Sesrisscesapecsesetetisststessestetgepirtet epee iistrtsetenstet rh peeee Eptetstetetsesttesesesssees srese SpeseneS Seite SaSSRCASSLESSSICECITICPeeEsESTE: Sipastesstitssssiscecesitissesersietes ispesreccteerstinresctectetten panied Socopseethebel = SEs spetetesepesessisiss ieee sitieseenstatersnopseerstpsesesestaee Septet pepehtiess secerbgccbiecesssrussbheesrs Hinuinncs sear Petisstatstssisg (pop pend ede ee ssasesatecsess Sefreseieiee toseeee corset Sebstetesteeseee Series SSsssbehes Sees ae 831 rbcteeststsetesesesss pebectgesscssestseesss Seestssieceotrerts pEstccitsteseeetssesttgiast iseabeerecesstontesese suaueassssebests pisipssesssibtivssitesseesro iesbe abit 3 Seastsastss pintpeatesatesseptesetresassiisesis ae SERENE EHS Sstttricesestrestgereriieseprassersseresresearaesestgess But M,,/N is the mass, m, of one “‘molecule,” and we then have kTdC,/dx = 6rnavNym The mass, in grams, of N,; molecules is Nim, or M. The product of v and Nym is the mass of solute flowing across unit area per second, or vN,m = dM /dt. Then we find dM kT dC, dt 6rna dz (2.5) Now, the diffusion constant, D, is defined by Fick’s law equation as =A (2.6) where A is area. Since we have considered unit area above, we derive from Eq. 2.5 that age = (2.7) OTna This important result was derived by Sutherland in 1905 and applied by him to determine the molecular weight of egg albumin from Graham’s diffusion data, he obtained the value 33,000. SIZE, SHAPE, AND HYDRATION OF VIRUSES Dik If nonspherical viruses are concerned, then the frictional drag coefficient is no longer 67a but can generally be written as f, so that the more general equation for the diffusion constant is D = kT/f (2.8) Diffusion constants, in practice, are measured by two methods. In the first, a sharp boundary is established by using a double cell, the upper part of which can be slid across until it forms an accurate continuation of the lower part. The two parts are filled separately, the lower with virus in buffer solution and the upper with buffer solution alone. When proper temperature equilibrium is established (the diffusion must be carried out under thermostatic conditions), the two parts of the cell are brought into line. The rate of diffusion can be measured by a refraction technique due to Lamm and Polson (1936) which consists of photographing a scale, by light from a mercury arc, through the cell. The boundary is marked by a change in refrac- tive index, and this causes a shift in the apparent position of the scale. From the amount of shift at different positions in the cell, the distribution of virus can be estimated. Initially this is, of course, a step function, but, as diffusion progresses, the dis- tribution becomes that of an error integral, and by evaluating the constant of this function as time passes, the diffusion con- stant can be obtained. Details are given by Neurath (1942). This method requires a rather elaborate, carefully made cell with a good optical system and a good thermostat. It also necessitates homogeneous, pure virus. Four determinations of diffusion constants have been made by this method: bushy stunt virus by Neurath and Cooper (1940), tobacco mosaic virus by Lauffer (1944), southern bean mosaic virus by Miller and Price (1946), and rabbit papilloma virus by Neurath, Cooper, Sharp, Taylor, Beard, and Beard (1941). Of these, there is excellent reason to believe that bushy stunt and southern bean mosaic viruses are accurately spherical, rabbit papilloma is probably spherical, and tobacco mosaic virus is definitely not spherical. The values obtained for the three spherical viruses, together with the derived radii, are given in Table 2.2. 28 THE PHYSICS OF VIRUSES TABLE 2.2 Dirrusion ConsTANTs AND Raptt ror THREE SPHERICAL VIRUSES Virus Diffusion constant (em?/sec) Radius (A) Bushy stunt oe Om: 187 Southern bean mosaic Sle ai These relations are all set out in Svedberg and Pedersen (1940, Eqs. 68—70b). Actual values for the constants applicable to 20° C are given there. It can be seen that, by employing Eq. 2.17, the results of sedimentation, diffusion, and partial-specific-volume measure- ment can, in the case of nonspherical viruses, yield a value of f/fo, the ratio of the frictional drag coefficient to the equivalent- sphere frictional drag coefficient. One obvious reason why f/fo should not be unity is the fact that the virus may have an asymmetrical shape. If this is known to be not the case—the virus is known to be spherical—one therefore predicts that the use of proper measurements together with Eq. 2.17 should give f/f) a value of unity. This is not found, and the explanation given in such a case is the presence of hydration, water which is bound on the surface and in the virus interstices so that the radius applicable to the frictional drag is not the radius of the dry particle. For the case of diffusion measurements, where the frictional drag term is all that is important, the effect of r gm of water (partial specific volume, V1) combined with one of virus (partial specific volume, J’) is to produce a frictional drag, f,, where (2.18) In the case of sedimentation, the buoyancy term is also of impor- tance, so the ratio to be applied as a correction factor for sedi- 34 THE PHYSICS OF VIRUSES mentation constants is fs/fo, where 1S. | Cea) é| fo \1—Vop +70 — Vip)} Both these relations are derived and discussed in the section by Kraemer in Svedberg and Pedersen (1940). ee (2.19) J0 SEDIMENTATION TECHNIQUE The technique of sedimentation as applied to viruses is quite varied. Because viruses are relatively large, their sedimentation constants are high, and elaborate long centrifugation processes are really not needed. One simple technique, used by Elford (1936), is to sediment in a capillary tube, held horizontally, and then to sample the virus at definite radii after exposure to the centrifugal action for known lengths of time at a known rate of rotation. He applied this to measure the sedimentation of bacterial viruses. The same method was used by MeIntosh and Selbie (1937) and more recently, for potato yellow dwarf virus, by Brakke, Black, and Wyckoff (1951). The capillary tubes used by these workers were 2 mm in diameter, and were placed in a centrifuge cup filled with water and spun in an International 1SB centrifuge for 5 hr or so. At the end of the centrifugation, a special fine capillary tube, turned to a hook shape at the bottom, was inserted, and samples taken out at known depths. The samples were then appropriately diluted and tested for infectivity. When such a method is used, the sedimentation constant is calculated from the formula derived by Svedberg and Pedersen (1940), namely Spay aatlinet seo) [in | (2.20) tw°neo(P»v — p) 3 where Soo is the sedimentation constant at 20° C, 7 is the vis- cosity of the solvent at experimental temperature, 720 is the viscosity at 20° C, po is the density of water at 20° C, p, is the anhydrous density of the virus, p is the density of the solvent at experimental temperature, ¢ is the time of centrifugation in seconds, w is the angular velocity in radians per second, 2, is the SIZE, SHAPE, AND HYDRATION OF VIRUSES 30 distance of the initial boundary from the axis of rotation, and x2 is the radius of the boundary after a time ¢. The sampling technique described above must be aimed at locating the position of the boundary. In place of finding the boundary at a known time, the time to reach a definite radius is measured. This is done by plotting the concentration on the upper side of a2 at different times and by interpolating between points determining the time at which the concentration has dropped to zero. ty” ta? is concerned with the description of the motion of the boundary, 1(P» — Po) N20(Pv — p) sedimentation to standard conditions at 20° C. When such measurements are made, it is usually found that the value of the sedimentation constant depends on the con- centration of the virus used. This is interpreted as being due to the presence of impurities which modify the rate of sedimenta- tion by introducing local variations of density, and the normal procedure is to plot the sedimentation constant as a function of concentration and extrapolate the line back to zero concentra- tion, where extraneous effects are assumed to be nil. It will be seen later that correction for the viscosity of the solution re- moves some of the dependence on concentration, a point made by Lauffer. The availability on the market of a single wire suspension, vacuum ultracentrifuge has widened the interest in this type of research. The Spinco ultracentrifuge, manufactured by Special- ized Instruments Corporation of Belmont, California, follows a design by Bauer and Pickels (1937) and is now found in many laboratories. It consists of a rotor of aluminum alloy, shaped for dynamical balance, with a hole cut through it about three inches from the axis of rotation. The hole accommodates a wedge shaped cell, with accurately ground, flat glass plates top and bottom, and within which the virus suspension can be placed. As rotation proceeds, this cell is brought, once per Equation 2.20 is the product of two terms. The term and the term is the term which reduces the observed Ss VIRUSE OF THE PHYSICS 36 ‘uses eq UBD yUIUOdWIOD puodss B pue aind 9}INb joU sI snJIA ay, “yyBU 0} 1°] WIJ SI UOTZEPUIUTIPIG ‘redsey Aq Uoye} ‘SNIIA OTBSOUL URI UI9T[JNOS JO] WIBISVIP UOTJVPUSUMIPIG “FZ “OT Qar SIZE, SHAPE, AND HYDRATION OF VIRUSES ol revolution, into a beam of monochromatic light. The centrifugal action causes a virus boundary to develop, with solvent on the inside and the outward moving virus on the outside. For viruses, this soon becomes very sharp, and, at the boundary, very rapid change of refractive index occurs. The position of this boundary can be made visible by Topler’s schlieren method, and the optical system accordingly includes a lens, which focuses an image of the cell onto a photographic plate, and an edge across the lens. The effect of a changing refractive index is to send behind the edge a part of the cell image and, accordingly, to have a part of the image missing on the photographic plate. This can be modified by using an oblique bar and a cylindrical lens to give an up and down deflection of the trace at the bound- ary. Such patterns are very familiar in the literature of macro- molecules today. One such is shown in Fig. 2.4, where the virus being spun is southern bean mosaic. The virus preparation can be seen to be not quite homogenous, and a filter placed across the light source produces a definite absorption at the boundary of the impurity. The main sedimentation occurs at the expected rate. This picture was taken by Mr. D. Caspar in the author’s laboratory. The speed of the ultracentrifuge is accurately controlled by a relay system, and pictures can be taken at known intervals so that the sedimentation constant can be measured directly. A very beautiful development of the ultracentrifuge has recently been made by Beams, Ross, and Dillon (1951). If a strong magnetic field has both a radial and an axial gradient, then a rotor of ferromagnetic material will seek the region of highest field and, having found it, will remain suspended there as long as the magnetic field is present. In Beams’ device, the rotor is brought up to speed, released of all material contact, and left to spin in an evacuated chamber with magnetic support. The rotor loses one revolution per second per day, and so the motion is essentially uniform. Two years would be required for the rotor to come to rest if left alone. This method is suitable for equilibrium studies in which the sedimentation drift is balanced by the tendency to diffuse. This may be of more 38 THE PHYSICS OF VIRUSES importance for protein studies but, as the purity of virus prepa- rations increases, will play a part in virus research. DirFusIoN-ConsTANT MEASUREMENT DuRING SEDIMENTATION A rough value for the diffusion constant of a virus can be obtained while a sedimentation run is in progress. The measure- ment is in terms of the gradual diffusion of the boundary. If C, is the concentration at a distance z from the boundary, C» the concentration in the solution where diffusion has not yet developed, then C, follows the form of an error integral, and 0, = Gf - 2 1 y e “dy 2.21 7, it y (2.21) By taking experimental values of C,, deduced from pictures taken during centrifugation, the value of y at any point z can be found. The diffusion constant, D, is then D = =. (2.22) where ¢ is time. The above was pointed out by Svedberg, and the method is described by Svedberg and Pedersen (1940). Such a method of measuring the diffusion constant, although useful since one experiment gives two pieces of data, is not too accurate because of the short times of diffusion, the lack of temperature stability, and the wedge-shaped cell used. Nevertheless, as Lauffer (1942) has pointed out, diffusion measurements made in this way can give very good additional evidence regarding the homogeneity of the preparation. HYDRATED PARTIAL SPECIFIC VOLUME The hydrated partial specific volume can be found by sedi- mentation measurements in solvents of different densities. The value of p, the solvent density, can be varied by introducing an additional solvent until the medium reaches the condition where pV») = 1, when there is no sedimentation. Actually it is SIZE, SHAPE, AND HYDRATION OF VIRUSES 39 not necessary to proceed to the actual point of no sedimenta- tion, for we can rewrite Eq. 2.13 in the form i, a and by plotting 7S versus p there appears a straight line of descending slope with intercept on the density axis where 8xlO ” Viscosity Times Sedimentation Constant 0 1,00 1.02 1.04 1.06 1,08 1.10 1.12 Solvent Density Fic. 2.5. Product of sedimentation constant and viscosity for PR 8 influenza plotted against solvent density as the concentration of serum albumin is in- creased, thus raising the density. The intercept value for the density deter- mines the hydrated partial specific volume. Data due to Sharp, Taylor, McLean, Beard, and Beard (1944). V.p = 1. Such a line for PR-8 influenza virus, plotted from data due to Sharp, Taylor, McLean, Beard, and Beard (1944), is shown in Fig. 2.5. The additional solvent material is bovine serum albumin, which is a relatively large molecule and so does not introduce effects due to osmotic pressure. The intercept at a 40, THE PHYSICS OF VIRUSES density of the medium of 1.104 gives the value 0.906 for the partial specific volume. The use of sucrose as a buoyancy variant substance has often been employed. This is a small molecule and so introduces osmotic effects. However, if the slope of the line at low concen- trations is used to extrapolate to the zero-force point, the figure obtained should be valid. For smaller, or thinner viruses, this method does not always vield consistent results, and Schachman and Lauffer (1949) have suggested that a layer of water, half the thickness of solute molecules, forms on the virus. For larger viruses this is not a very serious correction. Before describing some actual measurements on viruses, a description of the place of studies of viscosity in virus research is in place, and then a general discussion of this approach can be given. VISCOSITY When very pure virus preparations are available, so that the virus solution can be treated as containing only virus particles and solvent, the measurement of the viscosity of the virus solution can give information regarding size and shape. The viscosity of a liquid is measured in terms of a rate of shear of the liquid, and, since a force is required to push one layer of liquid over another at a certain rate, viscosity is essentially a process in which mechanical work is continually being dissi- pated. The rate of such dissipation is measured by the quan- tity 7A(dv/dx)v, where v is the velocity of the liquid, A is the area of a plane surface of the liquid, dv/dx is the rate of change of velocity with distance at the area A, and 7 is the coefficient of viscosity. Einstein (1906, 1911) investigated the flow of liquid around a small sphere—small, yet large compared to molecular separations—and derived an expression for the energy dissipation due to viscous flow around this sphere. He then examined the energy dissipation for a very large number of such spheres and derived the approximate expression n/no = 1+ 2.5¢ (2.24) SIZE, SHAPE, AND HYDRATION OF VIRUSES 41 where ¢ is the fraction of the volume occupied by the spherical particles, and 7 and 7 are the viscosities of the solution and the medium, respectively. This method, combined with diffusion, was suggested by Einstein as a method of measuring molecular radii and so of obtaining Avogadro’s number. In Einstein’s first paper, published when Avogadro’s number was still in process of being determined, the constant 2.5 was given as unity. The resulting low values of Avogadro’s number deter- mined by this useful method were thought of as in reasonable enough agreement. The later paper corrected the figure, and accurate values of Avogadro’s number resulted. Notice that the essential character of the study of viscosity is the study of a total volume which interferes with the sliding of planes of water over one another. This total volume is, of course, the number of particles times the volume of each, but the volume concerned is basically the volume due to each particle which does not enter into slipping. So any water held by the particle is to be included in the volume ¢. Thus viscosity measurements differ from sedimentation measurements in that, although bound water can be argued as equivalent to buoyant water for centrifugal action, and so not concerned in the motion, there is no question of buoyant action in viscosity. So one can turn a dark and a light shade of gray into black and white and assert that the particle mass determined by sedimentation and diffusion is the dry mass, while the volume determined: by viscosity is the hydrated volume. This is probably true for protein molecules but is not so apt to be true where viruses of complex internal morphology are concerned. Nevertheless we are going to continue with the black and white idea because all that can be done is to try out reasonable hypotheses in the hope that a fairly large category of viruses will fit them to the first approximation. From there, as measurements improve, the second approximation can be made. So we point out the value of viscosity studies as measuring the size of a particle which fails to slip and which is, therefore, the virus plus its hydration. There are many ways of measuring viscosity. An absolute value can be obtained by measuring streamline flow in a capillary 42 THE PHYSICS OF VIRUSES or by the rotation of one cylinder inside another with liquid between. Once absolute values are established, relative values can easily be found by timing the flow of a fixed volume of fluid through a certain length of capillary under the action of gravity, or by timing the rate of fall of a small sphere through the liquid. Thus viscosity is a relatively easy measurement. O'S 010 0.05 10 20 3.0 Grams of Virus in 1OO ml Fic. 2.6. Plot of 7/no — 1, the relative viscosity less unity, for solutions of SBMV of different concentrations. The circles and triangles refer to physically and chemically purified virus. The slope of the line enables a determination of V/m, the volume fraction of the virus, to be made. Data of Miller and Price (1944). The Einstein equation is seen to be very powerful in the case of purified spherical viruses. The number of virus particles per milliliter can be measured in terms of the mass of dry virus per milliliter, and the mass of the virus found by sedimentation and diffusion. If C is the mass per milliliter and m is the mass of each virus particle, then the number of particles per milliliter is C/m. Now if the actual volume of each, water included, is V, we have ¢ = CV /m, the number per milliliter times the volume of each. So a measurement of 7/7 as a function of C tells us the SIZE, SHAPE, AND HYDRATION OF VIRUSES i) value of V/m. Now mV ,q is the actual volume of the particle, so V — Vom so ere m V — mV is the associated volume of water. Then V m conventional method of expressing degree of hydration. This ratio is denoted by r. This method is well exemplified by the work of Miller and Price (1946) on southern bean mosaic virus. Their results are — Vo, is the mass of water per gram of anhydrous virus, the shown in Fig. 2.6. The measured values for - — 1 are plotted 0 against C, the gram concentration of virus. The points fit a straight line quite well, so that Einstein’s relation is obeyed. In these studies, the virus was purified by chemical precipi- tation and by ultracentrifugation, and viscosity determinations were made for each. The agreement is very satisfying. From the slope of the line, ¢ is found to be 1.76 and so V/m is 1.76. Pycnometric measurements give the unhydrated partial specific volume as 0.70, so the mass of water per gram of an- hydrous virus is found to be 1.06. ASYMMETRIC PARTICLES The pleasantness and simplicity of working with spherical particles ceases to hold if the viruses are rod shaped and becomes unmanageable if some description in terms of ellipsoids is not applicable. This doesn’t mean that queer shapes do not diffuse and sediment in a regular way, but that measurements do not tell us their shape. Virus work is still at an early enough stage so that we are content to take any information and add it up. Nevertheless, the sedimentation of phage-shaped particles is not a powerful way of studying their form. The central point to study is clearly the viscous flow of odd shapes. Neither the centrifugal reaction forces nor the “‘os- motie’’ forces which apply in sedimentation and diffusion are dependent on shape, but the viscous drag does definitely depend on shape. The problem of viscous drag experienced by ellipsoids was solved by Gans (1928). Ellipsoids permit precise solutions 44, THE PHYSICS OF VIRUSES of hydrodynamic equations and so can be handled mathe- matically. The application of these results to diffusion was made by Herzog, Ilhig, and Kudar (1934) and F. Perrin (1936). Their results are equivalent and lead to the expressions below. The ratio of the diffusion constant D, for an ellipsoid of revolution (semi-axis of revolution of length a, the other, b) to that, Do, for a sphere of the same mass and volume is Db ae V1 = (6/a)? es (2.25) Do Ge € ay = aa ey) be Ue reas = al b/a for prolate ellipsoids, and Deel CMO Oa eee 7 ONe fe AE eee 8 : (7) are tan V(b/a)? — 1 for oblate ellipsoids. We can consider these as measurements of the ratio f/fo, where f and fy are the frictional constants for ellipsoids and spheres. The extension of this idea to the calculation of the viscosity is much harder. Guth (1936) and Simha (1940) have derived expressions for the viscosity of solutions of prolate and oblate particles. These are not as firmly established as the Einstein equation but they represent the best available. The relations express viscosity in terms of concentration and the force con- stant for the particular shape, which can accordingly be found. The shape is, however, only determined as far as the ratio to spherical is concerned, and this depends on the true mass of the hydrated particle. There is thus no clear separation of hydration and shape. Now, in the measurement of f from diffusion studies, it will be remembered that the viscous-drag term corresponds to what- ever actual particle is being pushed through the medium. If some water is bound to the particle and changes its radius or surface, this must be included. So the measurement of f by the diffusion measurement will not yield b/a unless the proper hydrated SIZE, SHAPE, AND HYDRATION OF VIRUSES 4S particle is being treated. Thus, again, an ambiguity between hydration and axial ratio exists. What is done is to assume a reasonable hydration and axial ratio to fit diffusion data and then to see whether a check against viscosity is obtained. Actually, there is no virus for which the whole elaborate technique of protein molecular measurement has been applied. Very nearly, it has been done for tobacco mosaic virus and southern bean mosaic virus, with results to be described in what follows. EXAMPLES OF THE USE oF Virus MoTION STUDIES Some examples of virus motion studies can be given here. These are by no means the only cases studied, but are chosen as representative of the kind of work that can be done. The first is the study of potato vellow dwarf virus by Brakke, Black, and Wyckoff (1951). The purification of this virus to a high degree is difficult, as it is not very stable and centrifugation has to be carried out near the freezing point. Nevertheless, concentrated preparations of high infectivity could be obtained, and these were centrifuged in horizontal capillaries. During the cen- trifugation a quite definite visible boundary developed, and it was possible to measure the sedimentation constant of this boundary. In addition, virus samples were removed by a fine capillary, and the sedimentation constant of the infectivity was determined. The constant varied with concentration. This was traced to the fact that the viscosity of the solution increased with concentration. By plotting the apparent sedimentation con- stant versus concentration, a reasonably good straight line was obtained which was extrapolated back to zero concentration to give a value of 1,150 S for water at 20° C. The variation of sedimentation rate with solvent density was plotted, using sucrose as the second solute. The results extra- polate to a zero sedimentation rate at a density of 1.17, so the hydrated density of the virus is 1.17. This may need correction for the osmotic effects of the small second solute molecule. The authors examined, with some care, several high concen- tration preparations of potato yellow dwarf virus in the electron 46 THE PHYSICS OF VIRUSES microscope. The field contained particles of rather irregular circular shape, with estimated volumes spreading from 5.0 X 10° A? to 1.3 X 10° A*. The mean volume was close to 8.5 X 108 A’. If the electron micrographs are taken as justification for treating the virus as approximately spherical, the authors deduce, from Eq. 2.13 for sedimentation, that the virus diameter is 1,100 A, the volume is 6.9 < 108 A%, and the ‘‘molecular weight”’ is 490,000,000. The hydrated density of 1.17 is rela- tively low and implies a high degree of hydration, which may partly account for the virus instability. The value of the above studies lies mostly in the fact that the correlation between the objects seen in the electron micrographs and the rate of sedimentation of infectivity is very good, so that it can be concluded that the electron microscope observations are not merely of plant debris. The electron microscopy thus acquires added strength, and a further proposal that possibly the virus particles are more ellipsoidal in character can be made. It is of interest that the visible boundary sedimented at the same rate, within experimental error, as the infectivity. This offers some more evidence that the virus particles are indeed the infectious bodies, but only cireumstantially so. The above study is chosen because it may well be representa- tive of virus work. Viruses, in general, are not exceptionally stable, can not be highly purified, and are hydrated so much that simple physical observations on them are difficult. The conclusions that can be drawn are nevertheless not trivial, they serve to characterize the virus particle as a definite object and are helpful in further studies. It is to be regretted that very few studies of the rate of sedi- mentation of plant viruses as measured by serological affinity have been made. This virus assay is rather easier than the local- lesion technique, and the results would add a further piece of information regarding virus size and shape. As a second example we can choose southern bean mosaic virus, studied by Miller and Price (1946). This is a spherical plant virus capable of being highly purified, and so is fully SIZE, SHAPE, AND HYDRATION OF VIRUSES AT suitable for detailed study. The preparations used were not crystalline but were purified by both sedimentation and chemical methods. Both processes gave the same results. Sedimentation measurements were made at various concentrations. The sedi- mentation constant slowly fell as the concentration increased. By plotting i/S versus concentration and extrapolating the resulting straight line to the value 1/S at zero concentration, the sedimentation constant at 20° C was determined to be 115 S. Diffusion measurements were carried out in an electrophoresis cell, with the result that the diffusion constant at 20° C was found to be 13.4 X 10°° em?/sec. Partial-specific-volume meas- urements on the dry virus gave the value 0.696 ml/gm. Putting these together, the particle molecular weight was found to be 6:63, < 10°. The individual sedimentation and diffusion measurements were then applied to Eq. 2.17 for the frictional drag ratio, with the result that a value of f/f) = 1.25 was found. The viscosity of the virus was measured as a function of con- centration, with the results shown in Fig. 2.6. The value of ¢ so found was 1.76 if the particles are assumed to be spherical and the Einstein relation, 9 /n) — 1 = 2.5¢, can be applied. Alter- natively, if the virus is supposed to be unhydrated, and an axial ratio is responsible for the large viscosity, the axial ratio deduced isia-0 LOmk. In addition to these measurements, the sedimentation rate in sucrose solutions of different density was measured. The sedi- mentation rate did not vary linearly with density, probably due to osmotic effects or combination between virus and sucrose. However, by carefully determining the slope of the line at very low sucrose concentrations and extending this to the point of zero net force, the density value for the sucrose solution was found to be 1.21, corresponding to a partial specific volume (hydrated) of 0.827. The curvature of the line was actually slight, though definite, and the data are so good that the above figures should be very reliable. We now have the following experimental facts about the virus. First, the particle molecular weight is 6.63 < 10°. Second, 48 THE PHYSICS OF VIRUSES diffusion measurements give f/fo, the frictional ratio, as 1.25. Third, viscosity measurements give ¢, the apparent volume fraction, as 1.76. Fourth, the dry partial specific volume is 0.696 gm/ml, and the hydrated partial specific volume is 0.827. These can be explained in only one way. If we suppose that the f/fo value from diffusion is due to unhydrated ellipsoidal particles, then the axial ratio deduced from Eq. 2.25 is a/b = 5. This agrees with the value found from viscosity measurements. However, the hydrated partial specific volume figure does not fit this idea. Lansing and Kraemer (1936) have shown that if Vo is the partial specific volume of a combination of two substances with separate values V, and V,, and if 7 grams of substance V, combine with 1 of substance V,, then (r + 1)Vo — rV y + Ve (2.27) Putting in the above figures, we find r = 0.76 gm of water per gram of dry virus. Now this radically changes the explanation of both the diffu- sion and the viscosity figures. In the former case, if we assume spherical viruses and apply Eq. 2.18 for f/f as due to hydration, the value of + so found is 0.78 gm water per gram of virus. This agrees beautifully with the direct measurements. Using the value of V/m = 1.76, together with the dry partial specific volume of 0.696, the relation r = V/m — Vo gives r = 1.06. This is rather high, but still in tolerable agreement. Miller and Price then con- clude that an average value of 0.83 gm of water of hydration is associated with each gram of virus; that the virus is spherical; and that its mass, independent of hydration, is 1.1 X 10~!7 gm, corresponding to a particle molecular weight of 6.63 < 10°. The hydrated particle has a diameter of 312 A, and the dry particle a diameter of 244 A, Very recently, Lauffer, Taylor, and Wunder (1952) have made quite extensive studies on the centrifugation of southern bean mosaic virus. They have examined very carefully the sedimenta- tion in the presence of bovine serum albumin and various alkali metal chlorides and also at different pH values and in sucrose. Their studies show that buoyancy methods can readily be sub- SIZE, SHAPE, AND HYDRATION OF VIRUSES 49 ject to systematic error and that several factors need to be considered before specific volumes are deduced. They conclude that rather less water is associated with the virus, giving the value 0.45 gm water per gram of virus. In consequence, the virus diameter is also smaller, being 280 A. It must be agreed that, used in this way, virus motion studies are highly informative. As a third illustration of virus motion studies we can consider tobacco mosaic virus, as described in papers by Lauffer (1944) and Schachman and Lauffer (1949). All the beauty and sim- plicity of the study of spherical particles are here absent. Tobacco mosaic virus, although it can be thoroughly purified, has a long rod structure which readily aggregates into multiple lengths. Thus sedimentation, diffusion, and viscosity measure- ments are all subject to the question of whether the virus has aggregated or not. Nevertheless, Lauffer carried out sedimenta- tion measurements on the preparation showing the least vis- cosity. In the course of these measurements he was able to show that the dependence of sedimentation constant on concentration is due to a single factor, the viscosity of the solution in which the virus is moving. In Fig. 2.7 is shown a plot of Lauffer’s data before and after the correction for the solution viscosity. The apparent sedimentation constant is plotted as a function of virus concentration, and it can be seen that the use of solution vis- cosity (which is changing markedly with tobacco mosaic con- centration) in place of solvent viscosity produces a reasonably constant set of values. The value found for S2> was 187 S. This treatment was also found to be valid for SBMV by Miller and Price. For this same preparation, the diffusion constant was found to be 2.62 X 107% em?/sec, and the unhydrated partial specific volume to be 0.73 ml/gm. Using these figures, a particle mass of 5.24 X 107!" gm, or a particle molecular weight of 31.6 x 105, can be calculated. There now arises the same question of axial ratio and hydration. Specific viscosity measurements combined with sedimentation measurements yield an axial ratio of about 20. However, hydration must play a part. To establish this, 50 THE PHYSICS OF VIRUSES Schachman and Lauffer made sedimentation rate measurements in both serum albumin and sucrose solutions, with the results shown in Fig. 2.8. It can be seen that the no-net-force point occurs for a solvent density of 1.127 in the first case and 1.266 in the second. These do not agree. The first requires hydration to the extent of 66% by volume per milliliter of virus, and the I60S- Sedimentation Constant 140S}- I20S ! 