Biophysical Journal Volume 73 November 1997 2836-2847

Mapping Fluorophore Distributions in Three Dimensions by QuantitativeMultiple Angle-Total Internal Reflection Fluorescence Microscopy

Bence P. Olveczky, N. Periasamy, and A. S. VerkmanDepartments of Medicine and Physiology, Cardiovascular Research Institute, University of California,San Francisco, California 94143 USA

ABSTRACT The decay of evanescent field intensity beyond a dielectric interface depends upon beam incident angle,enabling the 3-d distribution of fluorophores to be deduced from total internal reflection fluorescence microscopy (TIRFM)images obtained at multiple incident angles. Instrumentation was constructed for computer-automated multiple angle-TIRFM(MA-TIRFM) using a right angle F2 glass prism (nr 1.632) to create the dielectric interface. A laser beam (488 nm) wasattenuated by an acoustooptic modulator and directed onto a specified spot on the prism surface. Beam incident angle wasset using three microstepper motors controlling two rotatable mirrors and a rotatable optical flat. TIRFM images wereacquired by a cooled CCD camera in -0.5 degree steps for >15 incident angles starting from the critical angle. For cellstudies, cells were grown directly on the glass prisms (without refractive index-matching fluid) and positioned in the opticalpath. Images of the samples were acquired at multiple angles, and corrected for angle-dependent evanescent field intensityusing "reference" images acquired with a fluorophore solution replacing the sample. A theory was developed to computefluorophore z-distribution by inverse Laplace transform of angle-resolved intensity functions. The theory included analysis ofmultiple layers of different refractive index for cell studies, and the anisotropic emission from fluorophores near a dielectricinterface. Instrument performance was validated by mapping the thickness of a film of dihexyloxacarbocyanine in DMSO/water (nr 1.463) between the F2 glass prism and a plano-convex silica lens (458 mm radius, nr 1.463); the MA-TIRFM mapaccurately reproduced the lens spherical surface. MA-TIRFM was used to compare with nanometerz-resolution the geometryof cell-substrate contact for BCECF-labeled 3T3 fibroblasts versus MDCK epithelial cells. These studies establish MA-TIRFMfor measurement of submicroscopic distances between fluorescent probes and cell membranes.

INTRODUCTIONTotal internal reflection (TIR) is used extensively in fiber-optics and biosensors. Light incident on a dielectric inter-face (from a higher to a lower refractive index medium) ata supercritical angle (defined by Snell's law) is totallyreflected back into the higher refractive index medium. Anexponentially decaying evanescent field is created in thelower refractive index medium. The exponential decay con-stant of the evanescent field intensity is typically 25-400nm and depends on media refractive indices, laser illumi-nation angle, and wavelength. Energy can be deposited inthe evanescent field if absorbing chromophores are present.The absorbed energy can be dissipated nonradiatively, or ifthe chromophore has non-zero quantum yield, by fluores-cence emission.The ability to excite fluorescent probes very near a di-

electric interface has been exploited in several biologicalapplications. Binding affinities of soluble fluorescent li-gands to surface-immobilized receptors are readily mea-sured by steady-state TIR fluorescence intensities (Thomp-son et al., 1997). Ligand binding rates are measured fromthe recovery of TIR fluorescence after irreversible photo-

Received for publication 27 May 1997 and in final form 30 July 1997.Address requests for reprints to Dr. Alan S. Verkman, CardiovascularResearch Institute, 1246 Health Sciences East Tower, Box 0521, Univer-sity of California, San Francisco, San Francisco, CA 94143-0521. Tel.:(415) 476-8530; Fax: (415) 665-3847; E-mail verkman@itsa.ucsf.edu.C 1997 by the Biophysical Society0006-3495/97/11/2836/12 $2.00

bleaching of bound ligands (Stout and Axelrod, 1994; Hsiehand Thompson, 1994; 1995). TIR fluorescence has alsobeen used to qualitatively map the surface topography ofcell-substrate contacts by the selective excitation of cell-associated fluorophores near a transparent substrate support(Axelrod, 1981; Axelrod et al., 1984; Lanni et al., 1985;Gingell et al., 1985; Reichert and Truskey, 1990). Ourlaboratory has utilized TIR fluorescence to measure relativecell volume from the dilution of soluble fluorescent probesin the cytoplasm (Farinas et al., 1995), and to quantify theviscosity of cell cytoplasm near the plasma membrane bymeasurement of time-resolved anisotropy (Bicknese et al.,1993) and photobleaching recovery (Swaminathan et al.,1996) of aqueous-phase fluorophores.

