Journal of Cell Science 101, 415-425 (1992)Printed in Great Britain © The Company of Biologists Limited 1992

415

Tracking of cell surface receptors by fluorescence digital imaging

microscopy using a charge-coupled device camera

Low-density Hpoprotein and influenza virus receptor mobility at 4°C

CATHERINE M. ANDERSON1, GEORGE N. GEORGIOU1, IAN E. G. MORRISON1,

GREGORY V. W. STEVENSON2 and RICHARD J. CHERRY1

^Department of Chemistry and Biological Chemistry, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, Essex, UK2Rhdne Poulenc Rorer, Rainham Road South, Dagenham, Essex RM10 7XS, UK

Summary

A fluorescence imaging system, based on using a cooledslow-scan CCD camera, has been developed for trackingreceptors on the surfaces of living cells. The technique isapplicable to receptors for particles such as lipoproteinsand viruses that can be labeled with a few tens offluorophores. The positions of single particles in eachimage are determined to within 25 nm by fitting thefluorescence distribution to a two-dimensional Gaussianfunction. This procedure also provides an accuratemeasure of intensity, which is used as a tag forautomated tracking of particles from frame to frame.The method is applied to an investigation of the mobilityof receptors for LDL and influenza virus particles onhuman dermal fibroblasts at 4°C. In contrast to previousstudies by FRAP (fluorescence recovery after photo-

bleaching), it is found that receptors have a low butmeasurable mobility at 4°C. Analysis of individualparticle tracks indicates that whilst some receptorsundergo random diffusion, others undergo directedmotion (flow) or diffusion restricted to a domain. Aprocedure is proposed for subdividing receptors accord-ing to their different types of motion and hencedetermining their motional parameters. The finding thatreceptors are not completely immobilised at 4°C issignificant for studies of receptor distributions per-formed at this temperature.

Key words: cell surface receptors, FRAP, lateral diffusion,domains.

Introduction

Measurement of the lateral mobility of membraneproteins such as receptors is important for a detailedunderstanding of a variety of cellular processes (Axel-rod, 1983; Peters, 1988). A number of techniques havebeen developed for such measurement, most of whichrely on fluorescence microscopy. In particular, methodsbased on photobleaching of fluorescent probes havebeen widely used (Axelrod et al., 1976; Jacobson et al.,1976; Jovin and Vaz, 1989; Peters, 1991). The basicmethod, often known as FRAP (fluorescence recoveryafter photobleaching), typically involves the photo-chemical destruction of fluorescent molecules in an areaof the cell surface by a brief pulse of intense laserillumination. Subsequent measurement of fluorescencearising from the same area reveals a recovery, the rateof which depends on the rate of diffusion of unbleachedfluorophores into the illuminated area. The veryextensive application of this and related techniques hasclearly demonstrated that the lateral mobility of mostproteins in cell membranes is highly restricted. Dif-

fusion coefficients are generally several orders ofmagnitude less than those measured for proteinsdiffusing freely in reconstituted bilayer membranes andimmobile components are also frequently observed.

Although FRAP has been very valuable for quantify-ing mobility of membrane components, it suffers thelimitation that it measures the average properties of alarge number of molecules. Thus the behaviour of sub-populations will be masked except for the distinctionbetween mobile and immobile components. A furtherlimitation is that the technique is poor at discriminatingbetween different types of motion. In principle, theshape of the recovery curve does allow one todistinguish between diffusion and directed motion(flow) (Axelrod et al., 1976). In practice, however,measurements with cells are generally interpreted by adiffusion model and it is very doubtful whether acombination of directed motion and diffusion could bedistinguished from pure diffusion. Finally, the FRAPtechnique measures diffusion over distances of theorder of 1 fan. It will thus fail to detect the mobility ofmolecules that are constrained in some way to move

416 C. M. Anderson and others

over sub-micrometre distances. Other methods ofstudying lateral diffusion that suffer from similarlimitations include fluorescence correlation spec-troscopy (Elson and Magde, 1974), measurement ofintermixing of membrane components after cell fusion(Frye and Edidin, 1970) and a recently described EPRtechnique (Shin, 1991).

An alternative fluorescence method for studyingdiffusion is to use a sensitive imaging system inconjunction with low-intensity excitation (minimal-photobleaching) so that the paths of individual fluor-escent markers can be tracked over a period of time.Such an approach largely overcomes the limitations ofthe FRAP technique and thus permits a more detailedanalysis of membrane protein mobility than washitherto possible. Webb and colleagues were the first tosuggest the feasibility of individual receptor tracking bydemonstrating that low density lipoproteins (LDL)labeled with about 40 fluorescent probes could bevisualised using an image-intensified video camera(Barak and Webb, 1981; Barak and Webb, 1982). Theyhave reported preliminary studies of LDL-receptormobility in which.the tracks of LDL particles bound tothe cell surface were obtained by taking time-lapseimages (Gross and Webb, 1988).