1.0 2.0 Concentration ( 9/100 cc) Fic. 2.7. Sedimentation constant of TMV versus concentration. The vis- cosity of the solution increases as the concentration increases and, if allowance is made for this, the dotted line results. Data and analysis of Lauffer (1944). second to 27%. Following a suggestion made by Kauzmann, they propose that a layer of water roughly half the thickness of the solute molecules is entrained by the virus. Correcting for this, they conclude that the hydration of tobacco mosaic virus is 15% of the wet particle, or about 0.12 gm water per gram virus. It is likely that the hydration of SBMV is less if this type of correc- tion is made. With this figure, the sedimentation, diffusion, and viscosity data fit with a rod-shaped virus of length 2,500 A and width SIZE, SHAPE, AND HYDRATION OF VIRUSES oil 140 A. It is truly remarkable that so difficult a virus to study should nevertheless be susceptible to correct characterization by these means. The fourth illustration is the study of rabbit papilloma virus carried out by Neurath, Cooper, Sharp, Taylor, Beard, and 100 (0) 1.10 1.20 1.30 Solvent Density Fic. 2.8. Buoyancy measurements by Schachman and Lauffer (1949) on TMV using two second solutes. The steep slope is for serum albumin, the gentle slope for sucrose. Differential entrainment of water is suggested to explain the two slopes. Beard (1941) and Sharp, Taylor, Beard, and Beard (1942). Rabbit papilloma virus can be obtained from warts in Western cottontail rabbits. The collection of material from four trapping seasons gave 430 gm of wart tissue. This was ground and extracted, and the virus separated by multiple centrifugation. 52 THE PHYSICS OF VIRUSES Since the wart tissues were stored at 2-5° C for several years, it is obvious that this is a stable virus. : Sedimentation measurements gave a value of Seo = 278 S. Diffusion measurements by the refractometric method gave Doo as 5.85 X 10-8 cm?/sec, and the anhydrous partial specific volume was found to be 0.754. These, when put together, give the particle mass as 7.81 X 10~'’ gm and the particle molecular weight as 47 X 10°. Putting together the sedimentation and diffusion data to calculate f fo, the value obtained is 1.486, which is rather high. If an unhydrated virus is assumed, the axial ratio deduced is 9 for a prolate ellipsoid and 11 for an oblate ellipsoid. However, there is no reason to assume an unhydrated virus, and if, instead, a spherical virus is assumed, the application of Eq. 2.18 gives 1S toner: In addition to sedimentation and diffusion measurements, the viscosity at various concentrations was observed. The data are very good and show a straight line with a slope of 0.063 for n/no — 1 plotted against gram-percent concentration of virus. The value of V/m is, accordingly, 2.52, and the resulting hydra- tion is 1.77 gm water per gram dry virus. This agrees well with the value above. Subsequent observation of the virus in the electron microscope showed a spherical particle of diameter 420 A, which fits the molecular weight of 47 X 10° reasonably well, if the partial specific volume of the dry virus as measured is used. The conclusion seems to be, therefore, that, in solution, rabbit papilloma virus is considerably hydrated but is still spherical. Lauffer and Stanley (1944) describe electron micrographs, sedimentation, specific volume, buoyancy, and viscosity meas- urements on PR8 influenza virus. The electron micrographs give a diameter of 1,150 A and an apparently spherical shape. The specific volume of the dry virus was 0.79. The density of sucrose for flotation was 1.18, so that the wet density is 1.18. The viscosity measurements did not show a linear increase in relative viscosity with virus concentration, a fact probably due to the presence of nonvirus components in the preparation. From these FO SIZE, SHAPE, AND HYDRATION OF VIRUSES ore) measurements, Lauffer and Stanley conclude that the particle diameter is about 1,000 A and the degree of hydration is 0.60 gm of water per gram of virus. Lauffer and Taylor (1953), with more modern buoyancy observations, find the sedimentation constant for the virus to be slightly higher and, from the two sets of data, conclude that the hydration is 0.32 gm water per gram of virus. It is hardly possible to tabulate here all the observations on virus motion studies. Bawden (1950, p. 224) tabulates the sedimentation constants of 11 plant viruses, and Lauffer, Price, and Petre (1949, p. 188) tabulate sedimentation constants for a variety of viruses, and diffusion constants for four viruses. Two cases are of some interest. The first is turnip yellow mosaic virus. This has been studied by Markham and Smith (1949). Preparations of this virus can be separated into two layers in the ultracentrifuge. The upper layer contains no nucleic acid and is not infectious, whereas the lower, denser layer is nucleoprotein, which is infectious. The serological properties of the two layers are the same, and the diffusion constant of the upper layer is 1.51 X 107~! cm?/sec, of the lower 1.55 XK 1071. So the particle size is slightly different. Yet the sedimentation con- stant for the lower layer is 106 S, and for the upper layer it is 50 S. There is, therefore, a considerable difference in virus mass. This ean, in part, be related to the nucleic acid. X-ray studies described in the next section indicate that, in addition, there is a higher density. A second case of interest is the Rothamsted variety of tobacco necrosis virus for which Ogston (1942) finds two sedimentation constants of 240 and 51S. Bawden and Nixon (1951) report that these are two spherical components of diameter 370 and 180 A. In comment on this work it should be pointed out that the basic physical methods of size and shape measurement by motion studies are vulnerable to errors of interpretation. It has already been seen that hydration and axial ratio can be confused. It is quite likely that a reconsideration of the actual physical factors involved may change detailed points of the measurement analy- sis. Thus the recent theory of Kirkwood and Shumaker (1952) 54 THE PHYSICS OF VIRUSES may modify conclusions regarding protein molecules. These modifications may extend into virus figures, although, in view of the excellent check given by the electron microscope, this is not likely. X-Ray DirrrRactTiIon APPLIED TO VIRUSES X-ray diffraction is a powerful physical tool which is being applied to supply evidence regarding crystalline protein struc- ture. For diffraction studies to yield really valuable information, relatively large, single crystals of material are needed. In any event, some order in the molecular arrangement is necessary. Only for some preparations of plant viruses has it been possible to apply this method. X-ray diffraction is concerned with three classes of measure- ment. The first concerns the regular atomic arrangements inside each virus particle. The second concerns the size of each particle, which appears as a repetitive diffracting distance. The third concerns the space between viruses, which may be a _ very regularly repeating value. All three types of diffraction have been observed. The first two are of use in describing particle size and shape and will be treated here. The intervirus spacing is of more interest later on and will be deferred until then. Diffraction arises from phase-related scattering. It is simplest to visualize this as due to regularly repeated scattering units, which will cause diffraction maxima at certain definite angles which are related to the repetition distance. The best illustra- tion of this is the reflection from planes rich in whole virus particles. A very beautiful picture of the nature of a small crystal of tobacco necrosis virus, taken with the electron microscope by Wyckoff, is shown in Fig. 2.9. It can be seen that there are regular, closely populated planes, and indeed it can be seen how the edges of the crystal are formed. Now any closely populated plane is one which scatters X-rays richly. Bragg pointed out that from such a plane equal angles of incidence and scattering give a diffraction maximum. If, in addition, there are many parallel planes, certain definite angles are selected, and these angles are related to the X-ray wavelength, A, the separation of the richly SIZE, SHAPE, AND HYDRATION OF VIRUSES 55 populated planes, d, and the angle of scattering, 0, by the Bragg relation nA = 2d sin 6, where n is an integer. An analysis of such crystals of tobacco necrosis virus was made by Crowfoot and Schmidt (1945). The crystals used had been grown for more than a year, and the largest was 2 X 1 X 0.5 mm. Both still and oscillation pictures were taken, with the Fig. 2.9. Electron micrograph of a small crystal of tobacco necrosis virus, taken by Wyckoff. Reprinted from Electron Microscopy by R. W. G. Wyckoff. Copyright 1949, Interscience Publishers, New York, London. result that the basic pattern corresponds to the packing in con- tact of a set of spheres of diameter 160 A. It is remarkable that over 500 hr of X-ray exposure could be given this crystal without any apparent change in its crystalline structure. This has an important bearing on other results involving radiation sensi- tivity. The great accuracy of more usual crystal analysis by X-rays is not present here since the crystalline perfection of chemical crystals is not matched by the virus crystals. With 56 THE PHYSICS OF VIRUSES still smaller crystalline preparations, Bernal, Fankuchen, and Riley (1938) found a spherical particle diameter of 270 A for bushy stunt virus. If in these crystals each virus could be identically oriented, it would be possible to find out some information about the internal atomic spacing. For spherical viruses this has not been done, but for tobacco mosaic virus, the long rod shape does frequently cause rather accurate mutual orientation. Using such prepara- tions, Bernal and Fankuchen (1941) found that there is an a 68A ee, os. a7A CE v2 act Fic. 2.10. Unit cell of tobacco mosaic virus as determined by Bernal and Fankuchen (1941). internal structure with a hexagonal lattice. To make their data fit this lattice, they found it necessary to use some fractional ralues of n in the Bragg formula, where n is supposedly integral. Bernal and Fankuchen point out that in a virus there is nowhere near an infinite atomic array. Hence the atomic planes do not select precisely integral values for scattering. If this interpreta- tion of their data is right, the unit cell they find is as shown in Fig. 2.10. The hexagon side is 87 A long, and the cell depth is 68 A. It is very gratifying that the precision electron microscopy applied by Williams (1952) to this virus also shows a hexagonal cross section of the same size. Thus Bernal and Fankuchen’s unit cell has one cross section which is that of the virus itself. The same method has been applied to tomato aucuba mosaic virus, enation mosaic virus, and cucumber viruses 3 and 4, all of which are related to tobacco mosaic virus. The same width SIZE, SHAPE, AND HYDRATION OF VIRUSES 57 of 151 A was found for all, except the cucumber viruses, which had a somewhat smaller width of 146 A. Bernal and Carlisle (1948) have made most interesting studies on turnip yellow mosaic virus. This virus is remarkable in that, as has been previously mentioned, the crystalline preparations separate ultracentrifugally into two factions, one contains nucleic acid and is infectious, and one has no nuclei acid and is non- infectious but has the virus serological properties. Bernal and Carlisle found that both classes of crystalline preparations had the same kind of X-ray structure, but that the virus repeat dimension for the infectious type was 228 A, whereas for the non- infectious, nucleic-acid-free particles 1t was 238 Aaor 10) A bigger. This remarkable fact suggests to Bernal and Carlisle that the nucleic acid holds the protein in a more tightly bound con- figuration. On drying, the interparticle distance shrinks and is the figure quoted above. When wet, the distance increases by 77 A or so. Very interesting interparticle regularities were also observed for TMV and will be discussed later. In the case of tobacco mosaic virus, Bernal and Fankuchen were able to secure sufficiently accurate orientation to observe reflections which correspond to some structure inside the unit cell. The difficulties of analyzing such reflections are very great, but they propose that in the hexagonal, unit cell there are platelets of dimensions 44 X 44 X 22 A which are arranged in regular order throughout the cell. The possibility of this type of analysis of internal structure makes further X-ray diffraction work on viruses of great importance. These X-ray studies can also be used to measure hydration, or at any event to act as a check on proposed values of hydra- tion. If observations on spherical viruses, or oriented, long, thin viruses, are made, the interparticle distance is found to be a function of concentration. In the case of TMV it was found that, as the virus was suspended in higher and higher concentra- tions of ammonium sulphate, the interparticle distance fell to a value of 178 A. In the dry gel preparations, in which the virus dries in an oriented way, the separation was found to be 151 A, 58 THE PHYSICS OF VIRUSES which is the separation for hexagonal rods in contact. Thus the effect of removing the dryable hydration cannot well be more than that produced in going from 178 A to 151 A. So extreme hydration proposals are not likely to be true. Actually, the values already quoted, as proposed by Schachman and Lauffer, fit these figures quite well. The shrinkage of bushy stunt virus on drying reduced the interparticle distance from 394 A to 318 A, and the process was reversible. Thus rather higher hydration is possible. SMALL-ANGLE X-Ray SCATTERING BY VIRUSES A method which promises to be very powerful has recently been applied to virus study by Kratky (1948) and by Ritland, GM Counter mane! Ni-Co Slits Scatterer ie) Filter X-ray Tube Fic. 2.11. Schematic arrangement for low-angle scattering of X-rays by viruses as used by Kaesberg, Ritland, and Beeman. A high-current rotating- anode X-ray tube supplies a beam which is filtered and collimated before en- countering the scatterer. This is a solution of virus. Scattering is measured as a function of angle with the Geiger-Miiller counter. Kaesberg, and Beeman (1950). The apparatus used by these last authors is shown schematically in Fig. 2.11. The virus solution is placed in a Lucite sample holder with properly oriented, thin polyethylene windows. The source of X-rays is a high-power, rotating-anode tube operating at about 30 kv and 100 ma, with a copper anode and a thin metal window. The X-rays are filtered through a nickel-cobalt filter and accurately collimated with SIZE, SHAPE, AND HYDRATION OF VIRUSES 59 fine slits. The scattered beam is observed through two slits which can be rotated around the scatterer. The whole equipment 1s about 6 ft in dimensions. Two theoretical features of the experiment need to be con- sidered. At very small angles of scattering, ¢, the theoretical scattered intensity 1s /(@), where 4? R2y? toy = Niele aoe (2°28) In this expression, N is the total number of particles irradiated, n is the number of electrons per particle, R is the “radius of gyration ’’* of the electrons in the particle, \ is the X-ray wave- length, and J, is the normal scattering by a free electron. This theory has been developed by Guinier (1939). A measurement of I(¢), therefore, gives the value of R?. Note that this concerns the electron distribution. Hence if there is any curious structural distribution of phosphorus, a high-electron element, and hydro- gen, a low-electron element, this should show up in the radius-of- gyration measurements. So far this feature has not been exploited, but it has promise. The second theoretical point involves larger angles, for which interference from the various internal sections of the virus plays a part. If the virus is spherical, the intensity has maxima and minima given by the expression : (= sin *\ 4D sin 6 (= sin *) 2 1 ———————)) cos Qn Qr Qn 4D sin 0\3 where J is the intensity at zero angle, and D is the diameter of the virus particle @ is the half-angle of scattering. A more elaborate expression can be derived for spheroids. One very important feature of this type of scattering experi- ment is that the essential scattering element is the electron distribution, which differs from water. Thus any hydration 1(6) = const X I (2.29) > * This “radius of gyration” is taken about the center and not about an axis of rotation. It is defined as R* = Ypdvr?/Zpdv, where p is density, v is volume, and r is radius, and so is formally like the mechanical radius of gyration. 60 THE PHYSICS OF VIRUSES which merely consists of water bound on the outside, or even mechanically seeped into cracks in the structure, will not con- tribute to the scattering. On the other hand, water, which causes a swelling of the whole virus, will produce an effect because the radius of gyration will be altered. Thus X-ray scattering offers a new measurement of size and shape, with a different response to water associated with the virus. More detailed information regarding hydration can thus be obtained for a virus which has been studied by sedimentation, diffusion, and viscosity, as well as by X-ray scattering. The price that has to be paid is the need for very pure prepara- tions of high concentration, concentrations of the order of 1% are needed, and any considerable amount of virus impurity is serious. For this reason, attractive studies of serological precipi- tates are not so easy to carry out. The small-angle scattering alone yields the value of R, the radius of gyration. If the molecular weight is independently known, it is possible to calculate the axial ratio for an assumed ellipsoid. This axial ratio is for the hydration-free molecule since the effect of water is deducted from the virus. By compar- ing the X-ray figures with axial ratios derived from the frictional ratio in sedimentation, which corresponds to the hydrated molecule, the degree of hydration can be inferred. A study of the two spherical viruses, southern bean mosaic and tobacco necrosis, by Leonard, Anderegg, Kaesberg, Schulman, and Beeman (1950, 1951) has enabled them to make measure- ments of the radius of gyration in each case using only the small angle scattering. The results are listed in Table 2.4. The inter- ference radius of bushy stunt is included. TABLE 2.4 Radius of | Corresponding Radius from Virus gyration (A) virus radius interference maxima Southern bean eel 143 149 + 3.3 Tobacco necrosis 119 154 Wes Doce sets) Bushy stunt 160 + 10 SIZE, SHAPE, AND HYDRATION OF VIRUSES 61 The internal interference scattering expression should apply to these viruses, and it has been found to hold. The results for southern bean mosaic virus are shown in Fig. 2.12, where it can be seen that the first five secondary maxima are visible. This is a very remarkable and most interesting result, for it shows that the conditions for large-angle scattering are closely fulfilled. Put in 60 es SBMV Curve Slits A 0 61x85mm B 0.61x 8.5mm C 0.81x!0 mm Intensity (counts per second) plane tend (es Now wa 5 |e se ve wes ee RO Oe 40 30 20 10 O 10 20 30 40 Scattering Angle (10? Radians) Fic. 2.12. X-ray scattering of SBMV taken by Ritland, Kaesberg, and Beeman (1950). Three sets of slits were used, and it can be seen that five sets of maxima are discernible. This means the virus is spherical to a close approximation. simple terms: because the virus particles are not arranged in any way, their perfect symmetry about the X-ray beam must be due to their own simple shape, and, in fact, the only shape simple enough is a sphere, and an accurate sphere to boot. The experi- ments show that the viruses are spherical to one part in 50, which is a remarkably accurate geometrical shape. They fully justify the use of equations for spherical particles in sedimentation, diffusion, and viscosity. Similar results on tobacco necrosis virus ’ e and bushy stunt virus have been reported, so that one class of 62 THE PHYSICS OF VIRUSES plant viruses, at least, is spherical, and so offers a simple geo- metrical shape for later speculation. This class of study adds one other datum to virus knowledge. Because any water attached externally will scatter like the water solvent, it cannot contribute to the actual net scattering. So any evidence for hydration cannot be due to water found on the surface. Now Miller and Price (1946), from sedimentation and diffusion measurements, found the value of the unhydrated virus volume to be 7.66 X 107'S cm*, whereas these X-ray experiments give 13.8 X 107'S cm? for the volume of the inter- nally hydrated virus. There is, therefore, 6.1 X 107'® cm%, or roughly 6.1 X 10-18 gm, of water for each 1.10 X 107~™ gm of unhydrated virus, which amounts to 0.55 gm water per gram virus. When this is compared with the total hydration of 0.67 gm water per gram virus, there is a residue of 0.12 gm water per gram virus, which is the external layer. This amounts to a thickness of about 4 A and corresponds very nearly to a mono- molecular layer. The same considerations can be applied to tomato bushy stunt virus with rather less accuracy. ‘The internal hydration is found to be 0.50 gm water per gram of dry virus. PICTURE OF A VIRUS One of the potential contributions of physical studies of viruses is some sort of pictorial representation of a virus. To some extent this can be begun as a result of the work described in this chap- ter. Taking as an example two of the best studied plant viruses, we deduce the appearances shown in Fig. 2.13. These are the bare canvases on which the real, detailed structure of the virus must be filled in. As further physical studies are elaborated, it will be seen that the open circle and long rod develop surface structures and internal constitutions. It should also be seen that it is far from hopeless to add a great deal of detail by patience and care. IDENTITY OF PuHysicaL PARTICLE AND INFEcTIOUS UNIT If the objects which are under study by these means are to be described in as detailed a way as we hope, it is plain that we SIZE, SHAPE, AND HYDRATION OF VIRUSES 63 should be certain that we are really studying the infectious unit responsible for the expected symptoms and not something which separates from highly infectious preparations and is only circumstantially related to the actual infectivity. There is a great deal of nonphysical evidence that crystalline, plant virus SBMV External monolayer of water 55% water inside 149A 79% protein 21% nucleic acid (a) non aqueous part 94% protein 6% nucleic acid Very little internal hydration TMV Monolayer | of hydration Fic. 2.13. Shape information regarding southern bean mosaic virus and tobacco mosaic virus as obtained from the physical studies described in this chapter. preparations have all the expected infective properties. These are briefly summarized by Bawden in his book, where he points out that the purified crystalline bodies, having recognizable chemical properties which can be extracted from infected plants, are never found in healthy plants. Moreover, when different kinds of plants are susceptible to the same virus, the same crys- 64 THE PHYSICS OF VIRUSES talline bodies can be found in the different plants which, while in the healthy state, have no common substances which are com- parable. The infectivity of purified preparations is very high and, if allowance is made for the expected loss of activity in purification, is high enough to account for all the infective agent being in the purified preparation. Finally, the antibodies pro- duced by clarified plant sap from infected plants combine specifically and strongly with the purified virus preparations. All these facts add up to make it most likely that the prepara- tions we call virus preparations are, in reality, strong concen- trations of the infectious principle, as they should be. A little extra confidence in this belief can be obtained by sub- jecting a virus preparation to ultracentrifugation and seeing whether the optical boundary of the concentrated nucleoprotein and the rate of transfer of infectivity comeide. By using a separation cell, in which a barrier across a sedimentation cell permits sedimentation through it under high acceleration, but does not allow rapid back diffusion, the rate of transfer of in- fectivity can be measured and compared with the rate of sedi- mentation by conventional means. This method has been ex- ploited by Lauffer in particular. For three viruses, tobacco mosaic (Lauffer, 1942), influenza (Lauffer and Miller, 1944), and southern bean mosaic (Epstein and Lauffer, 1952), the infectivity follows the optical sedimentation. The identity of the two princi- ples is therefore the more likely. The diffusion measurements of Polson and Shepard (1949) on T-3 and T-4 bacteriophages showed, at high concentration, that the diffusion constant was in reasonable agreement with the shape of the particles seen in electron micrographs. This argues that the phage particle is indeed the infectious unit. The fact that electron micrographs of bursting bacteria show about the right population of sperm-like objects is further evidence. However, it should be realized that, whereas the virus may have one shape and structure between residences in a host, the whole of this structure may not be needed for multiplication inside the host. So there is still left a question as to the nature of the object on which the biophysicist should concentrate his attention when making theoretical speculations regarding virus multiplication. SIZE, SHAPE, AND HYDRATION OF VIRUSES 65 Virus DIMENSIONS We conclude with a table of virus dimensions which is prob- ably nowhere near complete but which represents some of the available information on viruses. At this stage it is worth while to see what kind of classification of viruses by shape is possible. One fact is readily apparent—many viruses are spherical. To TABLE 2.5 Virus Dimensions (A) References* Psittacosis 4,500 diameter Vaccinia 2,600 & 2,100 Herpes simplex 1,500 diameter Rabies 1,250 diameter Influenza 1,150 diameter Newcastle 1,150 diameter Staphylococcus phage T-2 coli phage M-5 megaterium phage T-1 coli phage Rabbit papilloma Tobacco mosaic Southern bean Tobacco necrosis Bushy stunt Lansing polio Coxsackie Texas 1 Yellow fever Louping ill Tobacco ring spot Japanese B encephalitis Alfalfa mosaic Foot and mouth disease 1,000 diameter head 2,000 long tail 600 < 800 head 1,500 long tail 760 diameter head 3,000 long tail 500 head, 1,500 tail 440 diameter 2,800 long; hexagonal cross. section, side 87 A 298 diameter 300 diameter 300 diameter 250 diameter 340 diameter 220 diameter 190 diameter 190 diameter 180 diameter 170 diameter 100 diameter Friedman and Franklin (1953) Fluke (1953) Williams (1952) Ritland, Kaesberg, and Beeman (1950) Ritland, Kaesberg, and Beeman (1950) Ritland, Kaesberg, and Beeman (1950) Melnick, Rhian, Warren, and Breeze (1951) * The authority for a large part of this table is from Stanley’s review article in Chem- ical and Engineering News (1947). Other references are specifically given. 66 THE PHYSICS OF VIRUSES some extent this is due to first-order examination of dried viruses in electron micrographs, wherein a roughly circular appearance is classed as spherical. However, the X-ray scattering studies described in this chapter show that, for three plant viruses in solution, reasonably accurate spherical shapes are found. This may well be true of many others. There are some long, rod-shaped viruses, but these are only found among plant viruses. Among bacterial viruses, a combina- tion of rod and sphere seems to be a plausible description, al- though as careful studies are made, the heads appear to be only very roughly spherical. In addition, the tails do not appear as definite rods but seem to be rather variable both in length and diameter. These physical shapes at once pose a sharp challenge to the physicist. Virus can make more virus out of the host. Presuma- bly, to some extent, the formation of duplicates is by physical forees—Van der Waals, valence, or electroionic. How does a spherical object so influence its surroundings as to generate a second spherical object? And if it doesn’t directly do so, how is its structure broken down for multiplication so that many others can be assembled as spheres from the parts? Physics and physical chemistry has not yet encountered this type of erystal- lization process in which a number of large atomic aggregates of identical size and complex composition are formed from the medium. The temptation is to say that virus multiplication must consist of rods or plates generating other rods or plates, using the short range forces we already know. But in spite of this “must,” nature efficiently produces spherical viruses. It would seem that some extra process must be present. However, it is unwise to invoke such a process until it is clear that the actual multiplicative unit is indeed the spherical virus and not some quite different sub-unit, suitably shaped for the action of physical forces. Research is rapidly bearing down on this most important question. REFERENCES For general reference on motion studies, Svedberg and Pedersen’s classic The Ultracentrifuge (Oxford University Press, New York, 1940) is excellent. SIZE, SHAPE, AND HYDRATION OF VIRUSES 67 The general survey of virus size measurement by Markham, Smith, and Lea [Parasitology 34, 315 (1942)| is very useful; and the article by Lauffer, Price and Petre in Advances in Enzymol. 9, 123 (1949) is to be recommended. Wyckoff’s Electron Microscopy (Interscience Publishers, Inc., New York, 1950) is excellent reading. Detailed references follow below. Anderson, T. F., J. Appl. Phys. 21, 724 (1950). Bauer, J. H., and Pickels, E. G., J. Exptl. Med. 65, 565 (1937). Bawden, F. C., and Nixon, H. L., J. Gen. Microbiol. 5, 104 (1951). Bawden, F. C., and Pirie, N. W., Brit. J. Expll. Pathol. 23, 328 (1942). Beams, J. W., Ross, J. D., and Dillon, J. F., Rev. Sci. Instr. 22, 77 (1951). Bernal, J. D., and Carlisle, C. H., Nature 162, 139 (1948). Bernal, J. D., and Fankuchen, I., J. Gen. Physiol. 25, 111, 147 (1941). Bernal, J. D., Fankuchen, I., and Riley, D. P., Nature 142, 1075 (1938). Black, L. M., Morgan, C., and Wyckoff, R. W. G., Proc. Soc. Exptl. Biol. Med. 73, 119 (1950). Black, L. M., Price, W. C., and Wyckoff, R. W. G., Proc. Soc. Exptl. Biol. Med. 61, 9 (1946). Brakke, M. K., Black, L. M., and Wyckoff, R. W. G., Am. J. Botany 38, 332 (1951). Bull, H. B., Physical Biochemistry (John Wiley & Sons, Inc., New York, 1952). Crowfoot, D., and Schmidt, G. M., Nature 155, 504 (1945). Einstein, A., Ann. Physik 19, 289 (1906); 34, 591 (1911). Elford, W. J., J. Pathol. Bacteriol. 34, 505 (1931); Proc. Roy. Soc. (London) 112B, 384 (1933); J. Exptl. Path. 17, 399 (1936). Epstein, H. T., and Lauffer, M. A., Arch. Biochem. and Biophys. 36, 371 (1952). Fluke, D. J., In course of publication (1953). Friedman, M., and Franklin, R., In course of publication (1953). Gans, R., Ann. Physik 87, 935 (1928). Green, R. H., Anderson, T. F., and Smadel, J. E., J. Exptl. Med. 75, 651 (1942). | Guinier, A., Ann. phys. 12, 161 (1939). Guth, E., Kolloid-Z. 74, 147 (1936). Heinmets, F., and Golub, O. J., J. Bacteriol. 56, 509 (1948). Herzog, R. V., Illig, R., and Kudar, H., Z. Physik. Chem. A167, 329 (1933). Kilham, L., Morgan, C., and Wyckoff, R. W. G., J. Immunol. 67, 523 (1951). Kirkwood, J., and Shumaker, J. B., Proc. Natl. Acad. Sci. U.S. 38, 855 (1952). Kratky, O., J. Polymer Sci. 3, 195 (1948). Lamm, O., and Polson, A., Biochem. J. 30, 528 (1936). Lansing, W. D., and Kraemer, E. O., J. Am. Chem. Soc. 58, 1471 (1936). Lauffer, M. A., J. Biol. Chem. 148, 99 (1942). Lauffer, M. A., J. Am. Chem. Soc. 66, 1188 (1944). Lauffer, M. A., and Miller, G. L., J. Exptl. Med. 80, 521 (1944). Lauffer, M. A., and Stanley, W. M., J. Biol. Chem. 135, 463 (1940); J. Exptl. Med. 80, 531 (1944). : Lauffer, M. A., and Taylor, N. W., Arch. Biochem. and Biophys. 42, 102 1953). 68 THE PHYSICS OF VIRUSES Lauffer, M. A., Taylor, N. W., and Wunder, C. C., Arch. Biochem. and Biophys. 40, 453 (1952). Leonard, B. R., Jr., Anderegg, J. W., Kaesberg, P., Schulman, S., and Beeman, W. W., J. Chem. Phys. 18, 1237 (1950); 19, 793 (1951). McFarlane, A. S., and Kekwick, R. A., Biochem. J. 32, 1607 (1938). McIntosh, J., and Selbie, F. R., J. Exptl. Pathol. 18, 162 (1937). Markham, R., and Smith, K. M., Parasitology 39, 330 (1949). Melnick, J., Rhian, M., Warren, J., and Breeze, S. S., Jr., J. Immunol. 67, 151 (1951). Miller, G. L., and Price, W. C., Arch. Biochem. 