Proc. Natl. Acad. Sci. USAVol. 77, No. 8, pp. 4904-4908, August 1980Immunology

Fluorescence immunoassay based on long time correlations ofnumber fluctuations

(diffusion/intensity autocorrelation/human IgG assay/microcomputer-based instrument)

D. F. NICOLI, J. BRIGGSt, AND V. B. ELINGSDepartment of Physics, University of California, Santa Barbara, California 93106

Communicated by George Feher, April 7,1980

ABSTRACT We report the development of a fluorescence-based immunoassay technique relying on the physical phe-nomena of random number fluctuations and diffusion, whichwe review. By determining the autocorrelation of the fluctua-tions in the fluorescent intensity, this method is able to measurethe amount of labeled antigen or antibody that is bound to mi-crometer-sized carrier particles in solution. The principal ad-vantage of this technique is its insensitivity to small, fast-dif-fusing sources. It also discriminates against weakly fluorescentcontaminants of size comparable to the carrier particles. Wedemonstrate these attributes by using two model systems: ahuman IgG assay and an idealized system consisting of poly-styrene fluorescent spheres and rhodamine dye.

Considerable effort has been devoted to the development offluorescence-based immunoassay methods to replace thetechnique of radioimmunoassay for some routine clinical tests.The radioimmunoassay method is very powerful, owing to itshigh sensitivity and specificity. Its principal disadvantage is itsreliance on expensive and potentially hazardous reagents thathave a limited shelf life and whose use requires special handlingand disposal procedures and expensive instrumentation.

Several fluorescence-based immunoassay techniques arecurrently in use or are undergoing clinical evaluation (1-4). Thispaper introduces an approach that relies on the existence oflong-lived correlations of fluorescently labelled complexes insolution. Our preliminary results, as well as theoretical analysis,indicate that this correlation technique inherently possesses highsensitivity.Our assay is an adaptation of a technique developed by

Weissman et al. (5) to determine the molecular weight of DNAmolecules (108 to 1011) by using fluorescent dye binding. Theultimate goal of the technique is to measure the concentrationof complexes Ag-Ab* or Ag*-Ab, which fluoresce due to la-beled antigen (Ag*) or antibody (Ab*) while remaining in-sensitive to the presence of unbound fluorescing molecules insolution (in particular, free Ag* or Ab*). The key to the methodis the requirement that the immunological reaction of interestoccur on the surfaces of large "carrier" particles (e.g., mi-crometer-sized acrylamide gel, polystyrene latex, etc.).The technique of Weissman et al. (5) relies on two physical

phenomena: number fluctuations of particles within a pre-scribed volume in solution due to random Brownian motion,and diffusion of particles, in which the diffusion coefficientis inversely related to particle size. To distinguish between large,slowly diffusing sources of fluorescence (due to Ag*-Ab orAb-Ab* attached to carrier particles) and small, rapidly dif-fusing ones, we simply keep track of the fluctuations in fluo-rescence intensity that occur for a given small volume element

in the solution. Clearly, any fluctuation in intensity that occursdue to a fluctuation in the number of particles present in thevolume will, on average, persist for a time which depends in-versely on the rate of diffusion of the particles into or out of thesampling volume. For the large tagged carrier particles thesefluctuations will be very long lived. For any small, freely dif-fusing fluorescing molecules there will effectively be no"memory" of a fluctuation having occurred at a finite timeearlier, provided that the sampling volume is made appro-priately small.

THEORYLet us assume that the solution containsN identical fluorescingparticles per sampled volume 5V. At any instant the numberof particles in 6V will fluctuate according to Poisson statistics;the root mean square magnitude of the fluctuations is N1'2. Aconvenient way to monitor these fluctuations is to evaluate thefamiliar intensity autocorrelation function,

