general electromagnetic theory of total internal reflection … · 2005-08-25 · general...

General electromagnetic theory of total internal reflection fluorescence:

the quantitative basis for mapping cell-substratum topography

D. GINGELL1, 0. S. HEAVENS2 and J. S. MELLOR'1Department of Anatomy and Biology as applied to Medicine, The Middlesex Hospital Medical School, Cleveland Street, London 117, UK2Department of Physics, University of York, York, UK

Summary

Total internal reflection fluorescence (TlKF) hasrecently been used to look at the contacts madebetween cells and a glass surface on -which theyare spread. Our method utilizes the fluorescenceof a water-soluble dye that acts as an extracellu-lar aqueous volume marker. Fluorescence isstimulated by the short-range electric field nearthe glass surface that exists under conditions oftotal internal reflection. Since fluorescence is nor-mally generated beneath a spread cell and notbeyond it, the fluorescence of the image is relatedto the size of the cell-glass water gap. Theimages obtained are remarkable for their detail,contrast and the absence of confusing granularitydue to cytoplasmic heterogeneity, which is com-monly seen in interference reflection (IRM)images.

We here develop a rigorous electromagnetictheory of total internal reflection in layered struc-tures appropriate for cell contacts and apply itto quantitative TIRF. We show that: (1) TIRF,unlike IRM, can report cell-glass gaps in a waythat is practically independent of the detailedphysical properties of the cell; (2) TIRF is alsofar more sensitive than IRM for measuring cell-glass water gaps up to =100 nm. These strikingresults explain the image quality seen by TIRF.As the initial step towards verifying our theorywe show that measurement of the fluorescencestimulated by total internal reflection at a simpleglass-water interface matches theoretical predic-tions.

Key words: electromagnetic theory, total internal reflectionfluorescence, evanescent wave, cell-substratum contact.

Introduction

Knowledge of the pattern of contacts between a celland the surface on which it is spread is basic tounderstanding cell attachment and movement on solidsubstrata. A decade ago the re-introduction of inter-ference reflection microscopy (IRM) heralded a majoradvance in the understanding of cell contacts and theirrelationship to the cytoskeleton. Nevertheless IRM hasvery serious drawbacks and although image interpret-ation has been placed on a quantitative basis (Gingell &Todd, 1979; Gingell et al. 1982) insufficient knowledgeof dimensions and refractile properties of the cellperiphery is still a substantial practical limitation. Evenqualitative misinterpretations of IRM images are easilymade (Gingell, 1981).

An alternative procedure to IRM employs totalinternal reflection fluorescence (TIRF). This powerfullight-microscopic tool was first used in cell biology onlyrecently to study the close approach of cells to glass

Journal of Cell Science 87, 677-693 (1987)Printed in Great Britain © The Company of Biologists Limited 1987

(Axelrod, 1981; Weiss et al. 1982). Here we present aquantitative basis for its use and show that it is farsuperior to IRM for studying cell contacts. We realizethat not all who are interested in the application ofTIRF will wish to do battle with the mathematics, soour paper is organized so that the results are fullyunderstandable without reference to the theoreticalsection (pp. 2-8).

The basis of TIRF is as follows. Consider a colli-mated beam of light in glass (refractive index H\),incident at an angle c(«2, «i) . In this case totalinternal reflection occurs; all the energy is reflectedback into the glass and no transmitted wave propagatesthrough «2- F° r the interface between a microscopecoverslip and water (for example), Snell's Law gives:

= arcsin(nz/«i).

677

Although there is no net energy flow into medium n-ithere is a very short-range electromagnetic disturbancein the second medium near the interface, called anevanescent wave. This will often have a complicatedwaveform but its amplitude falls exponentially intomedium n-i normal to the interface, and dies out in lessthan a wavelength. This phenomenon has a longhistory and was anticipated by Newton. It forms thebasis of a type of beam-splitting prism and, mostimportantly, occurs in fibre optic transmission lines.The relatively recent interest shown by chemists in thisseemingly rather arcane phenomenon stems from thefact that if a fluid medium contains dissolved fluor-escent molecules, emission can be stimulated by theevanescent wave in a very restricted zone within onewavelength of the glass surface. This has been usedfor several decades to study the adsorption of fluor-escent macromolecules at optical interfaces (see Hladyet al. 1985) but it is only in the past few years that cellbiologists have become aware of the subject and haveused it to look at cells spread on glass. Axelrod (1981)reported the use of the fluorescent lipid analogue Dil tolabel cell surfaces and he was the first to demonstratestrictly localized fluorescence where cells come close toglass.

