-
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
[email protected] 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
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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
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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
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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
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Volume 73 November 1997
mum deviation from the true h value was
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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
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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.
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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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