[1]in which I(t') is the fluorescent intensity originating from OVat time t' and the symbol (... )tt indicates an average of theintensity product over a large number of sampling times t'.We now periodically sample the fluorescent intensity at

hundreds of locations within the solution, using in each case avolume of the same size (bV 10-6 cm3). The large numberof samples increases the signal/noise ratio of function C(t).When time t equals an integral multiple of the repetition periodT, the two intensities that form the product in Eq. 1 refer to thesame volume element, for a given t'. The usefulness of the au-tocorrelation function in our application depends upon the factthat a number fluctuation in WV has a finite lifetime, r. Fig. lais an idealized trace of the intensity I(t') showing two fluctua-tions, each of which repeats after the period T (»>> T). In re-ality, the intensity fluctuations do not resemble the regular,symmetric pattern of Fig. la; rather, they appear as "random"noise (as illustrated in Fig. 2). This idealization was chosen topermit a simple algebraic computation of C(t) as discussedbelow. We assume a mean number of particles N per volumebV, each particle fluorescing with intensity I, giving a meanintensity I-N. For simplicity we arbitrarily choose a positive anda negative fluctuation in intensity, with the size of each fluc-tuation given by the root mean square value, I-N1'2. Due to thedeliberate physical overlapping of the sampling volumes insolution, there is a finite perisistence width At' of the fluctua-tions in Fig. la.We now evaluate C(t) for the I(t') shown in Fig. la, aver-

aging the time t' over one period for convenience. Computing

t On leave from Department of Physics, Colby College, Waterville,ME 04901.

4904

The publication costs of this article were defrayed in part by pagecharge payment. This article must therefore by hereby marked "ad-vertisement" in accordance with 18 U. S. C. §1734 solely to indicatethis fact.

C(t) = Mt') - IW - 0) t,

Proc. Natl. Acad. Sci. USA 77 (1980) 4905

type particles can dominate in the correlation result if they area bright enough (i.e., if Ib is large enough).

We can significantly enhance the detection of bright b-typeparticles relative to weak f-type sources if the fluctuationlifetime Tb happens to be much longer than if. This will be thecase if the b-type particles are much larger than the f-typeIf particles, provided that diffusion is the dominant effect gov-erning the motion of these particles. Then the period T can bechosen such that Tf << T << Tb, resulting in no "memory" off-type fluctuations occurring in a given volume 3V at a time

V t = T later, regardless of the relative magnitudes of the twotypes of fluctuations. Effectively this means that Nf can be setequal to zero in Eq. 4.

Diffusion causes a number fluctuation An in a cubic volumeb of dimension e to relax exponentially with a diffusional lifetime

given by

T-At' T T+At' 2T t

FIG. 1. Idealized trace of the intensity in time (a) and the re-

sulting autocorrelation function versus the separation time (b).

C(t) for the special case t = T, the scanning period, clearlymaximizes C(t), yielding

(T) At,' [12 (N + N'/2)2 + j2 (N - N'/2)2]T -2At'IJ2N2

+ TT-At

=12N2 + 2 At, 2N. [2]T

Calculating C(t) for separation times t substantially differentfrom T (i.e., t < T - At' or t > T + At' but t not near 2T, 3T,etc.) gives C(t) = 12N2. This is simply the square of the meanintensity and forms the uncorrelated part of Eq. 2 (i.e., thebaseline). Fig. lb shows the resulting C(t) computed for all

times t. Thus, when the fluctuation lifetime r is much greaterthan T, the height P of the correlation peak above the uncor-

related baseline is given byAt'P c -N.2. [3]T

Next we explicitly consider a two-component system: Nbb-type particles, each of intensity Ib, plus Nf f-type particlesof "unit" intensity, per volume SV. (Ib is the number off-typeintensity units on each bead.) Subscript b denotes fluorescencebound to large carrier particles, and subscript f denotes thefluorescence due to free molecules. Assuming statistical inde-pendence of the two species, we obtain from Eq. 3 the depen-dence of the correlation peak height on the above parame-

ters,

P x (NbIg + Nf) [4]

in which it is assumed that fluctuation lifetimes Tb and Tf areboth much greater than the period T. If Nbi >> Nf, the cor-

relation peak height is almost entirely due to the fluctuationsof b-type particles, in which case measurement of P then allowsthe relative determination of either Nb or Ib. Even when theaverage fluorescent intensity due to b-type particles is com-parable to that of the f-type particles (i.e., NbIb - Nf), the b-

TD_ e2/14-D- kT Rh. [5]

We have used the Stokes-Einstein equation to relate the dif-fusion coefficient D to the particle hydrodynamic radius Rh;X is the solvent viscosity, k is Boltzmann's constant, and T is theabsolute temperature. Eq. 5 is an estimate of the diffusionallifetime of a fluctuation that is centered in the (cubical) sam-pling volume. Clearly, in general there will be a distributionof decay lifetimes due to the spatial distribution of fluctuationswithin the volume. For geometries other than a cube, a similarresult is obtained, with a different numerical factor. Taking eto be approximately 100l um, we find that, at room temperaturein water, the diffusional lifetime of number fluctuations forparticles of radius Rh (in Mm) is