In order to obtain detailed statistical sampling of thediffusion processes, an automated system is desirablewhereby particles can be traced from frame to frameeven in crowded areas of the surface. Here we describethe development of a system based on a charge-coupleddevice (CCD) camera for measuring motions ofindividual particles by fluorescence digital imagingmicroscopy. A cooled slow-scan CCD camera waschosen as the image sensor for its excellent linearityover a wide dynamic range and lack of geometricdistortion as well as great sensitivity (Hiraoka et al.,1987). Software has been developed to identify thespots in each image, and accurately quantify the localbackground and peak intensity by least-squares fitting aGaussian function in two dimensions to each spot. Thenoise in the CCD follows well-defined statistics, so thefitting procedure can assign errors to both position andintensity, and the goodness-of-fit is a normalised chi-squared function that assists in the identification of anyartefacts. Automatic tracking of spots from frame toframe is facilitated by the intensity coding of each spot.We have applied the method to two types of diffusingparticles, namely LDL and influenza virus, on culturedhuman fibroblasts using the fluorescent lipid probe Rig(octadecylrhodamine B chloride) to label the particles.A preliminary account of these studies was previouslypresented (Morrison et al., 1990).

LDL is a roughly spherical particle of mean radius 20nm. It consists of a core of cholesterol esters boundedby a monolayer containing phospholipids, free choles-terol and a single protein, apoprotein B-100, part ofwhich embodies the binding domain recognised by theLDL-receptor (Hillyard et al., 1955; Kane, 1983). It haspreviously been shown that ~40 molecules of the highlyfluorescent lipid analogue dil (1,1-dioctadecyl-3,3,3',3'-tetramethylindocarbocyanine) can be incor-

porated into the particle without affecting binding tothe LDL-receptor (Barak and Webb, 1981).

Since its discovery in the 1970s, the LDL-receptorsystem has been the subject of much interest. This is inlarge part due to the positive correlation found betweenthe incidence of heart disease and high levels of LDL inplasma (Goldstein and Brown, 1977). In addition, theconcept of receptor-mediated endocytosis, which wasfirst formulated to describe the entry of LDL into cells,has consequently been found to be applicable to theuptake of a wide variety of important macromoleculesand small particles (Brown and Goldstein, 1979;Goldstein et al., 1985).

Influenza viruses are particles of ~100 nm diameterenveloped by a lipid bilayer. Embedded in the lipidbilayer are the spike glycoproteins, the majority ofwhich are haemagglutinin (HA). HA binds to sialic acidmoieties on cell surfaces and at acidic pH undergoes aconformational change that promotes fusion of the viralenvelope with the membrane to which it is attached(White et al., 1983). In the normal course of infection,influenza virus enters cells by endocytosis and fuseswithin internal acidic compartments (Marsh, 1984). Thelipid probe Ris, originally used as a self-quenchingfluorophore for fusion studies (Hoekstra et al., 1984),can readily be incorporated into the viral membrane.We have previously reported studies of the fusion ofRi8-labelled influenza virus with erythrocytes thatdemonstrate the feasibility of imaging and trackingindividual virus particles (Georgiou et al., 1989).

It is generally assumed that cell surface receptors areimmobile at 4°C. This assumption is largely based onFRAP experiments that place an upper limit on thediffusion coefficient of typically 5 X 10~12 cm2 s"1. Herewe exploit the greater spatial resolution of singleparticle imaging to demonstrate that receptors for LDLand influenza virus do have significant mobility at 4°C.This finding is of interest in relation to methods used todetermine receptor distributions.

Materials and methods

CellsHuman dermal fibroblasts (D532) were obtained from FlowLaboratories. The cells were grown in Dulbecco's ModifiedEagle's Medium (DMEM) containing 10% fetal calf serumand supplemented with penicillin G (100 units ml"1),streptomycin sulphate (100 mg ml"1) and L-glutamine (2mM). Cells were grown at 37°C in 7% CO2. For imagingexperiments, trypsinised cells were seeded onto 8-well Lab-Tek slides (Gibco) and cultured for a further % h. For LDLexperiments, LDL receptors were upregulated by incubatingcells in lipoprotein-deficient growth medium during the last48-72 h, essentially as described by Brown et al. (1974).

LDL and influenza virusLDL was prepared from freshly drawn human blood bysequential flotation ultracentrifugation (Hatch and Lees,1968). The purity of the preparation was confirmed by agarosegel electrophoresis. Samples were stored in 150 mM NaCl, 10mM Tris-HCl, 1 mM EDTA, pH 7.4, prior to use. Influenzavirus, strain X47, grown in embryonated chicken eggs was

Tracking cell surface receptors All

generously provided by Professor C. Pasternak (St. GeorgesHospital Medical School).