Gingell et al. (1985) demonstrated that strikingimages showing the topography of the cell-glass appo-sition zone can be obtained using a fluorescent extra-cellular water-soluble dye acting as an aqueous volume

D

A v /i i.}-,.£,.,

Fig. 1. Layered dielectric model of cell-glass apposition.Light is incident at an angle (f> (which exceeds the criticalangle) on the interface between glass (>i\) and a film ofaqueous medium («2) of thickness t\. The cell membraneis represented by an isotropic dielectric film of thicknesstz~h and refractive index n3. The average cytoplasmicindex is W4. Complex waves (£1 ...E4) have complexamplitudes in the positive .v direction (A...Z5) and negative.v direction (A' ... C'). Quantities /3r, yr are defined in thetext.

marker. This produces dark contacts against a brightbackground by virtue of exclusion of the extracellularaqueous volume at contacts. The essential point of thistechnique is that no fluorescence is normally stimulatedfrom the aqueous medium beyond the cell, since theevanescent wave does not penetrate the several micro-metres necessary to cross the cytoplasm. It is forprecisely this reason that the volume marker techniqueis able to provide a unique map of the cell-glass contactzone by reporting variations in the thickness of theaqueous region between a living cell and its transparentsubstratum.

In the following analysis we develop rigorous ex-pressions for the electrical energy in the cell-glass gapunder conditions of TIR illumination, by solvingMaxwell's equations for all the conditions likely to ariseat cell contacts. From these equations we predict thevariation in the stimulated fluorescence with cell-glassseparation and discuss several factors that may influ-ence the results. A critical comparison of TIRF andIRM is made. Finally, we compare the experimentallymeasured fluorescence at a simple glass-water interfacewith our theoretical predictions.

(a) (b)\E \E

\ E V\

Vn, 7fc

*C(»4.«|) < 4» 0C

(c) (d)

\E

Fig. 2. The four situations that can arise when anevanescent wave E exists in medium n2 are: in case (a) thewaves in media 3 and 4 are also evanescent; in (b) acontinuous wave C exists in medium 3; whereas in (c) itexists in medium 4. In case (d) the media 3 and 4 supportcontinuous waves. The relationships between the incidentangle <p and critical angles <pc(nr,)i\) are explained in thetext.

678 D. Gingell et al.

Theoretical

We confine the analysis to the case of a plane s-polarized wave with electric vector perpendicular to the plane ofincidence (i.e. parallel to the reflecting interface), incident at angle (f>c(n2,nl) on a glass-liquid interface(x = 0). The bilayer membrane and the aqueous gap beneath it are simply represented as two thin films of thicknesst2 — t\ and *i, respectively. The symbol" represents a complex quantity. A diagram of the layered system is shownin Fig. 1 in which the y direction is perpendicular to the plane of the paper. The amplitudes EVT will in general becomplex. The incident wave has components Ey in the y direction but Ex = E~ = 0. Amplitudes Evr and refractiveindices nr are referred to media r = 1... 4. The quantities yr, /Jr are defined below. A ...D are complex amplitudecoefficients (phasors) of waves in the ±x direction. In all that follows, ti\ > n2, but distinct and interesting casesfor the different relative magnitudes of n\, «3 and na, will emerge. In region r, the appropriate form of Maxwell'sequations for plane waves of amplitude Ey are:

dxl -nrkl)Ey (1)

o • ax • (2)

where , „ /.

