Proc. Nat. Acad. Sci. USAVol. 68, No. 10, pp. 2365-2369, October 1971

Optical Activity of Membrane Suspensions: Calculation of Artifacts byMie Scattering Theory

(spherical scatterer/electromagnetic radiation/optical activity spectra/erythrocyte ghosts)

D. J. GORDON AND G. HOLZWARTH

Departments of Chemistry and Biophysics, University of Chicago, Chicago, Illinois 60637

Communicated by Paul Doty, July 13, 1971

ABSTRACT The circular dichroism, optical rotatorydispersion, and optical density of a suspension of erythro-cyte ghosts are calculated from the measured opticalproperties of solubilized ghosts by classical general scat-tering theory (Mie theory). The ghost is represented by asolvent-filled spherical shell 7 nm (70 A) thick and 3.5 sm inradius. The 3- to 5-nm red shifts and unusualband shapesobserved in the circular dichroism and optical rotary dis-persion of suspensions of the intact ghosts, but not in thesolubilized membranes, are reproduced by these calcula-tions. Both differential absorption and differential scat-teringofleft-and right-circularly polarized lightcontributesignificantly to the calculated circular dichroism spectra.The artifacts of small membrane vesicles are shown to beless than those of intact ghosts. It is concluded that thecharacteristic anomalies in the optical activity of mem-brane suspensions are artifactual.

The measurement of optical activity in the far ultraviolethas been valuable in establishing the conformation of manysoluble proteins. In the past five years, several investigators(1-8) have sought to extend this technique to obtain similarstructural information about the insoluble proteins of cellularmembranes. Only recently, however, has it been generallyappreciated that optical activity spectra may be stronglydependent upon particle size, because of light scattering andabsorption statistics. The resulting distortions in these spectraobscure their molecular informational content; from a biolo-gist's point of view, they are therefore artifacts. In thispaper these artifacts are calculated by rigorous classicalMie scattering theory. The calculated spectra agree withobserved data.The circular dichroism (CD) and optical rotatory disper-

sion (ORD) spectra that have been obtained on suspensions ofmembranes of rather diverse biological origin are quitestriking in their similarity. Their qualitative features areroughly those of a soluble protein of 30-50% a-helix content.However, the CD and ORD of membrane suspensionsconsistently differ from those of soluble proteins in tworespects: (a) the membrane spectra appear to be shiftedto the red by as much as 5 nm (50 A), and (b) the 220-nmCD band appears to be enhanced relative to the 207-nmband.Some investigators have proposed that these recurrent

anomalous spectral characteristics of membranes reflect acommon molecular structure or environmental feature shared

by the proteins of all membranes. Ji and Urry, (6) were thefirst to present experimental evidence that these anomaliesmight instead be artifactual, when they showed that sus-pensions of poly(iglutamic acid) [(Glu)n] aggregates exhibitthe same red shift and distortion in their CD spectra. Theexperiments of Schneider et al. (8), which demonstrate boththe diminution of these anomalies upon sonication of erythro-cyte ghosts and their enhancement in the CD of partiallyhemolyzed erythrocytes, provide further convincing experi-mental evidence for a significant artifactual component in theoptical activity of membranes. There have also been someattempts to develop a quantitative theory to account forthe observed optical activity of membranes (9-14); noneof these has been truly satisfactory.

THEORYThe objective of the Mie theory (15, 16) is to calculate theelectric field E and magnetic field H that satisfy Maxwell'sequations at a large distance from a spherical scattererexposed to electromagnetic radiation. Every particle isconsidered to be a discrete, independent scatterer. Forapplication of scattering theory to membranes, a suspensionof compound spheres, each consisting of an isotropic sphericalcore of radius R-A and a surrounding isotropic shell of thick-ness A, was taken as the simplest realistic model. Mie'stheory has been extended to this geometry by Aden andKerker (17); only the major features of their solution aregiven here.The orthogonality of E and H reduces the problem to

finding two independent solutions u and v of the scalarwave equation at all points in space. It is convenient to estab-lish a spherical coordinate system with origin at the center ofthe particle. In each of the three regions of space, designated1, 2, and 3 for core, shell, and suspending medium, respec-tively, the general solution of the scalar wave equation canbe expanded as an infinite sum of spherical Bessel functionsj.(kr) and spherical Hankel functions of the second kindh,(kr). Here r is the radial coordinate and k is the appropriatecomplex propagation constant. Each term in these series isweighted by an angular factor and an arbitrary coefficient.The 12 resulting sets of expansion coefficients are determinedby the boundary conditions of the model. These conditionsare that u and v remain finite as r -.Oand vanish as r-o c,and that the normal and transverse components of E and Hsatisfy the appropriate continuity conditions at inner andouter shell boundaries; these require specification of thecomplex refractive indices mI, im2, and m3in the three regions.