Labeling with fluorescent probesLDL was labeled with either dil or R18. The probe wassolubilised in DMSO (1.7 mM) and 120 /il of the solutionincubated with 1.21 mg of LDL in approximately 400 /A for 1 hat 37°C under nitrogen. Labeled LDL was separated from freeprobe on a PD10 column (Pharmacia) eluted with 150 mMNaCl, 10 mM Tris-HCl, 1 mM EDTA, pH 7.4, and stored at4°C. Protein was determined by the method of Markwell et al.(1978) and probe concentration by absorbance measurementassuming molar absorption coefficients of 117,000 M"1 cm"1

for dil and 93,000 M"1 cm"1 for R18 (Haugland, 1989). Theaverage number of probes per LDL particle was calculatedassuming that protein constitutes 25% by weight of LDL andthe average Mr of the particles is 2.75 x 106 (Goldstein andBrown, 1977). Labeling ratios were typically found to be 30-50probes/LDL particle.

Influenza virus was labeled with Rtg essentially as describedby Hoekstra et al. (1984). Protein concentration was deter-mined according to Lowry et al. (1951) and probe concen-tration by optical absorbance. The average number of probesper virus particle was calculated using a conversion factor of1.75 x 10 virus particles per mg protein. Although influenzavirus particle can incorporate a high concentration of RJS(Hoekstra et al., 1984), about 100 probes/particle weresufficient for imaging. Haemolysis and haemagglutinationassays were used to check that labeling had no effect on viralactivity.

Fluorescence microscopyD532 cells on Lab-Tek slides were labeled with fluorescentLDL at 4°C using a procedure modified from that describedby Barak and Webb (1981). Chilled cells were washed threetimes in phosphate-buffered saline (PBS) and then once inDMEM supplemented with 10 mM HEPES and 2 mM Ca2+ atpH 7.4 (buffer A). Labeled LDL was diluted to 50 ̂ g/0.45 [Ain buffer A. Cells were incubated with labeled LDL at thisconcentration for 10-30 min at 4CC. They were then washedthree times in PBS supplemented with 2 mM Ca2+ andincubated for 10 min in PBS supplemented with 2 mM Ca2+, 2mg ml"1 bovine serum albumin and 10 mM Tris-HCl at pH7.4. After washing cells once more in buffer A, the slides weretransferred to a microscope stage maintained at 4°C. Non-specific binding was checked by incubating cells with labeledLDL in the presence of a tenfold excess of unlabeled LDL.Similar procedures were used with influenza virus, except thatthe incubation and washing buffers consisted of 137 mMNaCl, 2.7 mM KC1,10 mM phosphate buffer, pH 7.4, and theincubation time was 5 min.

Fluorescence Digital Imaging Microscopy was performedusing a Nikon Diaphot inverted fluorescence microscope withOmega Optical Inc. filters and dichxoic mirrors. For dilobservations, the light source was a 50 W mercury lamp; forR18 a 100 mW beam of 514.5 nm light from a Coherent Innova90 argon-ion laser was used, directed from above at an angleof ~20° to the plane of the slide.

The Wright Instruments CCD camera was attached to thevideo port of the microscope, and the image focused, with aHanimex f2.8 wide angle lens, on to the EEV P8603 detector(576 x 384 pixels). This device has a maximum quantumefficiency of around 35% and a mean readout noise equivalentto 7 electrons/pixel. Image acquisition, storage and displaywere performed using the Wright Instruments ATI imagecontrol software, running on an IBM-AT compatible com-puter equipped with Wright Instruments image store and

display cards. Images were typically recorded every 1 or 2 minwith an exposure time of 10 s.

Spot position and intensity determinationIndividual LDL or virus particles or small clusters of particleshave dimensions less than the resolution of the microscope.The fluorescent images of these particles are thus diffraction-limited spots with a Gaussian intensity distribution. Fluor-escent spots in each image were located by a simple imageanalysis routine, which identifies peaks having approximatelythe diffraction limited width.

The intensity distribution in individual spots is then fitted bya specialised iterative non-linear least-squares algorithm to afunction consisting of a uniform background Zo and a two-dimensional Gaussian function with peak height Zn and widthWn at position coordinates (Xn,Yn) as:

f{x,y) = Zo + Znexp{ - [(* - Xnf + (y - Yn)2]/Wn

2} . (1)

The data values are the pixel contents from a square boxdrawn around the estimated peak centre; box size varies withthe objective lens used and is chosen to give the bestcompromise between speed and accuracy. Since the noise ineach pixel of a CCD follows well-defined statistics, the datapoints can be weighted in proportion to the contents and thegoodness-of-fit characterised by a normalised chi-squaredfunction; this enables standard deviations of the variableparameters to be determined.

When spots are closely spaced, two different techniques areused for overlaps:

(i) When another spot lies just outside the optimal box, thepixels surrounding the second spot are zero-weighted up to aradius equal to half the interspot distance.

(ii) When a neighbouring spot falls within the box, the boxsize is increased and the spots are fitted simultaneously; arecursive method is employed to identify all spots within aclose group of this kind. Up to nine spots can be treated as agroup, but at a cost of computer time and accuracy as theincreased box size may give rise to background non-uniformity. (A function with sloping background has beentried, but the fitting algorithm is less stable; in any case thepeak widths and heights are changed by less than the standarddeviations when compared with the uniform backgroundcase.) In practice, groups of more than three spots are rarelyfound; these will typically require twice the computing time ofsingle spots.

