A STUDY OF THE DIFFUSION PROPERTIES OF R 17 VIRUS BY TIME-DEPENDENT LIGHT SCATTERING

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A STUDY OF THE DIFFUSION PROPERTIES OF R 17 VIRUS BY TIME-DEPENDENT LIGHT

SCATTERING

P. Pusey, D. Schaefer, D. Koppel, R. Camerini-Otero, R. Franklin

To cite this version:

P. Pusey, D. Schaefer, D. Koppel, R. Camerini-Otero, R. Franklin. A STUDY OF THE DIFFU-

SION PROPERTIES OF R 17 VIRUS BY TIME-DEPENDENT LIGHT SCATTERING. Journal de

Physique Colloques, 1972, 33 (C1), pp.C1-163-C1-168. �10.1051/jphyscol:1972129�. �jpa-00214919�

JOURNAL DE PHYSIQUE

Colloque C l , supplément au no 2-3, Tome 33, Février-Mars 1972, page Cl-163

A STUDY OF THE DIFFUSION PROPERTIE S OP R 17 VIRUS BY TIME- DEPENDENT LIGHT SCATTERING

P. N. PUSEY, D. W. SCHAEFER, D. E. KOPPEL

1. B. M. T. J. Watson Research Center, Yorktown Heights, New York, 10598 R. D. CAMERINI-OTERO and R. M. FRANKLIN

Department of Molecular Biophysics

The Public Health Institute of the City of New York, Inc., 455 First Avenue, New York, 10016

Résumé.

- Des solutions de bactériophage R 17 ont été étudiées par diffusion de lumière dépen- dant du temps, en employant un corrélateur digital

canaux multiples pour mesurer la fonction d'autocorrélation des photons diffusés. La limite

concentration nulle du coefficient de diffusion est

1,540

0,015

10-7 cm2/s. Cette valeur a étéutilisée pour calculer le rayon hydro- dynamique

139 + ^1,4 A, et, en combinaison avec des valeurs publiées de la constante de sédimentation et du volume spécifique partiel, pour obtenir unpoids moléculaire, 3,81 + ^{0,14 x 106,}

et le degré de solvation, 1,11 k 0,13 cc de solvant par gramme de virus. A des concentrations virales plus élevées, D ~ o , ~ est une fonction de la concentration virale et de la force ionique de la solution. Cet effet s'explique par I'écrantement de l'interaction électrostatique entre particules.

Pour des forces ioniques élevées, on peut définir le volume d'exclusion apparent dépendant de la force ionique, alors que pour des forces ioniques faibles les interactions semblent acquérir une longue portée, et conduisent

des dépendances angulaires inhabituelles de l'intensité et du spectre de la lumière diffusée.

Abstract. -

Solutions of the bacteriophage R 17 have been studied by time-dependent light scat- tering, using a multichannel digital correlator to measure the photocount auto-correlation function.

The zero-concentration limit of the diffusion coefficient was D;o,w

1.540 + 0.015 x 10-7 crnzls.

This value was used to calculate the hydrodynamic radius,

139

1.4 A, and, in combination with literature values for the sedirnentation coefficient and partial specific volume to yield a mole- cular weight, 3.81

0.14 x 106, and the degree

solvation 1.11

0.13 cc solvent per gm virus.

At higher virus concentrations, D ~ o , , is a function of both virus concentration and solution ionic strength. This effect is explained in terms of screened interparticle electrostatic interactions. At high ionic strength an effective excluded volume dependent on ionic strength can be defined, whereas at low ionic strengths the interactions appear to become long range leading to unusual angular dependences of both the magnitude and time-dependence of the scattered light.

1. Introduction. - In this paper we present measu- rements of the time-dependence of light scattered by solutions of the bacteriophage R 17. R 17 is an E. coIi virus containing about 30 % RNA and 70 % pro- tein [l]. Electron microscopy has shown the R 17 virus particle to have jcosahedral symrnetry and to be spheri- cal in shape with a radius of approximately 120 A [2].

Our data span wide ranges of virus concentration and solution ionic strength. The measurements were per- formed by photocount autocorrelation in time of scattered laser light, using a twenty channel digital correlator.