10, 467 (1946); 11, 337 (1946). Miihlethaler, K., Umschau 10, 18 (1952). Neuman, 8S. B., Borysko, E., and Swerdlow, M., J. Research Natl. Bur. Standards 43, 183 (1949). Neurath, H., Chem. Revs. 30, 357 (1942). Neurath, H., and Cooper, G. R., J. Biol. Chem. 135, 455 (1940). Neurath, H., Cooper, G. R., Sharp, D. G., Taylor, A. R., Beard, D., and Beard, J. W., J. Biol. Chem. 140, 293 (1941). Ogston, A. G., Brit. J. Exptl. Path. 23, 328 (1942). Perrin, F., J. phys. radium 5, 497 (1934); 7, 1 (1936). Pickels, E. G., Chem. Revs. 30, 341 (1942). Pickels, E. G., and Smadel, J. E., J. Exptl. Med. 68, 583 (1938). Polson, A., Nature 154, 823 (1944). Polson, A., and Shepard, A. B., Biochim. et Biophys. Acta 3, 137 (1949). Ritland, H. N., Kaesberg, P., and Beeman, W. W., J. Chem. Phys. 18, 1237 (1950); J. Applied Phys. 21, 838 (1950). Schachman, H. K., and Lauffer, M. A., J. Am. Chem. Soc. 71, 536 (1949). Sharp, D. G., Taylor, A. R., Beard, D., and Beard, J. W., Proc. Soc. Exptl. Biol. Med. 50, 205 (1942). Sharp, D.G., Taylor, A. R., McLean, I. W., Jr., Beard, D., and Beard, J. W., J. Biol. Chem. 156, 585 (1944). Simha, R., J. Phys. Chem. 44, 25 (1940). Smadel, J. E., Pickels, E. G., and Shedlowsky, T., J. Exptl. Med. 68, 607 (1938). Stanley, W. M., and Lauffer, M. A., in Rivers, Viral and Rickettsial Diseases of Man (p. 29, J. B. Lippincott Co., 1948). Stanley, W. M., Chem. Eng. News 25, 3786 (1947). Stanley, W. M., and Anderson, T. F., J. Biol. Chem. 139, 325 (1941). Williams, R. C., Biochim. et Biophys. Acta 8, 227 (1952). Wyckoff, R. W. G., Proc. Nail. Acad. Sci. U.S. 37, 565 (1951); Nature 168, 651 (1951). CHAPTER THREE IONIZING RADIATION AND VIRUSES Ionization is, to a very large extent, caused by the passage of very fast, charged particles through matter. These particles have atomic dimensions or less (much less in the case of fast protons, deuterons, or alpha particles), and because of their high speed they are relatively unaffected by the vast majority of the atoms near their path. Thus these fast charged particles can readily penetrate into the interior of viruses, and may in- deed produce no effect at all until some internal action is pro- duced. For this reason, fast, charged particles are probes of virus structure. In addition they produce transient excitation effects in the solvent, which carry energy and can produce action on the large molecules of biology. The study of this should one day add still more to the knowledge of virus structure. The importance of studying the effect of ionizing radiation on viruses therefore lies in the fact that it is concerned mainly with the internal organization of the virus, something which is not measured by the techniques of the last chapter. The basic idea underlying the use of ionizing radiation is that it is a localized, destructive agent. The average energy release, which, as will soon be seen, is confined within a region of 7 A radius (on the average), is 110 electron volts or 2,500,000 calories/mole. It is likely that all ionization energy releases exceed 25 ev. This will destroy any sensitive function in its vicinity. So, by bombardment in this way, the loss of certain kinds of viral behavior can be studied. There are many of these, and for each there can be found a volume or an area related to the bombardment. Thus loss of infectivity, serological affinity, hemagglutination ability, bacterial killing power, and ability to adsorb, can each be measured. In the very limited number of 69 70 THE PHYSICS OF VIRUSES cases where several properties of a virus have been studied, the behaviors have been different. This is of great importance be- cause each function probably occupies a different part of the virus, and the radiation action is demonstrating the fact. To repeat in a rather different way, the use of radiation is aimed at exploiting the space relationships of high-energy re- leases in terms of effect on the virus. It is, accordingly, vital to know what these relationships are, and to conduct experiments so that the original relationships are retained. NATURE oF ENERGY Loss By Fast CHARGED PARTICLES The energy loss of a fast, charged particle occurs as a result of its passage near an atom. If it causes an atom to become excited or to lose an electron (i.e., to be ionized), the energy gained by the atom is lost by the particle. This process occurs in terms of a probability only. That is to say, the fast, charged particle can approach 100 atoms in exactly the same way, and for, say, five of these, some sort of excitation can happen whereas the other 95 are entirely unchanged. This method of operation is that required by modern atomic theory. The probability of 0.05 is determined by some quite simple considerations, but it is always no more than a probability. The considerations are as follows. Suppose a charged particle (e.g., a proton) is approaching an atom situated as at A in Fig. 3.la. As the particle moves along its track, the electric field at A takes values something like the indications in Fig. 3.1b. Now while this field is present, the atom, or molecule, is in a highly strained condition, and as a result of this strain may change its configuration to one of the possible excited states, or it may ionize, or, if in a molecule, dissociate. If the flying particle is fast, the field, as a function of time, rises and falls rapidly. If it is slow, the rise and fall is relatively slow. This is indicated in Fig. 3.1¢e. This time plot shows two very important features of radiation action. First, the slow particle produces the strain in the atom or molecule for a longer time and so increases the chance of response by excitation or ionization. Second, the field which rises rapidly and falls rapidly has an equivalent fre- IONIZING RADIATION AND VIRUSES WA quency spectrum with many high-frequency components, whereas the other has mainly lower frequency components. Since we have the familiar equivalence HE = hy, where FE is energy, his Planck’s constant, and v is frequency, the very-high- energy transitions are less likely for a slow particle than for a fast particle. (a) Position of Particle Slow particle Field (c) Fast Particle | Time Fig. 3.1. (a) represents the flight of a fast particle past an atom at A. (b) shows schematically the electric field at A as the particle passes. (c) shows the same referred to time, allowing for the velocity of the particle. Notice that, because all that is important is the field, the mass of the flying particle is unimportant. This whole process has been subjected to rigorous theoretical analysis, for the case where A is a hydrogen atom, by Bethe (1930) and Bloch (1931). A simple and clear account of the theory is given by Fermi in his book Nuclear Physics (1949). The extension to more complex atoms can be made by a mixture ie THE PHYSICS OF VIRUSES of experiment and theory. Two basic relations are derived. The first concerns the number, dn, of ionizing processes (primary ionizations) of energy between W and Ws, and is Onset (I 1 dn = aro NZ ba — ra da (eI) where z is the number of elementary charges on the flying particle, e is the electronic charge, N is the number of atoms traversed per unit length, Z is the number of electrons per atom, dx is the distance traveled, m is the mass of the electron, and v is the velocity of the flying particle. If we consider energy-loss values between W and W + dW, then the above formula becomes Wnr27e4 dW d-n = ING mv WW? da (Ge) where, now, d’n is the number of primary ionizations of energy between W and W + dW in the length of path dz. The rate of loss of energy is also important. In principle, it is given by the integral of Eq. 3.2 over all possible values of W. This is complicated by the fact that a somewhat different rela-. tion holds for excitations, which have discrete energies, and by the fact that both an upper and a lower limit to the possible values of W exist. The upper limit is set by the fact that energy transfers in excess of the conservation of momentum may not take place, and the lower limit by the fact that the first excited state of the atom must be reached. When these are duly processed, the result obtained (for heavy particles, not electrons) is, to a first approximation, , ANT Dmin? dE 4re!*NZ : | ma (3.3) dx mv? I where —dH/dz is the rate of energy loss with distance, and I is an equivalent excitation potential which must be found by experiment. IONIZING RADIATION AND VIRUSES to Equation 3.3 has been checked very accurately in nuclear physics and cosmic-ray work. Its use, within the proper ap- proximation limits, is therefore justified. For electrons there is the added feature of the possibility of exchange between the flying electron and an orbital electron. This modifies the result to dE 2%re*NZ mov2k’ 2 2 dx one {in 217(1 — B?) Geo) the IE 7b a) esa item (3.4) where E’ is the kinetic energy of the electron, and 8 is the ratio of electron velocity to that of light. One important point arises regarding loss of energy by com- pounds. Chemical binding runs around 5 ev per bond, whereas ionization processes are around 100 ev. It is therefore reasonable that chemical binding should not affect particle energy loss, to a good approximation. Preiss has verified this for C,Ho, C.H., and CH,, where the loss of energy is measured to be essentially that of an atomic mixture in the right chemical proportions. Some useful values of J are given in Table 3.1. TABLE 3.1 VALUES OF THE ErrecTIvE Excitation PoTENTIAL FOR ELEMENTS Element IT (ev) Reference H 16 Siri (1949) Cc 64 Preiss and Pollard (unpublished) N 81 Siri (1949) O 99 Siri (1949) 1p 173 Siri (1949) Returning to viruses, the energy lost in traversing the diam- eter of southern bean mosaic virus by various classes of particle is given in Table 3.2. It can be seen from the table that a 0.5-Mev deuteron, which can readily traverse a virus particle, releases a very large amount of energy per virus. Loss of function after receiving this much energy is not surprising. On the other hand, for a 10-Mev pro- 74 THE PHYSICS OF VIRUSES TABLE 3.2 Rate or Eneray Loss spy Various Kinps or PARTICLE Energy loss in ev per ° Particle 100 A in average protein Loss in SBMV 0.5-Mev deuteron 839 9.517 1.0-Mev deuteron 597 1,791 3.0-Mev deuteron 279 837 10.0-Mev deuteron 97 291 10.0-Mev proton 64 193 10.0-Mey alpha particle 746 2,240 2.0-Mev electron 215 8.25 ton, the loss of energy is less by a factor of 10, and for a 2-Mev electron it is quite small. SPACE DISTRIBUTION OF PRIMARY IONIZATIONS The actual energy loss is in no sense a continuous process but oecurs in discrete events, primary ionizations and primary excitations. The number of the former along an electron track can be measured in a Wilson cloud chamber, and in this way the average energy release per primary lonization can be estimated. This can be done, and the process is described by the author (Pollard, 1953). The figure found is 110 ev, on the average, for a primary ionization. Associated with each primary ionization are about three primary excitations with an average energy of 10 ev each. Each primary ionization has secondary electron tracks associated with it, but the ionization produced by these, averag- ing two ion pairs, is mostly within 7 A of the primary event. The picture to carry in mind is represented in Fig. 3.2. The kind of energy loss for four representative particles along the length of the track is shown in Fig. 3.2a. The ionization and excitation events are confined to about 5 A distance from the track for a deuteron, and about 25 A for an electron. In Fig. 3.2b, the appearance looking down the track is shown. The virus traversed is supposed to have a thickness of 500 A. Exploitation of these space relationships can be made in three ways. (a). Heavy particles, which are unavoidably randomly IONIZING RADIATION AND VIRUSES 75 (a) —&$—————_.—+, +_ Qo Bier Deuteron ° e 2 0.8-Mev. (c) 20 ° ° e Deuteron oC 4Mev. (4) Cap Ofer SP GOI IGS hips particle (a) O© PRIMARY IONIZATION --o-- SECONDARY IONIZATION e EXCITATION Fic. 3.2. Events along, (a), and across, (b), the track of fast particles. The large circles are primary ionizations, the small circles secondary, and the black dots are excitations. The very large circle in (a) is about the size of a protein molecule, as the vertical dashes are 100 A apart. 76 THE PHYSICS OF VIRUSES distributed in area, are fired at the virus, and it is supposed that along the track there is dense enough ionization to produce a detectable effect. For this purpose, slow deuterons or alpha particles are suitable. The resulting measurement yields a ‘“‘eross section,” or equivalent area. (b). Faster heavy particles, which ionize more sparsely, are used for bombardment. These produce primary ionizations spaced somewhat like the dimensions of the element of the virus under study. By varying the particle speed, and hence the ion spacing, the effective depth of the radiation-sensitive region can be studied. (c). Fast-electron bombardment is used. This essentially gives lonizations which are random in volume because the ion- ization is sparse, is laterally spread, and the electrons scatter readily. This kind of bombardment measures the volume of the sensitive element. By this triple attack, it is possible to get an estimate of the size and shape of a single, sensitive element, or the size and num- ber of a multiple element. The method is relatively new in this kind of application but has yielded quite valid information in studies of enzymes, hormones, and antibiotics. These studies are described in the review article quoted (Pollard, 1953), and, to summarize the findings briefly, it can be said that the arrival of a primary ionization in a dry enzyme or hormone, in 15 separate measured cases, results either in the removal of its biological function, or in the removal of a definite fraction cor- responding to a definite unit of substructure (as for catalase). The premise that a primary ionization can be used to “feel out” the sensitive shape is therefore justified, as far as a pre- liminary study goes, at all events. In using the method, it must be borne in mind that in the preceding description no explanation of the action of 1onizing radiation has been given. All that has been done is to suppose it is drastic and disruptive. In actual fact, evidence is accumulat- ing to the effect that only some of the observed consequences of ionizing-radiation action in the dry state are due to such high- energy disruption. A part is more gentle and possibly more IONIZING RADIATION AND VIRUSES C00 widespread. This shows as a part which is temperature sensitive and also possibly depends on the previous treatment of the virus. As understanding of this dual action proceeds, radiation studies will become more powerful. EXPERIMENTAL METHODS AND SOME RESULTS It has been pointed out that the space relationships of ioniza- tion must be retained in the bombardment technique. To be reasonably sure of this, the virus must be bombarded dry and in vacuum. It will be seen later that this is not absolutely necessary, but this conclusion can not be drawn until dry bombardment has been carried out. Dry bombardment of TMV by X-rays was first employed by Gowen (1940) and by Lea, Smith, Holmes, and Markham (1944), who were clearly aiming at exploiting the physical action of radiation just described. X-radiation of sufh- cient intensity requires somewhat specialized equipment. Much shorter exposure times can be used if electrons, deuterons, or alpha particles are used. Lea made some use of alpha-particle bombardment, but, until recently, radioactive sources of suf- ficient purity, homogeneity, and intensity have been hard to come by. The modification of a cyclotron for deuteron bombardment is shown in Fig. 3.3 in schematic fashion. The deuteron beam is defined by an insulated, positively charged diaphragm, and en- ters a bombardment chamber without striking any metal except a brass shutter or the sample holder. The beam entering the chamber is slowly diverging and, because the bombardment chamber is 8 ft from the cyclotron vacuum chamber, is uniform in cross section over a diameter of about 5¢ in. The beam is measured by a calibrated galvanometer which reads current col- lected by the whole bombardment chamber, which is insulated. The samples are placed on glass coverslips attached by a spot of grease to a brass disk. These are shown in the lower part of the figure. ‘These are successively rotated into place with the cyclo- tron off, the beam is turned up from the control room, and the shutter is electrically operated from there for the appropriate time. 718 THE PHYSICS OF VIRUSES Deuterons of different energy are obtained by putting foils over the samples. The whole unit is evacuated to the cyclotron vacuum of about 10-° mm mercury. Insulated Diaphragm E+ [m/e il ea Samples Shutter Insulating Gasket Fic. 3.3. Use of a deuteron beam from a cyclotron to bombard viruses. The upper drawing shows the side view, and the lower is an enlarged view of the end with the sample holder and shutter indicated schematically. Results of deuteron bombardment of T-1 bacteriophage are shown in Fig. 3.4. The data are due to Pollard and Forro (1951). It can be seen that a semilogarithmic relation between the per- cent of infectivity surviving and number of deuterons per square centimeter employed in bombardment holds. This is the charac- IONIZING RADIATION AND VIRUSES 79 teristic relation for random bombardment which is expected to produce the result (see, for example, Pollard, 1953) ln Se) (S25) Ny 100 50 Percent Survival i \ | aihe 20 40 60 80 100 x10” Deuterons /opp2 Fic. 3.4. Percent survival of T-1 phage after various amounts of deuteron bombardment. The relation In (n/no) = —SD is seen to be obeyed (Pollard and Forro, 1951). where 7 is the initial measure of infectivity, n 1s the amount left after a “dose” D of deuterons per unit area, and S is the effective cross section. S is determined from the above relation, and the problem of interpretation is to take this theoretical number and show its significance in virus structure. It will be 80 THE PHYSICS OF VIRUSES seen later that this is simple for some viruses. It is quite hard for T-1. In Fig. 3.5 are shown some unpublished results of Fluke, who subjected T-1 phage to electron bombardment, using 2-Mev electrons from a Van de Graaff accelerator. Again, a semilog- arithmic relation is found when percent survival is plotted aa SES ° 2 ) a) & re) ro) > a ia) — =) op) ° ie) ° ° | 4 6 8 10 12 Microcoulombs of Beam Fic. 3.5. Electron bombardment of T-1 phage. The survival ratio fits the relation In (n/no) = —VJ. Data due to Fluke. against primary ionizations per cubic centimeter. This relation corresponds to a bombardment which is random in volume, and so fits the equivalent relation eee et Vai (3.6) no where V, the inactivation volume, now takes the place of S, the cross section. I is the number of primary ionizations per IONIZING RADIATION AND VIRUSES 81 cubic centimeter. Again, the interpretation of V in terms of virus structure has to be made. The third type of experiment is illustrated by Fig. 3.6 where the effective cross section, S, taken from deuteron bombard- ment experiments, is plotted against the energy loss on the part of the deuteron for four viruses: TMV, SBMV, T-1 coli, and M-5 megaterium phage. The deuteron energy loss is varied by aloe T —@ —-¢-—M-5 Phage - 2 Oe é —O_-— Tmv 2x10 ‘cm? Oo ae rae —A__ +. T-| Phage a A ——>—_ SBMV a Be 7 oe © ae @ ee 6 Hi De ae ero 3 We ee =i) a 7) af is Ts 5; Rr RN wl 4 ea eee 3 / 2m L 7? a eae re) / ee Ve ES © yy Oe y, Cae & / Ze 100 200 300 400 500 600 700 800 900 Energy loss in ev per |OO A Fic. 3.6. Inactivation cross sections of TMV, M-5, SBMV, and T-1 for bombardment by deuterons of various energies and, hence, rates of energy loss. The cross section approaches a maximum for TMV, M-5, and SBMV, but not for T-1. interposing foils in the path of the beam, thus reducing the velocity of the particle and increasing the rate of energy loss. Three types of curve are seen which illustrate three classes of virus and probably express three different internal morphologies. The first, for TMV (a purified preparation assayed by lesion count on Nicotiana glutinosa), shows no change in S as a func- tion of ion density, or rate of energy loss. Within reason, S corresponds to the whole area (actually 80%) of the infectious unit of TMV. The second, for southern bean mosaic virus, shows an increasing cross section which flattens at high ion density 82 THE PHYSICS OF VIRUSES to give an area which is about that of the whole dried virus. The value of S for more sparse ionization is definitely less. The third case, a large bacterial virus, M-5 megateriwm phage, shows a definite flattening in cross section area, and so is similar to SBMV, but also has a lower cross section for fast deuterons. The total cross section at high deuteron energy loss is probably less than that of the whole virus, but since it is a definite value over a finite range of energy loss, there seems to be reason to believe that a definite part of the virus is radiation sensitive. The fact that not all of a large virus need be radiation sensitive was pointed out by Lea (1947). The fourth case, of T-1, shows a steady rise in effective cross section, which may perhaps be showing some flattening if correction is made for the fact that alpha-particle bombardment, which was used for the extreme point, brings with it a larger number of energetic, secondary electrons (delta rays), and these may give an excessively high apparent efficiency to an alpha particle. This correction is indicated by the dotted line. ANALYSIS OF BOMBARDMENT RESULTS It has been stressed that these findings are to be expressed in terms of the space relationships of energy loss by the bombard- ing particle. These are most simply (but not fully) described in terms of the occurrence of average primary ionizations at an energy cost of 100 ev per event. Using this description, the events in the three cases are shown schematically in Fig. 3.7. In this representation, the two extremes of low- and high-energy loss are shown in terms of the distribution of primary ionizations (black dots) along the particle track. It is clear that for TMV one primary ionization removes the infectivity. For SBMV, more than this is required, but probably between one and three repre- sents the number which will destroy infective function. On the other hand, for 'T-1 there is a steady increase in effectiveness as the deuteron specific ionization becomes greater. It is clear that all viruses do not behave in the same way as regards primary ionization. The only simple case that can be easily treated is TMV. The assumption can be made that one IONIZING RADIATION AND VIRUSES $3 primary ionization anywhere in some sensitive volume can in- activate the virus. Then the results of electron bombardment and deuteron bombardment can be combined to deduce the shape of the virus. This has been done by Pollard and Dimond (1953) as follows. The experimental deuteron cross section is 19 & 107!” TMV ial SBMV aA~ Fig. 3.7. A schematic representation of the passage of (a) a deuteron losing 200 ev per 100 A, and (b) 600 ev per 100 A, through three viruses. In all cases, more than one primary ionization occurs in the virus. This inactivates purified TMV, but more energy is needed for SBMV, and this is supplied in case (b). T-1 can survive even this. T-1 thus presumably has a more complex morphology. em”. Assuming that the target is randomly oriented, the true cross section is 4/7 times this, or roughly 24 & 107~!? em?®. Elec- tron bombardment gave an inactivation volume of 3.1 X 107" em*. Suppose the virus is a cylinder of radius r and length 1. Then co rl = 97 << 10 em? rat = anh < We enn 84 THE PHYSICS OF VIRUSES which lead to r = 98 A, and I = 1,200 A. The radiation data therefore fit a long, thin virus, rather fatter and shorter than that fitted by the electron microscope data. The measurements are not accurate enough to do more than claim a fair check and to conclude that not quite all (about 80%) of the virus is highly sensitive. Unfortunately, TMV is the only virus so far studied for which a consistent analysis can be made. To show the kind of trouble encountered, the figures for SBMV are here analyzed. The deuteron cross section is 6.2 X 1072 em®. The inactivation volume from electron data is 3.4 X 107!8 em?. Now we have already stressed that SBMV is spherical (though it may not be so in the dried state). So if we assume a radius 7, we have mr? = 6.2 X 10-” em?; r=141A can — "3.40 >< VOm Siem: r=93 A Although these are not way out of line, from a crude point of view, the “‘electron”’ radius is too small. Also, if the critical volume is as thick as even 186 A (twice the “electron” radius), then deuterons of low ion density should certainly produce one primary ionization in it. Yet if they do, they seemingly don’t al- ways inactivate, because S is not the full value for fast deuterons. Notice that one figure seems to be very reasonable. The radius for maximum deuteron action is a little less than that of the virus in solution, and corresponds rather closely to the radius of the virus less hydration as observed in the electron microscope. To weasel out of the dilemma, it can be supposed that as the virus dries it flattens. The actual sensitive volume is then less than that for the spherical virus. Assuming it to be a flat cylinder, of height h and radius 141 A, the value of h turns out to be 76 A. This effective thickness fits the variable-energy deuteron data of Fig. 3.6 quite well, for in such a thickness, the chance of a deuteron passing through without producing a primary ionization is 22%, so that the observed smaller cross section is quite plausible. The loss in volume from the X-ray scattering volume is 10.4 X 10718 em’, which is rather great to correspond to the known hydration of the virus, There is, there- IONIZING RADIATION AND VIRUSES 85 fore, something more about the action of ionizing radiation on SBMV which must be invoked to explain the data. Further studies will be needed to bring this out. The case of M-5 phage is somewhat similar to SBMV. The deuteron cross section for very high ion density is 2.05 107'! em’, which is not far from that of the whole virus as seen in electron micrographs. The electron inactivation volume is not in agreement with the above figure for a spherical sensitive region. The value found is 4.0 X 107'8 em’, and applying the same con- siderations as for TMV, without correction for random orienta- tion, we find zr2l = 4.0 X 107!8 and 27l = 2.05 X 10-1", so that r = 12.5 A and 1 = 8,200 A. The sensitive part is, therefore, long and thin and must be coiled up in the virus. Unfortunately, this does not fit the ion-density curve, for this indicates that there is an average of one primary ionization per target thickness at an energy loss of 250 ev/100 A, giving a target thickness of 100 X 110/250 = 44 A. The diameter calculated above is 25 Av about half of this. It is once again likely that a critical energy must be expended in M-5 phage before inactivation can occur. There seems, however, to be no doubt that the sensitive volume is long and thin, perhaps of the order of 50 X 3,000 A. Turning to the fourth virus, T-1 phage, there is a clear neces- sity for some added feature beyond the sensitivity of a certain part of the virus to one primary ionization. At all events, this part can not be concentrated in one vo!ume. In the first place, no definite maximum area can be assigned. In Fig. 3.6 an attempt to correct the cross section for fast secondaries (delta rays) has been made and is shown as the dotted line. Making a guess at the maximum value we get 15 X 107! cm’. The inactivation volume found by Slater (1951) for electron bombardment is 2.4 50%) due to primary ionization, but that in dilute solution it is largely due to the indirect effect of secondary prod- ucts produced in water. SUMMARY OF Utinity or RapIATION STUDIES We can now summarize the value of radiation work. Infectwity. (a). Bombardment of dry virus at high specific ionization should give the virus cross sectional area. (b). Variation of specific ionization should give evidence of the presence of internal structure. (c). Bombardment of dry virus by electrons should give an inactivation volume to be correlated with the results of (5). Detailed Virus Properties. (a). Dry bombardment at high specific ionization should give the total area involved for such factors as adsorption, killing power, and serological affinity. IONIZING RADIATION AND VIRUSES 91 (b). Varying the specific ionization should show the approxi- mate depth of the units responsible for these factors. (c). Dry electron bombardment should give the total volume of each factor. (d). Wet bombardment should enable some idea to be found of the degree to which these factors are involved with the surface. ReEsuuts oF INFEcTIVITY STUDIES An excellent account of some of the earlier studies on viruses is given by Lea (1947). Among the first of these were studies by Gowen and Lucas (1939) on vaccinia and by Gowen (1940) on tobacco mosaic virus. The probable complication from the indirect effect of radiation was not properly realized at first, although Gowen’s work on TMV includes dry inactivation. The best summary of data up to 1946 is undoubtedly that of Lea, who concludes from the data then available that the inacti- vation volume can be used as a measure of the virus size for the smaller viruses. It has been pointed out that this cannot be maintained in view of more recent work under what should be better conditions. Nevertheless, the use of ionizing radiation as a means of determining some critical volume of importance to infectivity seems to have been suggested by Gowen (1940), Wollman, Holweck, and Luria (1940), Lea (1940), and Luria and Exner (1941) at very nearly the same time. Of particular interest among work done at this time is Lea’s analysis of the available data on vaccinia. Remarkably advanced studies on this virus were made by Lea and Salaman (1942). The virus was irradiated dry, by gamma rays, X-rays, and alpha particles. The inactivation dose for vaccinia is 80,000 r. At this figure there is 37%, or e~1, survival. Using the conversion factor of 6.13 XK 10" primary ions em? for 1 rep, and assuming roent- gens and rep to be equivalent, the inactivation volume is found to be 2.04 X 107'7 em?. The actual volume, judged from electron micrographs, is roughly 9 X 107 ecm‘, so that the volume sensitive to one primary ionization is only one four-hundredth of the whole virus, in round numbers. The inactivation dose for alpha particles was 211,000 r, which can be reduced to number of particles per square centimeter by using the fact that 6.5 X 104 92 THE PHYSICS OF VIRUSES particles em? correspond to 1 r (no use of rep here), and thus the sensitive area, S, can be found. It is 7.3 * 107!! em?. The whole virus area is 5.5 X 107!° em?, which is eight times larger. Lea proposes to reconcile all these figures by supposing that there is an internal genetic structure which is radiation sensitive. It consists of n units each of radius 7, as a first approximation. Putting in the two relations n(4/3)mr3? = 2.04 X 107!" and nrr? = 7.3 X 107!!, we deduce 296 units of radius 21 A. This is only a very first trial of such radiation analysis of internal structure, but it is significant that electron micrographs show clearly that there 7s a substructure; and 296 units in it is not a hopelessly implausible figure. The danger of this type of reason- ing lies in the fact that the nongenetie part is still somewhat radiation sensitive, so that the alpha-particle cross section may contain a part which is not genetic. This would modify that conclusion to give fewer, bigger, units. When the various features of radiation sensitivity have been sorted out and understood, the deductions regarding internal structure will be of the utmost value. Before passing on to consider some of the more recent work on viruses and ionizing radiation, we give a table of some of the measured inactivation cross sections and inactivation volumes, TABLE 3.3 INACTIVATION DIMENSIONS Virus Virus Cross Volume area volume Radiation Virus section (A?) (A3) (A2) (A3) reference TMV 2.05 X 105 3.7 X 107 Ot x 08 4.5 X 107 Pollard and Dimond (1953) SBMV 6.2 X 104 3.4 X 106 6.2 X 104 11.8 X 108 Pollard and Dimond (1953) M-5, phage 2.10 X 105 4.0 X 108 3 X 105 Friedman and Pollard (1953) T-1 phage 1.6 X 105 2.4 X 108 3X 105 7.5 X 107 Pollard and _ Forro (1951) Influenza 3 X 10° (rough) -= 106 8 X 107 Woese and Pollard (1953) Bushy stunt Sex 104 3.62 X 106 5.4 X 104 7.4 106 Lea and Smith (1942) Vaccinia 7.3 X 105 2.0 X 107 5 X 108 9 X 109 Lea and Smith (1942) Tobacco necrosis — 2.9 X 106 6.0 X 104 11.0 X 106 Lea and Smith (1942) Newcastle disease 6.9 X 105 — 106 8 X 107 Woese and Pollard (1953) IONIZING RADIATION AND VIRUSES 93 with the virus dimensions given for comparisons. It can be seen that the cross sections of the smaller viruses, as determined from heavy-particle bombardment at high rates of energy loss, are in fair agreement with the accepted area. These do not depend on the concept that one primary ionization inactivates the whole virus, but often correspond to 10 or 20 such ioniza- tions for the effect to be produced. The volume figures, based on this assumption, do not (in general) agree with the whole virus, which can be taken to mean that there is an internal structure of different sensitivity. Radiation measurements should be able to shed some light on this. However, more must be known of radiation action before this can be determined; and to show what other features are present we consider two other experiments which bear on this, though they do not as yet clear it up. CoMBINED THERMAL AND IONIZING-RADIATION ACTION ON A Virus Heat, or perhaps more properly, exposure to temperature, inactivates viruses. It does so by a persistent low-energy agita- tion of some sensitive molecular structure which after a while, aided by fluctuations, gives way to produce inactivation. The threshold energy at the sensitive point turns out to be of the order of 30,000 calories/mole or thereabouts, which is about 1.3 ev. This is far below the 110 ev of a primary ionization, and so one would think that it could confidently be asserted that changing the temperature of a virus while it is being irradiated should have no effect. This turns out to be partly true and partly not true. If the radiation is volume random, so that no more than one average primary ionization can occur in a sensi- tive volume at a given time, the measured inactivation volume is (for one bacterial virus—T-1) constant from —80° C to 45° C. This was found by Adams and the author (1952). Above 45° C, the inactivation volume rises rather sharply. These results are shown in Fig. 3.8a. Moreover, if the radiation is densely ionizing, there is a thermal effect even as low as liquid-air temperatures, as can be seen from Fig. 3.8b. The thermal effect becomes more marked at higher temperatures, indicating that at about 45° C an 3 cm 35 ™ wn Variation of T-I sensitivity to X-rays with temperature -18 Inactivation volume in 10 a bombarded dry ™ So Ss - 80 - 60 -40 -20 0 20 40 60 80 100 Temperature in °C (a) 8 Ofo 7 ° Variation of T-1 Phage cross section (deuterons) with temperature ° 6 So 5 N O E on . © 4 <= c 6° = 3 = : 3 to} z i= Oe, ! 0 50 100 150 200 250 300 350 400 450 Temperature in “Kelvin (b) Fig. 3.8. Effect of combined primary ionization and temperature on T-1. (a) shows the effect of X-rays, and (b) deuterons. There is clearly a differential sensitivity corresponding to two types of radiation action, one intense and the other more gentle and depending on the condition of the virus. 