There are several reasons for this type of approach. Firstly,the spot position (i.e. Gaussian peak position) is identified toan accuracy of —0.1 pixel, or 25 nm when using a x40microscope objective. Secondly, artefacts can be recognisedon the basis of: (a) peak width; wide spots are artefacts,narrow ones are noisy pixels (e.g. cosmic rays); (b) widtherror; a poorly defined peak width indicates artefacts or closedouble peaks; (c) chi-squared; high values suggest artefacts oruneven background values.

Spots can be excluded from the analysis on any one of thesefactors. Thirdly, the intensity of the spot above localbackground is determined far more accurately than by justusing the central pixel value and an estimated background.

Spot motion trackingTo link a spot in an image with the corresponding spot in thenext frame of a time sequence, the following technique isemployed. For each pair of coordinates, probabilities areassigned to nearby spots in the next frame as:

P = exp{-[AR/Rd]2} x exp{[-AZ]2/Zn} , (2)

where AR is the change in position, Rd is a measure of the

418 C. M. Anderson and others

expected change in position, AZ is the change in peakintensity and Zn is the mean peak intensity of the spot. Insome cases where changes of focus are noticed as the particlediffuses, the intensity (changing inversely with spot width)varies too much for this formula to be used; replacing AZ andZn with the corresponding values for the total integratedsignal under the peak is better. Clashes (i.e. cases where morethan one spot in a frame could correspond to a single spot inthe next) can then be resolved on the basis of higherprobability.

Some limitations have to be included in this method, asspots may disappear due to aggregation, endocytosis ordetachment of the fluorescent particle from the membrane.This can best be achieved by setting a minimum probability,so that if the best match falls below this minimum then thetrack is deemed to have terminated.

Background motion of the slide is seen in some cases. This isobserved as apparent synchronised flow of all spots. It can beremoved by subtracting the motion of off-cell particles. Off-cellparticles also act as a control to ensure that any motion detectedfor on-cell particles is not a methodological artefact.

Results

LDL-receptor mobilityFig. 1A shows an example of the images obtained forRi8-labeled LDL bound to D532 fibroblasts. Non-specific binding was low for R18-LDL but was oftensignificant for dil-LDL. All the results reported herewere therefore obtained with R18-LDL. As described inMaterials and methods, the spots in each image areanalysed for intensity and position enabling individualparticles to be tracked over the duration of theexperiment. The integrated intensities above back-ground of individual spots typically corresponded to100-150 detected photons. The background corre-

sponded to about 60 detected photons/pixel. Fig. 2Ashows examples of the tracks observed for LDL; notethat for clarity the tracks have been enlarged relative tothe coordinates of their starting positions.

Individual tracks may be analysed by determining themean square displacement (r2,) as a function of timeinterval ndt. For random diffusion in two dimensions:

(3)i)=4D(ndt),

where D is the diffusion coefficient. For uniformmotion with velocity v:

{j2) = ^{ndtf. (4)

Particles that are constrained to move within adomain may move according to equation (3) for smallndt values but at longer times the mean squaredisplacement will reach a maximum value, r^M. For thiscase we use the following empirical expression, whichreduces to the correct formulae at short and long times:

(/n) = 'max[l ~ exp(~4Drt(5l'/r^lax)] . (5)

The value of (r2) for the time interval ndt, where n isthe number of frames and dt the time betweensuccessive frames, was computed according to:

j-n ,_i

where r, ,+n is the distance moved between frames i andi+n, and; is the total number of frames obtained. Notethat the time intervals are overlapping so that values of(r2) are not independent but there are insufficient datapoints to average sensibly non-overlapping time inter-vals. Error bands for each point can be calculated fromthe positional uncertainty of the spot in each frame

Fig. 1. Digital fluorescence images of: (A) R18-labeled LDL, (B) R18-labeled influenza virus, on fibroblasts. Inset in A is a3x enlarged area showing how closely associated spots can be analysed for position and intensity; the central boxed area,13 pixels square, is fitted with two Gaussian peaks (technique (ii)), with some pixels (shown black) zero-weighted toremove the effect of neighbouring spots (technique (i)). The variable background in B illustrates the need for individualspot computer analysis.

Tracking cell surface receptors 419

220

Fig. 2. Relabeled LDLparticles diffusing on afibroblast lamellipodium,tracked over 20 imagesrecorded at 2 minute intervals.To permit the individual tracksto be seen, they have beenexpanded by a factor of 8compared with the interspotdistances; starting positions aremarked by circles. The nucleusof the celi is out-of-frame onthe left-hand side.

(obtained from the original spot fitting procedure). Thepoints from n=\ to m, half the number of imagesobtained, were weighted in inverse proportion to theseerror bands and fitted to equations (3)-(5) by a non-linear least squares analysis. Points for n > m becomeincreasingly random due to insufficient averaging(though correlated with one another because of exten-sive overlap in the time intervals) and were not includedin the fitting. Fig. 3 shows examples of individualparticle tracks together with the corresponding plots of{r%) against ndt and the fits to equations (3)-(5).