In the presence of relatively high concentrations of sodium chloride (0.015 M to 1 M) the observed corre- lation functions decay exponentially, with a rate linear in K2, the square of the magnitude of the scattering vector. Such behavior is consistent with a single diffu- sive mechanism for the decay of the concentration

fluctuations which cause the light scattering [3], [4]

The observed diffusion coefficient was in general a function of both virus concentration and salt concen- tration. A tentative explanation for this concentration dependence will be given in terms of an excluded volume due to electrostatic interactions whose magni- tude depends on salt concentration. Information of biophysical interest is obtained from D;,,,, _{the value} of D extrapolated to zero virus concentration and corrected to standard conditions. D;~,, was found to be 1.54 f 0.015 x cm2/s

using the Stokes- Einstein relation, the hydrodynamic radius of the virus Rh

139 + ^{1.4 A} was obtained. Combination of D&,, with literature values for the sedimentation coefficient and partial specific volume yields a value for the virus molecular weight M

3.81 f 0.14 x IO6, and the degree of solvation, 1.11

0.13 cc solvent per gm virus.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972129

Cl-164 P. N. PUSEY,

D.

.,

Finally a sample of R 17 virus in pure water was

studied, and found to exhibit quite unusual behavior.

Firstly the total scattered intensity increased markedly with increusing scattering angle. Such behavior indi- cates repulsive interparticle interactions, presumably electrostatic in origin, extending over several hundred

A [5]. In addition the observed photocount correlation function could no longer be described by a single exponential, and the mean decay rate showed marked departure from linearity in K2.

2. Experimental methods. - 2.1 THE

- The experimental apparatus will be described in detail elsewhere [6], but its important features will be mentioned here. The light source was a Krypton Ion laser, and most of the data to be presented was obtain- ed using the 5 682 A line. The laser beam was focussed into a 1 cm x 1 cm square sample cell, which was placed on the axis of a cylindrical thermostatted water bath. The collection optics, consisting of imaging lens, slit, aperture and photomultiplier tube (PMT), were mounted on an optical bench, free to rotate about the axis of the watei- bath. The scattering angle could thus be changed rapidly without the need for optical realignment. The exposed photocathode area was about one coherence area. The pulses emitted by the PMT were amplified and shaped by standard instrumenta- tion.

The time autocorrelation function of the detected photons was measured using a twenty-channel digital correlator similar to that described by Foord et al. [7].

It was operated in the single-clipped mode, so that the measured quantities were < nk(t) n(t + mT) >,

< nk(t) > and < n(t) >. Here n(t) is the number of photons detected by the PMT in a sampling time of duration T centred at time t, and m, the channel number, runs from 1 to 20. The clipped count nk(t) is defined by

nk(t)

1 for n(t) > k n,(t)

O for n(t) < k .

We used clipping levels k of O, 1, 2 and 3, the higher levels being used when sufficient scattered light inten- sity was available. For Gaussian Iight, the measured quantities are related to the scattered electric field auto- correlation function

by the equation

Here S , is the experimental

signal », and p is in general a complicated function of < ⁿ >, T, k and the geometry of the optical components. However under certain conditions, which were usually fulfilled in this

work, is independent of m and can thus be regarded as a constunt unknown parameter for a given experi- mental run [8].

The correlator was interfaced to a time-shared computer system allowing a ralpid comprehensive data analysis to be performed in about two minutes follow- ing data accumulation. The experimental run time itself was frequently as short as 30 seconds and ranged up to several minutes.

2.2 DATA

W hen the concentration fluctuations causing light scattering by a macro- molecular solution decay via a single diffusive mecha- nism, the electric field correlation function is given by

with r

DK2, and

Here D is the translational diffusion coefficient of the macromolecules, K the magnitude of the scattering vector, n the solution refractive index, A the light wave- length in vacuo, and 0 the scattering angle. The decay rate

was determined by a weighted, two-parameter, least-squares fit of the twenty values of the signal Sm (see eq. 1) t o p exp(- ïmT), ~with fi and r regarded as unknown parameters.