Abbreviations: CD, circular dichroism; ORD, optical rotatorydispersion; (Glu)n, poly(iglutamic acid); SDS, sodium dodecylsulfate.

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2366 Biochemistry: Gordon and Holzwarth

The experimentally important solutions of the waveequation are those for region 3 at very large r. Since thefunctions j3(2irms/X) have the wrong asymptotic behaviorfor large r, the solutions u and v in this region are simplysums of h3(2wrmg/X), in which the coefficients are indicated,respectively, by a. and b.. In the forward direction at largedistances from the particle (r>> R), the intensity drop (extinc-tion) and phase lag* due to interference of the scatteredand incident wave are proportional to the real and imaginary

parts, respectively, of E (2n + 1) (a. + bW). The total scat-n-1

tered intensity, obtained by integration of scattered intensity

over all angles, is proportional to another simple sum,n*i

(2n + 1) (1a,12 + Ib.I2). The total absorptive loss is obtainedas a difference between the total extinction and the scatteringloss. The accuracy of our program for calculating the scat-tering by compound spheres was checked against independentcalculations for dielectric spheres (18), absorbing spheres (19),coated dielectric spheres (20), and hollow, absorbing shells(unpublished results of Battan and Herman, Institute ofAtmospheric Physics, University of Arizona, Tucson, Ariz.85721). In every instance exact agreement was obtained.The extension of the model to optically active particles

follows directly from considerations of symmetry [refs. 14and 15 (chap. 5) 1. For light scattered directly forward(i.e., in the direction of the incident beam) there is no uniquescattering plane, so that the only possible sensitivity topolarization must arise from the inherent anisotropy of thescatterer. Therefore, by substituting the complex refractiveindices for left- and right-circularly polarized light into theMie equations, one directly obtains the extinction and phaselag for these two polarizations. The difference between theextinctions gives the CD; the difference in phase lag gives theORD.Two limitations of the theory must be mentioned, both of

which are found experimentally to be insignificant for sus-pensions of erythrocyte ghosts:

(a) Multiple scattering is neglected. This assumption ismade reasonable by the observation that the optical density(OD), CD, and ORD of erythrocyte ghost suspensions aredirectly proportional to concentration in the range usedexperimentally;

(b) It is assumed that the solid angle of scattered lightintercepted by the detector is sufficiently small that lightscattered at non-zero angles may be neglected. We have foundexperimentally that the OD and CD of erythrocyte ghostsdo not measurably change when the acceptance angle of thedetector is severely reduced with an iris diaphragm.

It may be useful at this juncture to contrast our theory, asoutlined above, with previous theoretical explanations forthe artifacts. Urry and coworkers (9-11) have presented asemiempirical analysis of the CD of (Glu). aggregates. Al-though this theory gives a useful qualitative picture of theartifacts, it contains theoretical assumptions about absorp-tion flattening that have been shown to be invalid (13).

* The extinction and phase lag given by scattering theory are

related by the Kronig-Kramers transforms (15). The same istrue of the CD and ORD (14). This is in contrast with the non-

conformity of the CD and ORD with these relations predictedby absorption statistics alone (13). A

A similar treatment of the CD of erythrocyte ghosts by Glaserand Singer (21) likewise incorrectly assumes that CD andabsorbance are flattened by identical factors. Calculationof differential scatter in the Rayleigh approximation for asuspension of 1-&m (Glu). spheres (12) predicts that theartifact greatly exceeds the natural CD.t However, theRayleigh approximation overestimates the scattering bylarge particles. The analysis by Gordon and Holzwarth (13)of the absorption statistics artifact is limited by the expressneglect of scattering effects and thus offers no explanationfor the red shifts observed in membrane optical activity.Finally, Schneider (14) has derived formal scattering matricesof optically active particles, but has not evaluated thematrix elements.