It has been recognized for many years that the depen-dence of the decay of evanescent field intensity on laserillumination angle can provide quantitative informationabout distances between fluorophores and a dielectric inter-face (Reichert et al., 1987; Hellen and Axelrod, 1987;Rondalez et al., 1987; Suci and Reichert, 1988; Burmeisteret al., 1994). As described in the Theory section, the z-axisdistribution of fluorophores can be recovered by inverseLaplace transform of fluorescence intensities measured atmultiple laser illumination angles. Fluorescence image ac-quisition can thus provide information about fluorophorez-distribution with a resolution of tens of nanometers, andx,y-distance information with resolution of under one mi-cron. Multiple-angle TIR has the potential to measure sub-microscopic distances in living cells that cannot be mea-

2836

Distance Measurement by Multiple Angle TIRF

sured by existing techniques. Possible applications includequantitative 3-d mapping of cell-substrate contact geometry,measurement of submicroscopic distances between cellmembranes and the underlying spectrin and actin skeletons,and kinetic analysis of vesicular endo and exocytosis events.The purpose of this study was to develop and evaluate the

theory, instrumentation, and practical experimental strate-gies to apply Multiple Angle-Total Internal Reflection Flu-orescence Microscopy (MA-TIRFM) for measurement ofsubmicroscopic distances in living cells. Instrumentationwas constructed to direct a narrow laser beam onto a cellsample at a series of precise angles and to collect high-magnification fluorescence images. The theory and imageanalysis routines were developed to compute 3-d fluoro-phore distribution maps from the image sets. The methodwas validated using a known fluorophore distribution, andapplied to quantify cell-substrate contact geometry in fibro-blasts and epithelial cells.

THEORYDistance determination by MA-TIRFMThe evanescent field established by TIR illumination at adielectric interface penetrates into the medium of lowerrefractive index and excites fluorophores near the interface.The evanescent field intensity, I(z), decays exponentiallywith distance z from the interface:

I(z) = 1(0) exp(-z/d) (1)where I(0) is the intensity at the interface. The exponentialdepth decay constant, d, is:

d = (AJ4 7r)(n2sin 20 - n"2)-12 (2)where n1 and n2 are the refractive indices of the high andlow refractive index media, respectively; A is the wave-length of incident light in vacuum, and 0 is the incidentangle. I(0) depends on incident angle and polarization of theincident light. For s-polarized light (used in our experi-ments), I(0) = 1A1I2COS 20/(1 - n2/n2) (Axelrod et al., 1984),where AS depends on beam intensity.The strategy to measure 3-d fluorophore distributions

using MA-TIRFM is to exploit the dependence of the decayconstant, d, on incident angle 0. If Dx y(z) is the z-distribu-tion of fluorophores (at each x,y position in the sampleplane), then the measured fluorescence intensity (at a givenx,y pixel in the image), FXy(0), is:

Fx,y(0) = IY(O, 0) Dx y(z) exp[-z/d(0)]dz (3)0

where Ix y(z = 0, 0) is the intensity of the evanescent fieldat the interface. It is noted that the expression for FX y(0)formally defines the Laplace transform of Dx y(z). Our strat-egy is to eliminate the angle-dependent factor Ix Y(O 0) bymeasuring the fluorescence, pef(0), of a known fluorophore

distribution for each incident angle. A practical choice forthe reference distribution has proven to be a uniformlydistributed fluorophore in solution, producing a fluores-cence intensity:

0Xe'(0) = Ix,y(O, 0)crefd(0) (4)where cref depends on reference fluorophore concentration,molar absorbance, and quantum efficiency. Quantitativeangle-resolved determination of:

Gxy(p) = Fx,y(0) d(0)/Fre(0) (5)where p = l/d(0), thus formally permits the recovery of theDX,y(z) distribution by inverse Laplace transform of Gx y(p).

For the measurements reported in this study, the func-tional forms of Dxly(z) are known, permitting the angle-resolved intensity distribution Gx,y(p) to be fitted directly toan analytic expression for the Laplace transform. In the caseof a top-hat function where the uniform fluorophore layerextends from z = 0 to z = h [Dx,y(z) = csaple for z < hx'yand Dxy(z) = 0 for z > hx'y where csample is related tosample fluorophore concentration, molar absorbance andquantum yield], the analytical expression for the Laplacetransform of DX,Y(z) is:

Gxl,(p) = k[(l/p) - (1/p)exp(-phxy,)] (6)where k is a global constant (identical for all pixels) equal tocsample/cref. If the same fluorophore at identical concentra-tion is used for sample and reference, then k = 1. For a deltafunction [DX Y = csa,pleS(z - hy)] which would apply toa fluorophore-labeled cell membrane:

Gx,y(p) = k[exp(-phx,y)] (7)For a shifted step function [D, Y(z) = 0 for z < hx y andDx,Y(z) = Csamp1e for z > hxy], which would apply touniform staining of cell cytoplasm:

Gx,y(p) = k(llp) exp(-phxy) (8)For Eqs. 6-8, the parameters [k and hx y] or hx y alone, arededuced by nonlinear least-squares regression of experi-mentally measured GX Y(p) (see below).