94 IONIZING RADIATION AND VIRUSES 95 additional effect becomes apparent. Similar results have been obtained independently by Bachofer (1953). These results show that a virus such as T-1 cannot be re- garded as homogeneous, even within that part which is radiation sensitive. The fact that there is an interplay between high- energy (ionization) and low-energy (thermal) effects indicates that either transfer of energy through the virus to a sensitive part, or damage to a larger part of the virus, is facilitated by irradiation at high temperature. A second experiment, carried out by Adams and the author (1953), sheds some light on this question. The latent period of 'T-1 was studied for those virus particles which had undergone many deuteron hits but had survived. It was found that the latent period for these survivors is increased significantly, in agreement with a finding of Luria (1944) that ultraviolet light produces such action. The increase in the latent period was a function of the number of hits received, and this indicates that there is apparently a part of the virus which does not determine whether the virus will multiply but does determine the rate. The results of deuteron bombardment of T-1, with consequent action on the latent period, are shown in Fig. 3.9. The ratio of the measured latent period to that found after deuteron bombardment is plotted versus the number of deuteron hits on an assumed maximum sensitive area of 2 X 1071! cm’. A linear increase is observed, with a doubling of the latent period for 15 hits. Some more recent work by Fluke indicates that the burst size for radiation survivors is diminished. It is tempting to suppose that a part of the virus consists of an enzyme system which is related to the bacterial chemical content and which produces virus precursors. By damaging individual enzyme molecules, the rate of multiplication, and also the amount of precursor material available for manufacture of virus, is reduced. So we conclude that the virus contains a rather large number of enzyme molecules which are only concerned with rate of multi- plication. Probably not many types of viral enzymes are involved. The enhanced effect of temperature is thus to be thought of as taking place on this enzyme-like system. The effect of tem- 96 THE PHYSICS OF VIRUSES perature is, therefore, to increase the volume inactivated and not to increase the sensitivity of a highly significant target volume. These two experiments show that the simple considerations advanced by Lea and used by him to deduce an internal struc- ture for vaccinia cannot be applied with certainty. First, the part of radiation action which seemingly inflicts damage, which can B25 - ® a e oO 5 I o E20 ros oO Ratio Latent Period“ (0) 5 10 15 20 25 Deuterons Threading Sensitive Area Fic. 3.9. Increase in latent period of T-1 phage due to deuteron bombardment. accumulate to be fatal, must be ascertained and eliminated from the calculations. Then the area and volume technique can be used for analysis of internal structure. STRUCTURAL DEDUCTIONS Applying this idea to T-1 phage turns out to be rather hard because the laborious experiments to determine the nontempera- ture-dependent cross section at high ion density have not yet been made. The figures now available show that the measured IONIZING RADIATION AND VIRUSES 97 area and volume values require either a highly multiple genetic structure for T-1 or else a long, thin genetic structure. The best guess at present is a long cylinder of radius 26 A and length 1,900 A. For the two plant viruses so far studied, the “ genetic’ part, which is essential for survival, seems to be very nearly the whole virus, at least the unhydrated part of the virus. Returning to T-1, we can make some analysis of the increase in latent period. Adams and Pollard’s data indicates that X-ray bombardment corresponding to 25 primary ionizations per phage particle will just double the latent period. Now if we suppose that there is some critical concentration of a virus precursor which must be reached very rapidly, we can suppose that the full burden of the manufacture of this special precursor falls on the virus itself. Perhaps it is this which converts the basterial metabolism so rapidly to virus synthesis. The 25 pri- mary ionizations can be thought of as inactivating 25 molecules responsible for this. Since the latent period is doubled by this bombardment, the rate of precursor synthesis is halved, so that 25 molecules are left, making an initial total of 50. Now, 15 deuterons produce the same effect. These deuterons each produce 15 primary ionizations in the virus, or a total of 225 primary ionizations. Thus the dense tracks of deuterons make an inefficient use of the primary ionizations, which indi- cates that each of the sensitive molecules is large—large enough to include several primary ionizations: If these hypothetical molecules are considered to be spherical, their radius must exceed 50 A. Actually, if we speculate that the whole virus volume is divided into 50 units, and consider these as spherical, the radius of each is 75 A. This would make the deuteron and X-ray data roughly fit. The molecular weight of each unit would be roughly 1,000,000. . These units are possibly nucleoprotein units of some kind since the total nucleic acid in the virus far exceeds the assumed purely genetic part. This type of estimate is a mixture of speculation and reality. The fact that 25 primary ionizations 5 98 THE PHYSICS OF VIRUSES only reduce enzymatic rates by a factor of two argues that there must be many enzymes. So the existence of a multiple enzymatic structure, capable of rapidly changing bacterial metabolism, is strongly suggested by these experiments. The speculation could be reduced and the validity of description increased by better experimentation, which lies ahead. VARIED EFFrects OF X-RADIATION ON BACTERIOPHAGE In aremarkable series of experiments, Watson (1950, 1952) has studied various actions of X-radiation on T-2 bacteriophage. Watson’s work is largely qualitative in that he seeks the nature of the radiation action and is only concerned with its magnitude in passing, so to speak. The studies involve many of the known properties of bacteriophage, such as adsorption, ability to kill bacteria, ability to multiply, and ability to be photoreactivated. Care was taken to distinguish between primary-ionization (direct) effects and indirect action as far as could be done. The direct effect was magnified by irradiation in broth suspension and studied first. The second paper concerns indirect action in dilute synthetic medium. The effect of X-rays on the individual phage properties was studied under the two limiting conditions for direct and indirect action. The numerical following up of Watson’s work with deuteron, electron, and ultraviolet irradiation will be of tremendous value in determining the internal structure of bacteriophage. From Watson’s paper the following facts can be determined. Adsorption. For an estimated bombardment of 1.9 10! pri- mary ionizations/em®, the loss of ability to adsorb was less than 5%. It can be concluded that the inactivation volume for adsorption is less than 6 X 10~?° em®. It is very likely that this inactivation process will turn out to be multiple hit. Valuable information about the bacterial surface should result from study- ing it. The molecular unit involved must have a molecular weight of less than 4,000. Virus Activity. Measured simply in terms of virus activity the inactivation volume of T-2, T-4, and T-6 is 4.2 X 107!" em’, which is one-sixth the electron-micrograph volume. This is IONIZING RADIATION AND VIRUSES 99 actually a rather larger fraction than is found for T-1 phage, and shows that some characterization of viruses in this way is possible. Bacterial Killing Ability. The results of studying the reduction of bacterial colony counts by T-2 phage after irradiation are shown in Fig. 3.10. It can be seen that a semilogarithmic in- activation of the killing fraction takes place. The inactivation Per cent Remaining Activity | 2 3xlO’r Dose Fig. 3.10. Inactivation of bacterial killing power (solid line) and ability to form plaques (dotted line) as a result of X-ray bombardment. Data due to Watson (1950). The killing power inactivation volume is clearly less. volume for this is one-third of that for virus activity, and so is about one-eighteenth of the whole virus. Lysis from Without. If enough virus particles attach to a bacterium, it is lysed without being entered by the virus. This ability is not destroyed by X-irradiation even when the ability to kill has been destroyed. Presumably this property also has a small inactivation volume. 100 THE PHYSICS OF VIRUSES STRUCTURAL INFERENCES FROM RapIATION STUDIES In Fig. 2.13 we showed the appearance of two plant viruses which results from studies of sedimentation, diffusion, and X-ray scattering. Since the most detailed radiation studies have been made on bacterial viruses, we show in Fig. 3.11 what can be GY Mg Infectivity OO-4 Killing power Kock" Latent period a Fic. 3.11. Schematic representation of the various radiation cross sections of a T-series bacteriophage. The various factors are not put in place, but their relative areas are indicated. inferred about bacterial virus structure from the considerations outlined in this chapter. The picture is unfortunately a composite of ‘T-1 and T-2 bacteriophage, which is probably an unjustified synthesis of two very different viruses. This is no great detri- ment since careful enough studies of any one virus have yet to be made. The picture is, therefore, meant to give a general impres- sion of two things—what the internal structure of a virus may be IONIZING RADIATION AND VIRUSES 101 like, and what factors can be determined by careful radiation study. The part of the virus which is needed for infectivity and which can be destroyed by one primary ionization is shown as long and thin, just above the tail of the virus. That it is long and thin is probable, that it is straight is pure guessing mixed with a little laziness in drawing. The smaller killing fraction is drawn double-cross-hatched. The 50 enzyme-like units are shown, crudely to scale, and the whole is encased in some outer part which is seemingly not very radiation sensitive. The reader should notice that this is wholly derived from electron microscopy (for the outer shape) and deductions from radiation work. The picture now has to fit other physical and chemical studies but, most importantly, it must check with all the purely biological findings. When a more complete picture, including information from ultraviolet action spectra and surface studies is drawn, an attempt to see whether the resulting picture ean work will be made. A very good analogy for the kind of information assembled in this way is a series of geographic maps of a nation in which climate, population, height, and mineral deposits are separately indicated. The sum of the maps should tell a lot about the general character of the nation, and all should mutually agree. We have here assembled an early version of one map of a virus in terms of radiation action. Others can be made and all should fit into an inferred, but true, structure. REFERENCES For general references on radiation action there are three valuableibooks: Lea, D. E., Actions of Radiations on Living Cells (Macmillan Co., New York, 1947); Timofeeff-Ressovsky, N. K., and Zimmer, K. G., Das Treffer Prinzip in der Biologie (Hirzel, Leipsig, 1947); and the Oberlin Symposium Report: Nickson, J. J., Symposium on Radiobiology (John Wiley and Sons, Inc., New York, 1952). The principles of using radiation to study molecular organization are elaborated by Pollard in Advances in Biol. and Med. Phys. 3, 153 (1958). The more detailed references follow below. Adams, W. R., and Pollard, E. C., In course of publication (1953). Adams, W. R., and Pollard, E. C., Arch. Biochem. and Biophys. 36, 311 (1952). 102 THE PHYSICS OF VIRUSES Bachofer, C.S, Science 117, 280 (1953). Barron, E. 5. G., and Dickman, 5., J. Gen. Physiol. 32, 595 (1949). Bethe, H. A., in Handbuch der Physik Vol. 24, 273 (Springer, Berlin, 1933). Bloch, F., Ann. Physik 16, 285 (1933). Dale, W. M., Biochem. J. 34, 1367 (1940); 36, 80 (1942). Evans, R. D., Advances in Biol. and Med. Phys. 1, 151 (1949). Fermi, E., Nuclear Physics, p. 27 (University of Chicago Press, Chicago, 1949). Fricke, H., and Petersen, B. W., Am. J. Roentgenol. Radium Therapy 17, 611 (1927). Fricke, H., Cold Spring Harbor Symposia Quant. Biol. 2, 241 (1934). Friedewald, W. F., and Anderson, R. 8., Proc. Soc. Exptl. Biol. Med. 45, 713 (1940). Friedman, M., and Pollard, E., In course of publication (1953). Gowen, J. W., Proc. Natl. Acad. Sci. U.S. 26, 8 (1940). Gowen, J. W., and Lucas, A. M., Science 90, 621 (1939). Guild, W. R., Arch. Biochem. and Biophys. 40, 402 (1952). Lea, D. E., Nature 146, 137 (1940). Lea, D. E., Actions of Radiations on Living Cells (Macmillan Co., New York, 1947). Lea, D. E., and Smith, K. M., Parasitology 34, 227 (1942). Lea, D. E., Smith, K. M., Holmes, B., and Markham, R., Parasitology 36, 110 (1944). Lea, D. E., and Salaman, M. H., Brit. J. Exptl. Pathol. 23, 27 (1942). Luria, 5. E., Proc. Natl. Acad. Sci. U.S. 30, 392 (1944). Luria, S. E., and Exner, F. W., Proc. Natl. Acad. Sci. U.S. 27, 370 (1941). McLaren, A. D., Science 113, 716 (1951). Pollard, E., and Dimond, A. E., In course of publication (1953). Pollard, E., and Forro, F., Jr., Arch. Biochem. and Biophys. 32, 256 (1951). Siri, W. E., Isotopic Tracers and Nuclear Radiations (McGraw-Hill Book Co., Inc., New York, 1949). Watson, J. D., J. Bacteriol. 60, 697 (1950); 68, 473 (1952). Woese, C., and Pollard, E., In course of publication (1953). Wollman, E., Holweck, F., and Luria, S. E., Nature 145, 935 (1940). CHAPTER FOUR THERMAL INACTIVATION OF VIRUSES One of the outstanding features of living things is their insta- bility when acted on by heat. This is not an all or nothing affair— some organisms, like bacterial spores, are stable over a wide temperature range, others are highly sensitive. Now heat is a physical agent, and the careful characterization of the action of heat on viruses should at least offer a guide in classifying them and possibly can give information about their structure. As in the case of radiation action, we propose first to give a description of the nature of thermal action. In doing this we are aided by many studies on the thermal denaturation of proteins and the thermal inactivation of enzymes which have been made and analyzed in terms of theory. The basic theory is set out by Glasstone, Laidler, and Eyring (1941), and, more specifically for proteins, by Stearn (1949). A brief account of this theory, modified to suit the present purpose, is here presented. OUTLINE OF THE THEORY OF THERMAL INACTIVATION A virus, or an enzyme, is a large and complex molecular structure. It owes its ability to function to the fact of having inherited a certain rather precise structure from the living cell in which it originated. Heat, the thermal agitation of the atoms that form the molecular structure, is steadily and ceaselessly vibrating the atoms back and forth, and twisting and stretching chemical bonds, and so exerts a steady tendency to alter the structure. It seems likely that biologically formed molecules are not ultimately stable, by which we mean that probably some similar configurations have a lower total potential energy; but they certainly possess a local stability, by which we mean that 1038 104 THE PHYSICS OF VIRUSES the functioning configuration corresponds to one minimum of potential energy, if not the lowest there is. The denaturation of such a molecule can be thought of as the changing of its con- figuration from the inherited form to one of perhaps greater ultimate stability but no longer of the proper form for its function. Now a virus, as we have seen, is not a molecule but an aggre- gate of molecules. Each of these has a function, or plays a part in some function. The loss of biological form on the part of one of these molecules may not necessarily influence the behavior of the virus—it will depend on what feature of its activity we are studying. If, of course, there exists some function which requires the entire virus to be intact, then the loss of this funetion would take place if one molecule were denatured. In practice, it seems as though infectivity is a function which requires at least a great part of the virus to be intact, and probably loss of infectivity follows when one key molecule is inactivated. This will certainly vary from virus to virus. Therefore, as a start, we consider the process of inactivating one large biological molecule and see whether the description of the process is apt for the description of inactivating viruses. In Fig. 4.1 is a token representation of part of a protein molecule. We have taken the Pauling-Corey-Branson (1951) helical structure as a basis for the figure, but this is not essential. There are three classes of bond: The backbone bond, which binds the polypeptide chain, consists of covalent bonds of energy between 3 and 5 ev per bond. These appear in the figure as the bonds forming the helix. There are then the intrachain bonds which make the helix tight and firm, these appear as dashed lines; and the interchain bonds which hold the helices together. In the figure, these are shown as thick dashed lines. These last two types of bond are probably varied in character and include sulfur bridges, hydrogen bonds, and ionic bonds, but they are certainly weaker per bond than the covalent backbone bonds. Such a molecule, possessing, say, eight chains bound together, although nowhere bound with great strength outside of the poly- peptide chain, has a considerable stability. It is instructive to construct a model of even one chain and notice that the THERMAL INACTIVATION OF VIRUSES 105 breaking of one bond does not seem to destroy the configuration. The nearby breaking of several does produce a marked collapse, and it is tempting to think of this as the process involved in denaturation. Now each bond vibrates, or can do so, and, because it is a confined system, the laws of quantum mechanics require that Covalent Bonded Backbone 22S S= Hydrogen Bonds in Helix = on Interhelix Bonds Fig. 4.1. Schematic representation of the three classes of bond in a protein. The helix has considerable binding energy per bond but the hydrogen bonds in each chain, and the interchain bonds, are weaker. only certain restricted vibrational energy levels are possible. We definitely do not intend to go into this whole subject, but we do need to assume that there is a ladder of levels for each form of vibration, and so we will assign to the rth level of a ladder the energy H,. If n of the possible bonds are in the energy level r, and no in that of the ground state, then the most likely configura- tion at a temperature 7’ degrees Kelvin is one for which sey b= eB kr (4.1) 106 THE PHYSICS OF VIRUSES where / is Boltzmann’s constant. The free energy, /, correspond- ing to this class of bond is then (Schrédinger, 1948, p. 13) F = kT In ) eset (4.2) : and by the definition of free energy in thermodynamic terms |p U — TS where U’ is the internal energy and S the entropy. Now U, the internal energy per form of vibration, is » EB eF Ligh "3 3 \ —Er/kT /_€ —_ r U (4.3) which is simply the energy times the population divided by the population to give total energy. We can, therefore, use these expressions to find S, the entropy involved. We then have explicitly: The internal energy, U (or H), per form of vibration is SD o—eVkT DE, Erik yy, eT adk T a The total interna! energy will be the sum of terms of this kind. The free energy per form of vibration is F = kT In) eever r The total free energy is again the sum of terms of this kind. The Entropy, S, for the case where no volume changes is S = pee STALE as }: In e Ek (4.4) Again this must be summed for each form of vibration. THERMAL INACTIVATION OF VIRUSES 107 Returning to the schematic drawing of part of a protein molecule shown in Fig. 4.1, the effect of thermal agitation is to cause excitation of many of the weaker bonds and, possibly to a lesser extent, of the covalent bonds. As the temperature increases, this excitation increases. The excitation is not uniform, except on a long time average, but abnormal excitations can oecur. If one such causes a bond to break, there is a chance that a general irreversible modification of the molecule can follow. This modification may destroy the biological function and, if it does, the assay procedure will detect it as an inactivated molecule. The number, dn, of such molecules inactivated will clearly depend on the time, dé, and on the number, n, of intact molecules present but, because it is not concerned with reaction with external agents in the chemical sense, it will not depend on concentration in any way. The reaction equation is then —dn/dt = kin, where ky, is the reaction constant. This can be integrated to give the relation In (n/no) = —/it, where n/no is the fraction of activity remaining at time f¢. This is usually easily measured, and so the measurement of k; is inherently not a difficult matter. Now the theory of absolute reaction rates (see Stearn, 1948) states that if a monomolecular-type reaction that obeys the above relation takes place, then kT es Ie, = i Coe (4.5) where AF? is the free energy of activation for the process, R is the usual gas constant and h is Planck’s constant. This can be written in terms of the heat of activation, AH, which is the change in internal energy for volume change, and the entropy, AS?, of activation by using the constant-volume relation AEE = NH ENS? If the variation in volume warrants it, the relation AF? = AH* — TAS? + PAV? must be used. 108 THE PHYSICS OF VIRUSES Consider now the three predominant classes of bond. The covalent bond has widely spaced energy levels, so that, for thermal purposes, only two or three values of the energy need be considered. The helix bonds and the interhelix bonds have more closely spaced levels, and so more energy values need to be considered. Eyring’s theory of the activated state supposes that if F is plotted against a general reaction coordinate, which 1s, broadly speaking, a bond length, then there exists a second configuration separated by an intervening hump as shown in | F Bond Distance Fic. 4.2. Representation of a free-energy potential barrier which must be crossed to permit inactivation of a biological molecule. Fig. 4.2. For a large molecule to attain the energy AF? cer- tainly involves many other bonds as well, so that AF? includes changes in covalent, helix, and interhelix bonds. A measured value of AF, therefore, can be analyzed into AH* — TAS}, and corresponds to a total energy requirement of AH? baianced by an entropy term which expresses the effect of a tendency to reach the most probable state. If this expression, AF? = AH*t — TAS}, is substituted into the Eyring formula for absolute reaction rates, it can be seen to yield kT a8! _ aut ky = oA (Beso ha (4.6) where, now, AS? appears as a positive exponent which aids the speed of the reaction, THERMAL INACTIVATION OF VIRUSES 109 In the inactivation of enzymes and the denaturation of proteins, it is common to find values of AS? of the order of 10-100 calories/mole/degree. These produce a drastic change in k,, and it is in order to examine what processes can operate to give a high entropy of activation. Examining Eq. 4.4 for entropy, we see that the first term corresponds to the effect of changing the energy per state of vibration. This can take place if there is considerable expansion (and some recent work by the author indicates that, for proteins, this may be so), but, since the range of temperatures covered in _ biological inactivations is quite small, the predominant cause of an entropy increase is the second term. This means there is an increase in the number of available forms of vibration. Two major reasons for this exist: the first is the opening up of chains, which permits a whole class of pendulum-like oscillations to take place; and the second is the release of bound water which is now free to rotate in two degrees of freedom per molecule where before these possible modes were held down. So when figures are seen later regarding entropies of activation, they are to be associated with these two possibilities. It will be seen, as is reasonable, that in the dry state activation entropies are quite small, so that probably a very large part of the entropy of activation is concerned with hydration. THERMAL INACTIVATION OF VIRUSES Many measurements of the thermal inactivation of viruses have been made since this is a primary piece of knowledge in the handling of pathogens. Not very many are suitable for measuring rate constants and so are not suitable for determining the activation—heat change and entropy change Just discussed. The usual procedure is to describe the 10-min thermal inactiva- tion point, which is obviously a very practical piece of informa- tion but is, alone, not too informative from our point of view. The fact that the thermal inactivation of a bacterial virus follows first-order kinetics was shown by Krueger (1931), who studied a staphylococcus phage. Careful studies on four plant viruses were made by Price (1940). Some of his results are 110 THE PHYSICS OF VIRUSES shown in Fig. 4.3. The natural logarithm of the virus concentra- tion, as determined by counting local lesions on the appropriate plants, is plotted against time, in minutes, for the four viruses tobacco ringspot, tobacco mosaic, tobacco necrosis, and alfalfa . ° Tobacco-ringspot 50C. O-—_ TMV 90C. Alfalfa \ mosaic 62.5C O 10 20 30 40 50 60 70 Time (Minutes) Fic. 4.3. Inactivation of four plant viruses as measured by Price (1940). The logarithm of the concentration is plotted versus time, and first-order kinetics are obeyed. mosaic at the temperatures indicated. In the case of tobacco mosaic virus, Thornberry, Valleau, and Johnson (1938) have studied the thermal inactivation in the dried leaf of the host plant, white burley tobacco, over a very wide temperature range. The data on the dried virus just mentioned can be analyzed according to the Eyring relation. The resulting values found THERMAL INACTIVATION OF VIRUSES 111 are AH* = 25,300 calories/mole and AS? = —7.4 calories /mole/ degree. Some unpublished experiments by the author and Dimond on purified, dry TMV give AH? = 27,000 and ASt = 0. The dry virus is, therefore, characterized by a low or zero entropy of activation and a moderate value of AH?. The low entropy is characteristic of dry substances (Pollard, 1951). The wet inactivation yields two sets of figures. Below about 85° C, the reaction constant varies relatively slowly with temperature, yielding AH? = 40,000 and AS? = 18 in some experiments made by the author and Dimond and which sub- stantially agree with the data obtained by Price. Above about 85° C, the temperature dependence rises markedly. Price’s figures for the undiluted virus correspond to a AH? of 195,000 earlories/mole and a AS? of 410, roughly. The very much larger value of AS* above 85° C speaks for a completely different process taking place. Lauffer and Price (1941) studied the denaturation of ‘TMV with thermal action. TMV behaves in a rather interesting manner at high temperatures. The small frac- tion of nucleic acid is removed from the protein binding, the protein becomes denatured, and goes out of solution. The rate processes for this were carefully measured by Lauffer and Price (1941) with the result that, at pH 6.8, the values of 153,000 for AH? and 370 for AS* were obtained. It is thus clear that infectivity and protein denaturation do not necessarily go together. The latter is characterized by very large entropies of activation, and the former by lower values. If the temperature is high enough, the thermal action on the protein part will stop the virus from functioning faster than will the other process, whatever it may be, which was causing the infectivity loss. It will be seen later that the loss of serological affinity follows a high-entropy type of kinetics and so is presuma- bly related to protein denaturation. The two processes are plotted in Fig. 4.4, in which the rate constants for TMV inactivation and denaturation are plotted versus temperature. The two separate processes of denaturation and infectivity loss are seen to combine in the one curve as measured by Price. It is tempting to suppose that the slow 112 THE PHYSICS OF VIRUSES process of infectivity loss is due to the inactivation of nucleic acid. It is regrettable that so little data on the thermal inactiva- tion of nucleic acid measured in some biologically functional way has been assembled. Some very preliminary work by Fluke and Drew on the transforming factor for pneumococci indicates a rather moderate entropy change. It may well be 10x10" Rate Constant (Fraction per Minute ) 70 80 90 ©. Temperature Fic. 4.4. The rate constant for inactivation (dotted line) and denaturation (sharply rising line) of TMV derived from Price’s (1940) data. The slower in- activation process is superseded by the faster denaturation process at higher temperatures. that this depends on the lightness of the combination between nucleic acid and protein. Similar results were found for tobacco ringspot virus but not for alfalfa mosaic or tobacco necrosis virus. Cherry and Watson (1949) observed a similar effect for a S. lactis phage, which showed a very rapid rate of inactivation at 65° C. The values deduced from their work are given in Table 4.1. A very careful study of the thermal inactivation of T-5 E. cola bacteriophage has been made by Adams (1949). He observed THERMAL INACTIVATION OF VIRUSES 113 TABLE 4.1 THERMAL CONSTANTS FOR THE INACTIVATION OF SOME VIRUSES AH* As? (calories/ (calories/ Virus Condition mole) mole/°C) Reference E. Coli T-1 phage dry 27,500 0 Pollard and Reaume (1951) wet (broth) 95,000 207 Pollard and Reaume (1951) T-2 phage dry 18,000 —12 Pollard and Reaume (1951) wet (broth) 71,700 139 Pollard and Reaume (1951) T-3 phage dry 19,100 —9 Pollard and Reaume (1951) wet (broth) 105,000 246 Pollard and Reaume (1951) T-4 phage wet (broth) 120,000 Adams (1949) T-5 82,000 165 Adams (1949) 1b dry 12,700 —29 Pollard and Reaume (1951) wet (broth) 60,700 114 Pollard and Reaume (1951) B. Megaterium phage M-1 wet (broth) 76,000 165 Friedman (1953) M-2 wet (broth) 82,000 183. Friedman (1953) M-3 wet (broth) 87,000 195 Friedman (1953) M-4 wet (broth) 136,000 347. Friedman (1953) M-5 wet (broth) 112,000 254 Friedman (1953) TMV dry 27,000 0 Pollard and Dimond (1953) wet (pH6.8) 40,000 18 Pollard and Dimond (1953) denaturing 195,000 410 Price (1940) process SBMV dry 17,000 —16 Pollard and Dimond (1953) wet 25,000 = S. Lactis phage wet 30-45° C 11,000 — Cherry and Watson 55-65° C 76,000 = (1949) Tobacco ringspot wet 45-56° C 79,000 — Price (1940) 56-65° C 27,600 — Tobacco necrosis wet 70-95° C 37,300 — . Price (1940) Alfalfa mosaic wet 50-62° C 75,000 — Price (1940) Influenza wet (pH 7) 34,000 39 Lauffer, Carnelly, and MacDonald (1948) 114 THE PHYSICS OF VIRUSES inactivation according to the first-order kinetics already described, and his measurements of the reaction constants for virus in broth lead to the values 81,000 for AH* and 165 for AS*. The important feature of Adam’s studies, however, lies in the effect of varying the concentration of monovalent and divalent ions on the over-all process of thermal inactivation. It was found that if the phage were maintained in phosphate buffer (0.00117), 0.15.7 NaCl, and a little salt-free gelatin, the activity at 37° C was lost in a matter of an hour or two. Adding small concentrations of divalent ions radically changed the rate of inactivation. In following this observation further, Adams measured the reaction constants in 0.1N NaCl and 0.1 sodium citrate at various concentrations in the absence of divalent ions and then in the presence of various concentrations of divalent ions. The kind of effect produced is illustrated in Fig. 4.5. The velocity constant in fraction per second at 50° C is plotted against the concentration of sodium or magnesium ions. The remarkable change in value is clearly shown together with the fact that the same range of rate change is covered at a much higher concentration of sodium than magnesium. For mag- nesium, the rate constant changes proportionally to the third power of the ion concentration, and for sodium it changes approximately as the sixth power. Adams suggests that the lower reaction rates are due to the formation of a complex between phage and magnesium which is much more stable. It is interesting that if AS* values are calculated for various concentrations of Mg**, the values do not vary monotonically but rise from 35 entropy units (calories/mole/°C) to 90 at 10°, fall to 40 at 1074, and rise to about 90 for 107°. and broth. This lack of a regular behavicr probably shows the inherent complexity of thermal inactivation. After all, every part of the virus, whether protein or nucleoprotein, is thermally sensitive, and, moreover, the virus unquestionably comprises many parts combined together by loose physical forces. The inactivation of the virus as regards its infectivity probably in- volves the change of specific structure of only one of these. THERMAL INACTIVATION OF VIRUSES PS Under some circumstances, different units may inactivate first and so be the rate setting unit. It would appear as though varying the ionic concentration causes a shift from one sensitive unit to another. The consideration which determines the par- ticular part is not an entropy but the actual rate at the chosen temperature. The curves of Fig. 4.5, if plotted for rate con- +3 +| Log Velocity Constant (min) -4 Log lonic Concentration Fig. 4.5. Effect of ionic strength on the rate constant for inactivation of T-5 phage. Data due to Adams (1949). stants at 30° C, show appreciable variation from what is shown, notably in a more rapid dependence on ion concentration. It must therefore be remembered that, although thermal- inactivation studies undoubtedly contain valuable information about viruses, the unraveling of the various factors involved will take time. It is of interest that thermal resistance can appear as a mutation. Adams and Lark (1950) have shown that a mutant 116 THE PHYSICS OF VIRUSES form, which transmits hereditarily, is much more stable at low salt concentrations. This mutant adsorbs in the same way and has the same serological affinity and the same latent period as the wild type. At high broth concentrations, the wild type and the mutant are the same. The latent period and the burst size of T-5 are both modified by citrate, which shows that a part of the virus which is not concerned with duplication itself, but rather with rate, exists. This follows the same line as has been mentioned for latent- period increase due to X-ray and deuteron bombardment. The thermal inactivation of four bacteriophages has been studied by Marjorie Reaume and the author (Pollard and Reaume, 1951). The inactivation, both wet and dry, was studied with results which can be seen from Table 4.1. The striking fact is that in the dry state the entropy is very greatly reduced and is actually very nearly zero. The entropy does not seem to be related to the size of the virus either