When the waves in media 2, 3 and 4 are evanescent, the solutions for the second-order differential equation take theforms:

Y < 0 F i = A e~'Y ~

tz>x>tx Ey3 = C e~p'x + €' ftA" '

x>tz

w h e r e

The relationship (eqn (2)) between electric and magnetic components gives:

Hai = {Ayt e~'YlX -A'YI e'Y'x)/ck0^

(5)

The Maxwell boundary conditions for the parallel components of the electric and magnetic fields are:

Eyl(0) = Ej2(0)

Ey2(ti) =Ey3(tl)Ey3(t2) = Ey4t2)

^ (6)Hzl(0) = Ha2(0)

Mapping cell-substratum topography 679

Setting the incident amplitude A = 1 we obtain a set of linear simultaneous equations:

A1 -B -B' 0

- A ' y , +iB~p2 -iB'Pz 0

0

0

0

0

0

0

0

0

- C ' e

-C'p3

+ C ' e

+ C'p3

eft''

ft'2

eft'2

- D f

+ Dp4

0

0

0

0

e-ft'z

+ 1 = 0

+ y. = o

0 = 0

0 = 0

0 = 0

0 = 0 .

(7)

These are solved using determinants to give the complex coefficients A', B, B', C, C', D. Substitution intoequations (3) and (5) gives the electric and magnetic fields in each medium as a function of x. Squared amplitudes,which are real quantities, are then obtained by multiplying each complex amplitude by its complex conjugate\EV\ = EV-E*. (AS an alternative, it is possible to derive a general recurrence relationship for fields in adjacentlayers, but quite a lot of algebra is needed to obtain the explicit solutions considered in this paper.) In a two-filmsystem, there are four different situations, which can arise according to whether the fields in media 3 and 4 are.continuous (transmitted, homogeneous) or evanescent (inhomogeneous). Diagrams of these cases are shown inFig. 2A-D. Consider the behaviour of the function fiT-»z as the angle of incidence <pc(ti2,>i\) varies:

when ti\ sin nr the root is positive and /3r is real. However, when n\ sin <p<.nr,

(8)

(9)

where j3r is purely imaginary and yr is real. Consequently, when this occurs the wave in medium r becomescontinuous. The significance of this switch is easily understood since Snell's Law requires that the angle ofrefraction in a medium adjacent to a dielectric film is independent of the refractive index of the film and dependsonly on the indices of the two bounding media. Therefore, we can define a critical angle between ti\ and « r :

n\ sin0! = «r

«? sin20, - n 2 = 0.

The relations: c

<t> {nr,nx)><pc(«2,«i)

imply /3r imaginary and Ev continuous in medium r. Alternatively:

implies /3r real and Ev evanescent in medium r.When «3 >«2 < W4 and n^ >«4 and (p is increased the sequence in Fig. 2 will be d—* b—> a but if 114 > n^ the

sequence will be d—*c—* a. The phenomenon of a continuous wave generated beyond a gap containing anevanescent wave is called frustrated total internal reflection (FTIR). While the relationships between nT and <p thatwe have described do indeed solely determine whether FTIR can occur, the power of the transmitted wave will fallexponentially with the width of the gap containing the evanescent wave. It falls to around zero for a gap in the orderof A. We shall return later to the subject of FTIR in relation to cell contacts. For a cell surface, medium 3 representslipid ( t t3~l-4; Ninham & Parsegian (1970)) and medium 4 represents cytoplasm (1-36 Sjn4 ^ 1-37 fromrefractometry; Bailey & Gingell (unpublished); Izzard & Lochner (1976)). Since W3 will exceed ;?4 situation cshould not arise in observation on cells.

Having calculated the squared amplitude |i?v2(.v)|2, which is proportional to electrical energy at a particulardepth (JC) in the water gap, we make use of the fact that stimulated fluorescence is proportional to the local electricfield energy (see Appendix 1). The coefficient of proportionality linking emission with stimulation will includequantum efficiency (Q) and fluorochrome concentration (M). The proportion of the emitted photons detected by a

counting instrument will depend on several factors that are a constant (S) for a given system. Thus detectedfluorescence (Fc) for an area beneath a cell where the water gap is t\ will be:

Fc = QMS \EvZ{x) |2dx = QMSI(tx).J o

The background fluorescence (F^) at a nearby area without a cell will be:

Fb = QMS f" \Ev2(x) \2dx = QMSI(»).J o

Therefore, relative fluorescence is given by:

(10)

(11)

)• (12)

The coefficient QMS drops out and the ratio F, obtained from experimental measurements of fluorescence beneaththe cell and in the background, gives the cell—glass separation.