The multi-layer problem for measurementsin cellsIn MA-TIRFM measurements of living cells, the dielectricinterface may not be a simple interface between a substrate(e.g., glass prism) and a homogeneous aqueous medium asmodeled above. MA-TIRFM measurements on cells thusrequire consideration of multiple layers- extracellular fluidbetween the substrate and cell membrane, the membrane,and the cytosol- each having different dielectric properties.The decay of evanescent field intensity is no longer mono-exponential. According to Gingell et al. (1987), the expres-sion for I(z) (which replaces Eq. 1) relevant for cell studies

Olveczky et al. 2837

Volume 73 November 1997

in which fluorophore is dissolved in cytoplasm is:

I(z) = 4KI2vB1332exp[-2134(z- t2)]/(ia2 + f3Pa2) (9)where

_Y1 = nikO-kz, 232 = k-zn2k; 3 = k-n 2(3okZ- n4kO, a3 = 13(/4 sinh /32tl + 12 cosh 32t)cosh 81 +(32(4cosh 32tl 32 sii 2t1) sinh , a4 = (3(14 cosh32tl + /32 sinh 32tl) cosh 81 + (/2/4 sinh 2t1 + 32 cosh(32tl) sinhl l, 81 = 33(t2 - tl), ko = 2ni/A, and k, = n1kosin0. Here, t1 is the thickness of the extracellular fluid layer(between prism and cell membrane), t2 - t1 is the mem-brane thickness, n1 is the refractive index of the glass prism(1.632), n2 is the refractive index of the extracellular fluid(1.337), n3 is the refractive index of the cell membrane(1.44), and n4 is the refractive index of the cell cytoplasm(1.37). It is assumed that the depth of cytoplasm is muchgreater than the evanescent field decay depth. This assump-tion may not be valid at the very periphery of the cell forangles very close to the critical angle. For this reason, onlyangles of >1 beyond the critical angle were utilized for thecell studies below, generally corresponding to a decay con-stant of

Distance Measurement by Multiple Angle TIRF

FIGURE 1 Schematic of MA-TIRFM instrument. The beam from acontinuous-wave argon ion laser wasdirected onto a spot on the prism sur-face. Beam incident angle was se-lected by setting the angles of tworotatable mirrors and a rotatable opti-cal flat. Emitted TIR fluorescencewas imaged by a cooled CCD camera.See text for details. Inset. Device forculturing mammalian cells on the F2glass prism. Culture medium contain-ing cells was contained in a cylinderin contact with the prism surface.Tight contact was made using an 0-ring and rubber band. The prism washeld vertically in a Teflon stand.

photodiode

Incident angles for TIR illumination were selected usingtwo rotatable mirrors and an optical flat. The angular ori-entation of the round mirror (diameter 15 mm, >99% re-flectivity at 488 nm, New Focus, CA), the rectangularmirror (20 X 100 mm), and the optical flat (thickness 1 mm)were controlled by three microstepper motors. The motorswere driven separately by three 5-phase stepping motordrivers (model UPS502; Nyden Corporation San Jose, CA),and software controlled using a multi-axis motion controller(model MAC-300; Nyden Corporation, San Jose, CA). Theangles of the mirrors defined the beam incident angle anddirection, and the optical flat controlled out-of-plane beamdeviation, compensating for imperfect mirror flatness andaxial alignment. In addition, two glass plates (thickness 500,um) mounted on continuously rotating (300 rpm) motors(model 1219M; Minimotor, Switzerland), with perpendicu-lar axes of rotation, were positioned in the laser beam toimprove beam uniformity by averaging speckle and diffrac-tion effects. The beam was directed to the vertical surface ofa right angle 2 X 2-cm F2 glass prism (nr 1.632 at 488 nm,polish 5/10 surface quality; Custom Optical Elements, LasVegas, NV) held in a prism-holder mounted on a 3-dmicromanipulator. The high grade of surface polish wasnecessary to minimize scattered (non-TIR) light escapinginto the sample. The prism was used to create the TIRinterface and also functioned as substrate for cells. Toprevent secondary reflections of the laser beam inside theprism from transilluminating the sample, a polished F2glass rod (diameter 2 cm, length 8 cm, Mindrum Precision,Rancho Cucamonga, CA) was coupled to the hypotenusesurface of the prism with a refractive index-matched laserliquid (Liquid code 5763; Cargille Laboratories, NJ) (lighttrap, Fig. 1). A black rubber bag filled with the laser liquidwas tied to the distal end of the glass rod to absorb the light.For the calibration (see below), a plano-convex fused silicalens (radius 458 mm) was mounted on a 3-d micromanip-ulator and positioned above the glass prism to make pointcontact with the prism near the optical axis of the microscope.