Although Fig. 3 suggests that different types ofmotion are present on the same cell, it is not possible tobe certain that any individual track represents adeparture from random diffusion. It is neverthelessimportant to attempt to subdivide the particles ifmeaningful parameters are to be extracted from thedata. In order to estimate the proportion of particlesundergoing the different types of motion, we haveanalysed all the particle tracks by comparing the chi-squared values for the best fits by equations (3)-(5). Weassume that a particle is undergoing random diffusionunless the chi-squared value is improved by more than20% when the data are fitted by either equation (4) orequation (5). There is no ambiguity in distinguishingbetween directed motion and diffusion within a domainas the curvature of the plots are opposite in the twocases. On this basis, the population of LDL particles isabout equally divided amongst the three types ofmotion for the cell illustrated in Fig. 2. We have someevidence that the distribution may vary from cell to cellbut this point requires further exploration.

Having sub-divided the population of particles in theabove manner, we can compute parameters for thedifferent types of motion. For directed motion, themean velocity of LDL particles is (0.26 ± 0.08) nm s"1.In the case of LDL particles undergoing randomdiffusion, diffusion coefficients range from 0.3 to 3(xlO~13) cm2 s"1 with a mean and standard deviation of(1.26 ± 0.98) X 10~13 cm2 s"1. For diffusion within acircular domain, it may be shown (see Appendix) thatd, the diameter of the domain, is related to r 2 ^ by:

d2 = 6 ^ M . (7)

For LDL, r ^ varies from 0.006 to 0.2 /zm2 correspond-ing to domain diameters of 0.2 to 1.1 /urn. The limitingcase of an immobile particle would correspond to adomain determined by the experimental uncertainty inmeasuring the particle position. The smallest observedvalue of rmax for LDL corresponds to approximatelythree standard deviations in the measurement ofparticle position. We cannot be sure that a particle withsuch a low value of rmax is not in fact immobile, but it isclear that the vast majority of LDL particles do have ameasurable mobility at 4°C. Diffusion coefficientsdetermined from equation (5) for LDL particlesdiffusing within a domain range from 0.6 to 11.0(xl0~ ) cm2 s - 1 with a mean and standard deviation of3.4 ± 3.1 (xKT13) cm2 s"1.

The parameters calculated in the preceding para-graphs are model-dependent. More complicatedmodels that combine different motions, for example,directed motion superimposed on random diffusion,

420 C. M. Anderson and othersrile 255

'500 ' 10001 15001 2000 0 0

280

30 T

2 0 ••

1 0 ••

X tpx]

100 T

' 500 ' 1000' 1500' 2

Fig. 3. Plots of (r2) against ndt for LDL particles (upper row) and influenza virus (lower). The left-hand panels illustratedomain diffusion and are fitted by equation (5); the middle panels show simple diffusion fitted by equation (3); on the rightare examples of flow fitted by equation (4). If error bars are not visible they are smaller than the symbol. Inset in eachpanel is a diagram showing the particle track in units of pixels of the CCD sensor; the scale is approximately 5 pixels to 1/an. Note the changes of scale in each panel and the insets.

can also be envisaged. Individual particles could alsoswitch from one type of motion to another during thecourse of the experiment. Irrespective of the details ofmotion, the distance a particle moves in a given time isclearly a crucial parameter for dynamic interactionsoccurring on the cell surface. One method of rep-resenting this information is illustrated in Fig. 4. Thisshows the experimental probability distribution of riji+n

for selected values of n, measured over all the particletracks on an individual cell. For random diffusion, thedistribution is given by:

P(r)dr = (r/2Dndt) (8)

As discussed above, we do not believe that a randomdiffusion model is applicable to many of the particles.Nevertheless, a quasi diffusion coefficient can bedetermined by fitting the data in Fig. 4 by equation (8)using a non-linear least squares regression with D as avariable. The diffusion coefficient calculated in this wayis dependent on the time interval ndt. For an interval of120 s, D = 0.93 ± 0.03 (xl(r1 3) cm2 s"1 falling to 0.61± 0.02 (xl0~13) cm2 s"1 for an interval of 600 s.

Influenza virus receptor mobilityFig. IB shows an example of the images obtained forRelabeled influenza virus bound to D532 fibroblasts.The activity of Ris-influenza virus was checked byhaemolysis and haemagglutination assays. The activityof the virus was unchanged after labeling with R18.

Tracking virus particles was more difficult thantracking LDL because the virus tended to detach fromthe cell during the course of the experiment, presum-ably due to the action of the viral neuraminidase. In oneexperiment, for example, 45% of the particles ident-ified in the first frame were lost over a period of 40 min.Fewer virus particles could thus be tracked for theduration of the experiment.