Case (a)

For the situation illustrated in Fig. 2(a) we obtain for the field in the second (aqueous) medium:

(13)

wherea, = (Pi + 02

a2 = - ( $ -a3 s /M/^4si

) sinh(5i + fizifiz + p*4) cosh(5i

34) sinhSi — ^3()34 — Pi) coshS]

(14a)

(14b)

^zh + P2sinh/?2/]) sinh<5i (14c)

coshd] + (y32p4 sinhp2t) + p3 cosh/32J 1) sinhS] (14d)

and

Whence:

and

|2 — (15)

(16)

(17)

When «3 = w4 the expression for \Ey\2 reduces to that for a single film with an evanescent wave in the third

medium:12

2 + /3i/3i(/32 sinhj82/,

and 2yf i [ - ^ ^ smh2pV,+p i3(cosh2p^1- l ) + <1(p-2--l

sinh/32/, )2 (19)

For the case £)—»°° (or ^ ^ 0 ; W3—»n2) we obtain the expression for I^Vl2 for an evanescent wave at a singleinterface between two bulk media:

1

4n 1 cos (pexp

f 4^x (20)

Setting the exponent equal to unity we obtain x, the characteristic wave penetration depth, namely the distanceinto medium 2 at which the squared amplitude has fallen to l/e of its value at x = 0. Thus:

x =vac

sin2<p -(21)

A compact expression for / is obtained as usual by integrating the squared amplitude from .v = 0 to infinity.

jMwy (22)

The form of the evanescent wave Ev{x,z) at an unbounded interface is relatively straightforward and it can beshown to be:

Ev(x,z) = 2«i cos(p • cos( cot - *nx sin0 - 8, | e~f c v, (23a)\ ^vac /

where the phase angle / 8 \a . ^ t a n - ' / , Pz ) .

\k0nicos<pj

The final consideration of case (a) involves solving for the field in the fourth medium:

(23b)

where a3 and a4 are given in equation (14c,d). Integration between x = t and infinity gives:

lit t \- 2tffePi7(11''2)-/B4(y?.§+ /&*)•

If the cytoplasm contained a fluorescent volume marker this expression would give fluorescence versuscytoplasm-glass distance t2. We shall use it in a simplified model where the cell membrane is omitted and medium«4 represents the aqueou9 medium on the far side of a thin sheet of cytoplasm (thickness t2~t\) separated from theglass by an aqueous gap t\.

Case (b)

If there is a continuous wave in the third medium (Fig. 2(b)) we replace P\ by — y3 and obtain:

|£2l = 22 2, 2

2 b 4

2 fl2, 2 > ( 2 6 )

b + p2bw h e r e = - ( y ! - j82j84) sind, + y3(/32 + j84) cosd

b3 = y3 (/34 sinh/32f, + /32 coshj32r,) cosd, + (^264 cosh^2«, - yf si

b4 s y3 (/34 cosh/32/, + B2 sinh/32^ 1) cos61 + (/32/34 s i ^

sinSi

sinS)

(27a)

(27b)

(27c)

(27d)

When the fourth medium supports a continuous wave /34 becomes — y\ leading to:

| 2 4y?[{cicosh/32(<1 - .v) + c2sinh^2(t1 - ,v)}2 + {c4 co8h/32(ti - JC) + c3

where

- P2) sinhj

1 + 74) COS

62t\ 'coshî + PZ(Y\

hB2t\ -cosh6i + (Yip

CI = /32y4sinh6]

C2 = /33y4COSh5,

c3=#sinh6,

c4 = /32/33cosh<51

y4 - Pl)coshB2t\ •'.

'3 • PzY*) sinnp2î

3inh6,}2

•sinh6,}2

(30a)

(30b)

(30c)

(30d)

and 8\ = Pi{tz—1\) as defined earlier. Setting the denominator of equation (29) toî and integrating with respectto x:

| ( C ' + °2 °3 + °4 ) sinh2j3t, + 2(cf - c2 - c2 + c2)^, + j - (c,c2 -fc3c4)(cosh2)32/l - 1 ) | . (31)P2 J2

682 D. Cn/ê// e< a/.

Case (d)In this situation continuous waves exist in both the third and fourth media (Fig. 2(d)). We set f}\ = — y\; /J2 = — y2.and defining &z = Y'i{ti~t\) obtain:

4rf[73(73 sin62 • sinh/32(<i - x) - fi2 cos<52 • cosh02(*, - x)}1

- ., +y5{y3 cos<52-sinhj82(f, -x)+/32sin<52 • cosh/32(*i ~ x)}2]ty2\ = . (32)

[73(71X4 — y3l)sinhyS2fi •cos62 + /32(yiy4 + yf)cosh/32ti -sin<52]2

[(7i73 - £2y4) sinhj82t, • sin<52 - y3£2(yi + y4) cosh£2«i • cos<52]2

d, = Y$ sin2<52 + 74-73 cos262 (33a)

d2 s yf/31 cos262 + yipz2 sin2<52 (33b)

d3 = 73^2(74 - 7!) sin<52 cosd2 . (33c)

Setting the denominator in equation (32) to J2 we have:

} (34)

When «3 = «4 we have a single film with a frustrated wave in the third medium:

- ' {(7i73-/3l)sinhyS2f1}2+{y32(y1 + y 3 )cosher ,} 2

and 2y

, XHZW1 , ,3,^o..p2H/ ^

Absorption

We finally consider the case of absorption in the second medium for case (a) only. If the aqueous medium absorbsthe evanescent wave it is convenient to define a complex index of refraction:

n2 = n2— iK2 , (37)

where K2 is the absorption coefficient and n2 is the real part of the refractive index. We replace n2 by iT2 in all fieldequations and obtain a complex fi2 (eqn (4)):

]}2 = ko{a-ib), (38a)

where 2 • 2_L 2a = n\ sin d> - n 2 •

(38b)

Real and imaginary parts of fi2 are obtained using de Moivre's theorem:

Pi — ^o(a + b ) < coslx] —t sin 1x1 > , (39a)

where

W e d e f i n e ^ { ^ 2 } - s ,

so that ^^2 = 5 ] + J 5 2 . (39c)

Mapping cell—substratum topography 683

This expression for /S2 is now substituted in equation (13) for the field Ey2. Using \Ev2\2 = Ey2 ' E*2

w e finallyobtain:

\E 12 = tiftf + Np1 y2] (NY+XS+NSrf+iNSAUYN^)2' V '

w h e r e jV s ' < ' ' -jV, = es'<''-*>fe, sinS2(t, - *+ e - i ' ( " - v ) t e 3 s inS 2 (< 1 -x)+^cos5 2 ( i 1 -x )} . (41a)

N2 = ts'^~x){gl cosS2(t, -x) -g2smS2(tl -x)}+ e - s . d , - * ) ^ ^ CosS2(*, _ x ) + f t s i n 5 2 ( f ] _ x)y . ( 4 1 b )

JV3 = y33(/34cosa2 • sinhCT! + Si coscr2 • cosher — 52sina2 • sinhaj) cosh^i

• cosher — 52^4 sin02 • sinhCTi + /3f cosa2 • sinhCTi) sinhdj . (41c)

oshai + 5 j sina2 • sinha] +52COSCT2 • cosha^coshSi

+ (5i/34sin02 • sinh<7i + 52/34 cosa2 • coshai + /3f sina2 • coshai) sinh6) . (41d)

Ns = /33()34 cosa2 • coshCT] + Si COSCT2 • sinhcrj - S2 sina2 • cosha^ coshdi

+ (S1P4 COSCT2 • sinh<7i — S2^34 sina2 • coshai + /33 COSCT2 • cosh<7i) sinh^i . (41e)

Nf, = j33(j34 sina2 • sinhCTi + Si sina2 • coshCT] + S2 cosa2 • sinhai) coshoj

+ (Si/34 sina2 • cosher + S2y34 COSCT2 • sinhCT] +^33 sina2 • sinhCTi) sinhoj . (41 f)

In equation (41) we have used:<5i = & ( ' 2 ~t\), Oi=Siti, oz=S2ti

= -{ft + S,j84) sinho, - (jr33yS4 + S,j83) cosho, (41g)

^3 = - ( $ - S,j84) sinho, - (fofa - 5,/33) cosh6, .