The objective used for the calibration was a 25X longworking distance lens (Leitz Wetzlar, Germany; dry, N.A.0.35) and for the cell experiments a 100X water immersionlens (Leitz; N.A. 1.2). Emitted fluorescence was filtered bya 515-nm long-pass filter (Schott) and imaged by a 512 X512 pixel, cooled CCD camera (model CH 250; Photomet-rics, Tuscon, AZ) with a 14-bit analog processor.To generate specified beam incident angles (generally

>15 angles), the angular positions of the two mirrors andthe optical flat were established before each set of experi-ments and stored as a look-up table. The look-up table wasaccessed for subsequent acquisitions of sample and refer-ence images. Incident angles corresponding to each set ofmirror angles were measured from the position of the exci-tation beam reflection (observed on a strip of white tape onthe dark room ceiling) off of the vertical surface of theprism. Incident angles were computed from the location ofthe reflected spot and Snell's law (to account for refractionin the prism). The prism was positioned in the prism-holderso that the laser beam reflection on the ceiling was insen-sitive to vertical displacement of the prism, ensuring align-ment of the prism surfaces. The optical components wererigidly mounted on a Technical Instruments custom micro-scope stand positioned on a floating optical table (1-2000Stabilizer, Newport) in a dark, temperature-controlled anddust-free room.

Software was written in Microsoft C and executed on aGateway 2000 PC, equipped with analog and digital I/Oboard (CIO-DAS08-AOH, Computerboards, Mansfield,MA) to measure photodiode signal and set AOM input. Thesoftware controlled and coordinated the positioning of themicrostepper motors with the photodiode signal, AOM an-alog output, and image acquisition.

Image analysisThe experimental procedure described below generated im-ages for the reference and sample distributions at each beam

Olveczky et al. 2839

Volume 73 November 1997

incident angle. In order to exclude "bad" pixels, the imageswere filtered prior to analysis using a pseudo-median filterwith length three as defined by Pratt (1991). The angle-resolved intensity distribution for each pixel, Gij(p), wasobtained from the ratio of sample, Fij(O), and reference,F'ijf(O), images multiplied by the decay constant d(O) (Eq.5). The angle-resolved intensity distribution, Gij(p), wascurve-fitted to an analytic expression for the Laplace trans-form of the anticipated fluorophore distribution (Eqs. 6- 8).Parameter(s) defining the fluorophore distribution were fit-ted using the Levenberg-Marquardt algorithm (Press et al.,1992). The fitted distance hxy was corrected for multiplesample refractive index layers (for cell studies) and nonuni-form collection efficiency as described in the Theory sec-tion. The analysis produced a 3-d map of the fluorophoredistribution.

METHODSCell culture and fluorophore loadingMDCK-1 cells (ATCC CCL no. 34; American Type Culture Collection,Rockville, MD) and Swiss 3T3 fibroblasts were cultured directly on the F2glass prisms in DME-H21 medium supplemented with 10% fetal calfserum, 100 U/ml penicillin, and 100 mU/ml streptomycin. Cells weremaintained at 37C in a 95% air:5% CO2 atmosphere. A prism support forcell culture was constructed in which cells were grown directly onto theprism without the need for refractive index-matched coupling fluid (Fig. 1,inset). A polysulphone cylinder (radius 2 cm, height 1 cm) with anembedded soft 0-ring (making contact with the prism) was secured on topof the prism with a rubber band to provide a well for the culture medium.Cells were used 18-20 h after plating and were labeled with 10 /iMBCECF-AM (Molecular Probes Inc, Junction City, OR) in PBS. Thereference fluorophore (FITC-dextran, Molecular Probes Inc, Junction City,OR) was dissolved in the same solution. After use, prisms were washedserially in ethanol, alkali, and acid, rinsed extensively with distilled water,and stored immersed in ethanol.