in the dry or wet state. This means that the virus inactivation is taking place in rela- tively small regions and is again indicative of structure and func- tion in the virus. The contrasting character of inactivation and denaturation calls attention to a minimum of two different parts of the structure. If it were true that thermal inactivation showed characteristic behavior for different substances, then the figures of Table 4.1 could be used to determine which proteins, nucleo- proteins, etc., were involved in the activity measured. Unfortu- nately this is only partly true. Possibly in the dry state, where very little work has been done, it is possible to characterize an enzyme or protein by its inactivation constants. In the wet state, many factors must first be considered. INACTIVATION AS A FuNcTION oF pH If the percent infectivity of T-1 phage, or of TMV, remaining after a fixed time of exposure to thermal action, is plotted against the pH, the type of result shown in Fig. 4.6 is obtained. There is a region of relative stability with rather sharp edges. Steinhardt (1937) has shown that for pepsin the rate of denaturation varies as the cube of the hydrogen-ion concentration, and concludes THERMAL INACTIVATION OF VIRUSES 117 that the changing of three ionically bonded groups is necessary for the unfolding, and hence denaturation, of pepsin. The T-1 inactivation-reaction constant varies more slowly, more nearly as the first power, and so perhaps corresponds to the changing of a single ionically bonded group. Much better data is really needed for this sort of analysis. survival after 24 hours Per cent a 0 2 4 6 8 10 12 (Sa aes Fia. 4.6. Percent survival of T-1 phage after exposure to different pH values for 24 hr. PRESSURE EFFECTS ON THERMAL INACTIVATION A systematic study of the effects of pressure on micro- organisms has been made by Johnson. By way of illustration of a case which behaves regularly and is susceptible of analysis in terms of the Eyring theory we show, in Fig. 4.7, data taken by Foster, Johnson, and Miller (1949) on T-5. The inactivation in the presence of a small concentration of Mgt? ions obeys first- order kinetics, and it can be seen that as the pressure is increased the rate of inactivation is lessened. This corresponds to a posi- tive change, or an increase in volume, to reach the activated state. The value of AV? found is 113 em’/mole, or 1.87 X 10722 em*/virus particle, The total volume of the virus is about 118 THE PHYSICS OF VIRUSES 3 X 107" em, so this corresponds to a percent volume change of 6.1 X 107°. Such a small change, seen as part of the whole virus, seems too minute to be effective. It is more likely to be thought of as a volume change in one sensitive molecule of molecular Survival Per cent 10 20 30 40 50 60 Minutes Time ~ Fia. 4.7. Effect of pressure on the inactivation of T-5 according to measure- ments of Foster, Johnson, and Miller (1949). Pressure reduces bond lengths and gives an increased stability. weight, say, 100,000 for which the volume change is about one- tenth of one percent or so. The figures obtained by Foster, Johnson, and Miller for AH? and AS? do not agree with previously quoted values obtained by Adams. Whereas this may well be due to the difference in salt THERMAL INACTIVATION OF VIRUSES 119 content of the broth used, it is quite possible that the effect of pressure is to cause a change in AV? such that different parts of the virus, with normally slower rate constants, become the rate determining factor. It must never be lost sight of, in this kind of work, that a virus is not a single molecule but, at best, a molecular aggregation. A rather different approach from the statistical-thermo- dynamical reasoning of the Eyring theory may be more signif- icant. It seems very likely that the nucleoproteins of viruses have very high changes in volume under pressure. This means that a fair fraction of the bonds are capable of changing their average spacing. If the energy of binding of such bonds is strongly distance dependent, the increased proximity of the bound groupings may increase the stability of the molecule as regards thermal agitation. The positive AV?, which means that the molecule must expand to inactivate, is thus to be linked with the idea that the molecule with high AV? contains bonds which are quite distance dependent. Since the above measurements were made on infectivity, which perhaps is related to nucleoprotein, a completely different set of values would be expected for change in serological affinity, which is related to the surface protein. Studies which could be used to measure AV? for such treatment have not yet been made. CONCLUSIONS FROM THERMAL-INACTIVATION STUDIES’ Virus inactivation seems to follow first-order reaction kinetics with an energy of activation in the dry state of around 1 ev. The constants in the wet state indicate that higher energy barriers have to be overcome, so that tighter binding of the whole structure holds in the wet state. This is at the expense of a high, positive entropy of activation, corresponding to the binding of considerable water, with consequent reduction in possible degrees of freedom, and renders the virus quite susceptible to inactivation if the temperatures are high enough. Thus, viruses seem to be stable when dry if the drying process can be con- ducted so as to retain the virus structure intact, but the tempera- ture must be kept low in many cases or the virus slowly gets 120 THE PHYSICS OF VIRUSES taken across the low potential barrier. On the other hand, wet viruses are highly stable at low temperatures but in a small temperature range may become inactivated very quickly. The high entropies of activation associated with the denatura- tion of proteins are not necessarily found for virus inactivation unless it is carried out at high temperatures. This fact will be seen to be very significant in studies on the serological behavior of viruses, and it turns out that serological affinity follows dena- turation behavior in many cases. Thus if a virus is inactivated rapidly at high temperatures, the virus protein is almost sure to be denatured, with consequent damage to the antigens. If it is slowly inactivated at medium temperatures over a period of days, there is good reason to believe that great loss of infectivity can occur with little or no loss in ability to combine serologically. Many more studies of thermal inactivation need to be made. Thus all the complex of properties studied by Watson for T-2 bacteriophage and described in Chapter 3 can also be studied for thermal inactivation. Actually, practically none of this rewarding work has been done; this chapter is accordingly short. Further mention of thermal studies in regard to the surface properties of viruses are contained in the next chapter. REFERENCES General references on thermal behavior are: Glasstone, S., Laidler, K. J., and Eyring, H., The Theory of Rate Processes (McGraw-Hill Book Co., Inc., New York, 1941), and Stearn, A. E., Advances in Enzymol. 9, 25 (1949). More detailed references follow below. Adams, M. H., J. Gen. Physiol. 32, 579 (1949). Adams, M. H., and Lark, G., J. Immunol. 64, 335 (1950). Boyd, G. A., and Eberl, J. J., J. Phys. & Colloid Chem. 52, 1146 (1948). Cherry, W. B., and Watson, D. W., J. Bacteriol. 58, 601, 611 (1949). Foster, R. A. C., Johnson, F. H., and Miller, V. K., J. Gen. Physiol. 33, 1 (1949). Friedman, M., In course of publication (1953). Johnson, F. H., Baylor, M. B., and Frazer, D., Arch. Biochem. 19, 240 (1948). Krueger, A. P., J. Gen. Physiol. 14, 493 (1931). Lauffer, M. A., Carnelly, H. L., and MacDonald, E., Arch. Biochem. 16, 321 (1948). Lauffer, M. A., and Price, W. C., J. Biol. Chem. 133, 1 (1941). Levy, M., and Benaglia, A. E., J. Biol. Chem. 186, 829 (1950). THERMAL INACTIVATION OF VIRUSES 121 Pauling, L., Corey, R. B., and Branson, R. H., Proc. Natl. Acad. Sci. U.S. 37, 205 (1951). Pollard, E., Am. Scientist 39, 99 (1951). Pollard, E., and Dimond, A. E., In course of publication (1953). Pollard, E., and Reaume, Marjorie, Arch. Biochem. and Biophys. 32, 278 (1951). Price, W. C., Arch. ges Virusforsch. 1, 373 (1940). Schrodinger, E., Statistical Thermodynamics (Cambridge University Press, Cambridge, 1948). Steinhardt, J., Kgl. Danske Videnskals Selskals, Mat.-fys. Medd. 14, 11 (1937). Thornberry, H. H., Valleau, W. D., and Johnson, E. M., Phytopathology 28, 129 (1938). CHAPTER FIVE THE SURFACE OF VIRUSES Viruses are perhaps the smallest functioning objects in nature. They are in the realm of colloids, and yet they have an internal structure and are able to use this internal structure to multiply when in a host. Their small size greatly exaggerates the relative importance of the virus surface. In a human being, the ratio of surface to mass is about 0.3 em?/gm, whereas in southern bean mosaic virus it is about 3-million em?/gm, or 10-million times larger. A human being functions considerably by reason of his surface, and so a virus must do so much more. So great is this surface-to-mass ratio that it is impossible to conceive of a virus maintaining any kind of metabolism out- side a host. If the remarkable relation between surface area and internal metabolism [as, for example, measured by respira- tion studies (see Brody, 1945)]| is extended down to viruses, the respiratory rate is such that a gram of virus would require an energy turnover 20 times that of a normal human being. This is much too high to be going on continuously, and so this very simple consideration indicates that outside the host a virus can be treated as nonliving. Inside the host it is quite different. This is a striking illustration of the importance of environment. The small size of a virus also influences the vapor pressure of water at its surface. If p’ is the vapor pressure at a surface of radius 7, and p is the ambient vapor pressure, then, for a liquid of density p, molecular weight MM, and surface tension y, the re- lation holding is (Adam, 1941, p. 14) RT in 2 ee (Ga) THE SURFACE OF VIRUSES os : {23 For southern bean mosaic virus p’/p = 1.08, so the vapor pres- sure is 8% higher than ambient. A virus, therefore, will tend to dry even in the presence of moderately high vapor pressures: It is essentially certain that all the water held by a virus is bound by some kind of moderately strong force not (necessarily) as strong as a covalent bond but of the order of a hydrogen bond in strength. SURFACE FUNCTIONS OF VIRUSES Many of the known properties of viruses are due to their surface. Those of great importance are now listed and briefly described. Adsorption. This is best understood for bacterial viruses but is almost certainly a factor for all viruses, with the possible exception of plant viruses. The facts known about adsorption for bacterial viruses will be considered in more detail later in the chapter. Serological Behavior. In some manner, the virus protein is able to condition the formation of antibodies in the blood serum of animals. These antibodies are then able to combine specif- ically with the surface virus proteins. This can be studied directly by measuring the precipitate formed, using various means for estimating small amounts of precipitate. Indirect means of various kinds have been devised, of which the most notable is neutralization of infectivity, by which the failure of a preparation to be infective at a certain dilution is taken as evidence that specific combination with antibody has taken place. Another indirect method is complement fixation, which is a remarkably sensitive technique embodying two separate serological processes. Sheep red cells can be dissolved by the joint presence of a thermally unstable substance present in normal serum, complement, and a specific antibody produced in rabbits after injection with sheep red cells. Complement is removed from serum by the combination of an antigen and an antibody. When complement is removed, the red cells are not dissolved. So the presence of specific combination between virus and antibody is inferred from the absence of complement, or the lack of dis- o>. 124 THE PHYSICS OF VIRUSES solution of sheep red cells. This is quite a sensitive, but laborious, method. The recent discovery that long polypeptides form a not highly specific and reversible combination with viruses has added a secondary aspect to serological work. The polypeptides are under better control as regards size and length than are anti- bodies and so can be used in different classes of experiment. Hemagglutination. Certain animal viruses agglutinate red cells in a manner which is relatively simple to study. Hemag- glutination may be followed by elution, wherein the virus releases itself from the red cells. Both properties are surface properties and both can be studied. ADSORPTION Although by far the greatest degree of study has gone into virus serology, it is simplest to consider the nature of adsorption because this forms the best introduction to the study of virus surfaces. Bacterial viruses lend themselves very simply to adsorption studies. The virus and bacteria are mixed so that a known amount of virus is initially present and there is an excess of bacteria. After a certain time, which is usually varied, the mixture is spun in an ordinary laboratory centrifuge and the supernatant examined for virus. Any change in the amount of virus is ascribed to adsorption on the bacteria. The results of this type of experiment show that the rate of adsorption is proportional to the concentration of bacteria, 6, and to the concentration of unattached virus, U, so that which, on integration, gives the familiar relation ee = kyBt (5.2) “a0 Measurements of U/Uo, the percent virus left unattached as a function of time, thus enable kh. to be measured if B is known. THE SURFACE OF VIRUSES 125 The values of ky so measured are of the order of 5 X 107'! cm?/ sec. Krueger (1931) showed that adsorption to live and dead bacteria followed the above relation and measured ky for staphylococcus phage. Schlesinger (1932) pointed out that if the collision rate expected from Brownian movement of the bacterium and the virus were the only agent responsible for this rate, the value of k. calculated is about what is found. Delbriick (1940) assumes that because the virus is removed by adsorption near the surface of a spherical bacterium, radius a, there exists a concentration function C(7), where By SC (1 = “) where r is the distance from the center of the bacterium, and C, is the concentration at infinite distance, 1.e., the average con- centration. There will then be a rate of flow, F, on to the bacterium given by the concentration gradient, 0C/d0r, times the area, 47r?, times the diffusion constant, D, so that Y F = 4qr? at = C,40Da or Since: / —ike02. we have kh. — 400, where i... is the maximal attachment constant. The fact that /, is so close to this figure argues that attach- ment occurs every time, that it does not depend on the orienta- tion of the virus, and so that the whole virus surface, or at least an equally distributed pattern of small units, is involved in this attachment. Alternatively, an attraction of a specific charge must occur. A great clarification of the nature of this process resulted from the very direct experiments of Puck, Garen, and Cline (1951). In studying values of ky by the method outlined above, they found that although T-1 and T-3 phages fitted the rapid adsorp- tion pattern, T-2 and T-4 did not until NaCl was added. This feature of virus attachment had been discovered by Hershey. (1946). Cherry and Watson (1949) observed that the lysis of Streptococcus lactis by a phage in the presence of MgSO, showed 126 THE PHYSICS OF VIRUSES a maximum at 0.007, of CaCl. at 0.02M, and of KCI at 0.02.M concentrations. They associated this with the adsorption process. Puck, Garen, and Cline then investigated the rate con- stant for the attachment of T-1 as a function of the salt con- centration for NaCl and CaCly. Their results are shown in Fig. 30010 “yin, § 200 ° w 5 ©) = t o E ie) rs) ~ 2 5 4% aq 100 Y a ‘ e li \ [ae \ we 000 A ~~ 7 a a“ I Q O aa -4 -3 -2 =| 10) 10) lO lO lO Salt Molarity Fic. 5.1. Variation of the velocity constant for attachment of T-1 phage to E. coli with salt concentration, as measured by Puck, Garen, and Cline (1951). These results show the strong effect of the ions in the medium on the attachment. 5.1. There is a rapid rise in attachment for the divalent ions and a similar rise at higher concentration for monovalent ions. Excess of either kind of ion diminishes the attachment. Further experiments showed that there is no lag period fol- lowing the addition of divalent ions. The rapid attachment of virus is very striking in such a case. Also the reaction con- stant, while increasing from 2° C to a maximum at 37° C, does THE SURFACE OF VIRUSES 127 not change very greatly. Part of the change is certainly due to the viscosity change of water. The virus is not firmly bound at first, and changes in the salt concentration can cause elution of the virus. This was shown by Garen and Puck (1951) who found that after a 10-min adsorption process, which gave a 98% attachment at 3° C, 43% could be eluted by raising the salt concentration. At 37° the amount that could be eluted was very much less. By studying the reversible attachment at low temperatures and the irreversible attachment which occurs as the temperature is increased, the following picture of virus attachment emerges. The first process of attachment is electrostatic in character. It arises because a certain specific, charged grouping on the virus matches a specific, similar grouping on the bacterium sur- face. Such charges on the surface of colloids are well known. The charges in this case are controlled by the heredity of the virus and the bacterium. In the absence of any ions in the solution, we can suppose these charges to be alike, so that there is repul- sion. Figure 5.2, taken from Puck, Garen, and Cline (1951), shows the kind of process. If, now, divalent ions are added, they can attach to the surface charges, and will do so in a preferential order. Suppose they first attach to the virus and not to the bacterium. Then the result will be a set of opposite charges, in the correct pattern, on the surface of the virus. The resulting attraction to the bacterium is then very strong. Quite simple considerations indicate that four charges which were accurately matched by four equal opposite charges can produce, at 10 A, a force of 107° dyne/virus. At 50,000 g in an ultracentrifuge, the force per virus is only 10~' dyne. The effect is thus 10-million times more potent than quite strong sedimentation. As the ionic concentration increases, the ions continue to fasten to surfaces until the less favored groups on the bactertum are covered. The result is now much the same as at first, and a net repulsion exists. The curves of Fig. 5.1 are thus nicely ex- plained. The divalent ion causes attachment at a low molarity, and also covers all surfaces to give repulsion at a high molarity. When only one type of surface (e.g., virus) is covered, the attrac- 128 THE PHYSICS OF VIRUSES tion is very strong. Monovalent ions are never as effective, oper- ate at higher concentrations, and again, in excess, cause repulsion. These experiments and the definiteness of this idea for the first attachment phase are relatively new. A complete theory in terms of modern ideas of colloids and ionic atmospheres should be capable of predicting the shape of the curves of Fig. Medium Virus Surface Cell Surface Result Water No attachment —\Mg° = _\mg]- -3 10 M MgCl, a) Mgt . Mg i. Attachment Mg|_ Mg = 10’ MMoCl, Mg Mg" No attachment = Mgt Mgt = Mg ]|-— Fia. 5.2. Puck, Garen, and Cline’s scheme for explaining the first phase of virus attachment. 5.1 and should then yield figures for actual charge distributions on the virus or the bacterium. One important point which must be cleared up by such a theory is the factor which determines why ions should attach first to one or the other, virus or bacterium, and not equally to both. It seems probable that the final description of the process in terms of ionic-solution theory may be more complex than that just given. THE SURFACE OF VIRUSES 129 One feature of this type of process is that, although specific attractions to identical surface distributions are very great, there is considerable attraction to any surface of opposite charge. The fact that viruses will attach to glass filters and other adsorbents has been known for some time. Delbriick (1940) found that reversible attachment of T-1 to a Jena glass filter was possible. Shepard and Woodend (1951) showed that T-2 phage can be adsorbed on to glass powder and celite filter aids and that the adsorption rapidly lessens above 107? molarity concentration. Puck, Garen, and Cline also demonstrated such nonspecific adsorption and, in addition, made the important point that a tryptophane-requiring mutant of T-2 would only attach to a glass filter in the presence of the needed concentra- tion of tryptophane. The surface groupings in this case therefore require tryptophane to be present before they are formed. Note that this electrostatic attraction is not temperature dependent except that the viscosity of the medium exerts a drag on the motion of the virus and this, being mainly water, changes rather slowly with temperature. The second phase of attachment is described by Garen and Puck (1951). It was found by them that a part of the virus attachment to a bacterium is reversible. This reversible attach- ment does not kill the bacterium, takes place predominantly at low temperatures, and, in the presence of Zn** ion, is the only kind of attachment. Reversibility was established by dilution in excess NaCl, which carries the virus to the low attachment point as seen in Fig. 5.1. The question arises as to the nature of irreversible attachment, which at 37° C is over 90% of the total attachment. In studying this, they found that it is strongly temperature dependent, with a AH?* of 18,000 calories/mole; that ultraviolet light applied to the bacterium inhibits it; and that ions are necessary for it to take place. They conclude that this second process is enzymatic in character. The whole picture is then as follows. Surface charges of like configuration and charge exist on both bacterium and virus. In the presence of ions, one or the other preferentially attracts ions, so that matching opposite charges now exist, with conse- 130 THE PHYSICS OF VIRUSES quent strong attraction. Once attraction has occurred and the virus and bacterium are in contact, an irreversible enzymatic process takes place which is temperature sensitive, and inhibited by Zn‘ in the case of E. colt. Some interesting deductions can be made from this story. In the first place, the ionic binding is so strong that the virus and bacterium should be tightly locked together. This being so, the fact that the enzymatic process is 90%, or more, effective at 37° C means that a large part of the bacterial surface must be substrate. Garen and Puck also made the observation that 4X 107 atoms of zinc are absorbed per cell of E. coli in order to block the enzymatic step. Assuming that these are all on the surface of the /. coli and that the bacterium is a cylinder ly in diameter by 2u long, the total surface available for distribution is roughly 6 X 108 A®. Since this is matched on the virus surface by an identical distribution, the specific groupings must occupy an area of 15 A®. This number is probably low because it is based on the assumption that all the zine goes in the surface of the bacterium. Nevertheless, the indication is that there exists a small charge grouping that is similar to that on the bacterium. Associated with this is an enzymatic type of surface. These powerful methods of study are just in their early phases. Quite detailed knowledge of the virus and bacterial surfaces can be expected to result. POLYPEPTIDE ATTACHMENT Some very remarkable work in which the combination of lysine polypeptides with tobacco mosaic virus has been studied is due to Stahmann, Graf, Patterson, Walker, and Watson (1951) and to Burger and Stahmann (1951). In the first of these papers, the formation of synthetic polypeptides from E-carbobenzoxy- a carboxy-t-lysine anhydride is described. The chain length ean be varied and measured by finding the proportion of termi- nal a-amino nitrogen. An elementary analysis of one such polypeptide gave Cy,366H1,751Ni91O291, which has a molecular weight of roughly 25,000. They show that such a polypeptide can cause the inhibition THE SURFACE OF VIRUSES 131 oO of infectivity of TMV as shown in Fig. 5.38. The inhibition of infectivity is reversible, as shown by diluting a 4:1 combination of virus and polypeptide. When diluted, the virus-polypeptide combination evidently loosens, as the infectivity returns to normal at low concentrations. In the second paper, the process is studied in more detail with the electron microscope and with a quantitative method of 100 Infective TMV fo) Per cent O 100 200 300 Polypeptide Concentration Fic. 5.3. Reduction of infectivity of TMV by lysine polypeptides in various concentrations according to the data of Stahmann, Graf, Patterson, Walker, and Watson (1951). determining the amount of precipitate formed when virus and polypeptide are mixed. In addition, they carried out studies of the amount of virus-polypeptide precipitate formed when the pH is varied. Their results show that: (a). The virus infectivity is reduced before a_ precipitate between virus and polypeptide is formed. (b). No precipitation occurs at pH2 or pH10. This is the region in which both the virus and the protein carry a net charge of the same sign. 132 THE PHYSICS OF VIRUSES (c). Virus inhibition is a logarithmic function of the poly- peptide concentration, a fact which is apparent from Fig. 5.3. (d). The percent infectivity remaining is a falling logarithmic function of the chain length, or the number of lysine residues. The longer the chain, the more the inhibition of infectivity, but only logarithmically so. (e). No precipitation of the virus occurs with free lysine. They propose as an explanation that charged groups on the virus can combine with charged groups on the polypeptide which can then link to a second virus particle to cause aggregation. Aggregation does not occur at low and high pH. The reversibility of the process suggests that the binding is not extremely tight. For this reason, the longer the polypeptide chain the more charged bonds can be formed and the better the combination and inhibition. In the electron microscope, the virus particles can be seen to be thicker and less uniform of surface. It is of interest that large aggregates can only form when the excess of polypeptide is not too great. It will be seen shortly that this is very much like the formation of precipitate with specific antibody. These experiments offer a new technique in virus work. It may well be that inhibition of infectivity is general for all viruses, or specific to some. Inhibition of bacterial infectivity does take place (Burger and Stahmann, 1951), so some fairly general property of viruses, as, for example, the covering of the surface specific charges needed for attachment, may be involved. Virus SEROLOGY All kinds of viruses are excellent antigens. Plant viruses, in particular, are so good that if an infected plant is used to give infectious sap, and this is injected into a rabbit, the majority of the antibodies formed are attributable to the virus. This is partly related to the size of viruses, which are larger than more usual protein molecules, but it is probably also related in some way to the strong function a virus can play in a cell—even in a THE SURFACE OF VIRUSES 133 cell which is not its host cell it is probably active, and one sign of this activity is the formation of antibodies. Serological Techniques. Excellent accounts of these exist, and references are given at the end of the chapter. Two features of the technique are important. It is assumed that, as far as possi- ble, an antiserum containing only the specific antibodies to the virus has been produced. This can be achieved by differential precipitation of all but the virus antiserum. The two features of importance are (a) appropriate concen- tration relation between antibody and virus, and (b) assay of the amount of virus-antibody combination formed. The former is of importance because as the amount of antigen (virus) is increased relative to antibody the amount of precipitate increases, stays constant, and goes down. Therefore, working in the region of antibody excess must be established or ambiguities can result. Preliminary work has to be done to establish that the proper conditions hold. The second feature, the measurement of the amount of combination between virus and antibody, can be done in several ways. The simplest is to estimate by eye the amount of precipitate formed under favorable lighting conditions for different dilutions of virus and antiserum. A new technique due to Moorhead and Price (1953) raises the sensitivity of this method by using fresh, washed, sheep red cells as an indicator. Any precipitate between virus and antibody will keep the red cells from settling, and thus they form a convenient indicator for the presence of precipitate. A quantitative method is to form the precipitate by incuba- tion with antibody for the appropriate time (varying from 3 hr to 48 hr depending somewhat on the character of the test being made), centrifuge, remove the supernatant, dissolve the pellet in NaOH, and look for protein absorption at 2,750 A in a spectrophotometer. A third method is to employ the loss of infectivity of the virus as a result of antibody combination. This is particularly useful for bacterial viruses where the infectivity assay is direct and easy. Since the question of neutralization of infectivity is of 134 THE PHYSICS OF VIRUSES some importance, a short description of the major findings in this subject will be given. NEUTRALIZATION OF INFECTIVITY If antibody is incubated for a standard (long) time with active virus, and the percent viable virus is plotted against the amount of antibody, three general types of curve are found. The first, which holds for 'T-2 phage (Hershey, Kalmanson, and Bronfen- brenner, 1943), is a semilogarithmic relation of the form n In — = —k,A Io where 7/70 1s the surviving fraction, A is the amount of antibody, and i; is a constant. Viewing this process as due to a progressive covering of surface by antibody until the virus is inhibited, it is possible to estimate how many antibody molecules are needed for n/no to be 37%, which represents a unity chance of virus inactivation. For T-2, the number found is 90. The second type of curve shows an initial logarithmic be- havior, but it flattens to a constant remaining activity. This is reminiscent of an equilibrium, but is not so. If further phage is added, precisely the same curve is obtained and the equilibrium point is not shifted. This type of relation holds for T-1. A simple explanation, given more for illustrating the type of process rather than claiming it to be true, is to suppose that two kinds of antigen exist. If one kind of antibody is predominently formed, and some cross reaction with the second antigen exists, then two rate constants would be found. The third type is the same but is actually a reversible com- bination. This holds for influenza. SURFACE INACTIVATION BY ANTIBODY The figure of 90 molecules for T-2 inactivation is interpreted by supposing that a certain fraction of the virus surface is essential for its multiplication. This can be phrased by saying that some bacierial receptors exist on the virus which are impor- THE SURFACE OF VIRUSES 135 tant, whereas antibody receptors are not. When any one bacterial receptor is covered, the virus is inactive. The number of receptors can now be estimated. If it is assumed that the antibody molecules are of molecular weight 160,000, with a length of 235 A and a diameter of 44 A, and that they attach end on, we have: Antibody attachment area = 7 X 22? ~ 1,500 A? Radius of T-2 phage = 350 A Surface area, ignoring tail, = 47 X 350? ~ 1.5 X 10° A? So total area is equivalent to 1,000 molecules. Now when 90 antibody molecules cover the appropriate spots, one bacterial receptor is just covered. This is one-eleventh of the whole surface and it can, therefore, be concluded that when one of 11 bacterial receptors are covered, the phage is inactive. This fact of there being eleven receptors is of importance as it is another datum in the structure of viruses. SEROLOGICAL INACTIVATION OF VIRUSES The techniques indicated in the two previous chapters should be applicable to the destruction of serological affinity. In fact, the technique of bombardment by ionizing radiation should be very suitable because we have just seen that something like a thousand antibody receptors must exist on a virus surface and so the size of each of these must be close to that of an enzyme molecule, which is inactivated by one primary ionization. The rather doubtful character of inactivation of infectivity, where it is questioned whether one primary ionization is sufficient, should not apply to the smaller molecules of the antibody receptors. We therefore describe some experiments in which the serological affinity of TMV, southern bean mosaic virus, and T-1 phage has been studied (Pollard and Dimond, 1952; Pollard and Jane Setlow, unpublished). In the case of the two plant viruses, the technique used was to bombard virus preparations by deuterons and to assay for the amount of precipitate formed by centrifugation, pellet solution, and spectrophotometry. The results for TMV and 136 THE PHYSICS OF VIRUSES southern bean mosaic virus are shown in Fig. 5.4. The data for TMV are not too satisfactory because of a marked tendency for the virus to precipitate without addition of antibody after the very heavy irradiations necessary. This was allowed for SBMV Small Antigen SBMV Large Antigen Activity Infectivity Per cent TMV Infectivity 10 20x10" Deuterons per square centimeter Fic. 5.4. Deuteron inactivation applied to the serological affinity of TMV and SBMV. The loss of activity is small compared to the loss of infectivity. The points for TMV fit best with a single antigen of surface area 1.5 X 1074 cm’, whereas for SBMV, two antigens of area 3 X 10714 and 1.5 & 107}3 em? are apparently present. as best could be done, and the points are plotted. For SBMV the data are better and form two semilogarithmic lines which can be analyzed into two effective sensitive sizes. The values found are: THE SURFACE OF VIRUSES 13 Virus Area TMV 1.5 X 1074 em? SBMV 3 X 10714 em? and 1.5 X 10713 em? AMI 1.5 X 105" em2 In the case of T-1 phage, similar results are found. The area per antigen is given in the table above. These results are remarkable in that they indicate that the surface antigenic unit is quite small and also possibly multiple in type. The smallness of the unit gives rise to some speculation as to whether there may not be a rather limited number of possible types of antibody. In the case of southern bean mosaic virus, the same ability to precipitate was measured after electron bombardment. The same type of double curve was obtained, again indicating two classes of antigen. It is possible, in principle, to apply the area and volume considerations of densely ionizing and sparsely ionizing particles. In the case of the small antigen, this can be done roughly, and the resulting sensitive volume is found to be about 7 X 1077! em? with a very roughly spherical shape. The molecular weight equivalent is about 6,000. The area of each antigen is about 3 X 10714 em?, and of the whole dry virus it is 3.5 X 10-1! em?, so there are presumably 1,700 such small antigens. The large antigen cannot be analyzed so well, but by pushing the data a little, a molecular weight equivalent of 15,000 is obtained, with a roughly spherical shape and an area per antigen of roughly 1.5 & 1071’ em?. Assuming these cover the virus surface, there are about 200 large antigens. The resulting picture of the virus is shown in Fig. 5.5. The large antigens alone are drawn in, but the subdivision of each into smaller units is also shown for one case. The warnings contained in Chapter 1 must be repeated here. Such pictures and such models are necessarily inferential. For instance, the second antigen may not prove to be part of the virus itself. Other evidence should support them before they ean be taken as valid. A certain amount of such evidence exists 138 THE PHYSICS OF VIRUSES and this will appear later. It is no surprise to anyone who has worked with the serological affinity of viruses that there are many surface antigens. The small-size antigen is perhaps more remarkable. The area of 3 X 107! em2, or 300 A2, was found by Hutchinson (1952) for the effective antigenic area of monolayers of bovine serum albumin. Quite small molecular units are, therefore, capable of specific combination. Probably four or az Small Antigen Large Antigen Diameter 298 A Fic. 5.5. Representation of the surface of southern bean mosaic virus as deduced from deuteron and electron bombardment and measurement of the serological affinity. The virus surface is composed of about 200 antigenic units of molecular weight about 15,000, and 1,200 subunits of molecular weight about 6,000. five amino-acid side chains in a specifically repeated pattern, throughout the virus surface, form the combining antigenic units. Since there are only 20 amino acids, the possible combinations of four of these is not so enormous a number as the possible protein molecules. This may mean, as has been mentioned before, that a fairly limited number of specific group combinations on anti- bodies exist. One byproduct of this type of work results. If the removal of serological affinity requires the inactivation of several hundred molecules, whereas the destruction of infectivity needs only a THE SURFACE OF VIRUSES 139 few, it should be possible by deuteron bombardment, and nearly as well by electron bombardment, to produce an inactive virus which will stimulate antibody formation very nearly as efficiently as the active virus itself. This has been tried, quite independently of the above work, by Traub, Friedemann, Brasch, and Huber (1951). These workers have prepared a rabies vaccine by electron bombardment. The technique used is to harvest brains from mice injected intracerebrally with stock virus, waiting until 24 hr after the first symptoms developed. These were ground up, broth added, frozen in polyethylene bags, and exposed to 3-Mev electrons in the frozen condition on a solid CO, support. They were then thawed and tested for antigenicity. This was done by injecting at various dilutions into rats and then injecting challenge doses of the original virus preparation at various concentrations. The results are shown in the table. Logarithm of infectivity Logarithm of Logarithm Dose titer of challenge of virus Logarithm of (10° rep) original virus control after vaccine protection 1.5 ih a 1.6 5.4 oh Oa 5.9 5.9 4. (5; 3.4 13) We 6.5 6.5 i eee 4.8 P45) 8.0 6.6 1.4 4.2. 