Integration gives:

+ fe.ft -«i) s.n2S2r, + feg2 +^3)(cos2S,., - 1) y _ (42)

where J 3 is the denominator of equation (36).The integral:

I(K2)=r\Ev\zdx, (43)

J owhich gives the fluorescence at an unbounded interface in the presence of absorption, can be obtained from ourresults by reducing equation (40) for the case t\ —* °o; tz^* t\. After much algebra all terms in /33 and /34 disappearand we obtain:

giving the characteristic decay depth x = 1/2S. Integration gives the background electric energy in the absorbingmedium:

I(K2) = \Ev\*dx = — ^ — - 2 - r , (45)

which reduces as required to the expression (eqn (22)) for a non-absorbing medium at a simple interface whenK2 = 0 (implying S2 = 0, whereupon Si = fi2).

Numerical results

The objective of this work is to show how the water gapbetween a cell and its substratum can be measured bythe TI R-induced fluorescence of a water-soluble dye inthe gap. Thus we compute curves of fluorescenceversus gap width. Since the electric field of theevanescent wave in the gap stimulates fluorescence, thecurves are strongly dependent on factors that affectfield energy, namely the angle of incidence <p of thelaser beam on the glass-water interface, and therefractive index ti\ of the glass. These two factors alsogovern how far the evanescent wave penetrates not onlyinto the gap but also into the adjacent cell. If the cell isvery thin the wave may even penetrate right through itand stimulate fluorescent molecules on the far side. Weshall present the results of calculations, using thetheory developed above, which show to what extentmeasurement of the water gap by TIRF depends on <pand 77] as well as on the physical properties of the celland its shape. We shall also discuss other factors thatmay influence the results and give a numerical compari-son of the sensitivities of TIRF and IRM.

Dependence of fluorescence on the width of the watergap for various incident angles (p and refractiveindices of the glass n/

Fig. 3 shows fluorescence (in arbitrary units) stimu-lated by light (A = 488 nm) incident at angles between70° and 85°. The curves show how fluorescencedepends on the thickness (t\) of the water layer inwhich the evanescent wave develops. Fig. 4 showscurves of relative fluorescence (F) (fluorescence ex-pressed as a fraction of the bright background value, asdefined in equation (12)) versus t\ for <p values between65° and 85° for both normal glass (wj = 1-539) andhigh-index glass (ii\ = 1-85). The optical properties ofthe cell are as shown in Fig. 3. The significant featureof these curves is the short range of TIRF: in all thesecases 90% of background fluorescence is reachedbefore the water gap reaches 160 nm. Penetration of theevanescent wave falls as <p increases. On high-indexglass at high incident angle 90 % of background fluor-escence is reached before the water gap reaches80 nm, giving an appropriate range for measuringcell-substratum gaps without the evanescent wavepassing right through the cytoplasm of thinly spreadcells (see below).

Relationship between fluorescence and gap width forvarious assumptions about the nature of the cellsurface

An important result is shown in Fig. 5. Whereas onnormal glass ((p = 75°; n\ = 1-539) setting the cytoplas*mic refractive index to either 1-37 or 1-40 makes asignificant difference even at small distances (=17%error at 20 nm) we find that on high refractive index

glass at the same incident angle the worst error is lessthan 2-5nm, right through the useful range from 0 to70 nm or more. At t\ = 10nm the error is 10%, fallingto 5 % at 30 nm. Furthermore, the presence or absenceof a membrane in the model makes even less differencethan the cytoplasmic variation discussed. We concludethat gap measurement on a high-index substratum isvirtually independent of assumptions about the refrac-tive index of the cytoplasm and the ce.ll membrane.

Comparison of TIRF with IRM for measuring cell-substratum topography

Figs 6 and 7 show comparisons of quantitative inter-ference reflection theory (Gingell & Todd, 1979) withthe present TIRF theory. In comparing the merits ofthese two techniques we define sensitivity as the changein signal/background with water gap, dR/dti. In thecase of TIRF, R = F (eqn (12)). The IRM theory hasbeen experimentally validated and is capable of highaccuracy (Gingell et al. 1982) provided the opticalproperties of the components are adequately known.This, however, can be a serious practical limitation formeasuring cell contacts. IRM is best on low-index

40

30-

20-

10-

(iY)

50 100Water gap /| (nm)

150

Fig. 3. Calculated fluorescence Fc (arbitrary units)generated by the evanescent wave in the aqueous gapbeneath a model cell (see Fig. 1) plotted as a function ofgap thickness t\. Curves are shown for several angles ofincidence <p= (i) 70°, (ii) 75°, (iii) 80°, (iv) 85°. Refractiveindices are as follows: glass n\ = 1-539; aqueous medium/?2 = 1-337; cell membrane n^ = 1-45 (thicknesst2~t\ = 4nm); cytoplasm «.» = 1-37. Wavelength of incidentlight A = 488 nm.