EXPERIMENTALHemoglobin-free erythrocyte ghosts were prepared fromfreshly drawn human blood by the osmotic hemolysis methodof Dodge et al. (22). Residual hemoglobin was estimatedfrom the absorbance in the Soret region and was generallyless than 2% of the total protein. Total protein was estimatedby the method of Lowry et at. (23), with bovine-serum al-bumin as a standard. Ghost suspensions were counted on aCoulter counter at various threshold settings, and the truecount was obtained by extrapolating the linear part of thecurve (corrected for coincidence) to zero threshold.The ghosts were divided into two equal aliquots. The first

aliquot was suspended in 20 mOsm phosphate buffer atpH 7.40. The second was dissolved in the same buffer, towhich sodium dodecyl sulfate (SDS) was added to a finalconcentration of 0.1%. (The addition of SDS causes imme-diate clearing of turbid ghost suspensions.) In this manner itwas assured that the ghost solution and suspension were ofidentical protein content, regardless of experimental uncer-tainty (about 10%) in absolute protein determination.Optical density was measured on a Cary 15 spectrophotom-eter. CD and ORD were measured on a Cary 60 spectro-polarimeter.

RESULTS AND DISCUSSIONThe major obstacle in attempting to account for the observedspectra of erythrocyte ghosts is that one has no reliabledata for the optical constants of the membrane material.(If these were known, one would have no need to measurethese properties in suspension.) The Mie theory providesfor calculation of suspension optical properties from thoseof the membrane material; however, there is no apparentway of reversing this process. We therefore took the fol-lowing simple approach, which requires a minimum of un-

t By an approach similar to that of Ottaway and Wetlaufer,we obtained the following expression for the contribution [9]. ofdifferential Rayleigh scattering to mean residue ellipticity:

[9]. = (16r2Mno2[jo]/3Xt)dn/dcwhereM is the particle mass in grams, no is the solvent refractiveindex, dn/dc is the absolute refractive index increment in cm3/gof the particle substance, and [0] is the mean residue rotation indeg-cm2/decimol. For a (Glu). sphere of 1-pm radius at X %

200 nm, we calculate that []1. -0--109 deg-cm2/decimol,which is about 106 times larger than the results of Ottaway andWetlaufer (12). On the basis of communication with these authors,we believe that their numerical results are in error, due largely toambiguities in the units of certain parameters which they used.

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measured parameters. We calculated the optical propertiesof spherical shells whose constituents have the known,measured optical properties of ghosts treated with 0.1%SDS, which is known to disperse the ghosts into protein-detergent and lipid-detergent complexes (24).The dimensions of the ghost model are taken to be R =

3.5 ,um and A = 7 nm. The core and the medium are

each given a fixed refractive index ml = ms = 1.4, corre-

sponding to water in the 190-260-nm region. Since refractiveindex in UV light is not readily measured, the mean realrefractive index of the membrane for unpolarized lightis also assumed constant and given the value nma; its disper-sion in the ghosts, as in the solvent, is neglected. Althoughn could be made more realistic by including dispersiveeffects, this would introduce additional unmeasured param-

eters into the calculation. We prefer not to do this.The complex refractive indices m2R and m2L of the mem-

brane for right (R)- and left (L)-circularly polarized lightat a given (vacuum) wavelength, X, are now expressed as

follows:

m2R = nm3 -i X A.1l/4ThNV - X (¢. -i6li)/360hNV

m2L = nm3 -i X As.1/4ThNV + X (,O, -i0801)/360hNV

where As., is the absorbance of the solution in base e, 4)ooand O0.. are the solution rotation and ellipticity in degrees,h is the path length, N is the (measured) number densityof particles in suspension, and V is the particle volume,as given by

V = 4Tr (3R2A - 3RA2 + A3)/3

The scattering loss, absorptive loss, total extinction, andphase lag for left- and right-circularly polarized light are thencalculated by the procedure of Aden and Kerker (17). Fromthe difference in each of these four calculated quantitiesfor the two opposite polarizations, one obtains the scatteringand absorptive terms of the CD, the total CD, and theORD of the model suspension. These may then be comparedto the measured optical activity of the real suspension.Similarly, from the mean values of the same four quantities,

10co

-.0

18(

'.0

. E

.0 "0

.0o

0 200 220 240 260

X,nm

FIG. 1. Circular dichroism of erythrocyte ghosts. Observedand calculated CD of erythrocyte ghost suspension, with N =

2.24 X 108 ghosts/cm3. Each open circle represents a separatecalculation. The CD of a solution of the ghosts in 0.1% SDS isalso shown. The protein content (so 0.12 mg/cm3) and pathlength(1 mm) are identical for the three curves. The solvent refractiveindex is assumed to be 1.4. A mean residue weight of 110 is as-

sumed in calculating the molar ellipticity (right-hand scale). (-),Observed solution; (-), observed ghosts; (0), ghosts, calculated.