3.9 GRO 6 93.58) 4.0 4.7 UD 6.6 Oe Vs 4.4 It can be seen that approximately 10,000 times as many original infectious virus particles are needed after such vaccina- tion. The amount of electron dose was found to diminish the loga- rithm of protection. If this fits a semilogarithmic relation (and the data are not complete enough to permit this deduction), then 26 X 10° rep are needed to cause a drop in the serological potency to 37%. This is 1.59 X 10° primary ionizations/cm®, so that the inactivation volume’*is 1/1.59 X 101°, or roughly 6 X 10-*° cm, corresponding to an equivalent molecular weight 140 THE PHYSICS OF VIRUSES of about 45,000. This is somewhere near equivalent to the large antigen for SBMV. This type of bombardment is probably a nearly equal mixture of indirect action due to free radicals and direct action due to primary ionization. The radicals act on the surface and many of them are needed for one inactivation. So indirect radiation action is a poor way to reduce infectivity and retain serological potency. For this reason, it is likely that the estimates made above give too large a size for the antigenic units. There should be great practical application for dry, or well protected, electron bombardment of viruses. Deuteron bom- bardment should be even better. THERMAL INACTIVATION OF SEROLOGICAL AFFINITY The question as to whether infectivity and serological affinity inactivate thermally in the same way is clearly interesting. Bawden (1950, p. 253) gives figures for the loss of infectivity and of serological titer for potato virus X and bushy stunt virus after 10-min heating at pH 6 and different temperatures. The two viruses behave quite differently. Bushy stunt loses all its serological affinity between 80° C and 85° C, whereas the infec- tivity gradually diminishes over the range 50° C to 85° C. On the other hand, potato virus X loses its infectivity over a range from 59° C to 68° C and loses its serological affinity at about the same rate. Bawden points out that at 50° C, potato virus X loses its infectivity slowly without much serological loss. Probably the denaturation point is reached rapidly for virus X but not for bushy stunt. Further studies, in which the logarithmic character of the loss of serological affinity is approximately demonstrated, have been made by the author and Dimond (1953) for southern bean mosaic virus and by the author and Jane Setlow (1953) for T-1 phage. Several curves for T-1 serological inactivation are shown in Fig. 5.6. These data were obtained by the technique of neutralization of infectivity. Inactivations were carried out, both wet and dry, with reasonable fit to a first-order reaction THE SURFACE OF VIRUSES 141 kinetics, except at very low temperatures. Some indication of a second type of antigen was found below 80° C. 100 ro, oO Per cent affinity remaining 5 10 15 20 25 30 minutes Time of inactivation Fig. 5.6. Thermal action on the serological affinity of T-1 phage as measured by the neutralization of plaque formation. a These results can be analyzed as in the table. The values found for infectivity are given for reference. Reaction Constants FoR T-1 INFECTIVITY AND SEROLOGY Infectivity Serology Condition AH? AS? AH? As? Dry 27,500 0 56,500 oil Wet 95,000 207 165,000 Sie The results found by Dimond and the author for SBMV in- dicate that there are curved lines on this logarithmic scale. These ean be analyzed into the sum of two lines and interpreted as the separate inactivation curves for two antigens. Approximately 60% of the antigenic activity has a rapidly changing reaction 142 THE PHYSICS OF VIRUSES constant corresponding to AH? = 159,000 and AS? = 370 (these figures are only approximate), whereas 40% has a slowly changing constant with AH* = 17,400 and AS = —22.5 (again only roughly). These two types of inactivation are identified with the two antigens found from deuteron and’ electron bom- bardment, the large antigen corresponds to the slowly changing constant and the small to the rapidly changing one. It may be coincidence, but the values for T-1 phage agree rather well, both in target size and AH?*, with SBMV. Clearly, many more such studies need to be made to see if this is a general type of antigen. HEMAGGLUTINATION Some of the phenomena which can be so effectively studied in the interaction of phage and bacterium can be looked into by ob- serving hemagglutination. This is a phenomenon discovered by Hirst (1942) which takes place for a fair variety of red cells and a moderate number of animal viruses, notably influenza, New- castle disease, and mumps. Studies comparable to those of Puck, Garen, and Cline should be possible, although they have not yet been carried out. We are here concerned with two physical studies of hemagglutination, the work “of Lauffer and Miller (1944) on influenza virus, and some recent work by Woese in the author’s laboratory on the action of ionizing radiation on Newcastle disease virus. In the experiments already quoted in Chapter 2, Lauffer and Miller showed that, for influenza virus, infectivity and re- fractive index move in the same way. The fact that this virus also possesses the property of agglutinating red blood cells enables a test to be made of the identity of the physical, infec- tive, and agglutinating units. The calculated sedimentation rate from boundary measurement is compared with the agglutination activity above the barrier in the sedimentation cell with the results shown in the table. It can be seen that hemagglutination follows the boundary in a very satisfactory way. Agglutination is thus an inherent property of this virus. The figures for in- fectivity and nitrogen content are shown for comparison. THE SURFACE OF VIRUSES 143 Fraction REMAINING IN Tor CoMPARTMENT (From Lauffer and Miller, 1944) Boundary measurement Hemagglutination Infectivity Nitrogen content 100 100 100 100 45 57 57 65 35 30 = 39 34 37 => 39 25 23 20 7s 15 12 15 = 0 2 =e The effect of exposure to temperature on hemagglutination was measured by Lauffer and Carnelly (1945). They found that the inactivation follows a form such that, at any one tempera- ture, the reciprocal of the square root of the agglutinating ac- tivity is proportional to time. This corresponds to a reaction of the three-halves order, which is hard to interpret literally. Lauffer and Carnelly point out that there is probably some kinetic process complication, as, for example, multiple sensitiv- ity of agglutination receptors. In any event, it is possible to characterize hemagglutination in this way even though it is somewhat empirical. Using this basis of measurement, Lauffer and Scott (1946) measured the rate constants at various temperatures and con- cluded that, for the loss of hemagglutination, the value of AH*, the energy of activation, is 110,000. The entropy of ac- tivation cannot be calculated, as the reaction is not of simple order. This value for AH? is considerably higher than the energy of activation for infectivity loss, which is 34,000 calories. This fits rather well with the behavior of serological affinity with regard to thermal action, and fits a protein figure rather than nucleoprotein inactivation kinetics. Studies of Newcastle disease hemagglutination have been made by Woese (1953). The rates of loss of hemagglutinating ability in both the wet and dry state were studied. In the wet state, first-order kinetics were obeyed to a reasonable approxi- mation. In the dry state, two reaction constants were clearly 144 THE PHYSICS OF VIRUSES observed. The relative proportions of slow-inactivating and fast-inactivating components are not, however, fixed, but as the temperature is increased, the fast reacting component in- creases in relative importance. Woese attributes this to an equilibrium between two forms of virus, both of which can be- come inactivated. He suggests that the equilibrium is condi- tioned by the amount of bound water remaining in the virus. The reaction statistics are given in the table. THERMAL INACTIVATION OF NDV HEMAGGLUTINATION State of virus AH?* (calories/mole) AS?* (ealories/mole/°C) Wet 125,000 320 Dry (fast component) 23,000 —4.8 (slow component) 22.000 +0.2 In addition to these thermal studies, Woese bas observed the effect of deuteron bombardment, in the dry state, on NDV hemagglutination. The radius of the unit which is responsible for this virus property lies between 40 A and 50 A and so has a molecular weight of the order of 300,000. NATURE OF THE VIRUS SURFACE By way of a conclusion to this chapter, a brief description of the virus surface, as deduced from the work described, is now given. The surface is covered with many similar groupings, each carrying a charge. These groupings are doubtless of the familiar type of organic acid-base combination, and so acquire a charge in a manner dependent on the hydrogen-ion concentration. The number of such groupings is certainly large, of the order of thousands, and when a similar group of the opposite charge is presented near the virus, a very strong force pulls the two together. These groups are probably part of, or close to, enzymatic elements, which can catalyse an irreversible reaction which may either bind the virus on to a cell or, in the case of elution from THE SURFACE OF VIRUSES 145 red cells, may destroy the surface pattern responsible for adsorp- tion in the first place. Probably the enzymatic part is also related to the antigenicity of the virus, for there appear to be many surface antigens, of the order of 1,000 small units and several hundred large units. These units must have a great many common properties, al- though they are not known to be identical. REFERENCES Adam, N. kK., The Physics and Chemistry of Surfaces (Cambridge University Press, New York, 1948). Brody, $., Bioenergetics and Growth (Reinhold Publishing Co., New York, 1945). Burger, W. C., and Stahmann, M. A., J. Biol. Chem. 193, 13 (1951). Cherry, W. B., and Watson, D. W., J. Bacteriol. 58, 601, 611 (1949). Delbriick, M., J. Gen. Physiol. 23, 643 (1940). Garen, A., and Puck, T. T., J. Exptl. Med. 94, 181 (1951). Hershey, A. D., Genetics 31, 620 (1946). Hershey, A. D., Kalmanson, G., and Bronfenbrenner J., J. Immunol. 46, 281 (1943). Hirst, G. K., J. Exptl. Med. 76, 195 (1942). Hutchinson, F., Arch. Biochem. Biophys. 41, 317 (1952). Krueger, A. P., J. Gen. Physiol. 14, 493 (1931). Lauffer, M. A., and Carnelly, H. L., Arch. Biochem. 8, 265 (1945). Lauffer, M. A. and Miller, G. L., J. Exptl. Med. 80, 521 (1944). Lauffer, M. A., and Scott, E. M., Arch. Biochem. 9, 75 (1946). Moorhead, E. L., and Price, W. C., Phytopathology 48, 73 (1953). Pollard, E., and Dimond, A. E., Phytopathology 42, 472 (1952). Pollard, E., and Dimond, A. E., In course of publication (1953). Pollard, E., and Setlow, J., Arch. Biochem. and Biophys. 48, 136 (1953). Puck, T. T., Garen, A., and Cline, J., J. Exptl. Med. 93, 65 (1951). Schlesinger, M., Z. Hyg. Infektionskrankh. 114, 136, 149 (1932). Shepard, C. C., and Woodend, W. G., J. Immunol. 66, 390 (1951). Stahmann, M. A., Graf, L. H., Patterson, E. L., Walker, J. C., and Watson, D. W., J. Biol. Chem. 189, 45 (1951). Traub, F. D., Friedemann, A. B., Brasch, A., and Huber, W., J. Immunol. 67, 379 (1951). Woese, C., In course of publication (1953). CHAPTER SIX ACTION OF ULTRAVIOLET LIGHT ON VIRUSES The biological action of ultraviolet light has been the subject of much study. The side of this work which is of most interest here is ably summarized by McLaren (1949). An important pioneer in the field of ultraviolet effects on viruses and enzymes was Gates (1930). The more recently available purified virus preparations have enabled some important new contributions to this field to be made and there is, therefore, considerable ma- terial for this chapter. In its simplest terms, ultraviolet light gives information about the absorption of ring aromatic com- pounds, purines and pyrimidines, and the peptide bond. The former are associated with proteins; the purines and pyrimi- dines, with nucleic acids, and the peptide bond is related again to proteins. So a separation of protein and nucleic-acid absorption is possible, and this is one of the first functions of ultraviolet studies. More refined studies can tell something of the relative importance of aromatic amino acids in various kinds of function. An additional feature of importance is the quantum yield of a biological result, a number which can be related to both structure and purpose. Mo.uecuLaR ABSORPTION OF ULTRAVIOLET LIGHT It is in order to consider first the mechanism of the absorp- tion of ultraviolet light. Light is electromagnetic radiation and so interacts with the electric and magnetic elements of molecules. In particular, it does so with oscillating electric dipoles, magnetic dipoles, and' electric quadrupoles; but in actual fact the degree of interaction is only appreciable for electric dipoles. So, for all intents and purposes, we can say that light is only absorbed by 146 ACTION OF ULTRAVIOLET LIGHT ON VIRUSES 147 a molecule which has a method of motion which is equivalent to the proper electric dipole. In the case of molecular absorption of ultraviolet light, the vibrations of atoms as a whole in the molecule are of far too low a frequency. Hence, the only suitable means of absorption is by a transition from one electronic state to another, which, as it primarily involves single electrons, has the proper frequency range. Inevitably associated with this electronic transition is some kind of vibration, and the combination of the two gives Potential Distance Energy Fic. 6.1. Electronic absorption from one state of vibration to another in which an electron is in an excited state. This is the major process of ultra- violet absorption. ; rise to an electronic-vibration band. Rotation is also possible, although in a large protein or nucleic-acid-like molecule it is probably not so important. Using the familiar representation of potential hollows in which vibration can occur, such a transition is represented as in Fig. 6.1. Three important features need to be remembered. The first is that, inasmuch as an electronic transition changes the state of the electron cloud around an atom, there may be a great weakening of the bond joining this atom to a neighbor. The second is that the vibrational levels, and indeed all levels, are broadened by the thermal agitation and electric-field overlap of the near neighbors. For these reasons, ultraviolet absorption 148 THE PHYSICS OF VIRUSES by a large molecule cannot be anything like as selective a matter as absorption by an atom in free space. The third feature applies in solution. Since the presence of free ions in a solution can profoundly modify the stable electronic configuration of a com- pound (particularly in the organic acid-base, or ‘‘zwitterion”’ compounds), the absorption spectrum in solution may well depend on the number and kind of ions present. In many cases the act of absorption can cause a bond to break. In a small molecule this causes dissociation. In a large molecule, however, the existing structure may be so strong that no actual atomic motion takes place and ultimately the energy is lost as radiation of some form, with consequent restoration of the bond. This process, known as the ‘“‘cage-effect,’’ or the Franck-Rabinowitsch effect, operates in the interior of a large molecule. The subsequent fate of the energy caught by the mole- cule in the act of absorption is complicated. In this respect the large-molecule constituents of viruses and the behavior of small crystals have much in common, so that virology has to look to developments and discoveries in solid state physics for an inter- pretation of some of the experimental findings in ultraviolet effects. One process of energy transfer has been discussed for photo- synthesis by Oppenheimer and Arnold (1950). They point out that the induction field of an excited bond may interact with another bond at a rather large distance and cause a transfer of energy without actually any radiation and absorption having taken place. This energy transfer process is similar to that of the “diffusion” of color centers in an alkali halide crystal, which has been experimentally studied by Apker and Taft (1950) and theoretically discussed by Heller (1951). Transfer of energy over distances as great as a micron are possible. This means that it is possible for energy to be transferred rapidly from any part of a virus to any other part. At the surface of a large molecule, de-excitation can occur as a result of collisions with the solvent. Because of this, and because of the cage effect just mentioned, the denaturation of proteins by ultraviolet light is relatively inefficient. ACTION OF ULTRAVIOLET LIGHT ON VIRUSES 149 ABSORPTION BY SOME DEFINITE MOLECULES Absorption spectra of simple substances such as benzene vapor are very sharp. In solution, or in the liquid state, the lines are broadened. When a simple substitution is made on a molecule such as anthracene, the relatively simple spectrum becomes changed, in general because certain resonant electronic con- figurations are no longer possible. Samples of various spectra are given in Fig. 6.2. An excellent review is given by Beavan and Holiday (1952). Of some interest is the sharpening of the absorption spectra of some organic com- pounds at low temperatures. This has been applied to molecules of biological interest by Sinsheimer, Scott, and Loofbourow (1950) and by Brown and Randall (1949). In general, one would expect a sharpening at low temperatures because of less molecular agitation. This is not found in practice. For example, purines show no sharpening, but pyrimidines definitely do. The absorption spectra of thymine and cytosine are shown in Fig. 6.2a and clearly have many distinct bands. The effect of the nature of the solvent on the absorption of tryptophane and tyrosine can be seen in Fig. 6.2b where data due to Holiday (1936) are plotted. Although the general shape is not changed, the details of the peaks are considerably altered. The effect of substitution is shown in Fig. 6.2c where data of Jones (1947) are plotted for anthracene and anthraldehyde in ethanol. The substitution of the aldehyde group for the hydrogen removes many possible absorption modes, as can be seen from the figure. The absorption spectrum of the pneumococcus transforming factor, a form of desoxyribose nucleic acid, taken by Fluke, is shown in Fig. 6.3. The absorption by the purines and pyrimi- dines causes the broad band at 2,600 A. The rise at 2,200 A is more doubtful. In Fig. 6.4, the absorption spectrum of insulin, taken by Suprynowicz is shown. This is representative of protein absorp- tion. A broad maximum occurs at 2,750 A, but in this particular substance six peaks [previously reported by Beaven and Holiday 150 THE PHYSICS OF VIRUSES Thymine H ONO ie a D o Oo 8 a Oo 2400 2500 2600 2700 2800 2900 Wavelength (a) 20 Cytosine 2° K Relative Absorption ro) 2200 2400 2600 2800 3000A Wavelength Fig. 6.2. (a) Absorption spectra of thymine and cytosine taken by Sins- heimer, Scott, and Loofbourow (1950) showing the sharpening observed at low temperatures. (b) Absorption spectra, taken by Holiday (1936), of trypto- phane I and II and tyrosine III and IV in N/10HCI and N/10NaOH, re- spectively, showing the shift in character due to the shift in acidic or basic character of these substances. (c) Absorption spectra of anthracene and an- thraldehyde, taken by Jones (1947), showing the removal of modes of ab- sorption by the introduction of the aldehyde group. ACTION OF ULTRAVIOLET LIGHT ON VIRUSES Absorption (b) 2650 Wavelength —_— — EO EE Log Extinction Coefficient 2200 3000 3800 4000 Wavelength A Fria. 6.2. (Continued.) 151 152 THE PHYSICS OF VIRUSES (1950) at 2,535, 2,585, 2,645, 2,681, 2,755, and 2,831 A] are found. These are presumably due to individual amino acids. Transforming J Factor Ol Density Optical ool OOO! 2200 2400 2600 2800 3000 3200 34005 Wavelength Fic. 6.3. Absorption spectrum of the pneumococcus transforming factor, a form of DNA, taken by Fluke. The broad band at 2,600 A is due to the purines and pyrimidines. The origin of the rise at short wavelengths is indefinite. THe ABSORPTION SPECTRUM OF ToBacco Mosaic VIRUS Very careful work on tobacco mosaic virus was carried out by Butenandt, Friedrich-Freksa, Hartwig and Scheibe (1942). The absorption curve found is shown in Fig. 6.5b. It can be seen to have a rather definite structure. In Fig. 6.5a, the separate absorptions of tryptophane, ribonucleic acid, tyrosine, and phenylalanine are given. These can be assembled in the propor- ACTION OF ULTRAVIOLET LIGHT ON VIRUSES 15s) tions indicated in the lower curves of Fig. 6.5b. The result is not a complete synthesis of the observed absorption spectrum but is clearly rather close to it. Some unpublished work by Brown and Randall (privately communicated by M. F. H. Wilkins) indicates that the ab- sorption spectrum of TMV sharpens at low temperatures. The 1.4 Density Absorption 0.2 2450 2500 2600 2700 2800 2900 Wavelength (A) Fia. 6.4. Absorption spectrum of insulin, taken by Suprynowicz. The con- tinuous line is at room temperature, and the dotted line at 80° K. Six peaks can be seen in a broad maximum at 2,750 A. There is some sharpening at low temperatures. absorption spectrum of TMV at room and _ liquid-nitrogen temperatures, as taken by Suprynowicz (1953), is shown in Fig. 6.6. The sharpening is quite apparent and can clearly be made use of in analyzing the internal structure of this virus. The wavelengths of the maxima observed are 2,578, 2,615, 2,644, 2,681, 2,811, and 2,905 A. Of these, 2,644 and 2,681 coincide with two peaks found in insulin. TMV is predominantly protein and so it is not surprising that the absorption extends so far to the long-wave end. Tryptophane (a) Absorption 2200 2600 3000 A Wavelength ps TMV 2 = 5 re) L<§ (b) $ ‘Oo hea aie 2200 2600 Z000A Wavelength Fic. 6.5. (a) Absorption spectra of tryptophane, phenylalanine tyrosine, and RNA, taken by Butenandt, Friedrich-Freksa, Hartwig, and Scheibe (1942). (b) The absorption curve for TMV and, below, a line representing the synthesis of absorption by 4.5% tryptophane, 5% RNA, 3.8% tyrosine, and 6% phenylalanine. The general, but not detailed, characters are reproduced in this way. Data due to Butenandt e¢ al. 154 ACTION OF ULTRAVIOLET LIGHT ON VIRUSES 155 The fact that tobacco mosaic virus consists of long, thin rods, and so can be oriented, means that the powerful tool of polar- ized ultraviolet absorption can be used. This was done by Butenandt, Friedrich-Freksa, Hartwig, and Scheibe. Tobacco mosaic virus is pressed into a fine capillary in a quartz tube and thereby acquires the orientation of the capillary. Light then passes through this capillary on to the slit of a spectrograph. Room Temperature 80° K Absorption Density ° ° fon) @ ° as 0.2 2450 2500 2600 2700 2800 2900 Wavelength Fig. 6.6. Absorption spectrum of TMV at room and low temperatures, taken by Suprynowicz. Some sharpening is apparent, but no great increase in structure over what can be seen by careful examination of plates at room temperature. At the exit end of the spectrograph is placed a sheet of crystal- line quartz cut perpendicular to its optical axis and tilted at a slight angle so that the light having one plane of polarization is displaced to a different point than is light having a perpendicu- lar plane of polarization. This occurs because the two classes of light have different refractive indices in the quartz. The spectro- graph thus gives two images, one polarized parallel to the TMV in the capillary, and one perpendicular to it. The relative in- tensities of these, as a function of wavelength, are then measured. 156 THE PHYSICS OF VIRUSES The most striking result of this kind of study is the fact that the characteristic small absorption peak of tryptophane at 2,900 A only shows for the case of light polarized perpendicular to the axis of the capillary, and hence of the virus. It is thus con- cluded that the aromatic rings of tryptophane are definitely oriented in the TMV particle. In a less clear way it can also be concluded that the nucleotides of ribosenucleic acid are also oriented. Butenandt concludes that the planes of the purine and pyrimidine rings are perpendicular to one another and _ per- pendicular to the long axis of TMV. So also is the indole ring of tryptophane. Seed and Wilkins (1950) consider that orienta- tion is necessary but that, in fact, it is parallel to the long axis of the virus. More work along these lines would be of the utmost value. ABSORPTION SPECTRA OF OTHER VIRUSES The absorption spectra of southern bean mosaic virus and T-1 phage, as taken by Suprynowicz (1953), are shown in Fig. 6.7. These are both less full of character than is TMV and, in addition, show no sharpening of absorption at low temperatures. This last may partly be explained by the inability to orient the viruses In any way. The same kind of broad analysis into protein ecmponents and nucleic-acid components is possible. The rather definite increase in absorption below 2,300 A is probably due to peptide bond absorption, which has been shown by Saidel and Goldfarb (1951) and by Setlow and Guild (1951) to be responsible for the rise in absorption of dipeptides below 2,300 A. [Further interesting work on this has been reported by Goldfarb, Saidel, and Mosovich (1951) and Hamm and Platt (1952).] ACTION SPECTRA Biological action spectra are, in principle, very powerful methods of study of the internal structure and mode of operation of viruses. The technique consists of irradiating the virus, either dry or in solution, with monochromatic ultraviolet light and measuring the survival ratio for a known amount of incident ACTION OF ULTRAVIOLET LIGHT ON VIRUSES 157 energy at that wavelengtb. For viruses, rather large amounts of light are necessary, so that either very intense ultraviolet sources or a monochromator with high aperture must be used. An inexpensive and quite adequate monochromator was de- signed and constructed by Fluke and Setlow (1951) using a large prism of distilled water enclosed with quartz plates and oO (os) ° o Relative Absorption ° rs 0.2 2500 2600 2700 2800 2900 Wavelength Fic. 6.7. Absorption spectra of T-1 phage and SBMV, taken by Suprynowicz. T-1 has a broad maximum around 2,600 A. The absorption of SBMV extends quite far to the long-wavelength end. two 8-in. astronomical mirrors coated with aluminum. The light source was a quartz mercury arc, and each line was isolated by an exit slit covering a bombardment chamber which could be employed either for stirred liquids or dry preparations. An important feature of this kind of work is the measurement of the radiant energy incident on the sample. For routine purposes this can be done with a calibrated photocell, but absolute measure- ments must be made now and again with a thermopile and sens1- tive galvanometer. 158 THE PHYSICS OF VIRUSES Careful studies have been made by Fluke (1953) on the action spectrum of T-1 phage, dry at room temperature, at liquid- nitrogen temperature, and wet at room temperature. In the dry state, it is found that the inactivation at any one wavelength follows the familiar relation In n/ny = —al where n/n is the survival ratio, I is the total energy incident on the specimen, and a is a constant depending on the amount of energy absorbed and the quantum yield in the process. In the wet state this relation sometimes holds, but in general it does not. The type of curve fits a so-called ‘“‘multiple-hit”’ process. The general formula for an inactivation requiring m inactivating events for each of N necessary parts of a virus, with a probabil- ity a per unit total dose applied, is where k is an integer. (Timofeeff-Ressovsky and Zimmer, 1947; Zirkle, Marchbank, and Kuck, 1952.) When only one necessary part requires one inactivating event, we have the familiar sur- vival curve n/no = e ”. For two inactivating events, the two- hit curve is n/N) = € “(1 + al), and so on. The multiplicity of hit is not definite and depends on the virus and the wavelength used. If an accurate survival-ratio curve is obtained, the num- ber of hits can be ascertained and a measured. For the relatively simple case of dry irradiated T-1, Fluke (1953) obtained the results shown in Fig. 6.8. The relative action on infectivity is plotted on a logarithmic scale versus the wavelength. This effectively means plotting a versus wavelength for survival. The virus was irradiated both at room temperature and liquid-nitrogen temperature. Slight but not very definitive differences are observed. It is interesting that the action spectrum does not entirely parallel the absorption spectrum. Most noteworthy is the fact ACTION OF ULTRAVIOLET LIGHT ON VIRUSES 159 that at the shorter wavelengths less effect on the virus is ob- served, whereas the absorption markedly rises. Since it is thought that this shorter-wavelength rise in absorption is due to the polypeptide absorption of proteins, it would seem as Action Room Temperature Action Liquid Nitrogen Action on Infectivity or Optical Density 0.01 2200 2400 2600 2800 3000 3200 3400 A Wavelength Fic. 6.8. Absorption and action spectra, taken by Fluke (1953), for T-1 phage. The action spectrum does not follow the absorption spectrum in detail, indicating that T-1 has a morphology, not all of which is concerned with sur- vival. In particular, the quantum yield definitely falls at short wavelengths where polypeptide absorption occurs. though either such protein absorption is unimportant or a con- siderable recovery takes place in bonds which have been excited in the polypeptide chain. On the other hand, absorption in the nucleotide or aromatic-amino-acid region seems to be quite 160 THE PHYSICS OF VIRUSES effective. The nucleotide absorption seems to be the most effective. Such an action spectrum, although of very great value, repre- sents only one step along a road that should lead to fundamental discoveries about viruses. From what has already been said, it is clear that the inactivation of a virus like T-1 is a complex process. It may be the result of over-lengthening of the latent period, which Luria (1944) has shown to occur following ultra- violet illumination, or it may be a lethal mutation in a genetic element, or possibly a destruction of specific surface groups. All of these various aspects of virus behavior have their separate action spectra, and only when a selection of these are available can the real power of the spectroscopic approach be apparent. This point is illustrated by some studies by Tamm and Fluke (1950) on influenza virus which are described below. INFECTIVITY AND HEMAGGLUTINATION ACTION SPECTRA OF INFLUENZA VIRUS The infectivity and hemagglutinating ability of PR-8 in- fluenza virus can both be readily studied. The former is meas- ured by inoculating 10-day-old embryonated eggs and deter- mining whether the inoculum results in a strong rise in virus in the egg due to active infection. The dilution at which this will occur is a measure of the activity of the virus. Hemagglutination is measured in a somewhat similar way by making twofold dilu- tions until one dilution fails to produce definite agglutination of red cells. Tamm and Fluke employed monochromatic ultraviolet light of four wavelengths. The virus was irradiated in a gold-plated cell with quartz windows on two sides. Radiation intensity on both sides of the cell was measured by a phototube which was calibrated by means of a thermopile. Exposures were made for various times at known intensities. The results are indicated in Fig. 6.9. The wavelength region covered is somewhat limited, notably in stopping short of the polypeptide absorption region, but it is clear that the maximum effect on infectivity is nearer to a nucleic-acid maximum, and is ACTION OF ULTRAVIOLET LIGHT ON VIRUSES 161 different from the hemagglutination curve, which has a pro- tein-like maximum. Perhaps most striking is the fact that, whereas the loss of infectivity followed an inactivation curve somewhere near a one-hit type, the hemagglutinating loss fol- lows a strongly multi-hit type. Tamm and Fluke point out that Infectivity SSeS Loss of Infectivity Hemagglutination ——-x— — or Agglutination Ability 2200 2400 2600 2800 3000 3200 Wavelength (A) A Be earl Uae Aaa 3023 A ~ \ ce) \ \ Agglutination i Y Titer \ | 2652A 28034 \ | a \ i \ * A 20 40 60 80 Dose ( Ergs/m2) Fic. 6.9. Action spectra and dose-effect curves for influenza virus, as taken by Tamm and Fluke (1951). The hemagglutination maximum is clearly in the protein region, whereas the infectivity maximum is more nearly nucleic acid in character. The multi-hit character of loss of agglutinating ability can also be seen. It is both striking and variable. 