Although fewer tracks were available for analysis,the movement of viral particles appeared to havesimilar characteristics to those of LDL. Essentially allviral particles exhibited measurable mobility at 4°C.Fig. 3 shows examples of individual tracks and theiranalysis by equations (3)-(5), which correspond to thethree types of motion observed with LDL. Rather fewparticles can be assigned to flow, their velocities are ofthe order of 0.4-1 nm s~J. Diffusion coefficients are

Tracking cell surface receptors 421

15 T

100 2001 300 400 500 600

Fig. 4. Histograms showing the probability distributions P(ru+n)dr for 1, 3 and 5 time intervals; left side, LDL receptors;right side, virus particles (a cell showing uniformly low mobility was used for this analysis). The lines are best fits ofequation (8) and give D = 0.93 ± 0.02 (n = 1), 0.66 ± 0.02 (n = 3), 0.61 ± 0.02 (n = 5) for LDL particles; D = 1.07 ±0.02 (n = 1), 0.59 ± 0.02 (n = 3), 0.55 ± 0.03 (« = 5) for virus particles, units (xlO~13) cm2 s"1.

highly variable, ranging from 0.4 to 70 (xlO 13) cm2

s . Domain sizes appear to be somewhat larger (d =1.1-3.5 ^m) than those found for LDL.

Fig. 4 shows the model-independent representationof the observed viral particle movements for the cellillustrated in Fig. IB. As with LDL a quasi diffusioncoefficient was calculated by fitting the data in Fig. 4 toequation (8). For a time interval of 120 s, D = 1.07 ±0.02 (xlCT") cm2 s~l whilst for an interval of 600 s, D= 0.55 ± 0.03 (xlO~u) cm2 s . The similarity of thesevalues to those quoted for LDL is no doubt somewhatfortuitous in view of cell-to-cell variation. As with LDLthe dependence of D on the time interval is againindicative of non-random movements.

Discussion

In this study, we have been principally concerned withdeveloping methodology for tracking sub-microscopicparticles attached to receptors on cell surfaces. We hereconfine ourselves to presenting data obtained at 4CC.

This has the advantage of avoiding complications due toendocytosis, which is negligible at this temperature.Moreover, the mobility of receptors at 4°C is relevant toattempts to determine receptor distribution, a subjectthat has caused controversy in the case of LDLreceptors (Wofsy et al., 1985; Sanan et al., 1987; Sananet al., 1989; Robenek et al., 1991).

The data presented here demonstrate that the cooledslow-scan CCD camera provides an excellent imagingsystem for tracking particles containing a few tens offluorophores. Analysis of the intensities of individualfluorescent spots by a two-dimensional Gaussian distri-bution permits accurate determination of the particleposition to within ±25 nm. This in turn enables rathersmall displacements to be detected corresponding todiffusion coefficients as low as 3 x 10~14 cm2 s"1.

An alternative method for tracking receptors that hasconcurrently been developed is Nanovid microscopy(de Brabander et al., 1991; Geerts et al., 1991; Lee etal., 1991; Sheetz et al., 1989). In this technique ligandsare labeled with small gold particles, typically 40 nm indiameter, which can then be tracked by video-enhanced

422 C. M. Anderson and others

contrast microscopy. It is of value to have differenttechniques available, since each has its own distinctiveadvantages and disadvantages. Gold particles have theadvantage of being completely stable and images can becollected at video rates, thus providing large numbersof data points. On the other hand, currently usedprobes are multivalent with typically 5-30 ligands pergold particle. Thus it is possible that receptors will becross-linked, hence reducing the information obtainedfor single receptors. Fluorescent probes suffer fromphotobleaching, although, as shown here, this can beminimised with an imaging system of sufficiently highsensitivity. In the case of LDL, the fluorescent ligand isunivalent, thus permitting the study of individualreceptors, and the variation in the number of fluoro-phores per spot is useful for identification purposeswhen particles are present at high densities. In a widercontext, fluorescence microscopy is a versatile tech-nique in which a variety of phenomena such asquenching, polarisation and energy transfer can beobserved. There is thus considerable scope for thefurther development of fluorescence imaging tech-niques that will provide more detailed information onthe events occurring at the cell surface (Jovin and Vaz,1989).

We have employed two different particles in ourinitial studies of receptor mobility by fluorescenceimaging. As mentioned above, LDL has the advantageof being univalent and, moreover, binds to a well-defined receptor. Influenza virus on the other hand ismultivalent and binds to heterogeneous sialic acid-containing receptors, which probably comprise bothglycoproteins and glycolipids. Because of these differ-ences it is of interest to compare the mobilities of thetwo types of particle on the cell surface.

Data analysisIn analyses of FRAP measurements of lateral diffusionit is normally assumed that receptors are eitherdiffusing randomly or are immobile. An importantadvantage of direct observation of tracks of individualparticles is that deviations from random diffusion canbe detected. In the present experiments, analysis ofindividual particle tracks indicates that some particlesundergo directed motion whilst others are restricted tomove within a domain.

The presence of different types of motion on thesame cell poses considerable problems of analysis.Ideally, particles should be divided into sub-popu-lations according to whether they undergo randomdiffusion, directed motion or diffusion within a domain.We have attempted to make such a division on the basisof chi-squared for the best fits of the data by equationsthat describe the mean displacement with time for thedifferent types of motion. We assign a particle torandom diffusion unless chi-squared is improved by atleast 20% by assuming an alternative type of motion.We recognise that the cut-off of 20% is arbitrary andthat the motion of an individual particle may combinedifferent types of motion. Nevertheless, we suggest thatsuch a subdivision can provide a useful basis for

comparing data obtained with cells under variousconditions. It also enables more meaningful determi-nation of motional parameters to be made than if theparticle population is treated as a whole.