TD (sec) - 3000 Rh. [6]

Of course, the occurrence of velocity currents in solution mayimpose a significantly lower limit on the fluctuation lifetimesof all species. Nevertheless, a significant result is obtained ifthere are two radically different sizes of fluorescing particlesin solution, with the fluctuation lifetime of the smaller speciesdiffusion limited. In that case, one can design an immunoassaywhich is highly sensitive to fluorescence bound to large particlesbut quite insensitive to fluorescing molecules that are part ofthe fast-diffusing "background."

EXPERIMENTAL APPARATUS

A simplified diagram of the fluorescence-fluctuation spec-trometer is shown in Fig. 2. Pinhole P (diameter, 100,um) isused to define the beam of light incident on the sample cell S.It was convenient to use an argon-ion laser, X = 488 nm (blue),to excite the fluoresein isothiocyanate-labeled molecules. Co-herence of the light source is not required-any suitably fil-tered incandescent source would suffice.Any labeled molecules that lie within the pencil beam volume

defined by P will emit fluorescent light. Lens L projects thisline image onto a photographic slit S at the face of the photo-multiplier detector PMT. Filter F (Corning no. 3-69) blocksthe 488-nm blue exciting light scattered from particles in so-

lution, leaving the yellow-green fluorescein emission plus anylong wavelengths emitted by fluorescing impurities. The widthof slit S is also 100Mgm. Thus, an effective illuminated/detectedvolume 3V of the order of 10-6 cm3 is defined by these op-tics.

As described thus far, the approach is identical to that usedsuccessfully by Weissman et al. (5) for DNA size determination.The significant change in design occurs in the choice of themeans of periodically sampling the intensity as a function of

C(t)

-NI2T Km

Immunology: Nicoli et al.

L I

i

Proc. Nati. Acad. Sci. USA 77 (1980)

pt

I I

X=488 nm

A//

//E

//F / /

.4p.A4

FIG. 2. Schematic of the experimental arrangement showi:sample cell S, vertically translated, in which the volume 5V Z10-is defined by the associated optics.

position within the sample solution. In the original DNAa cylindrical sample cell was uniformly rotated (T ; 5 soa slow-speed synchronous motor and drive belt. Instead, wea linear translation scheme. The sample cell is a cylindricathat is uniformly translated in an up/down vertical motifusing a loudspeaker. Two sizes (outside diameter) of tubesused in these experiments: 6-mm disposable culture tube2-mm 100-,dl micropipets. These tubes were centered va standard 1-cm fluorimeter cuvette filled with water ftpurpose of index-matching the incident light beam to minstray reflections. Sample solution volumes as small as 20easily achieved in the small tubes.The sample tube is translated up to 0.8 cm according

triangular waveform, with the period adjustable from 0.2sec. The triangular driving waveform in reality consistrising and falling staircase of discrete steps, adjustalnumber from 64 to 1024. Each step corresponds to a dirtime bin of width 5t used to approximate the autocorrelfunction C(t) of Eq. 1. Typical values of bt range from 1msec. An important innovation is the use of a microcom(Motorola 6800) to synchronize the sample position wittime base used to form C(t). Hence, the sample cell is "lo(into the autocorrelation time base and performs perfect]riodic motion. The run time can be arbitrarily long, wishort-term "jitter" or long-term slippage of position withthereby enhancing the sensitivity of the instrument toweak intensity fluctuations.The PMT photocurrent is converted to a voltage, wit

justable gain, dc offset, and filter time constant. This allowsignal to be optimally matched to the input range of aanalog-to-digital converter. In the instrument, successiveX 4-bit multiples are used by the microcomputer to for]autocorrelation function.

In addition to displaying the contents of the correchannels on an oscilloscope, the microcomputer determinebaseline and the correlation peak height. These valuenormalized by the number of sample intervals in the elrun time. In practice one scans the solution until the normpeak height settles to a constant value-i.e., when C(t) idetermined.