We have developed a procedure for testing how well the data can be fitted to a single-exponential correla- tion function, a procedure wllich can also be used in many cases to characterize non-exponential correlation functions. We take al1 possible sets of four consecutive data points and perform a least-squares fit as above, of each set to the function pi e:<p(- Ti mT). This leads to 17 values of T i (i

2.5, 3.5 ... 18.5). T i is then plotted against iT, and the slope and intercept T, _{of a} straight-line fit of these values are computed. The normalized slope a

slope/ri can be used as a measure of the goodness of fit to a single exponential. For a single-exponential correlationi function T i should, of course, be independent of i and, hence a should be zero.

For many frequently encouritered scattering mecha- nisms leading to a non-exponential decay, such as highly polydisperse samples, or the presence of some

((

unshifted » scattered light,

decreases with increas- ing i, and a is negative. We fiind that computation of a frequently detects non-exponential behavior which is not evident from visual inspection of a plot of ln Sm against mT.

If a is found to be non-zero, to within experimental error, and there is no a priori reasonable mode1 to which the data can be fitted, the problem arises as to how to characterize the correlation function. One can perform a fit of the data to a siingle exponential anyway, but in this case r will be a firnction of the number of decay times, l / r , spanned by the correlator channels.

However, assuming that the observed correlation

A STUDY OF THE DIFFUSION PROPERTIES OF R 17 VIRUS Cl-165

function can be described by a distribution g(T) of

exponentials, so that

it is easy to show that the limiting slope as mT

O of a plot of - In 1 y(mT) 1 against mT is just the mean decay rate 7, where

If r, T is small enough, this limiting slope is simply TO, a quantity which can therefore be used to characterize the decay mechanism of any photocount correlation function which can be described by eq. (2).

2.3 SAMPLE

The preparation and purification of the bacteriophage R 17 involves minor modifications of standard techniques and will be described elsewhere [6]. By several physical and che- mica1 criteria these preparations were pure and homo- geneous. The sample cells were cleaned, and flushed with several hundred ml of filtered distilled water, using a closed system. The sample was then introduced through a 0.2 y Gelman filter, and the ce11 was sealed.

The virus concentration of the sample was determined from the optical density at 260 nm using an extinction coefficient of 7.66 cm2 mg-' [6].

2 . 4 MEASUREMENT

The sample refractive index n is needed to correct the scattering angle for refraction (a correction < 0.5 % in this work), and to calculate the value of K. It was determined by measuring the angle of minimum devia- tion of the laser beam through a corner of the square sample cell.

The diffusion coefficient D T , determined at arbitrary temperature TOC, in solvent S, was corrected to standard conditions, 20 OC and water as solvent, by the equation

where y represents viscosity. The viscosities of the NaCl solutions were obtained from standard tables [9].

Most of the data was taken at 25.0 f 0.1 OC.

3. Results and discussion. - 3 . 1 EXPERIMENTS

MODERATE AND HIGH IONIC STRENGTH SOLUTIONS. -

Figure 1 is a plot of the data as a function of virus concentration for three relatively high values of the solvent NaCl concentration. The solutions were un- buffered and had measured pH values between six and seven. Each data point in figure 1 is the average of about six independent runs. In general two or more runs were taken at each of the (uncorrected) scattering angles 8

75, 90, 105 or

70, 90, 110. The decay rate r was found to be linear in K2, to within experi-

mental error, over this range of

In addition, the quality parameter a (see Section 2.2) was generally O + 0.02, indicating a good fit to a single-exponential correlation function. This single-exponential correla- tion function, with K2 dependent decay rate, indicates that the concentration fluctuations decay by a single diffusive mechanism with diffusion coefficient

The quantity plotted in figure 1 is the corrected diffu- sion coefficient Dz0,, (see Section 2.4). Error in the values of D,,,, is believed to be less than one per cent.

This estimate includes both random error and syste- matic errors due to uncertainty in the solvent viscosity and to possible optical misalignment. The error bars in figure 1 represent this 1 % uncertainty.