Experimental protocolThe prism containing cultured cells was aligned and secured rigidly in theprism-holder by a Teflon screw. The positions of the three microsteppermotors for the incident angles were then established as described above.Generally the angles were incremented by -0.5 degrees, starting from thecritical angle. Image acquisition time was set to avoid saturation whilemaximizing the dynamic range of the pixels. Images of the sample werethen acquired in succession at each of the specified laser incident angles.The cells were carefully washed off the prism surface using STV (0.25%Trypsin and 0.2% Versene in saline; UCSF Cell Culture Facility) andwater, and were replaced by a uniform film of dissolved fluorescent dye.The excitation beam was attenuated by the AOM for the brighter referencesample. Laser intensity was recorded just before and after each imageacquisition and the average was taken to represent the intensity during theexposure. The complete experimental procedure took -15 min, with -2min for multiple-angle image acquisition of the cell sample. A repeat imageat the initial angle was recorded after the multi-angle image acquisition toevaluate photobleaching.

convex lens (radius 458 mm) onto a layer of dissolved fluorophore until thecurved surface of the lens made point contact with the horizontal surface ofthe right-angle prism near the center of the field of view (Fig. 2). Afluorescent dye [di-O-C6-(3); Molecular Probes Inc., Junction City, OR] ina DMSO/water mixture was refractive index-matched to the fused silicalens (nr 1.463 at 488 mm) by immersing the lens in a bath of DMSO whileilluminating the prism with the laser beam through the bath. Water wasadded until the direction of the laser beam exiting the bath was insensitiveto movement of the lens. Images were acquired using the 25 x dry objec-tive. Reference images were acquired after elevating the lens -1000 nmabove the prism surface.

RESULTSTheoretical simulationsPredicted angle-resolved intensity functions G(p) (Eq. 5)were computed for three fluorophore profiles, D(z), of sig-nificance for biological measurements: delta function (Fig.3 A), top-hat function (Fig. 3 B), and step function (Fig. 3C). The simulations showed a strong dependence of abso-lute G(p) values and the G(p) curve shape on distanceparameter h. It is this dependence that is exploited to de-termine fluorophore-interface distance from fluorescenceintensities measured at multiple incident angles.The influence of experimental noise on the accuracy of

parameter recovery from G(p) data was evaluated. Fig. 3 Dshows fitted curves to G(p) (for a top-hat function with 14incident angles) with random noise (average noise-to-signalamplitude 30%) added to each point. Fitted curves areshown for a two-parameter fit (fitting k and h, see Eq. 6),and a one-parameter fit (fitting h only). The recoveredvalues for h were excellent (100 and 97 nm for 1- and2-parameter fits, respectively). Simulations at different h(25-250 nm) and noise levels (up to 50%) indicated recov-ery of h values to generally better than 4% accuracy with the1-parameter fit and 15% accuracy for the 2-parameter fit.Similar results were obtained for simulations using theshifted step function and the delta function. These simula-tion provide justification for the determination of fluoro-

objective elevatesilica lens

>0fused silica lens

n=1.463_

prismn=1.632 I

di-O-C6-(3)in DMSO/H20

n=1.463sample

Distance calibration using a knownfluorophore distributionTo validate the accuracy of distance determination by MA-TIRFM, aknown 3-d fluorophore distribution was established by lowering a plano-

FIGURE 2 Evaluation of MA-TIRFM instrument performance using aknown fluorophore distribution. A spherical film of di-O-C6-(3) in DMSO/water was created by making point contact between a fused silica plano-convex lens and the F2 glass prism (left). A uniform "reference" fluoro-phore distribution was created by raising the silica lens by - 1 ,um (right).

2840 Biophysical Joumal

Distance Measurement by Multiple Angle TIRF

A incident angle64 66 6870 74 8090

4=50 nm D(z)"

3 100 h zG(p)

2 2001 40

800.0 2 4 6 8 1012141618 20

p [im-1]

B8(

64

4'

21

incident angle64 66 68 70 74 8090

AO00D(z)I

h=800 nm h z

00 40 100 5

0 2 4 6 8 1012 1416 18 20p [Im-11

C incident angle000 64 66 68 70 74 80908000800 i D(z)

600 h=800 nm h z400

400 I 200100

200 50

00 2 4 6 8 101214161820p [Im 1l

D incident angle64 66 68 70 74 8090

90l ..-

80

70

60

50

o \0

\

40'0 2 4 6 8 1012 1416 18 20p [I'm-']