RESULTSHuman IgG Model System. For this series of experiments

we utilized the Immunofluor reagents supplied by Bio-RadLaboratories. These consist of human IgG molecules, which werefer to as the antigen, Ag; rabbit antibody to human IgG (i.e.,anti-immunoglobulin) which has been tagged with fluoresceinisothiocyanate, Ab*; and 3- to 5-,gm-diameter acrylamide gelbeads to which antibody molecules, Ab, are covalently bound.We denote the latter by the symbol Abb, b denoting bindingto the carrier particle.To perform this particular assay, known amounts of the an-

tigen, IgG, were added to solutions of carrier particles (107-108beads per cm3). During incubation the antigen binds to theacrylamide particles. Each solution was then flooded with anexcess of tagged antibody, nAb*, resulting in the reaction

nAb* + Abb + Ag-Abb (n - 1)Ab* + Abb+ Ab*-Ag-Abb. [7]

At this point the standard fluorimetric intensity assay consistsI' of spinning down the acrylamide particles (to which are bound

the complexes Ab*-Ag-Abb), discarding the supernatant, andng the measuring the mean fluorescent intensity, which should be6cm3 proportional to the initial IgG concentration

Our first test was to compare the results based on the corre-study lation measurement with those of fluwrimetry. For bothec) by methods the fluorescent "signal" is plotted in arbitrary unitse used versus IgG concentration (,gg/ml) (from dilutions of an IgGJ tube standard, 3200 mg/dl) (Fig. 3). For the fluorimetric assay (curveion by B) that signal is simply the mean intensity. For the correlationwere assay (curve A) the signal is the square root of the peak height~sand (Eq. 4); Nb is the mean number of carrier particles in 5V andsthand Ib equals the number of fluorescing complexes, Ab*-Ag-Abb,

v thn per particle. Nb should be fixed; Ib is the unknown to be mea-oriz. sured. Because we discard the free Ab* in solution, Nf shouldAilare be zero. The correlation result closely parallels the simple4u are measurement of total intensity. Both methods saturate .at

moderately high IgG concentrations, where a substantialg to a fraction of the active antibody sites Abb have become occupied. to 20 by IgG. Furthermore, at very high IgG levels both methodsAs ofa display a curious reverse behavior, in which presumably theae mscretelationto 10iputerth theeked"ly pe-ith noLtime,very

th ad-ws the4-bit

> 4-bitm the

lationies thees areapsedalizedLs well

100

z-

or

-Jz0(f)

10

0.1 10IgG (,pg/ml)

FIG. 3. Measured signal (in arbitrary units) versus the IgG con-

centration. Curve A gives the correlation result (P1/2 - Nlf Ib); curveB gives the fluorimetry result (average intensity -c NbIb).

x

Ax

x

B

4906 Immunology: Nicoli et al.

Proc. Natl. Acad. Sci. USA 77 (1980) 4907

number of available Abb sites on the carrier particles has beenreduced due to substantial aggregation of the gel particles,promoted by the divalent IgG molecules.

Unlike fluorimetry, our assay is particularly sensitive to theformation of aggregates of the carrier particles. These aggre-gates occur because the divalent IgG crosslinks two Abb mole-cules belonging to two different carrier particles: Abb-Ag-Abb.The formation of aggregates increases the fluorescent intensityper carrier (Ib in Eq. 4) while proportionately decreasing thenumber of carriers per volume 5V (Nb). Because the correlationpeak height scales like NbIL the formation of aggregates willenhance the signal. This is probably the cause of the "bowed-ness" of the correlation assay data shown in Fig. 3. (Computersimulations support this conclusion.)The ability of the correlation assay to determine the amount

of IgG bound to the carrier particles in the presence of varyingamounts of free Ab* was also investigated. From Eq. 6 we es-timate the diffusional lifetime of the 4-,m-diameter acrylamidebeads to be roughly 6000 sec. The corresponding lifetime forthe Ab* molecules was deduced from dynamic light scatteringtto be approximately 25 sec.