'

2

* 5 J ; 1 ? ' é I ; CONCENTRATION (mg/ml)

FIG. 1 . -

Diffusion coefficient

function

concentration,

D,,,, is in general a function of both virus concen- tration and Salt concentration. This result will be discussed later, and for the moment we will concentrate on the information of biophysical interest which can be obtained from the quantity D:~,,, the result of extra- polating the data to zero virus concentration. From figure 1 the value OiO,,

1.54 & 0.015 x 1OP7 cm2/s is found. This value is independent of salt concentra- tion, indicating that the diffusion properties of the virus molecules are not affected by the presence of Salt when interparticle interactions are negligible. In this limit, for a spherical molecule, is given by the Stokes-Einstein relation [IO]

Here k is Boltzmann's constant and Rh is the hydro-

dynamic radius of the virus molecule. From eq. (3),

Rh

139 f 1.4 A, a value which can be compared

Cl-166 P. N. PUSEY, D. W. SCHAEFER, D. E. KOPPEL 2, R. D. CAMERINI-OTERO ANID R. M. FRANKLIN

with the radii determined by electron microscopy 121, 120 + 5 A, and by small angle X-ray scattering, 133 + ⁵ A [ll], [12].

Our value of D : ~ , , can be combined with literature values of the partial specific volume,

and the sedimentation coefficient,

through the Svedberg equation 1141

to yield the virus molecular weight,

Here N is Avogadro's number and p,,,, the density of water at 20

In addition the degree of solvation can be determined by comparing the solvated volume,

M -

5 ^{n ~ : ,} with the dry volume

1141. The degree of

3 N

solvation found is 1 . l l & 0.13 cc solvent per grn virus. A cornparison between the values of Rh, 139 A,

and the X-ray scattering radius, 133 A (taking the latter as an estimate of the spatial extent of matter in the virus particle) implies that this solvation is mostly interna]. Despite the solvent associated with the virus particle, it appears to have a rigid structure. This is suggested by the fact that D Z ~ , ~ was found to be independent of the pH in the range 6 to 10. Over this range of pH, the charge on the virus particle should change considerably, and electrostatic forces might be expected to alter the size of a non-rigid particle.

We now return to the data of figure 1 and offer a tentative explanation for the dependence of D2,,, on both salt and virus concentration. At relatively low, but non-zero, virus concentrations the diffusion coefficient can be described by the expression [14]

293 (1 + Be).

D20,w

f20,w

Here

is the concentration in mg/ml, and B is the second virial coefficient, the same quantity which characterizes the first-order departure from linearity in concentration of osmotic pressure and conventional light scattering. The frictional coefficient f also depends on virus concentration and can be described by [14]

where f

20,w

nq20,w Rh for a spherical molecule, and B' is an empirically determined quantity.

Thus

to a first approximation. For uncharged molecules the main contribution to B is the excluded volume with B given by 1141

B E - N 2

1 0 - ~ cm3/mg .

M 3

The virus particles can how~:ver carry an electronic charge varying from zero up to several thousands. Even for a charge as small as 10, 1.he electrostatic energy between two particles, assunled to be unscreened, would be greater than the thermal energy for interpar- ticle separations 5 700 A. We propose that the data of figure 1 can be explained in terms of Equations 4 and 5 with Rh replaced by an effective hard sphere radius RHs

2 RH, is a measure of the interparticle separation at which the electrostatic interaction energy is equal to the thermal energy. RH, will depend on the degree of screening produced by the salt solution, as well as on the total charge on the virus particles. An explanation similar to this was proposed by Doty and Steiner t o explain effects seen in a convi:ntional light scattering study of bovine serum albumiri [5]. The interaction of two shielded macroions cannot, of course, strictly be described by a hard sphere potential, but this simpli- fying approximation provides

qualitative explanation of the observed effect. In table 1 are listed the experi- mental values of B - B' and B, and RH, calculated from eq. (4) and (5). Br

9.32 x cc/mg) was obtained from the data of Enger et al. [13] for the concentration dependence of the sedimentation coeffi- cient, and was assumed to be independent of NaCl concentration. The values of RHs increase with decreas- ing salt concentration as would be expected for the decreasing screening effect of the salt. It is gratifying that the value of RH, for the highest salt concentration is close to the actual hydrodyniamic radius.

Virial coeficients, ( B

Br:) and B, and hard sphere radii, RH,, determined from data of jigure 1. B' was obtained from the data of Enger et al. [13]. L, is the Debye-Hückel shielding length.