a,

-e

ICO

Xnm

Fig. 2. Optical rotation of erythrocyte ghosts. Observed andcalculated ORD of erythrocyte ghost suspension. Conditions asin Fig. 1.

one obtains the mean turbidity, absorbance, optical density,and refractive index of the suspension. Thus, by uniformapplication of a single model, all of the optical propertiesof the suspension are calculated. The results are shown inFigs. 1-5.The observed CD of a ghost solution and suspension,

and the CD curve calculated by the Mie theory for n = 1.20,are shown in Fig. 1. The CD of the dissolved ghosts is typicalof soluble proteins of -40% a-helix content ([01225 =-14,000deg-cm2/decimol). It displays a peak at 192 um, a crossover

at 199 nm, and overlapping negative bands at 207 and 220am, of which the former is decidedly more intense. Onthe other hand, the CD bands observed in the suspendedghosts appear to be red-shifted by 3-5 nm from their posi-tions in the solution. Also, the relative amplitudes of the twonegative bands are reversed in the suspension. These charac-teristic anomalies of the observed erythrocyte-ghost CD are

reproduced in the CD calculated by the scattering methodoutlined above. The positions of each of the bands and ofthe crossover point of the calculated curve are in excellentagreement with the observed CD. The amplitude of the calcu-lated CD is also in quite good agreement with experiment, al-though it appears to be somewhat low in the 210-230-nmregion and high at longer wavelengths; the minor descrepan-cies probably reflect the neglect of refractive-index dispersionand perhaps possible solvent effects.A similar display of the ORD of erythrocyte ghosts is

shown in Fig. 2. The ORD spectrum of the dissolved ghostsis not qualitatively distinguishable from that of a solubleprotein containing -40% a-helix. The rather intense peakat 199 nm, the pronounced shoulder at 210-220 nm,the 220 nm crossover, and the shallow trough at 232 nmare all fairly typical of such proteins. The ORD of the sus-

pended membranes, however, exhibits the same general 3-

5-nm red shift as the CD. Also, the peak is less intense, thetrough is shallower, and there is greater rotation in theshoulder region than is seen in the ORD of the solubilizedghosts. As in the case of the CD, all of these anomalies are

quite well reproduced in the ORD calculated by Mie theory.One may ask how sensitive the calculated curves of Figs. 1

and 2 are to the parameters R, A, and n, and how nonsphe-ricity of real suspended particles may influence the scattering.Calculations at selected wavelengths of CD and ORDversus shell radius, with A = 7 nm and n = 1.20, demon-strate that 85-95% of the changes between R - 0 and R

= 3.5,m generally occur at radii less than 1 Mum; for R > 1

2~~~~~~~~~~~~~~~~~~~~~~~~~~.

02 - /9\ 2

~~/S/\ \ ~~~~~n- 1.200% A \°-a 7rm (70 A)-.\IO R - 3.5iFm

20 0

I~~~~~~~~~0

*2

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2368 Biochemistry: Gordon and Holzwarth

( 0-0.01

180 200 220 240X,nm

Fig. 3. Calculated contributions of scattering (es) and absorp-tion (OA) to the total CD (GT) of an erythrocyte ghost suspension.Total CD and conditions as in Fig. 1. (-), OA; (---@) Gs;-( ),OT.

pm, the calculated CD and ORD are quite insensitive to R.Moreover, the choice of A for the erythrocyte ghostis not critical, provided that n-1 is changed proportionately.The CD and ORD spectra of a 3.5-,um ghost calculated forthe rather extreme choice of A = 3.5 nm and n = 1.40agree closely with the curves for A = 7 nm and n =1.20. Although we cannot dismiss the possibility of complica-tions due to biconcavity of the ghost surface, these observa-tions strongly suggest that the CD and ORD of randomlyoriented nonspherical shells, all external dimensions of whichexceed 1 pm, will not differ measurably from the correspondingspectra of true spherical shells.The choice of n and the neglect of its dependence on wave-

length in Figs. 1 and 2 might appear arbitrary. However,parallel calculations for n = 1.12 and 1.33 show only modestsensitivity to choice of n. The distortions were somewhatmore prominent for n = 1.33 and less prominent for n =1.12. The neglect of dispersion in n might appear to be moreserious, since the calculations are performed in an absorptiveregion. However, application of the Kronig-Kramers trans-