In order to use diffusion to discriminate against the free Ab*,one should use a scanning period T of the order of 100 sec.However, we found that the fluctuation lifetimes of all species,large and small, were limited to about 10 sec, presumably dueto velocity currents in the sample. These currents may be par-tially a consequence of the accelerations set up due to the up/down motion of the sample cell and partially due to thermalgradients. Hence, for the IgG experiments a short repetitionperiod T was required (we used 1.2 sec); consequently, thecontribution of the free Ab* to the correlated peak height couldnot be avoided.Curve A in Fig. 4 is a plot of the correlation result (expressed

in relative units) as a function of the amount of free taggedantibody Ab*, normalized to the bound intensity. The units ofthe x axis thus are NfJ/NbIb obtained by measuring mean flu-orescent intensities (i.e., Nf + NbIb and NbIb). In this test wekept the IgG concentration and the carrier particle densityfixed. From curve A we see that, when the background freefluorescence is 10 times the carrier particle fluorescence, thereis virtually no change in the correlation result for bound fluo-rescence. Thus, we have confirmed experimentally that thecorrelation assay does achieve a level of selectivity even whenboth fluorescing species are large and have long enough life-times to contribute to the correlation. The fact that the corre-lated signal increases at high Ab* concentrations demonstratesthat the fluctuations of Ab* are indeed being correlated.

It is instructive to use the results of curve A to estimate themean number of fluorescent complexes bound to a carrierparticle. Eq. 4 shows that the correlation result, pl/2, will in-crease by 21/2 when NbIj = Nf. Because the x axis is given byNf/NbIb, the corresponding x axis value is Ib. From Fig. 4 weestimate that Ib - 31. The IgG concentration used in estab-lishing curve A was 3.2 ,ug/ml. According to Fig. 3, this IgGlevel corresponds to approximately 33% saturation. Hence, weestimate a maximum of ut100 fluorescent complexes per carrierparticle (Bio-Rad Laboratories estimated 1000 antibodies perbead, of which 12-15% are active).

Finally, it should be mentioned that curve A does not strictlyfollow the response predicted by Eq. 4, if Ib is to remain con-stant at all Ab* concentrations. We believe that the discrepancy

5 10 50 00N.t/NbI/

FIG. 4. Relative correlation signal, P1/2 cc (NbI2 + Nf)112, versusthe ratio free fluorescence/bound fluorescence (equal to Nf/NbIb).Curve A, system acrylamide bead-Abb-Ag-Ab* + Ab*; curves B andC, polystyrene fluorescent spheres + rhodamine, at T = 1.2 sec andT = 10.2 sec, respectively.

is explained by a decreasing Ib, perhaps due to the increasinglikelihood of the reaction

Abb-Ag-Ab* + Ab* Abb + Ab*-Ag-Ab* [8]as the concentration of Ab* increases.

Idealized Model System. We next devised an experimentin which the fluctuation lifetime of the smaller ("free") fluo-rescing species is diffusionally limited. To achieve this we usedcommercially available fluorescent spheres (Duke Scientific,no. 267 diameter, 4.3 ,m) for the large species and the dyerhodamine 6G for the fast-diffusing species. The latter has amolecular weight of 530 with an estimated hydrodynamic ra-dius of 6.7 A (based on a globular molecule of protein-likedensity). For this series of experiments we attempted to reduceflow currents due to sample motion plus thermal gradients bydrastically reducing the sample cell diameter. For the cell weused a portion of a standard 100-,Ml micropipet (1.3 mm insidediameter), resulting in an active solution volume of less than20,gl. This was centered in a fluorimeter cuvette filled withwater for index matching as well as thermal sinking. From ananalysis of the resulting fluctuating signals, we concluded thatuse of the small-diameter tube coincidentally reduced thevolume 3V by a factor of 3, due to the focusing lens effect ofthe glass tube. The resulting diffusional relaxation times out ofthis reduced volume for the polystyrene spheres and the rho-damine 6G are estimated, from Eq. 5, to be about 3000 and 1.0sec, respectively. Thus, we expect that scanning periods T onthe order of 10 sec should allow us to discriminate effectivelyagainst the background fluctuations of the rhodamine 6G,whereas at T = 1 sec we expect only marginal discrimina-tion.