100 20x 10” this could be exploited for the preparation of vaccines, assuming that the serological behavior follows more the hemagglutination behavior. Ultraviolet inactivation has been successfully applied to produce rabies vaccine by Levinson, Milzer, Shaughnessy, Neal, and Oppenheimer (1945). This work shows clearly that the study of action spectra does not yield a monotonous repetition of a nucleoprotein absorption 162 THE PHYSICS OF VIRUSES spectrum, but clearly enables the differentiation of various virus properties in terms of their chemical constitution and, possibly, their position in the virus. Thus, a virus having a sensitive region consisting of nucleic acid imbedded in protein will produce an absorption spectrum which is a composite of both protein and nucleic acid. The action spectrum, as regards the nucleic-acid part, will only show strong effect in the nucleic- acid absorbing region. Work which could be extended to viruses has been carried out by Morowitz (1953) on B. subtilis spores. The lethal action spectrum and the action spectrum for two deficiency mutants were observed and compared with the absorption spectrum. Definite differences were observed. ACTION SPECTRA FOR DIFFERENT VIRUSES A summary of earlier work on the action spectra of viruses was given by Hollaender and Oliphant (1944). Figure 6.10 shows a composite plot, adopted from their paper, for five viruses. The remarkably low sensitivity of Rous sarcoma virus at 2,470 A and the high sensitivity of TMV at 2,300 A are the most interesting features of these studies. It is also interesting that, although the absorption spectrum of TMV extends out to 2,900 A, the quantum yield at that wavelength is very small. This kind of experiment is difficult and laborious. However, it is clear that if the character shown in the five curves plotted is not due to experimental uncertainty, then virus action spectra should be useful in characterizing viruses. QuaNntTUM YIELD One important datum in ultraviolet studies is the quantum yield for various kinds of inactivation processes. McLaren (1950) has made a careful study of quantum yields (ratio of number of molecules inactivated to number of photons absorbed) at 2,537 A and has concluded that the larger the molecule (including viruses) the lower the quantum yield. Inverting the figure and talking of photons per inactivation, this number seems to be ACTION OF ULTRAVIOLET LIGHT ON VIRUSES 163 roughly proportional to the surface area of the molecule. On | rather slender evidence, McLaren (1951) has proposed that the ionic yields for the indirect action of ionizing radiation also obey this relation. Relative Sensitivity \ \ eo As Influenza Rous Sarcoma 2200 2400 2600 2800 A Wavelength Fic. 6.10. Action spectra for five viruses, taken from Hollaender and Oli- phant (1944). The phage acts on Staphylococcus aureus. If this idea is right then the photons per inactivation should give some idea of the size of the unit being inactivated. Far too little data is at present available, but it represents an im- portant region for future physical studies of viruses. The quantum yield for inactivation of TMV at 2,537 Ais 4.3 X 10-5 (McLaren, 1950), and for T-1 phage at 2,600 A it is 3 X 107% (Fluke, 1953). 164 THE PHYSICS OF VIRUSES Mu.utieuicity REACTIVATION AFTER ULTRAVIOLET TREATMENT It was discovered by Luria (1947) that T-2, T-4, T-5, and T-6 phages, when inactivated by ultraviolet light and then caused to infect bacteria, multiply and show a much higher yield of still active phage than is the case if single infections alone are allowed. This shows that the virus is apparently partly inactivated, so that the single infection cannot quite achieve the process of multiplication, but yet has viral potency in some degree. If two viruses are used to infect a bacterium, there is now a chance that the residual potencies can combine to supplement each other in such a way that a whole virus results, with the usual consequences. This is spoken of as multiplicity reactiva- tion and was originally analyzed in terms of a genetic recom- bination process (Luria, 1947; Luria and Dulbecco, 1949). This analysis depended rather critically on the one-hit nature of phage inactivation, and, since this does not necessarily hold, the precise conclusions may not be valid. Nevertheless, the numerical considerations are sufficiently interesting to be worth mentioning here in simplified form (following Luria, 1947). Suppose a number, 7, of essential units (not necessarily genetic) exist in each virus particle, and suppose r of these have been inactivated. Then the average “hits”’ per unit is r/n, and the probability of no inactivation is e’’” per unit. The proba- bility of at least one hit is 1 — e~”’”. If k particles are used to infect, the chance that a particular unit has been hit in every one of k particles is ql) = GM and the chance that one has not been hit is 1— (1 — Cua) The chance that a bacterium receives active representatives of all n units is y, where p= {1 Sr e t/n)k\n This reasoning ignores the possibility that two hits may occur on one unit, and so has to be modified somewhat. This modifica- ACTION OF ULTRAVIOLET LIGHT ON VIRUSES 165 tion was made by Luria and Dulbecco (1949). For low doses, where r Protein Nucleic Acid Water JUN I Nucleoprotein RQ SS e SS a Se SSiasrar IS aeons e ees ea’ Fia. 8.4. Suggested structure for T-1 bacteriophage. The hook shaped central part is the nucleic acid essential for multiplication. If one-third of this is intact, the virus will kill bacteria. About 50 enzyme-like molecules are re- quired to produce a short latent period; these are indicated as nucleoprotein. The whole is surrounded by a protein sheath, unessential for operation in the bacterium. An enlarged view of the antigenic part, with surface charges for attachment, is shown. the protein. To indicate this in a token way, it has been placed as a long rod in the center of the virus, with protein units at- tached to it. Obviously, other ways exist, but it seems plausible that the nucleic acid extends down the virus. The second point concerns the antigenic units, which are small. In the figure, they 198 THE PHYSICS OF VIRUSES have been represented as a pattern of aromatic amino acids, which Butenandt has shown to be oriented in the virus. The pattern continues throughout the whole volume, and so has been Nucleic Acid NDV =<} Protein Fig. 8.5. Newcastle disease virus. This has an outer layer of lipid, through which project the hemagglutinins. The structure is simple and must be capable of unrolling in the infectious state. It is probably heavily hydrated. shown on the end. A small layer of hydration has been indicated, perhaps rather overconfidently, as bound on the surface. The third virus pictured is T-1 bacteriophage. Radiation studies show this to have a complex morphology, and an attempt to represent it schematically has been made. The nucleic acid is shown as made up of eight units, all attached to protein. The VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 199 ultimately highly vulnerable part of the virus is this, and unless it is damaged the virus will survive, although with impaired properties. The eight units are thought of as eight genetic com- ponents. They can mutate and, if such forms are stable, reeom- bination could occur. The outer layer of protein, which does not enter the bacterium, is shown as an intact sheath. The protein units which control the latent period are shown as white blocks. The tail of the virus (the most convenient part to draw) is shown in more detail and is broken into a mosaic of antigenic units carrying a pattern of charge distribution which is specifically related to the charge distribution on the bacterium. Undoubtedly the virus is hydrated inside, and this is shown. The outer hy- dration has been omitted, as its thickness is a pure guess. Finally, on very slender evidence, we show Newcastle disease virus. This is guessed at as spherical in the resting state, but is probably formed by coiling up an elongated structure which is the form it takes in the host. The lipid fraction is shown on the outside, with islands of protein penetrating through to form the hemagglutinins, which are of about the size indicated by deute- ron bombardment. The virus is certainly very much hydrated, and this has been indicated as partly in the center and partly extending between the nucleoprotein units. The virus is a poor antigen, probably due to the lipid layer. It is very radiation sen- sitive, almost as much so as TMV, which argues for a salle simple internal structure. We feel like insisting that these pictures be treated as specula- tive and tentative. However, in the author’s experience, they have excited much interest and, after all, presumably viruses do have a functional internal structure—so why not say so. It is only in the event that these pictures should be treated as author- itative descriptions of the viruses that harm could be done. Prob- ably in five years such authority can be justified—but not at the present time. THe ENercGy TURNOVER IN THE Host One basic process which must be concerned with virus multi- plication is the energy turnover, or metabolism, of the host. This 200 THE PHYSICS OF VIRUSES is taking place rapidly, as in all active living systems, and the nature of the process is of deep interest. In many of the systems with which physics and chemistry have to deal, the transfer of energy requires the generation of a certain amount of random thermal motion and its transfer partly to different random mo- tion (at a lower temperature) and to definite linear motion. This is inherently impossible in biological systems which are at one uniform temperature. Schrédinger (1945) has pointed out the general mechanism by which this biological energy transfer takes place, and Delbriick (1946) has shown very clearly how it oper- ates in one or two special cases. Energy turnover takes place by means of atomic rearrange- ments. These do not take part in a statistical system, they have no “temperature,” but rather involve a direct and very efficient method of moving energy from one form to another. Thus a loosely bound phosphate group can become a tightly bound group with the release of 2 or 3 ev of energy. However, the re- leased energy does not have to cause random thermal agitation, but can produce the necessary excitation to break a bond and permit a new configuration which carries a high percentage of the original released energy. Almost certainly the function of en- zymes is to hold systems in place so that such energy transfer can take place through the enzyme molecule and effect the required change. The energy shift is rapid and at high efficiency. The host cell has thus an equipment comprising specialized enzyme molecules, small co-factor molecules which can form temporary structural unions, as well as a basic medium of small molecules and ions. A part of the necessary behavior of the cell is the assembly of nucleic acid and protein structural units. These are formed from the simple molecules of the medium supplying the host, either directly after assimilation through a membrane as in the ease of a bacterium, or through the more complex proc- esses of an animal or plant. These units evidently carry with them a specific character, probably imposed by the general na- ture of the enzymatic protein, which is a simple repetition of a rather limited number of amino-acid side chains in the case of a small polypeptide precursor, or an order to the nucleosides in the VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 201 case of a nucleic-acid precursor. It is this intimate specific charac- ter which is expressed in the antigenic nature of the bacterial contents. In the bacterium, use is made of the nucleoprotein precursors either as enzymes for causing the synthetic metabolism to pro- ceed rapidly and effectively, or as units which form part of the new genetic material necessary to carry the basic cellular char- acter over into the next division. None of this process is clearly understood at the present time. It seems speculatively reasonable, however, that rather rapid chemical rearrangements can be made, utilizing energy by direct transfer to form either nucleic-acid units of molecular weight 2,000 or so, or small proteins of the same size. Let us guess that the nucleic acid is first made: the egg before the hen. (The order is not important, protein could be made first.) This nucleic acid is then specifically attached to protein molecules already in the cell and, as the spacing of the nucleosides is rather flexible (Wil- kins, private communication), this local attachment causes the opposite side of the nucleoside to form the same protein pattern, but in terms of bases or sugars. The small proteins now being formed then find themselves able to attach to the bases or sugars if their over-all pattern fits the proper structure, which is that of the protein of the parent cell. Any other di- or tripeptides do not attach and prob- ably suffer a new enzymatic digestion until they are reassembled in the correct way. Thus the nucleic acid serves to transfer the parental pattern to the new molecular generation. Thus there rapidly develops a population of new protein and, in turn, this prints its design on new nucleic acid until the cell carries a high proportion of subunits ready for assembly. The assembly process in the host follows the orderly develop- ment of the cell. In a virus-infected cell it conforms to the as- sembly needs of the virus. All the above is speculative. It may be words and no more. It is the kind of basic thinking which will one day lead some- one to the truth and we therefore include it with no great apology. 202 THE PHYSICS OF VIRUSES We need now to consider how the assembly of viruses from moderately large molecules can take place. Forces OPERATIVE IN ViruUS MULTIPLICATION We have seen how the process of virus multiplication involves a dramatic change in the manufacturing processes of the bac- terium so that the actual small pieces themselves are different, as exemplified by the virus antigens, which are small yet differ from the bacterial antigens. Although this is a most important fact, there is the equally important fact that in some way a virus, or part of a virus, can grow until it either divides or is the equiva- lent of two viruses. This requires an ordered growth, and the ordering process requires some kind of forces to be acting. We propose to consider here the kinds of forces which can be ealled on to explain ordered growth, and to make a speculative sug- gestion as to how they act. There are essentially two ways in which an ordered array of matter can be made to develop. One is by the establishment of a concentration gradient of some kind, and subsequent diffusion. Thus if a cell is filled with small units of nucleic acid, and these are condensed into a solid phase at some point in the cell, there will be established a concentration gradient toward that point, and diffusion will occur. This diffusion will produce a steady accretion of nucleic acid at the condensation point. There is no doubt that this is an important feature of many cellular proc- esses. However, the measured diffusion constants of protein molecules indicate that this process is far too slow to account for the very rapid virus multiplication. Accordingly, we turn to the second way, which requires the action of forces. All forces between molecules are electrical in character, if we exclude very weak forces. They have their origin in the Coulomb field of a charged particle and owe their nature to the distribu- tion of charge in the two systems which attract or repel each other. We have already seen that the first stage in virus attach- ment is electrostatic and must be due to the attraction of charges of opposite sign. If two elementary charges are involved, and they are separated by a distance r em in a medium of dielectric VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 203 constant AK, the mutual potential energy is (4.8 X 1071°)?/Ar ergs. When r is 100 A, and for K = 80, which applies to water for static or low-frequency fields, the potential energy 1s 29 X 10-" erg. The energy kT, which is a representative ther- mal agitation energy, is 4.1 X 10714 erg at 300° K, or 27° C. This is 14 times larger. Hence, such attractive forces are only capable of providing an energy able to hold a second molecule in place, in spite of thermal agitation, at distances of a few Angstrom units or less. It is, however, not necessary that a field be sufficient to ac- count for a binding energy. If the field is sufficient to produce relatively rapid motion in a definite direction, this can cause two charges to come close enough together to produce binding. Now the electric field of a single, elementary charge in a medium of dielectric constant 80, at 100 A, is 1,800 volts/em. The measured electrophoretic mobilities of proteins are such that, in a field as high as this, a protein molecule can travel 100 «/sec, or cover the 100 A necessary to become bound in 10~ sec. Thus forces due to free charges must be taken very seriously and probably account for some of the efficiency of assembly of molecular architecture. The difficulty in the way of explaining the whole of the order- ing of submolecular units in this way is the existence of ions in the bacterial cell. Whenever a free charge exists on the surface of a protein or nucleic-acid molecule, there will rapidly result an ionic atmosphere around this charge, and the consequent force at a distance becomes totally different. In fact, the most likely effect of the interaction of such charges and their atmospheres is a repulsion. We can now consider these ionic atmospheres, or double-layer forces. Tonic ATMOSPHERE, OR DouBLE-LAYER ForCES For many reasons, a large molecule may either lose or gain surface charge and so acquire a net positive or negative charge. If this molecule now finds itself in a medium full of ions, the ions of opposite sign are attracted to the molecule and there results a double-layer as indicated in Fig. 8.6. The positive charges at the surface of the molecule attract negative ions, 204 THE PHYSICS OF VIRUSES which approach closely to the molecule. However, these, in turn, attract more positive charges behind them, and so an atmosphere results in which, on the whole, there is more negative charge near the molecule, but in a rather diffuse way, with positive charge mixed in with it. This is called a double-layer, which is an ap- proximately correct description. The forces due to double-layers have been treated in colloid theory, notably by Verwey and eo he ue ® ® OF+ 2 Ol+ ) . ©9 @ © ® “Olt 5 @® I+ Oo @® © >) i) + @ oe 26 Sutmee sire oat Oo © eh +| 5 ® ) oC ® Oj+ +o iS) eS “alk % oy) ae CNG Ct) @® @ Oo © Fic. 8.6. The ionic atmosphere around a bacterium, drawn schematically to show the character of a double-layer. Overbeek (1948). Two cases have been worked out in some de- tail—the cases of flat sheets and of spheres. A skeleton account of the theory is given here, less for the reason of deducing the re- sults quoted than because it enables an understanding of the reason for the forces to be gained. A very clear genera] descrip- tion of ionic processes and of the Debye-Hiickel theory is given by Gurney (1946) which can serve as a background for the following material. The double-layer is due to a fixed set of charges on the virus surface which influences a charge distribution in the solution con- VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 205 taining ions. This charge distribution is conditioned by the fact that an electrical potential energy is possessed by an ion near the virus surface, and this potential energy is a factor in the Boltz- mann distribution of the ions. Thus, if we consider the virus surface to be a plane, there will be a potential V at a point near the plane, and so for an ion of charge multiplicity (valence) m, where the elementary charge is e, the ratio of the number of positive or negative ions, v4 or n_, per unit volume to the average number, 7, is ny = emev/kT aS emev/kT rn These are not the same, which is an elaborate mathematical way of saying that a double-layer will form. Now the charge density, p, at any point can be calculated from n, and n_ and is simply p = me(n, — n_) However, the charge density, p, is itself related to the potential by Poisson’s equation: Ores iO Van Oren __ 4p dx? ' dy? ' dz? K so that we can, in principle, use these equations to calculate the electrical potential due to this ionic distribution. If we make some simplifications, which limit the range of operation of the result but do not fundamentally alter the theoretical processes involved, we can assume that all ions have the same valence, so m is the same (as indeed has already been written above), and can assume JV is small, so that the first two terms of the exponential series are sufficient to describe the Boltzmann exponentials given above. Then ny = 7 € = | 206 THE PHYSICS OF VIRUSES Hi —Inme?V igs kT and therefore 02V 02V 02V Sirnme2V 5 i Oy? Th og UNE Now for a plane surface which accumulates an ionic atmos- phere, we need only consider the a-coordinate and, if we put p? = 8rnm’e?/KkT, we have the very simple equation d?V nae dr? ph for which the general solution is V = (Cye®? 4— Cheese where (, and C, are constants determined by the physical conditions present. Since, V = 0 for x = © we have C,; = 0. And since V = Vo, the potential at the surface, for x = 0, we have V = Vy The double-layer potential has then dropped to 37% (or 1 /e) of its original value in a distance of 1/p em, or a distance Ne Ge me N 8xn and somewhat on n, the average concentration of the ions. Now if two double-layers are formed at a distance 2d apart, there will be an interaction between them which will result in a repulsive force and hence a net potential energy which is a function of 2d, their separation. It is possible to calculate this repulsive potential, V;, in several ways (see Verwey and Over- beek, 1948, p. 66), and an approximate value for this is - This depends sharply on m, the valence of the ions, > AL fu I DON 2 tel 64nk7 |: | ppd J R p 7 ep/2 1 VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 207 An approximate value for the force, F, between two such plate double-layers is : fc aa Se I = 64nk7 Esl ie: This foree depends on the concentration of ions and also on p. The greater the value of p, the more rapidly does the force fall off with distance. This type of force is remarkably interesting from a biological viewpoint, and it is undoubtedly one of the factors in the organization of large molecules into the pattern of a virus or a chromosome. A living cell which is metabolizing is the seat of rapid energy turnover, of rapid molecular change, and of synthesis. It is surrounded by a membrane capable of selective passage of ions. As a result, the ionic strength of the inside of a cell is continually changing as the development of the cell proceeds. The expression for the force between two large mole- cules (which, for the present, we can think of as represented by planes) is dependent critically on the ionic concentration and also on p, which contains both the concentration and the valence. Thus the degree of repulsion between two large mole- cules is wnder control by the condition of the cell. We shall see shortly that attractive forces of a different character exist, and the balance between these will determine whether two large molecules remain near each other or will be repelled apart. We have seen that Luria’s mutation studies indicate that virus multiplication consists of an exponential growth involving some- thing like a growth, division, and separation. The separation is almost certainly constrained to take place because of the repulsive force due to ionic atmospheres. Evidence for this repulsion as a factor in virus action was ob- tained by Bernal and Fankuchen (1941) in their X-ray studies of tobacco mosaic virus. The preparations of this virus showed strong birefringence, and the orientation causing this persisted even on drying. In order to study the process, they constructed a small-angle X-ray diffraction camera, using slits in place of circular openings in 208 THE PHYSICS OF VIRUSES order to observe the reflections corresponding to the large separations between whole virus particles. They found sharp reflections and were able to make accurate measurements of the interparticle distances. The X-ray diffraction pattern corre- sponded to a hexagonal, close packed array. The interparticle distance varied with the virus concentration in the manner shown in Fig. 8.7. The interparticle distance R, in A, was found to be R = 1,650/N”, where N is the number of 500 BSS 8 300 8 Inter Particle Distance A 100 (@) | 2 + Aram Concentration) Fic. 8.7. Variation of the intervirus distance for TMV at various concen- trations, as observed by Bernal and Fankuchen (1941). The fact that a linear relation with the reciprocal of the square root of concentration is observed means that a close packed array exists. grams of dry virus per 100 cm®. The plot in the figure is R versus the reciprocal of the square root of the concentration. This separation into a hexagonal array can be explained by a repul- sion between the particles, causing them to fit the space in the container with as much distance between particles as possible. The results have been analyzed by Oster and Onsager and can be fully explained by repulsive forces only. The repulsive potential due to the double-layer interaction for two spheres, radius a, can be calculated for a variety of cases. For a thin double-layer, corresponding to a moderate ionic concentration (about one-tenth molar for example), VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 209 Verwey and Overbeek give the approximate value for the repul- sive potential, Uz, as Uz = Kay,"[}4 In (1 + e7*&™)) where K is the dielectric constant; Wo is the surface potential; which is of the order of 30-150 my, corresponding to 4.8 & 10714 erg; T is pa or [8Srnme?/KkT]*a; and s is the ratio of the separation of the centers of the spheres to the radius of each. 300 ° Interparticle Distance (A) 200 100 2.0 3.0 40 5.0 6.0 70 80 pH Fig. 8.8. Variation of intervirus distance with pH for TMV. A minimum occurs at the isoelectric point, which indicates that forces exist which are dependent on ionic atmospheres. Data due to Bernal and Fankuchen (1941). The fact that the force between virus particles is dependent on the ionic atmosphere is shown by the way in which inter- particle distance for TMV was found by Bernal and Fankuchen to depend on pH. This is shown in Fig. 8.8. It can be seen that there is a minimum distance at the isoelectric point, pH 3.4, with a rise on each side. It is quite clear that repulsion alone cannot explain the assembly of macromolecules to form a virus unit. Some kind of 210 THE PHYSICS OF VIRUSES attraction is necessary. Two types of attractive processes exist, and probably both play a part in virus synthesis. VAN DER Waats Forces BETWEEN MACROMOLECULES The forces between neutral molecules which give rise to liquefaction of even spherical molecules like helium, and which are known generally as Van der Waals forces, have been ex- plained by London (1930, 1937). According to quantum me- chanics, an electron associated with a positive nucleus to form an atom does not occupy a smoothly regular orbit, but has a chance of occupying many different positions with respect to the nucleus. Thus, although the average location of the electron may be such that no net-time-averaged dipole moment exists, there may be very large instantaneous dipole moments, and a mean-square dipole moment may have a considerable value. Now each ephemeral dipole produces an electric field around it, distorts nearby atoms, and produces induced dipoles in them. These induced dipoles now interact with the originating transient dipole and cause an attraction. There are thus two factors to consider—first, the size of the transient electric field due to the random position of the electron in the first atom, and second, the readiness of the second atom to change its configuration to produce a dipole and so become attracted. Once the originating and induced dipoles have assigned values, the mutual potential energy due to their interaction (which is attractive) is easy to compute. The electric field due to a dipole varies as 1/h*, so the induced dipole will have a strength dependent on this, and the attractive potential between two dipoles also depends on 1/R’, so that the over-all attractive potential depends on 1/A°. The magnitude of the constant of proportionality depends on the polarizability,* a2, of the second atom and the polarizability, a,, of the first. In addition, if the frequency for an electronic transition from a state L to a state AK, of energies F, and Ex is Vz, SO that hie = E, San Ex * Polarizability is the induced dipole moment per unit applied electric field. VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 721A and vy is the lowest possible frequency of such a transition, London deduces that the factor (34)hvo is also involved. The mutual potential energy, U, is then ee SAV payjas 4R® Actually this calculation is difficult to make, and other ver- sions exist. In general we can put U = B/R®, where B is a con- stant for any pair of atoms. From our point of view, two vital considerations exist. The first is that these forces are additive, so that one fluctuating atomic dipole influences and attracts all other polarizable atoms. The second is that the size of viruses on the molecular seale is large, and the electric field accordingly takes time to travel to all points in the virus, a time which is admittedly very short but not short compared to the rate of fluctuation of the inducing dipole. This means that remote atoms in the virus may be influenced by a field which does not correspond to the existing dipole and so will be out of phase with it and thus much less attracted. The first consideration leads to the remarkable result that between large molecules the attractive potential diminishes quite slowly with their distance apart, d; in fact, over a small range, the potential varies as 1/d?. The second consideration limits the range in which forces can be treated as additive and, indeed, may require that repulsive forces be considered. So for distances exceeding 100 A, the attractive potential varies more rapidly with distance and, in fact, falls very quickly in value. The forces between plane surfaces of infinite extent and finite thickness, neglecting the finite-velocity effect mentioned above, were calculated by de Boer (1936), and Hamaker (1937) has considerably extended the calculation to include spherical particles. For the case of two parallel plates of thickness y, the additive feature of the forces is readily exploited, and by two quite simple integrations (see Verwey and Overbeek, 1948, p. 101) an expression for the potential, U, can be derived. It is 912 THE PHYSICS OF VIRUSES pee Bid 2 i a2 (ag) SEs aie) 48 where N is the number of atoms per unit volume of the plane material, and B is the constant in the relation for the potential energy of two atoms. In the case of two spheres, radius a, placed so that the shortest distance between their surfaces is H, we can use the parameter ae H a . Thus S is the ratio of the total separation of the centers to the diameter of one sphere. Then the resulting poten- tial energy (Verwey and Overbeek, 1948, p. 160) is | 2 Se *] 82 2 Maicauate Serene aS or, approximately, ae w?N?Ba + yal For a rough guide, we can follow Verwey and Overbeek and put w?N?B = 10 ergs, so we have UOC aE In actual cases, the macromolecules are immersed in a medium which intervenes between them. This does not, however, dimin- ish the field strength except in the usual way in terms of the dielectric constant. At the frequencies involved, there is no opportunity for wholesale rotation of polar molecules but only for the electronic adjustments in each. Thus the dielectric con- stant to be used is the square of the refractive index [about (44)?]