Salt Concen- (B - B') x 103 .B X 103 RHS LD tration

(Molar) (cm3/mg) ((:m3/mg) (A) (A)

-

-

0.015 M 12.8 & 4.2 22.1 f 4.2 161 f 10 25.2 0.15 M 6.3 & 1.6 15.6

+=

1.0 M - 1.6 1: 2.4 7.7 & 2.4 113 & 12 3.08

Although the Debye-Hückel theory of screening cannot be expected to apply exactly in the present case for such large electrostatic energies [14], the theory does give an estimate of the degree ,of screening ; the Debye- Hückel screening lengths L,, are listed in table 1.

It should be pointed out that the values of RH, at the

two lower ionic strengths are only of qualitative

significance, since the macroionic charge is expected to

Vary with both virus concentration and ionic strength.

A STUDY O F THE DIFFUSION PROPERTIES OF R 17 VIRUS Cl-167

A more complete study of the dependences of D on macromolecular concentration and ionic strength should include measurement of the macroionic charge, as well as measurement of B by conventional light scattering and an investigation of the dependence of Br on ionic strength.

Finally if should be emphasized that the above treatment assumes that the only effect of the salt is to screen the macro-ionic charge. It is, in fact, possible that Donnan effects

and other interactions [15]

which occur in multi-component systems could affect the macromolecular diffusion. The magnitudes of such effects in this system remain to be estimated.

3.2 EXPERIMENTS

Finally we present data for conventional and time-dependent light scattering by a virus solution of concentration 0.565 mg/ml in water, where the macroionic charge is expected to be much less effectively screened. Figure 2 shows that the average scattered intensity increases dramatically with increasing scattering angle. This result indicates spatial correlations of virus particles extending over distances comparable to 1/K

600 A).

The repulsive electrostatic interactions causing these correlations must have a varying energy comparable to k T over this range of distances. It remains to determine the actual form of the interparticle potential from these data. It is of interest to note that for larger macroionic charges, which should be attainable by the addition of acid or base to the solution, the ordering of the virus particles might become even more pro- nounced. Under these conditions, at somewhat lower virus concentrations, one might observe a maximum in the average scattered intensity near the angle which satisfies the condition for Bragg reflection from planes spaced by the mean interparticle distance.

Figure 3 shows the time-dependence of the scattered light for the same virus sample. The quantities plotted against K2 are ï o / K 2 and ï / K 2 . ï0 is the initial decay rate (see Section 2.2) and

is the decay rate obtained by fitting the data to a single exponential correlation function. (The twenty correlator channels spanned a time range = 1.75/ï s). The fact that

ïo indi- cates, of course, distinct non-exponential behavior

the quality parameter a was generally - 0.25 + 0.03.

In addition it is seen that both r / K 2 and ï o / K 2 Vary by almost a factor of two over the range of K2 covered.

These two facts imply that an interpretation in terms of a simple diffusional decay is no longer valid. Since the range of interaction,

600 A is the same order of magnitude as the mean interparticle spacing,

2 200 A

a theoretical treatment of the effect must take into account collective modes of motion of the virus particles.

FIG. 3. - Dependence of r/K2 and ro/K2 on K2 for R 17 in water at virus concentration of 0.565 mg/mi. r i s << one-exponen-

tial » decay rate and

ro

Finally, is should be stated that following data collection the sample was dialyzed back to high salt.

Here ï / K 2 was found to be independent of K2, and the correlation function to be nearly exponential, though D

f / K Z ) was about 15 % lower than its normal value, indicating some degree of aggregation or dena- turation. However the trends in figures 2 and 3 are in the wrong direction to be explained by such effects.

Furthermore examination of such a sample under the electron microscope showed little or no detectable difference from virus solutions at high ionic strength.

Also there was no loss of viral infectivity after extensive

FIG. 2. - Dependence of average scattered intensity on K2

for R 17 in water at virus concentration of 0.565 rnglrnl.

dialysis against water'

Acknowledgernents. The authors have profited A similar disymmetry in the angular dependence of greatly from several discussions with Dr. S. H. Koenig.

conventional light scattering was observed by Doty and They are also pleased to acknowledge discussions with

Steiner in bovine serum albumin [5]. Professor M. J. Stephen and Professor B. J. B rne.

Cl-168 P. N. PUSEY, D. W. SCHAEFER, D. E. KOPPEL, R. D . CAMERINI-OTERO AND R. M. FRANKLIN

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