It should be noted that the distinction betweenrandom diffusion and diffusion within a domaindepends upon relative values of diffusion coefficient,size of domain and duration of observation. It could bethat particles assigned to random diffusion are in factconstrained to a larger domain whose limits are notrevealed within the time of observation. It should alsobe emphasized that random diffusion is not synony-mous with free diffusion. The very low diffusioncoefficients of randomly diffusing particles indicate thatalthough their direction of motion is random, their rateof displacement is nevertheless highly constrained.

Segregating particles according to their type ofmotion is an important step towards determiningmolecular interactions that occur at the cell surface.Such an approach is, however, inevitably model-dependent. It is therefore valuable to have a model-independent way of evaluating the experimental data.In Fig. 4 the measured probability distributions forparticle displacement in a given time are plotted. Theserepresentations involve no assumptions about the typeof motion or the continuity of motion of individualparticles. For a homogeneous population of randomlydiffusing particles, the distribution function would begiven by equation (8). Fitting the data by this equationis a means of extracting a quasi diffusion coefficientfrom the data for comparison with FRAP and othermethods that yield an average diffusion coefficient. Thisapproach further provides an important confirmation ofthe non-random nature of receptor motion. Thedecrease in quasi diffusion coefficient with the timeinterval over which the distribution function ismeasured is expected if significant numbers of particlesare restricted to a domain. Although directed motion isexpected to have the opposite effect, its perturbation ofthe distribution function is small for the time intervalsemployed.

Functional processes occurring on cell surfaces, suchas capture by coated pits, depend on how far a particlemoves in a given time. Distribution functions such asthose in Fig. 4 may provide a useful basis for calculatingthe rates at which such processes occur withoutassuming any particular type of motion to be present.These representations will also be useful when com-paring receptor mobility measured under differentconditions.

Discussion of resultsA significant population of LDL particles appears toundergo directed motion as illustrated in Figs 2 and 3.This cannot be due to movement of the whole cell, asother particles move randomly. The simplest expla-nation of directed motion is that the receptors areattached either directly or indirectly to moving cyto-skeletal elements. This possibility, together with thealternative possibility that receptors are carried alongby lipid flow, has been much discussed in relation to cell

Tracking cell surface receptors 423

locomotion (Abercrombie et al., 1970; Bretscher, 1976;Bretscher, 1984; Bretscher, 1991; Heath, 1983; Holi-field et al., 1990; Lee et al., 1990; Sheetz et al., 1989). Inour experiments, cells are not visibly motile and thusthe data do not directly bear on the mechanism of celllocomotion. Nevertheless, it is noteworthy that thedirection of motion (Fig. 2) is generally away from theedge of the cell towards the nucleus, as has long beenobserved for large particles (Abercrombie et al., 1970),and recently for colloidal gold particles (de Brabanderet al., 1991; Sheetz et al., 1989), in motile cells. It is thuspossible that the very slow directed motion that weobserve at 4°C is a vestige of the much larger-amplitudeevents that occur in motile cells. As it seems unlikelythat lipid flow could be generated at 4°C by membraneinternalisation/recycling, our data tend to support otherrecent reports that favour coupling of receptors tocortical cytoskeletal flow (de Brabander et al., 1991;Lee et al., 1990; Sheetz et al., 1989).

Plots of {rf,) against time for individual LDL andinfluenza virus particles and the time-dependent distri-bution functions in Fig. 4 strongly suggest that manyparticles may be constrained to move within a domainof limited size. At 4°C it is conceivable that domains areformed by lipid phase segregations. However, evidencefor domains at higher temperature has also beenobtained from measurements with colloidal gold par-ticles (de Brabander et al., 1991) and from FRAPmeasurements in which the size of the bleached spotwas varied (Yechiel and Edidin, 1987). In a recentexperiment, Edidin and Stroynowski (1991) showedthat class I MHC molecules appear to be constrainedwithin domains when anchored in the membrane by atransmembrane polypeptide but not when anchored bya glyocolipid. This result strongly suggests the involve-ment of cytoskeletal elements in domain formation.

It has long been clear from FRAP measurementsthat, with few exceptions, proteins in cell membranesdo not undergo unrestricted random diffusion in thelipid bilayer. Our present experiments also do notdetect any motion of LDL or influenza virus receptorsat rates expected for free diffusion. However, furtherexperiments at higher time resolution and lowerparticle densities would be required to be sure that noreceptors at all undergo free diffusion. A differentquestion is whether any receptors undergo randomdiffusion (i.e. their displacements obey equation (3))but with low diffusion coefficients. According to ouranalysis, about one third of the LDL and virus particlesexhibit displacements that are indistinguishable fromsuch a motion. Diffusion may be reduced by proteincrowding and/or by the presence of barriers such ascytoskeletal elements (Eisinger et al., 1986; Abney etal., 1989; Saxton, 1989a,b). The percolation model ofSaxton (1989a,b) is attractive in that it predicts both areduced diffusion coefficient and, at sufficiently highconcentration of barriers, domains formed from perco-lation clusters. Above the percolation threshold, thediffusion coefficient is expected to decrease withincreasing time interval of measurement, as found inthe present experiments.