I, 'I F-

.04- CIRCULAR DICHROISM OPTICAL ROTATION

.03 L

.02;

b C

-01 1.20A 7om (70Ol)

-.0280 200 220 240 200 220 240 260

Xnm

Fig. 4. Optical activity of membrane shells as a function ofshell radius. The calculated CD and ORD of a whole ghostsuspension (R = 3.5 pm), a suspension of small vesicles (R = 0.1pm), and the observed curves for a ghost solution (R - 0) in0.1% SDS are shown. Protein content is 0.12 mg/cm', pathlength is 1 mm, and solvent refractive index is 1.4. ( ), R - 0;(- ----), R = 0-1 ism; (--- -), R = 3.5 can.

190 200 210 220 230 240

X,nm

Fig. 5. Optical density of erythrocyte ghosts. Sensitivity of Miecalculation of OD to choice of n. All other conditions as in!Fig.1. ( ), Ghosts, calculated; (-), ghosts, observed; (- - -),solution, observed.

forms to the measured absorption spectrum of the SDS-treated material shows that the 190-nm absorptionband contributes a maximum variation in n of only 0.09.Thus, the wavelength-dependent variations in n will fallwithin the range of n already explored.We have seen that the calculated anomalies are quite

insensitive to the choice of R, A, and n; one may then seekthe physical origin of the effects. The breakdown of thecalculated erythrocyte-ghost CD into absorptive and scat-tering terms, displayed in Fig. 3, provides insight into thesource of the anomalies. The absorptive term resembles theCD of the solution, but in rough agreement with considera-tions of absorption statistics (13, 25), it becomes increasinglyflattened as one scans toward shorter wavelengths. Thescattering term, in rough agreement with the results ofUrry et al. (10, 11) and of Ottaway and Wetlaufer (12),resembles the ORD curve in shape. Absorption statistics andscattering both make important contributions to the totalCD spectrum. The red shift is almost entirely a result ofscattering. Both artifacts contribute to the flattening of the207-nm band relative to the band at 220 nm. The twoartifacts oppose each other in the region X <200 nm, s0 thatthe solution and suspension differ little in the amplitude oftheir positive CD band in this region.

It has been shown experimentally that sonication of ghostsuspensions generates small solvent-filled vesicles for whichthe CD anomalies are much reduced (8). In Fig. 4, one mayobserve the CD and ORD calculated for such vesicles of0.1-,pm radius. In agreement with experiment, the anomaliesare intermediate between those of the solution and thoseof the whole ghosts. The quantitative interpretation of suchexperiments is, however, more hazardous than for intactghosts because the accurate measurement of count, size,and size distribution is much more difficult for small vesiclesthan for whole ghosts. The vesicle preparations may also bequite heterogeneous.

t Previous theoretical treatments have considered absorptionstatistics and scattering as independent artifacts. However,- theabsorptive loss of light energy in fact depends on both the real andthe imaginary part of the refractive index. Similarly, the scat-tered intensity depends on both the imaginary and the real partof the refractive index. In the present analysis, as in that ofSchneider (14), no such artificial separation of these two artifactsis made.

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Although the optical activity of membranes is of muchgreater interest than their absorption spectra, comparisonbetween observed and calculated OD can provide usefulinsight into the limitations of the Mie calculations. Unfor-tunately, optical-density calculations, unlike those of opticalactivity, are quite sensitive to choice of real refractive indexn for the membrane. This is illustrated by Fig. 5, which showsthe measured solution and suspension spectra, as well as cal-culated spectra, for n = 1.12, 1.20, and 1.33. It can be seen

that a value of n between 1.0 and 1.2, with appropriate dis-persion, would fit the observed data.Mie scattering calculations for solid spheres of optically

active material (Gordon, 1971; manuscript in preparation)reveal artifacts similar to those reported here for thin sphericalshells. Indeed, such artifacts are likely to be present in the CDcurves of other optically active, scattering particles such as

viruses and ribosomes; one may anticipate that the scatteringterm will resemble the ORD of the particles. It shouldbe noted that these artifacts are not instrumental; theyoriginate in the optical activity of the scattering particle.The same artifacts are not expected for optically inactivescatterers in a dilute optically active solvent or for tandemcells of scatterer and optically active solution.