FIGURE 3 Predicted G(p) curve shapes and theoretical accuracy of parameter recovery. (A-C) Angle resolved intensity distributions, G(p), for indicatedfluorophore profiles. (A) Delta function, D(z) = c5(z - h). (B) Top-hat function, D(z) = c for 0 < z < h and 0 for z > h. (C) Step function, D(z) = 0for z < h and c for z > h. Parameters for (A-C): n, = 1.632, n2 = 1.463, A = 488 nm. (D) Recovery of parameter h from simulated experimental datacontaining random noise. G(p) values were simulated at 14 incident angles for a top-hat function with h = 100 nm. Random noise (30%) was added toeach point. G(p) vs. p data were fitted to the inverse Laplace transform of a top-hat function (Eq. 6). Fitted curves for a 1-parameter fit (dashed curve, h =100 nm) and 2-parameter fit (solid curve, h = 97) are shown.

phore-interface distances from experimentally derived G(p)ratios.The recovery of distances in the presence of multiple

layers of different refractive indices in the evanescent field(as in cell experiments) was evaluated. G(p) was computedfrom Eqs. 5 and 9 for a multi-layer configuration consistingof an F2 glass prism (nr 1.632), a layer of aqueous buffer (nr1.337) of variable thickness, a 4-nm thick membrane (nr

1.44), and cytoplasm containing fluorophore (nr 1.37). Thepredicted G(p) (circles in Fig. 4 A) were fitted to the inverseLaplace transform of a top-hat function (as in Fig. 3 D)assuming a uniform refractive index of 1.37. The G(p) datawere very well fitted even though the refractive index in theevanescent field is not uniform in this multi-layer simula-tion. Fig. 4 B shows a correction plot of actual versusrecovered h for a shifted step function distribution. Maxi-

A 62 64 67 71 76 90

30 qX incident angle

G(p) 20-

10

10 12 14 16 18 20 22p (gm-1)

D

12 14 16 18 20 22p (m-,)

BE-

a

500 line of _ __400 identity ,

300

200 /

100 /00 100 200 300 400 500

real h-value (nm)

E 64 66 6870 74 809080

incident angle70

G(p)60

50

402 4 6 8 101214 1618 20

p (grm-)

C

Q(z)

0.6 N.A.=1.3370.50.40.3 ~~~~1.20.3 / ~

0.2 .0

0.10 .0 100 200 300 400 500distance from interface, z (nm)

F500 calibration .y

SE 400am

Volume 73 November 1997

mum deviation from the true h value was

Distance Measurement by Multiple Angle TIRF

binations (e.g., FITC-dextran, glycerol/water) for minimalA _00 E i surface adsorption. Additional precautions included exten-

sive cleaning of the prism and lens surfaces before use, andrapid data acquisition after applying the fluid layer.

Measurement of cell-substrate contact geometryThe topology of cell-substrate contact was measured forSwiss 3T3 fibroblasts and MDCK epithelial cells stainedwith BCECF. Images were acquired at 17 incident angles.Computations were performed using a sample refractiveindex of 1.37, correcting for the multi-layer refractive indexdistribution using the plot in Fig. 4 B. Fig. 7 shows fluo-rescence intensity images of a 3T3 fibroblast (top) andMDCK cell (bottom) for three incident angles. Image inten-sities depended strongly on incident angle. The regions ofclosest cell contact with the substrate are preferentiallyilluminated as the evanescent field penetration depth de-

w D _30nm creases with increased incident angle. Cell images were30 ,um quite nonuniform for the 3T3 fibroblasts, indicating wide-

spread presence of close contacts (as defined by Izzard and30 gm

Lochner, 1976).30 p.m The angle resolved intensity distributions, G(p), were

fitted to the inverse Laplace transform of a shifted stepB function (Eq. 8), assuming uniform staining of cytoplasm.

160 Since different fluorophores were used in the sample andD(r) reference acquisitions, k was taken as a fitted global param-

140 r eter that is the same for all pixels. Fig. 8 A shows theE 120 / r /deduced 3-d cell contours at the cell-substrate interface and__ 120[ / / /Fig. 8 B shows a gray-scale contact map. Representative 1-d_ 100 plots of contact geometry along dashed lines in Fig. 8 B are

shown in Fig. 8 C. The data for 3T3 fibroblasts indicate the6 80 measured D(r) close contact regions to be between 20 and 45 nm from theCt 60 / / surface. These results are in very good agreement with15460 previous studies on fibroblasts using electron microscopy

40 actual lens and interference reflection microscopy (Abercrombie et al.,20 /profile

20

0 50 100 150 200 250 300 350distance from center, r [gLm]

FIGURE 6 3-d distribution of solution thickness from data set shown inFig. 4. (A) 3-d contour plot reconstruction of the fluid layer between the flatprism (bottom) and curved surface of plano-convex lens (top). (B) Solution incident 59.3 61.7 64.6thickness as a function of distance from lens-prism contact point, D(r), angledetermined by radial averaging of data from (A). Actual lens profiledetermined from manufacturers specification of 458 nm lens radius.