Barak and Webb (1982) have measured LDL mo-bility by FRAP on JD fibroblasts in which a mutation inthe LDL receptor prevents binding to coated pits. At10°C they found that at least 80% of receptors wereimmobile (D < 0.25-1 (xl0~n) cm"2 s"1). Themotions of individual LDL particles that we detect at4°C are such that they would appear immobile in theFRAP measurement. Aroeti and Henis (1986) haveperformed FRAP measurements on a variety of cellswith bound Sendai virus, which is similar to influenzavirus and also binds to sialic acid receptors. They foundunder all conditions that the virus was immobile (D < 5x 10~12 cm2 s"1). Again, the low mobilities of virusparticles that we observe are quite compatible with theFRAP measurements. These results underline the factthat the tracking method is able to measure much lowermobilities than the FRAP technique.

The present finding that receptors have a small butmeasurable mobility at temperatures as low as 4°C isrelevant to studies aimed at determining receptordistributions. In the case of LDL receptors, there isdisagreement concerning the distribution of newlyinserted receptors in the plasma membrane of culturedfibroblasts (Robenek et al., 1991; Robenek and Hesz,1983; Sanan et al., 1987; Sanan et al., 1989; Wofsy et al.,1985). The point at issue is whether newly inserted LDLreceptors are dispersed in the membrane prior toentrapment in coated pits or whether they are insertedand remain as pre-existing clusters. Experiments todetermine LDL receptor distribution involve incu-bation of cells with LDL at 4°C and fixation proceduresthat may extend over one to two hours, prior to electronmicroscopy. Our experiments show that the receptorscannot be regarded as completely immobile and manywill move distances of 0.5-1 fim in this time. This iscomparable to the average distance between clusters(or coated pits). Thus it cannot be safely assumed eitherthat no clustering of dispersed receptors or that nodispersal of clustered receptors has occurred during thepreparation of the samples for electron microscopy.Differences in procedure may possibly account for thedifferent results obtained by different groups.

In the case of LDL, 60-70% of receptors are believedto be located in coated pits at 4°C (Anderson et al.,1978; Carpentier et al., 1979). On this basis, our datawould suggest that even those receptors in coated pitshave detectable mobility, presumably reflecting mo-bility of the coated pit itself. Receptors could also beentrapped in flat clathrin lattices as described fortransferrin receptors by Miller et al. (1991). Inprinciple, receptors clustered in coated pits can bedetected on the basis of their higher spot intensities(Gross and Webb, 1986). We do indeed find that thereis some correlation between spot intensity and mobility.The weakest spots have the largest range of mobilitieswhilst the most intense spots tend to have only very lowmobility. This correlation is only observed if the particlepopulation is analysed for the different types of motionand is not apparent if it is assumed that all particles areundergoing random diffusion. This emphasises theimportance of subdividing the particle population when

424 C. M. Anderson and others

analysing the data. Influenza virus is expected to bind toa heterogeneous population of receptors, which includeglycolipids (Marsh, 1984). It is therefore not surprisingthat the mobility is more variable than for LDL. Ascoated pits occupy only about 2% of the cell surfacearea (Goldstein et al., 1981), it is probable that only avery small fraction of the virus particles is bound toreceptors in coated pits.

In conclusion, the present studies reveal low butcomplex mobilities of both LDL and influenza virusreceptors on the surface of dermal fibroblasts at 4°C.Both directed motion and motion restricted to a domainare present. A number of recent investigations withvarious cells and receptors at higher temperature arealso indicative of such motions (de Brabander et al.,1991; Edidin and Stroynowski, 1991; Sheetz et al.,1989), suggesting that the phenomena are rathergeneral. The details of receptor movement haveimportant implications for any biological process thatinvolves dynamic interactions in the cell surfacemembrane. Further development of the imaging tech-niques described here promises to make a significantcontribution to the quantitative understanding of suchprocesses.

We are grateful to the Wellcome Trust and the SERC forfinancial support.

Appendix

Consider a particle that is constrained to move within acircular domain of diameter d. At sufficiently long timeintervals, the initial and final positions of the particlewill be completely randomized within the domain. Letthe initial and final polar coordinates of the particle be(ri,a) and (r2,a+ff), where rur2 < d/2. Then thedisplacement of the particle, r, is given by:

r2 = r\ + r\ — 2r\

Thus

J dfl Cdfl Cln .

o Jo JoCdfl Cdfl C2n

Jo Jo Jo= d2/6.

Hence in a tracking experiment, the relation betweendomain diameter and the maximum mean displacementof the particle is:

d2 = 6rl^.

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{Received 24 September 1991 - Accepted 12 November 1991)