. So the effect of the medium will be to modify downward, by a factor of about two, the value of the interaction potential. FLucTUATING PROTON CHARGE FoRCES One of the characteristics of proteins is the fact that many of the side chains consist of amino acids containing dissociating groups. Groups such as —NH, can attach a hydrogen ion to be- come —NHs, and a group like —COO7 which has already lost a VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 213 hydrogen can reattach one to increase the local positive charge. In the ordinary way, there are many of these groups and not a great deal of reason why one should have hydrogen attached to it, rather than another. The charged groups produce dipole mo- ments which, on the whole, average to a small value, but which ean, by fluctuations in the positions of the attached protons, cause quite large mean-square dipole moments. Kirkwood and Shumaker (1952) have pointed out that such fluctuating dipoles can influence the migration of protons in a second protein mole- eule and thus induce dipoles which are attracted to the first molecule. [f one were constructing a large-scale model to illus- trate the nature of the London-Van der Waals forces, this would serve very well; the reason for the fluctuations is totally different, and the factors influencing their size are also quite different, but the net effect of producing attraction is the same. The theory developed by Kirkwood and Shumaker can be used to explain the fact that small concentrations of protein in solu- tion produce a large change in dielectric constant, a fact which was previously ascribed to the presence of large, permanent (or nearly so) dipole moments. If, instead of such moments, there is supposed to be a lability of the protons which are attached to the kind of groups just described, then the influence of an external electric field will be to modify the proton distribution and bring forth induced dipoles, which are large, on the average, and so cause an increase in the dielectric constant. For the four proteins G-lactoglobulin, ovalbumin, hemoglobin; and serum albumin, the mean-square dipole moment found experimentally agrees quite well with the theoretical predictions. In view of this fact, the value for the interaction energy be- tween protein molecules calculated by the same authors is of considerable interest. If U is the interaction energy (Agi)? (Aqz)? Were where (Aq,)? and (Aqz)? are the average, total charge fluctuations of the two molecules. The energy falls off as 1/R?, which is very 214 THE PHYSICS OF VIRUSES similar to the rate of change of energy for the Van der Waals forces between large molecules. A force of this nature is dependent on the average charge fluctuations in the molecules, and these will, in turn, depend on conditions in the solution which attach or detach protons from ionic groups. Therefore, the condition of the molecule can have a considerable effect on this variety of force. This kind of force is not inherently specific; that is, it does not depend on the presence of similar groups or complementary structures. However, the interaction energy may well be in- creased in value if certain kinds of complementary groupings exist in the two molecules. Kirkwood and Shumaker point out this fact, but make no definite calculation of interprotein forces numerically. We now have three classes of force to consider, one repulsive and under metabolic control by changing the ionic strength and one attractive and also dependent on whatever cellular con- ditions determine the proportion of charge subject to fluctua- tion. The third force, the Van der Waals force, is not under con- trol by the nature of the solvent in the cell at all. PoTeENnTIAL ENERGY DIAGRAMS FOR ‘Two MACROMOLECULES There is not a great deal of value in trying to plot accurate potential diagrams for the interaction between two biological molecules since neither the size nor the structure of these mole- cules is accurately known. Nevertheless, it is worth while to get some idea of the order of magnitude of the potential energies involved so that suggestions for the physical processes in virus multiplication can be made. To make a definite case, in Fig. 8.9 we plot the potential- energy curve for two southern bean mosaic virus particles ac- cording to the attractive-force formula of Hamaker and the repulsive-foree formula given by Verwey and Overbeek. The value of the surface potential, Yo, has been chosen quite arbi- trarily as k7'/e for a temperature of 300° K. It can be seen that the potential energy, U, is slightly negative at large distances, VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 915 which means there is a small attraction between the particles. This is not significant because thermal agitation is sufficient to prevent any important binding between virus particles at this range of separation. As the distance apart becomes less, there 2xl0 erg Repulsion to Double Layer H ° Surface separation, HinA Fia. 8.9. Potential energy between two southern bean mosaic virus particles, The double-layer repulsion and the Van der Waals attraction produce a potential barrier. This varies in character with ionic strength, and may be a factor in keeping constituents together during growth and then forcing them apart at division. is a sharp increase in the mutual potential energy, which means a quite definite repulsive force in this region. At a distance of about 6 A, the Van der Waals attraction makes up for the double-layer repulsion, so that within a range of 6 A there is quite strong binding between the two particles. 216 THE PHYSICS OF VIRUSES We can now imagine a process about as follows. The original virus invades the host cell, and probably a long nucleoprotein molecular aggregate unwinds and presents a large area of specifi- cally active surface. This starts a strongly competitive system of enzyme manufacture, and possibly also of direct enzymatic action, which sets going a new process of synthesis of virus pre- cursor material, both nucleic acid and protein. The nucleopro- tein units so formed become attracted by Van der Waals attrac- Fic. 8.10. Token representation of the process of self-duplication. The nucleoprotein units are attracted to an original chain, aggregate near it to form adjacent chains, experience a change in ionic atmosphere, and are forced tion and held in place so that near the original unit a second set of nucleoprotein molecules accumulates. This will grow, but only within the 6-A attractive distance, so that a second, long, thin nucleoprotein is formed. This will continue to thicken and develop as the metabolic processes of the host pile up more nucleoprotein until the thickness of both original and new nu- cleoprotein exceed about 200 A. Under these conditions, the Van der Waals attraction may begin to lessen on account of the fact that the additive feature of the intermolecular forces may cease VIRUS GENETICS, MULTIPLICATION, AND PHYSICS PANT to hold because of the finite velocity of travel of the electric field. Thus if the effective frequency of an electronic fluctuation is 10'® per sec, the time for the field to be established at a distance of 100 A is the distance divided by the velocity of light, or 10-°/3 X 107°, or 3.3 X 107" sec. This means that the induced dipole will not be in phase with the original fluctuation dipole and no attraction will occur. So this may well mean that the n/AN/ VA (d) apart to form two chains. Part of one chain can go with the other at this stage, and the second chain can be completed from a unit near by. attraction to the original nucleoprotein chain is too little to hold within the 6-A critical distance. As soon as this is exceeded, the strong repulsive forces of the ionic atmosphere take over, and the two units are forced apart, ready to start a second pair of chains, and so on. It is interesting, though speculative, that the size of a genetic unit is thus restricted by the finite velocity of light, so that ulti- mate cosmological laws can be seen influencing the intimate details of a living system, 218 THE PHYSICS OF VIRUSES The kind of process envisaged is shown in Fig. 8.10. The center, internally active part of the virus is thought of as long and thin and comprising nucleoprotein units joined together by a mixture of Van der Waals forces and hydrogen bonds. The units are firmly, but not inseparably, bound. This long, thin unit offers a large surface area to the metabolizing bacterium and, as a result, rapidly changes the molecular environment so that fresh nucleoprotein begins to be formed. As this takes place, the immediate neighborhood begins to be populated by subunit nucleoproteins, each capable of influencing protein and nucleic- acid synthesis as described earlier. These are attracted to the original nucleoprotein and also to one another and begin to form alongside the first virus element as shown in Fig. 8.10b. As they aggregate to form new lines along the old virus, the ionic atmos- phere changes to make possible a repulsion. As soon as there are several lines formed on each side of the parental virus, the Van der Waals attraction ceases to be enough to overcome the ionic repulsion, and the new units are driven out. Some are complete and some are not. Each unit now starts its double process, of charging the metabolic synthesis mechanism and of mutual accretion. This process will develop exponentially, and before long the cellular metabolism will have become almost wholly a virus me- tabolism contained in the cellular envelope. At a stage, which is about three-quarters of the whole duration of single cell develop- ment, the nucleic acid synthesis becomes essentially complete. A further protein synthesis continues until the virus particles are covered with a protein sheath which includes the enzymes necessary to produce cellular lysis and entry in the first place. These are able to produce lysis in any event and, in the case of bacterial viruses, do so, liberating a burst 1n the well-known way. We have mentioned that some incomplete virus chains will be formed. To some extent, these must remain until the burst occurs and must be part of the whole debris which is found at that time. However, there must also be some over-all checking proc- ess, as suggested by Dancoff (1949), which renders the multi- plication of smaller units unfavorable. Perhaps this can be found VIRUS GENETICS, MULTIPLICATION, AND PHYSICS 219 in more specific attractive forces due to special arrangements of charges on the surfaces of the virus chains which act to make the attraction of subunits considerably less unless the whole chain is complete. It can be seen that the multiple mating process falls into this scheme. Each genetic unit is thought of as being one of the nucleoprotein building blocks shown in Fig. 8.10. It is quite easy for the separation of two chains to carry away part of the first; in fact, the whole process is one of ordered assembly of separate units rather than of the splitting of one individual into two halves. So it is not surprising if a genetic unit which started in one chain finds itself part of another chain. It is also clear that the generations need not be synchronized, but only approximately so. This last part of this chapter has been frankly speculative. In truth, all that can be said is that we have some small idea of the probable nature of the virus precursors, that there exist attrac- tive forces between large molecules up to a certain size, and also repulsive forces due to ionic atmospheres, which are somewhat controllable by the cellular state. What has been done above is to try to invent a scheme using these ideas. The interest and value of such a scheme is not essentially in its truth but rather in its suggestiveness. We have said before that virus multiplication may form an elementary test of the adequacy of physical laws to explain fully biological processes. Using some simple facts regarding large molecules in solution, it can be seen that known physical laws contain at least some of the necessary features demanded of them. This is encouraging, but it remains for the virologist to provide fuller information about the parts and pieces and the biological processes, for the virus physicist to make their information fully quantitative and handy for accurate thought, and for the theorist to put all the informa- tion correctly together to see whether known natural laws can accurately interpret and predict events in virus development. Physical studies of viruses aid in this goal, and it is because they aim toward a solution of an outstanding problem of hu- manity that even preliminary steps, as we have described here, 220 THE PHYSICS OF VIRUSES are worth description. Far greater development of these studies is needed and is going forward. It is with a keen eye to the prom- ise of the future that we conclude this chapter. REFERENCES Bernal, J. D., and Fankuchen, I., J. Gen. Physiol. 25, 111 (1941). Burnet, F., and Lind, P. E., J. Gen. Microbiol. 5, 59 (1951). Dancoff, 5., Brookhaven Seminar (1949) (unpublished). de Boer, J., Trans. Faraday Soc. 32, 21 (1936). Delbriick, M., Problems of Modern Biology in Relation to Atomic Physics (Committee on Growth, National Research Council, 1946). Delbriick, M., Michigan Biophysics Symposium (1951). Delbriick, M., and Bailey, W. T., Jr., Cold Spring Harbor Symposia Quant. Biol. 11, 33 (1946). Gurney, R. W., [ons in Solution (Cambridge University Press, New York, 1946). Hamaker, H. C., Physica 4, 1058 (1937). Hershey, A. D., and Rotman, R., Genetics 34, 44 (1949). Kirkwood, J., and Shumaker, J. B., Proc. Natl. Acad. Sci. U.S. 38, 302 (1952). Kozloff, L. M., and Putnam, F. W., J. Biol. Chem. 182, 229 (1950). London, F., Z. Physik 63, 245 (1930). London, F., Trans. Faraday Soc. 33, 8 (1937). Luria, S. E., Cold Spring Harbor Symposia Quant. Biol. 16, 463 (1951). Maaloe, O., and Watson, J. D., Proc. Natl. Acad. Sci. U.S. 37, 507 (1951). Schrédinger, E., What is Life Cambridge University Press, New York, (1945). Verwey, E. J. W., and Overbeek, J. Th. G., The Theory of the Stability of Lyophobic Colloids (Elsevier Publishing Co., Inc., 1948). Author Index Numbers in italics indicate the pages on which the references appear in the bibliographies at the end of each chapter. A Adam, N. K., 122, 145 Adams, M. H., 112, 113, 114, 115, 118, 120 Adams, W. R., 95, 97, 101 Anderegg, J. W., 60, 68 Anderson, R. S., 89, 102 Anderson, T. F., 17, 67, 68, 172, 173, 177, 178, 179, 182 Apker, L., 148, 167 Arnold, W. F., 148, 168 B Bachofer, C. S., 95, 102 Bailey, W. T., Jr., 184, 220 Barlow, J. L., 178, 182 Barnes, D. K., 170, 182 Barron, E. S. G., 89, 102 Bauer, J. H., 35, 67 Bawden, F. C., 14, 21, 53, 63, 67, 140 Baylor, M. B., 120, 170 Beams, J. W., 37, 67 Beard, D., 27, 31, 39, 51, 68 Beard, J. W., 39, 51, 68 Beavan, G. H., 149, 167 Beeman, W. W., 58, 60, 61, 65, 68 Benaglia, A. E., 120 Bernal, J. D., 56, 57, 67, 207, 208, 209, 220 Bethe, H. A., 71, 102 Black, L. M., 20, 21, 34, 45, 67 Bloch, F., 71, 102 Boggs, S., 172, 173, 182 Borysko, E., 19, 68 Boyd, G. A., 120 Brakke, M. K., 34, 45, 67 Branson, R. H., 104, 121 Brasch, A., 139, 145 221 Breeze, S. S., Jr., 23, 65, 68 Brody, S., 122, 145 Bronfenbrenner, J., 134, 145 Brown, B. B., 171, 182 Brown, G. L., 149, 153, 167 Bull, H. B., 67 Burger, W. C., 130, 132, 145 Burnet, F., 184, 220 Butenandt, A., 152, 154, 155, 156, 167, 198 C Carlisle, C. H., 57, 67 Carnelly, H. L., 113, 120, 143, 145 Caspar; D., 36), 37 Chase, M., 178, 179, 180, 182 Cherry, W. B., 112, 113, 120, 125, 145 Christensen, R. J., 171, 182 Cline, J., 2, 125, 126, 127, 128, 129, 142, 145 Cooper, G. R., 27, 31, 51, 68 Cooper, K. W., 170, 182 Corey, R. B., 104, 121 Crowfoot, D., 55, 67 D Dale, W. M., 89, 102 Dancoff, S., 219, 220 de Boer, J., 211, 220 Delbriick, M., 14, 125, 129, 145, 181, 184, 186, 200, 220 Dickman, S., 89, 102 Dillon, J. F., 37, 67 Dimond, A. E., 83, 92, 102, 111, 113, 121, 135, 140, 141, 145 Duggar, B. M., 167 Dulbecco, R., 164, 165, 166, 167, 168 aS) cS) we x E Eberl, J. J., 120 Einstein, A., 40, 41, 42, 48, 44, 47, 67 Elford, W. J., 22, 34, 67 Epstein, H. T., 64, 67 Hvans, R. D., 88, 102 Exner, F. W., 89, 90, 91, 102 Kyring, H., 103, 120 Fr Fankuchen, I., 56, 57, 67, 207, 208, 209, 220 Fermi, E., 71, 102 Fluke, D. J., 16, 19, 65, 67, 80, 95, 112, 149, 152, 157, 158, 159, 160, 161, 163, 166, 167, 168 Forro, F., Jr., 78, 79, 92, 102, 172, 182, 187, 191 Rosters RAC. 117. 118s 720 Franklin, R., 65, 67 Frazer, D., 120, 170 Fricke, H., 89, 102 Friedemann, A. B., 139, 145 Friedewald, W. F., 89, 102 Friedman, M., 65, 67, 92, 102, 113, 120, VQ LS 2 Friedrich-Freksa, H., 152, 154, 155, 167 Fry, F. J., 169, 182 ryan Wide LOO ne? G Gans, R., 43, 67 Garen, A., 2, 125, 126, 142, 145 Gates, F. L., 146, 167, 168 Glasstone, S., 103, 120 Goldfarb, A. R., 156, 167, 168 Golub, O. J., 22, 67 Gowen, J. W., 77, 91, 102 Graf, L. H., 130, 131, 145 Green, R. H., 67 Guild, W. R., 87, 102, 156, 168 Guinier, A., 59, 67 Gurney, R. W., 204, 220 Guth, E., 44, 67 5 TADS UstOe AUTHOR INDEX H Hamaker, H. C., 211, 214, 220 Hamm, J. S., 156, 167 Hartwig, S., 152, 154, 155, 167 Harvey, I. N., 170, 182 Heinmets, F., 22, 67 Heller, W., 148, 167 Herriott, R. M., 178, 182 Hershey, A. D., 125, 134, 145, 178, 180, 182, 184, 185, 186, 220 Herzog, R. V., 44, 67 Hirst, G. K., 142, 145 Holiday, E. R., 149, 150, 167 Hollaender, A., 162, 163, 167 Holmes, B., 77, 102 Holweck, F., 91, 102 Horton, J. P., 182 Horwood, M. P., 182 Huber, W., 139, 145 Hutchinson, F., 138, 145 Illig, R., 44, 67 Johnson, E. M., 110, 121, 170 Johnson, F. H., 117, 118, 120 Jones, H. N., 149, 150, 151, 167 K Kaesberg. P., 58, 60, 61, 65, 68 Kalmanson, G., 134, 145 Kekwick, R. A., 31, 68 Kilham, L., 21, 67 Kirkwood, J.. 53, 67, 213, 214, 220 Knight, C. A., 7, 14 Kozloff, L. M., 187, 191, 220 Kraemer, E. O., 34, 48, 67 Kratky, O., 58, 67 Krueger, A. P., 109, 120, 125, 145, 182 Kuck, K. D., 158, 168 Kudar, H., 44, 67 179, fal AUTHOR INDEX L Laidler, K. J., 103, 120 Lamm, O., 27. 67 Lansing, W. D., 48, 67 Lark, G., 115, 120 Lauffer, M. A., 7, 14, 23, 27, 31, 38, 40, 48, AG) 502 bile) 2a 00.1005 045,607, Go, LTS 113, 120, 142, 143, 145 IL@HI5 IDS 1g, Wi, PAS ONE Wirls tee fish, TOD LOE 92, 96, 101, 102 Leonard, B. R., Jr., 60, 68 Levinson, A. B., 161, 168 Levy, M., 120 Lind, P. E., 184, 220 London, F., 210, 211, 213, 220 Loofbourow, J. R., 149, 150, 168 Lueas, A. M., 91, 102 Luria, S. E., 89, 90, 91, 95, 102, 160, 164, 165, 168, 188, 189, 191, 194, 207, 220 M Maaloe, O., 187, 191, 220 MacDonald, E., 113, 120 Malkiel, S., 173, 176, 177, 182 Marchbank, D. F., 158, 168 Marcus, A., 167 Markham, R., 102 McElroy, W. D., 170, 182 McFarlane, A. S., 31, 68 McIntosh, J., 34, 68 McLaren, A. D., 89, 102, 146, 162, 163, 167, 168 McLean, I. W., Jr., 39, 68 Melnick, J., 23, 65, 68 Miller, G. L., 27, 31, 42, 43, 46, 48, 49, 62, 64, 67, 142, 143, 145 Miller, V. K., 117, 118, 120 Milzer, C. D., 161, 168 Moorhead, E. L., 133, 145 Morgan, C., 20, 21, 67 Morowitz, H., 162, 168 Mosovich, E., 156, 167 Miihlethaler, K., 19, 68 Murphy, J. B., 168 Is} 8}, ak, WS Kekely “Wf N Neal, J. D., 161, 168 Neuman, S. B., 19, 68 Neurath, H., 27, 31, 51, 68 Newton, N., 171, 172, 173, 174, 182 Nickson, J. J., 101 INixonesieniie Qi ooss67, O Ogston, A. G., 53, 68 Oliphant, J. W., 162, 163, 167 Oppenheimer, F., 161, 168 Oppenheimer, J. R., 148, 168 Oster, G., 172, 173, 174, 175, 182, 208 Overbeek, J.T. G., 204, 206, 209, 211, 212, 214, 220 P Patterson, E. L., 130, 181, 145 Pauling, L., 104, 121 Pease, D. C., 170, 182 Pedersen, K. O., 33, 34, 38, 66 Perrin, F., 44, 68 Petersen, B. W., 102 Petre, A. W., 53, 67 Pickels, E. G., 35, 67, 68 Pirie, N. W., 67 Platt, J. R., 156, 167 Pollard, E. C., 74, 76, 78, 79, 83, 92, 95, ViSTOR 1022 Mihi ASG. Lets oe 140, 141, 145, 172, 182 Polson, A., 27, 28, 64, 67, 68 Price, W. C., 21, 27, 31, 42, 43, 46, 48, 49, Te (A (Oi, (ei, UO), WO, Ih, ial U3. 120) 127, 133. 045 Puck, T. T., 2, 125, 126, 127, 128, 129, 130, 142, 145 Putnam, F. W., 187, 191, 220 R Randall, J. T., 149, 153, 167 Reaume, M., 113, 116, 121 Rhian, M., 23, 65, 68 Riley, D. P., 56, 67 224 Ritland, H. N., 58, 61, 65, 68 Rivers, T. M., 14, 168 Ross, J. D., 37, 67 Rotman, R., 185, 186, 220 S Saidel, L. J., 156, 167, 168 Salaman, M. H., 91, 102 Schachman, H. K., 40, 49, 50, 51, 58, 68 Scheibe, G., 152, 154, 155, 167 Schlesinger, M., 125, 145, 180 Schmidt, G. M., 55, 67 Schrodinger, E., 106, 121, 200, 220 Schulman, S., 60, 68 Scott, E. M., 143, 145 Scott, J. F., 149, 150, 168 Scribner, E. J., 171, 182 Seeds, W. E., 156, 168 Selbie, F. R., 34, 68 Setlow, J., 135, 140, 145 Setlow, R. B., 156, 157, 167, 168 Sharp, D. G., 27, 31, 39, 51, 68 Shaughnessy, O. M., 161, 168 Shedlowsky, T., 68 Shepard, A. B., 28, 64, 68 Shepard, C. C., 129, 145 Shumaker, J. B., 53, 67, 213, 214, 220 Simha, R., 44, 68 Sinsheimer, R. L., 149, 150, 168 Siri, W. E., 102 Slater, M., 85 Smadel, J. E., 67, 68 Smith, K. M., 14, 15, 23, 53, 67, 68, 77, 92, 102 Stahmann, M. A., 130, 131, 132, 145 Stanley, W. M., 7, 14, 23, 31, 52, 53, 67, 68, 171, 182 Stearn, A. E., 103, 107, 120 Steinhardt, J., 116, 121 Sturm, E., 168 Suprynowicz, V. A., 149, 153, 155, 156, 157, 168 AUTHOR INDEX Svedberg, T., 30, 33, 34, 38, 66 Swerdlow, M., 19, 68 it Taft, E., 148, 167 Takahashi, W. N., 171, 182 Tamm, I., 160, 161, 168 Taylor, A. R., 27, 31, 39, 51, 68 Taylor, N. W., 48, 67, 68 Thornberry, H. H., 110, 121 Timofeeff-Ressovsky, N. K., 101, 158, 168 Traub, F. D., 139, 145 Tucker, D., 169, 182 V Valleau, W. D., 110, 121 Verwey, E. J. W., 204, 206, 209, 211, 212, 214, 220 Ww Walker, J. C., 130, 131, 145 Warren, J., 23, 65, 68 Watson, D. W., 112, 113, 120, 125, 130, 131, 145 Watson, J. D., 90, 98, 99, 102, 187, 191, 220 Weissler, A., 182 Whiteley, A. H., 170, 182 Wilkins, M. H. F., 153, 156, 168, 201 Williams, R. C., 17, 20, 56, 65, 68 Winters, B. C., 172, 173, 182 Woese, C., 92, 102, 142, 143, 144, 145 Wollman, E., 91, 102 Woodend, W. G., 129, 145 Wulff, V. J., 169, 182 Wunder, C. C., 48, 68 Wyckoff, R. W. G., 20, 21, 34, 45, 54, 55, 67, 68 Z Zimmer, K. G., 101, 158, 168 Zirkle, R. E., 158, 168 Subject Index A Absolute reaction rate theory, 107 Action spectra, see Ultraviolet action spectra Adsorption of viruses, 124 Agglutinins, 9 Alfalfa mosaic virus, 65, 110, 113 Anthracene, 149 Anthraldehyde, 149 Antibody receptors, area of, 137 number of, 135 Antigen-antibody reaction, 8 Antiserum preparation, 9 Asymmetric particles, viscosity and dif- fusion of, 43 Attenuation of viruses, 6 B B. megaterium, 12 B. subtilis spores, 162 Bacterial virus multiplication, 186 Bacteriophage, M-1, M-2, M-3, M-4, thermal constants of, 113 M-5, inactivation cross section of, 81, 92 size and shape of, 65 thermal constants of, 113 Megateriwm, Sonic action on, 172 S. lactis, adsorption of, 126 thermal constants of, 113 Staphylococcus, adsorption of, 125 size of, 65 thermal inactivation, 109 U.YV. action spectrum, 163 T-series, sonic action on, 172 T-1, absorption spectrum, 156 deuteron bombardment, 79 dimensions, 5, 65 combined radiation and thermal ef- fects, 94 Bacteriophage, T-1, electron bombard- ment, 80 electron micrograph, 18 inactivation cross section, 81 mutual interference, 6 picture, 197 quantum yield, 163 reaction constants for loss of serology, 141 serological affinity, 135 thermal constants, 113 U.V. action spectrum, 158 U.V. action spectrum at low tempera- tures, 159 wet X-irradiation, 90 T-2, chemical composition, 7 dimensions, 65 mixed yield, 6 multiplicity reactivation, 165 picture, 179 recombination genetics, 185 thermal constants, 113 T-3, diffusion, 64 thermal constants, 113 T-4, diffusion, 64 mixed yield, 6 thermal constants, 113 T-5, pressure effects, 118 thermal constants, 113 thermal inactivation and ionic strength, 115 T-7, mutual interference, 6 thermal] constants, 113 Bombardment by ionizing radiation, 77 at varying ionization density, 81 results, SBMV, TMV, T-1, 82 Bovine serum albumin monolayers, serol- ogy of, 138 Buoyancy measurements, 39 Burst, 3 Burst size, 3 225 226 am SUBJECT INDEX Bushy stunt virus, chemical composition, 7 diffusion constants, 28 dimensions, 5, 65 filtration, 24 inactivation dimensions, 92 mass by motion study, 31 purified preparation, 10 radius from X-ray scattering, 60 thermal action on infectivity and serol- ogy, 140 X-ray hydration studies, 58 C Cabbage blackring virus, lack of observed particle, 22 Cage effect, 148 Capillary tube sedimentation, 34 Cauliflower mosaic virus, lack of observed particle, 21 Cavitation, 170 Checking process in multiplication, 219 Chemical composition of viruses, 7 Collision rate for viruses, 125 Color center diffusion, 148 Combined radiation and thermal action, 93 Complement, 123 Coxsackie virus, dimensions, 65 filtration, sedimentation and electron- microscopy, 24 Cross section, see Sensitive cross section Cucumber mosaic virus, amino acid con- tent, 8 rod shaped particles, 22 X-ray diffraction, 56 Cytosine, 149 D Debye-Hiickel theory, 204 Delta rays, 82 Desoxyribonucleic acid, absorption spec- trum, 149, 152 Deuterons, 73 Diffusion, 24 Diffusion constants for ellipsoids, 44 Diffusion constant measurement during sedimentation, 38 Double layer forces, 203 Doughnut heads, 4 E J Electron microscopy, 15 Enation mosaic virus, X-ray diffraction, 56 Energy loss, by fast charged particles, 70, (5 te) rates for various particles, 74 Energy turnover in host, 199 Entropy, 106 Equine encephalomyelitis virus, diffusion of, 28 Excitation potentials for elements, 73 Excitations, 72 F Fast charged particle, see Energy loss Fluctuating proton charge forces, 212 Foot and mouth disease, dimensions, 1, 5, 65 Free energy per form of vibration, 106 activated state barrier, 108 Free radicals, 88 collision with solute molecules, 88 G Graded collodion membranes, 22 H Hemagglutination, 9, 124, 142 sedimentation constant, 143 thermal constants, 143, 144 Hemocyanin, 23 Hemoglobin, 23 Henbane mosaic virus, lack of observed particle, 22 Herpes simplex, dimensions, 5, 65 Hydrated partial specific volume, 38 Hydrated viruses, frictional drag, 32 SUBJECT INDEX I Identity of physical particle and infectious unit, 62 Inactivation volume for random bombard- ment, 80 Indirect action of radiation, 89 Inferential character of virus study, 14 Influenza, buoyancy studies, 39 chemical composition, 7 dimensions, 5, 65 electron microscopy of infected mem- branes, 21 hemagglutination, 142 inactivation dimensions, 92 infectivity sedimentation, 64 recombination in, 184 thermal constants, 113 U.V. action spectrum, 160, 163 U.V. action on hemagglutination, 160 Insulin, absorption spectrum, 153 Interaction energy between protein mole- cules due to fluctuating charge, 213 Internal energy per form of vibration, 106 Internal structure of viruses, 17 Tonic atmosphere, of bacterium, 204 forces, 203 Tonic strength inside cell, 207 Tonization, 69 J Japanese B encephalitis, dimensions, 65 IL; Large angle scattering, see Scattering Latent period, 3 effect of radiation on, 95 Lesion counting, 11, 12 animal viruses, 12 Local lesions, 11 Logarithmic survival, area bombardment, 79 volume bombardment, 80 Lysine polypeptides, infectivity reduction by, 131 ysis,3, 11 Lysogenesis, 12 227 M Magnetic ultracentrifuge, 37 Molecular absorption spectra, 149 low temperature, 149 Motion of viruses, 24 Multiple hit processes, 158 Multiple infection, 5 Multiple mating process, 219 Multiplicity reactivation, 164 Mumps virus, hemagglutination, 142 Mutagenic agents, 5 Mutation of viruses, 5 Mutual interference, 6 N Neutralization of infectivity, 9, 134 Newcastle disease virus, chemical compo- sition, 7 dimensions, 65 electron microscopy of infected mem- branes, 21 hemagglutination, thermal action on, 143 inactivation dimensions, 92 picture of, 198 Nicotiana tabacum, 21 Non-spherical viruses, frictional drag, 32 Nuclear physics methods, 13 O Optical microscopy, 15 Origin of viruses, 12 Osmotic effects on viruses, 177 Osmotic ghosts, 177 absorption of, 178 Osmotic shock, release of DNA, 178 P Partial specific volume, 30, 31 Particle weight measurement, 31 Peptide bond absorption, 156 Phenylalanine, 152 Phosphorus turnover in phage duplica- tion, 187 Photo reactivation, 165 Photosynthetic energy transfer, 148 Physical forces, 66 228 Plaque technique, 11 Plate double layers, forces between, 206 Pneumococcus transforming factor, 112 absorption spectrum of, 149 Poiseuilles flow law, 22 Poliomyelitis, Lansing, dimensions, 5, 65 Polypeptide attachment, 130 Polypeptides and virus surfaces, 124 Potato leaf roll virus, lack of observed particle, 21 Potato paracrinkle virus, lack of observed particle, 22 Potato virus X, rod-like particles, 21 thermal inactivation, serology and in- fectivity, 140 Potato virus Y, lack of observed particles, Q2 Potato yellow dwarf virus, buoyancy, electron microscopy and sedimenta- tion, 45 sedimentation, 34 Potential energy distance diagrams for macromolecules, 214 Precipitin method, 9 Pressures in sound waves, 169 Primary ionization, linear distribution, 72 space distribution, 74, 75 Protective action against free radicals, 89 of broth, 90 Protein coating of virus, 179 Protein internal bonding, 105 structure, 104 Provirus, 12 Psittacosis virus, dimensions, 5, 65 growth in membranes, 22 optical microscopy, 15 Purified virus preparations, 10 Purine absorption, 149 Pyrimidine absorption, 149 Q Quantum yield, 162 R Rabbit papilloma virus, chemical com- position, 7 diffusion constants and radius, 28 dimensions, 65 SUBJECT INDEX Rabbit papilloma virus, motion studies, 51 particle mass, 31 Rabies virus, dimensions, 65 vaccine, by electron bombardment, 139 by U.V. action, 161 Radiation inactivation dimensions, 92 Radiation sensitive element, 76 Radiation studies, on infectivity, 91 on vaccinia, 91 structural inferences from, 100 utility of, 90 Radical yield for virus inactivation, 89 Radius of gyration for X-ray scattering, 59 Recombination of free radicals, half life, 88 Red cell receptors, 10 Relative viscosity plot, 42 Ribonucleic acid, 152 Roentgen, 88 Roentgen equivalent physical (rep), 88 conversion factor to primary ionizations per cc, 88 Rous sarcoma virus, U.V. action spectrum of, 163 Ss Scattering, X-ray, 58 and hydration, 62 large angle formula, 59 small angle formula, 59 Schlieren method, 37 Secondary radiation effects, 88 Section technique in electron microscopy, 19 Sedimentation, 24, 29 constant, 30 as function of concentration, 50 diagram, 36 technique, 34 Selfelution, 9 Sensitive cross section, M-5 phage, 85 for random bombardment, 13, 79 southern bean mosaic virus, 84 T-1 phage, 85 tobacco mosaic virus, 83 SUBJECT INDEX Serological inactivation of viruses, 135 Serological techniques, 133 Shadowing technique, 15 Size and shape of viruses, 4 Sonic effects on viruses, 171 Sonic irradiation procedures, 170 Southern bean mosaic virus, absorption spectrum, 156 chemical composition, 7 diffusion constants and radius, 28 dimensions, 5, 65 electron micrograph, 18 inactivation cross section, 81 inactivation dimensions, 92 infectivity sedimentation, 64 motion studies, 46 mutual potential energy of two par- ticles, 215 outline picture, 63 particle weight measurement, 31 picture, 195 purified preparation, 10 sedimentation pictures, 36 serological affinity studies, 135 thermal constants, 113 X-ray scattering, 61 radius of gyration from, 60 Spherical double layers, force between, 209 Stokes law for motion in viscous fluid, 32 Structural deductions radiation action, 96 Sugar beet mosaic virus, lack of observed particle, 21 from Sugar beet yellows, lack of observed par- ticle, 21 Surface charges on viruses, 127 Surface forces in electron microscope preparations, 19 Surface inactivation by antibody, 134 Svedberg unit, 30 An Theory of thermal inactivation, 103 Thermal constants of dry viruses, 116 Thermal inactivation, ionic strength, 115 pH, 116 229 Thermal inactivation, plant viruses, 110 pressure effects, 117 serological affinity, 140 viruses, 103, 109 thermal constants for, 113 Thermally resistant strain of virus, 115 Thymine, 149 Tobacco etch virus, particle, 22 lack of observed Tobacco mosaic virus, absorption spec- trum of, 152 at low temperatures, 155 by polarized light, 154 amino acid content, 8 chemical composition, 7 dimensions, 5, 65 early radiation studies, 91 electron micrographs, 19, 20 inactivation cross section, 81 inactivation dimensions, 92 infectivity sedimentation, 64 interparticle distance and concentra- tion, 208 ionic atmospheres, 207 motion studies, 49 outline picture, 63 particle weight, 31 picture, 196 quantum yield for inactivation, 163 serological studies, 135 sonic action on, 173 sonic action on serology of, 176° surface amino groups, 7 thermal constants, 113 thermal inactivation, 110 thermal] inactivation tion, 111 ultraviolet action spectrum, 163 unit cell, 56 X-ray diffraction, 57 Tobacco necrosis virus, crystals of, 55 dimensions, 65 electron micrograph of crystal, 54 inactivation dimensions, 92 and denatura- purified preparation, 10 radius of gyration, X-ray scattering, 60 thermal constants, 113 thermal inactivation, 110 Tobacco necrosis virus (Rothamsted) two spherical components, 22, 53 Tobacco ringspot virus, dimensions, 65 spherical particles, 22 thermal constants, 113 thermal inactivation, 110 and denaturation, 112 Tomato aspermy virus, lack of observed particle, 21 Tomato aucuba mosaic virus, X-ray diffraction, 56 Tomato bushy stunt virus, see Bushy stunt virus Tomato spotted wilt virus, lack of ob- served particle, 21 Transforming factor r to III pneumo- coccus, 5 Tryptophane, 152 Turnip yellow mosaic virus protein and nucleo protein, 53, 57 Tyrosine, 152 U Ultracentrifuge, 66 Ultrafiltration, 22 Ultrasonic waves, 169 Ultraviolet action spectra, 13, 156ff. summarized, 166 Ultraviolet light, molecular absorption of, 146 V Vaccinia virus, chemical composition, 7 dimensions, 5, 65 in membrane, 21 inactivation dimensions, 92 Lea’s analysis of internal structure, 92 optical microscopy, 15 ultraviolet action spectrum, 163 Vacuum ultracentrifuge, 35 Van de Graaff accelerator, 80 Van der Waals forces, 210 additivity of, 211 between parallel planes, 211 spheres, 212 Vapor pressure at virus surface, 122 Virology, 2 Virus adsorption, 123 SUBJECT INDEX Virus adsorption, and salt concentration, 126 antigens, 181 antiserum combination, 21 assay, 10 attachment, enzymatic, 129 reversible, 129 and surface charges, 128 Virus description, 194 dimensions, 5, 65 energy turnover, 122 fact summary, 191 genetic unit and velocity of light, 218 genetics, 184 hydration, 33 mating, 186 motion studies, examples, 45 multiplication, 3, 192 and physical laws, 219 forces in, 202 spontaneous mutation study, 188 template idea, 186 recombination, 184 self duplication assembly, 216 serology, 8, 123, 132 size, 15 surfaces, 122 description of, 144 titer, 10 Viscosity, 24, 40 and hydration, 41 and volume fraction, 42 measurement, 42 xX X-radiation, and bacterial killing ability, 99 and bacteriophage activity, 98 and bacteriophage adsorption, 98 and lysis from without, 99 X-ray, action on 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