averaging of the 3-d distribution (Fig. 6 B), was in very U..good agreement with the known lens profile (458 nm radiusof curvature). The non-zero predicted z-distance at the cen- incident 61.5 65.7 72.5ter of the distribution was a consistent finding, and might be anglerelated to unavoidable adsorption of the fluorophore to the

FIGURE 7 Fluorescence intensity images of a Swiss 3T3 fibroblast (top)prism surface and/or to imperfect lens-prism contact. The and MDCK cell (bottom) at indicated laser incident angles. Cells werechoice of a cyanine fluorophore and DMSO/water solvent cultured directly on the F2 glass prism, cytoplasm was stained withwas made after testing a series of fluorophore/solvent com- BCECF, and cell were imaged as described in Methods. Bar = 5 ,um.

blveczky et al. 2843

Volume 73 November 1997

150 nm

10 sLmIi af

On

120 a

a)cnc1 20

120 [\ b

2vLW/\10 nm is readily achievable for bright fluorophores anddefined fluorophore geometries. A priori specification ofthe fluorophore distribution profile permits determination ofdistance parameters by nonlinear least-squares regression toan analytical form of the Laplace transform of the fluoro-phore distribution. It is noted that the z-resolution of MA-TIRFM can be improved by increasing the number of inci-dent angles used for the parameter regression; however,extended data acquisition times and photobleaching limitthe practicality of collecting data at >25 angles. Simula-tions indicated that the resolution can be improved, not onlyby increasing the number of angles, but also by optimizingthe sampled angles for the expected fluorophore distribution(Fig. 3, A-C). Our impression is that recovery of fluoro-phore distributions of arbitrary functional form by directinverse Laplace transform (e.g., by complex integrationusing the Heaviside expansion theorem; Boas, 1983) or bythe maximum entropy method (Livesey and Brockon,1987), is not practical at this time. An additional complexityin the recovery of an arbitrary distribution function wouldbe correction for nonuniform collection efficiency.

Notwithstanding these caveats, the MA-TIRFM approachhas a number of potential applications to biological prob-lems in living cells where existing methods cannot be ap-plied. The measurements here of cell-substrate contact con-firmed the results from previous studies (see Results) andprovided quantitative 3-d surface contact maps. The MA-TIRFM approach should be useful to measure skeleton-plasma membrane distances, such as the spatial distributionof the spectrin membrane skeleton in erythrocytes (Mc-Gough and Josephs, 1990; Winkelmann and Forget, 1993).TIRF has been applied recently to visualize agonist-inducedexocytosis of intracellular granules after labeling by fluo-rescent weak bases (Steyer and Almers, 1997; Oheim et al.,1997). MA-TIRFM should permit the quantitative determi-nation of membrane-granule distances, the correlation ofdistances with granule properties (such as pH and calcium),and the measurement of kinetics of granule movement toand fusion with the plasma membrane. Another potentialapplication of MA-TIRFM is analysis of cell locomotion,where the topological changes that occur as cells crawl

optical effects. Lanni et al. (1985) corrected the experimen-

Olveczky et al. 2845

could be quantified.

Volume 73 November 1997

APPENDIXThe theory developed by Hellen and Axelrod (1987) was adapted tocompute the distance-dependent collection efficiency, Q(z), introduced inEq. 10. The equations presented below apply to the case of a fluorophoredistribution with random dipole orientation, excited by s-polarized light.To avoid confusion it is noted that the symbol 0 is here used to denote theazimuthal angle, not the incident angle as previously.

The system under investigation consists of a single interface between anaqueous layer containing the fluorophore (refractive index n2) and a glassprism (nl). The plane of origin (z = 0) is taken to be the interface, and zis positive in medium 2. The location and orientation of a dipole is givenby r'(z, 4', 0'), where z is the distance from the interface, and theazimuthal angle 4)' and polar angle 0' define the orientation of the dipole.The observation point is specified by r(r, 0), where r, and arespherical coordinates. S(r,r') is the radiated emitted intensity from afixed-amplitude dipole oscillator at r' observed at r. As discussed in theTheory section, the fluorophore is modeled as a fixed power and variableamplitude dipole. The intensity S(r,r') is thus divided by the total powerdissipated by the fixed amplitude dipole, P7Ar'), resulting in the radiatedintensity per unit of absorbed power S(r,r') = S(r,r')/PAr'). The productof S and the excitation intensity, I,, (in the case of evanescent waveexcitation Ie4 is given by Eq. 1), gives the intensity radiated from a fixedpower dipole: I(r,r') = Iex(z) S(r,r'). For a fluorophore distribution, D(z),with random dipole orientation, the intensity observed at r is:

,(r) = k j I(r,r')D(z) sin 0'd4'dO'dz (Al)

where k is a proportionality constant. The total fluorescence collected by amicroscope objective, 9;, at a distance r, is the integral of J(r) over theobjective's aperture:

=(r)= r2 O(r) sin 0 do dO (A2)

where O,.. = arcsin(NAIn2) is the polar observation angle, and NA is thenumerical aperture of the objective.