Curves B and C in Fig. 4 are plots of the relative correlatedsignal as a function of the ratio of free to bound fluorescencefor T = 1.2 and 10.2 sec, respectively. In both cases, the insen-sitivity to the "free" fluorescence is better than in curve A. Thisresult could be explained by assuming that the fluorescentpolystyrene spheres are more fluorescent relative to the freespecies (i.e., that Ib is a larger number) than are the Ab*-Ag-Abb complex-coated particles of curve A. However, rho-damine 6G molecules do correlate less efficiently at longerrepetition periods than do the free Ab* molecules, owing to thefact that the former diffuse faster than the latter by 1 order ofmagnitude. The significance of this difference is seen bycomparing curves B and C. The latter curve is essentially flatall the way out to a free fluorescence intensity 200 times largerthan the bound value. This is our principal result. It clearlydemonstrates the high level of insensitivity of this techniqueto fast-diffusing sources of fluorescence.

tWe filtered the scattered light (incident, X = 488 nm) with a bluefilter to remove the fluorescent light. A 4-bit autocorrelator was usedto determine the mean diffusion coefficient (see ref. 6). Given anestimated molecular weight of 150,000 for Ab*, we conclude thatAb aggregates are common.

Immunology: Nicoli et al.

Proc. Natl. Acad. Sci. USA 77 (1980)

DISCUSSIONDetailed comparison of this fluorescence correlation assay withthe radioimmunoassay (as well as other fluorescence techniques)requires further testing on systems of clinical significance. Inorder to evaluate the practical sensitivity of the proposedmethod it is necessary to consider the level of fluorescent con-tamination. For the case in which there is negligible backgroundcontamination, the correlation technique is no more sensitivethan a simple measurement of total intensity. For example, inour IgG model assay we are able to detect approximately 1fluorescent complex per carrier particle, which corresponds toa concentration of 107-108 labeled molecules per cm3. How-ever, the correlation method retains sensitivity in situations inwhich there is a background of fluorescent sources. We havedemonstrated (curve C of Fig. 4) that this new method is highlyinsensitive to fast-diffusing background fluorescence. Instraightforward intensity assays, unwanted small sources mustbe removed by a separation step (e.g., filtering, centrifugation,etc.). The correlation assay inherently provides a filter againstsmall sources. We have also demonstrated a level of insensitivityto relatively large unwanted sources. In curve A of Fig. 4, boththe labeled antibody molecules and the carrier beads contrib-uted to the signal. The selectivity in favor of the carrier particlesresulted from their relative brightness (i.e., their large Ib).Hence, in situations in which contaminants are individuallymuch dimmer than, but of the same size as, the primary par-ticles (i.e., size-based separation techniques would not work),this immunoassay technique would still be insensitive to thecontaminants. From curve A and Fig. 4, we see that this in-sensitivity persists to somewhat beyond the point where the netfluorescent intensity of the contaminants is 10 times larger thanthat of the carrier particles (for Ib - 30).A number of technological details influence the overall

performance of this method. One of these is the bit resolution

of the analog-to-digital converter; another is the scheme usedfor scanning the sample volume. We experimented with ascanning scheme in which the sample cell was kept stationary,but we encountered troublesome artifacts in the signal due tooptical limitations. Although the overall performance of theassay method may be improved by further attention to thesedetails, we believe that sample-related factors will provide theultimate limitation. For example, in our IgG experiments weexperienced difficulties associated with carrier particleaggregation. In other assay systems one may encounter large-particle fluorescent contamination. In summary, we have al-ready demonstrated the potentially high sensitivity of this newtechnique. It remains to be determined whether this methodoffers a fundamental improvement for fluorescence-basedimmunoassays.

We thank G. Feher for useful suggestions regarding the experimentalmethod and the manuscript, D. Sears for helpful conversations con-cerning immunology, and D. Pfost for help in constructing the mi-croprocessor-based autocorrelator. This work was supported by a grantfrom the National Institutes of Health (5 R01 AI 15073-02) as well asfunding from the campus research committee of the University ofCalifornia, Santa Barbara.

1. Burgett, M. W., Fairfield, S. J. & Monthony, J. F. (1977) J. Im-munol. Methods 16,211-219.

2. Kronick, M. N. & Little, W. A. (1975) J. Immunol. Methods 8,235-240.

3. Watson, R. A. A., Landon, J., Shaw, E. J. & Smith, D. S. (1976) Clin.Chim. Acta 73,51-55.

4. Dandliker, W. B., Kelly, R. J., Dandliker, J., Farquhar, J. & Levin,J. (1973) Immunochemistry 10, 219-227.

5. Weissman, M., Schindler, H. & Feher, G. (1976) Proc. Natl. Acad.Sci. USA 73,2776-2780.

6. Chu, B. (1974) Laser Light Scattering (Academic, New York).

4908 Immunology: Nicoli et al.