In conclusion, the agreement between the calculationsfor the ghost model and the observed data argues for twodistinct points: (a) that Mie scattering leads to substantialeffects on the optical properties of particles the size of eryth-rocyte ghosts, and (b) that the average intrinsic opticalproperties of the ghost material must be quite similar tothose of the SDS-treated ghosts. However, one cannotclaim that the dilute detergent has no effect whatever on theconformation of membrane proteins. One might, for example,hypothesize from the difference between observed and cal-culated ghost CD at 223 nm that a small loss of a-helix hasoccurred in the SDS-treated material. Much further experi-mental work, supported by artifact calculation, is necessary

before firm conclusions can be reached on such points.Recognizing these limitations, one may nevertheless concludethat the characteristic shifts and distortions of membraneoptical activity as they occur in erythrocyte ghosts are no

more than artifacts of their particulate nature.

We thank Drs. Louis Battan and Benjamin Herman for per-forming some sample Mie scattering calculations for hollowspherical shells at our request. We also thank Dr. CliffordOttaway for providing us with a sample calculation of differ-

ential Rayleigh scattering by a 1-/Am (Glu). sphere, and Drs. P.Urnes and E. W. Taylor for critical reading of the manuscript.This work was supported by Grant NS-07286 from the NationalInstitute of Neurological Diseases and Stroke, U.S. PublicHealth Service. Moreover, D. J. G. was supported by U.S. PublicHealth Service Training Grant No. HD 00001 from the NationalInstitute of Child Health and Human Development.1. Wallach, D. F. H., and P. H. Zahler, Proc. Nat. Acad. Sci.

USA, 56, 1552 (1966).2. Lenard, J., and S. J. Singer, Proc. Nat. Acad. Sci. USA, 56,

1828 (1966).3. Urry, D. W., M. Mednicks, and E. Bejnarowicz, Proc. Nat.

Acad. Sci. USA, 57, 1043 (1967).4. Wrigglesworth, J. M., and J. Packer, Arch. Biochem. Bio-

phys., 128, 790 (1968).5. Gordon, A. S., D. F. H. Wallach, and J. H. Strauss, Biochim.

Biophys. Acta, 183, 405 (1969).6. Ji, T. H., and D. W. Urry, Biochem. Biophys. Res. Commun.,

34, 404 (1969).7. Glaser, M., H. Simpkins, S. J. Singer, M. Sheetz, and S. I.

Chan, Proc. Nat. Acad. Sci. USA, 65, 721 (1970).8. Schneider, A. S., M.-J. T. Schneider, and K. Rosenheck,

Proc. Nat. Acad. Sci. USA, 66, 793 (1970).9. Urry, D. W., and T. H. Ji, Arch. Biochem. Biophys., 128, 802

(1968).10. Urry, D. W., and J. Krivacic, Proc. Nat. Acad. Sci. USA, 65,

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Biophys., 137, 214 (1970).12. Ottaway, C. A., and D. B. Wetlaufer, Arch. Biochem.

Biophys., 139, 257 (1970).13. Gordon, D. J., and G. Holzwarth, Arch. Biochem. Biophys.,

142, 481 (1971).14. Schneider, A. S., Chem. Phys. Letters, 8, 604 (1971).15. Hulst, H. C. van de, Light Scattering by Small Particles (J.

Wiley& Sons, New York, 1957).16. Kerker, M., The Scattering of Light and Other Electromag-

netic Radiation (Academic Press, New York, 1969).17. Aden, A. L., and M. Kerker, J. Appl. Phys., 22, 1242 (1951).18. Gumprecht, R. O., and C. M. Sliepcevich, Tables of Light

Scattering Functions for Spherical Particles (EngineeringResearch Institute, University of Michigan, 1951).

19. Chromey, F. C., J. Opt. Soc. Amer., 50, 730 (1960).20. Kerker, M., J. P. Kratohvil, and E. Matijevic, J. Opt. Soc.

Amer., 52, 551 (1962).21. Glaser, Michael, and S. J. Singer, Biochemistry., 10, 1780

(1971).22. Dodge, J., C. Mitchell, and D. Hanahan, Arch. Biochem.

Biophys., 100, 119 (1963).23. Lowry, 0. H., N. J. Rosebrough, A. L. Farr, and R. J.

Randall, J. Biol. Chem., 193, 265 (1951).24. Engelman, D. M., T. M. Terry, and H. J. Morowitz,

Biochim. Biophys. Acta, 135, 381 (1967).25. Duysens, L. N. M., Biochim. Biophys. Acta, 19, 1 (1956).

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