Using the above equations, the collection efficiency Q(z), as defined inEq. 10, can be expressed in terms of single integrals. The equations tocalculate Q(z) for the special case here (single dielectric interface, s-polarized excitation light, observation through the aqueous medium) aregiven. For a rigorous derivation of the general expression for Q(z), seeHellen and Axelrod (1987).

Q(z) can be expressed as the weighted linear combination of thecollection efficiencies for dipoles oriented parallel, Q1(z), and perpendic-ular, Ql(z), to the interface:

Q(z) = [wI' Qll(z) + w-Q-(z)]I(w'1 + wl) (A3)where the weighting factors are:

f

ssn5i 'dO'W Sin2 0' + [r,(Z)]l1 COS2 0'(A4)

JT sin3 0' cos2 O'dOw cos2 0' + [71(z)] sin2 0'

and i(z) = TI4(z)/PT(z), where JIOTI(z) are the total powers dissipated byfixed-amplitude dipoles oriented parallel and perpendicular to the interface.

'(z) = [c,j241/4n'] Re f v(l -2)- 12

*{(1 + r'exp(i2k2z(1 - _,2)1/2)) + ((1 - v2) (A5)

(1 - r exp(i2k2z(l - v2) '2)) } dv]

PT(z) = [ctL2k/2/2n']ReJv[ (1 - ,2) -1/2(l + re exp(i2k2z(l v2)1/2)) dv

(A6)where c is the speed of light in vacuum, k2 = 2mn2/A, and j, is the dipolemoment. The integration variable, v, is the sine of the polar angle of theemitted light and goes from zero to infinity to account for the complexwavenumbers corresponding to the near field of the dipole. re and e are thereflection coefficients for p and s-polarized light respectively, and can beexpressed as a function of v:

(1- I-2)1/2 - E21(E12-p2)1/2=P(1 - j2)1/2 + E21(Eq2 - 2)1/2

(1- p2)1/2 - (E2_- 2)1/2(1-v2)g12 + (E12 - 1')1/2

(A7)

(A8)

where (E2 = (nl/n2)2, and E21 = (n2/n1)2. The parallel and perpendicularcollection efficiencies are:

('1

Q"'l(z) = 2irr2 (S)11 (z, 0) sin 0 dO0 (A9)where (S)11l are the 4)-averaged and normalized intensities radiated bydipoles parallel and perpendicular to the interface:

(S)I (z, 0) = cn2(IEPI2 + IEsI2)/16sn.4(z);

(S),(z, 0) = cn2lEzl2/8,wPT(z)(AIO)

where EP, ES, and EZ are electric fields produced by dipoles oriented alongthe directions p, s, and z at a distance z from the interface and observed ata point defined by r and O.p and s are parallel to the interface, withp beingparallel to and s perpendicular to the plane of observation. z is the along thez-axis. In the aqueous medium the electric field intensities are:

IEP12 = [pU2k/4r2]COS2 0 IexP(-i2k2z cos 0) -rI2 (A1)IEsl2 = [j52141n4r2] lexp(-i2k2z cos 0) + r 12 (A12)1Ez12 = [Ea2k42Ir4r2]Sin2 0 Iexp(-i2k2z cos 0) + $12 (A13)The collection efficiency, Q(z), was computed by numerical integration ofEqs. A4, A5, A6, and A9. For the improper integrals (A5 and A6), theextended midpoint rule was used, while the closed integrals were computedwith the extended trapezoidal rule. The program to compute Q(z) forspecified nl, n2, NA, and A was written in C and is available upon request.

2846 Biophysical Journal

Olveczkv et al. Distance Measurement by Multiple Angle TIRF 2847

The authors thank Catherine Chen for cell culture, Laszlo Bocskai in thephysiology machine shop for construction of the MA-TIRFM microscope,Dr. Daniel Axelrod for helpful advice on instrumentation and theory, andDr. Edward Hellen for valuable assistance in computations of nonuniformcollection efficiency.This work was supported by NIH Grants DK43840 and DK16095, andFogarty Collaborative Research Award TW00704.

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