80 100Water gap (,

Fig. 4. Calculated relative fluorescence F developed in avariable aqueous gap / | . Upper three curves, refractiveindex of glass n\ = 1-85; lower three curves, n\ = 1-539.Incident angles (<p) 65°, 75°, 85° as shown. Otherparameters as in Fig. 3.

10 20 30 40 50Water gap f, (nm)

60 70

Fig. 5. Calculated relative fluorescence F developed in avariable aqueous gap t\ showing the limited dependence offluorescence on cell properties. Upper three curves;

ti\ = 1-85; lower two curves rt\ = 1-539. In curves (i) and(iv) cytoplasmic refractive index n+ = 1-40; in (iii) and (v)tit, = 1-37. In (ii) setting nj = 114 gives a situation where themembrane is (optically) absent.

glass, where the differences in amplitudes reflectedfrom glass and the cell surface are minimized. In thissituation (Fig. 6) it is clear that the IRM image onlybegins to give useful information about the cell-glassgap when it exceeds 30nm or so; at smaller distancessensitivity is very poor. Furthermore, the result isdependent on the cytoplasmic refractive index becauseIRM image formation depends on phase retardationdue to the refraction of light through the cytoplasm aswell as reflection at the cell periphery. The reflectedamplitude is a function of the refractive indices of thevarious layers of the cell surface and the interpretationof IRM images depends on the details of the assumedproperties of this region. Even under optimal con-ditions of high illuminating numerical aperture wherethe contribution of cell thickness to image formation isminimized, this contribution still depends critically onthe cytoplasmic refractive index (Bailey & Gingell,unpublished), and it is for this reason that cytoplasmicinhomogeneities give IRM images a characteristicgranularity.

IRM

TIRF

10 20 30 40 50 60Water gap I, (nm)

70

Fig. 6. Comparison of (i), (ii) IRM with (iii), (iv) TIRF.Relative signal (i.e. signal/background) appropriate to eachmethod is plotted against the aqueous gap t\. For IRM theparameters used are glass n\ = 1-539; medium n2 = 1337 ,t\ variable; lower lipid membrane iij = 1 4 5 , 4 n m ;cytoplasm « 4 = 1-40 (i) or 1-37 (ii), 1000 n m ; uppermembrane (as lower); upper medium (as lower). ForT I R F , w, = 1-539; « 2 = 1-337, t, variable; #i3 = 1-45, 4 n m ;«4 = 1-40 (iii) or 1 3 7 (iv). A = 488nm; angle of incidencetf> = 75°only.

Although TIRF developed on low-index glassdepends to a limited extent on the cytoplasmic refrac-tive index (lower curves, Fig. 6) the sensitivity of themethod is very high. On high-index glass (Fig. 7) IRMis useless below 50 nm but on the other hand TIRF isseen to be a very sensitive function of the width of thewater gap, rising to almost half the background valuein 30 nm. Even 2nrn is probably measurable (seeAppendix 2).

Dependence of fluorescence on gap width for thespecial case where the cytoplasm is very thin

Evidence from quantitative IRM and supported byelectron microscopy shows that cells can make ultrathinperipheral cytoplasmic lamellae, of ~100nm (Gingell& Vince, 1982; Mellor & Gingell, unpublished). Theseappear as dark areas in IRM, similar to intimatecell-glass contacts. When such lamellae have formed itis difficult if not impossible to measure their separationfrom the substratum by IRM when their thickness isunknown. If lamellae have a refractive index differentfrom bulk cytoplasm the matter is even more uncertain.In contrast, TIRF offers a way of measuring cell-glassgaps beneath thin lamellae, utilizing the low wavepenetration available with- glass of high refractiveindex. In addition there is the advantage that uncer-tainty in assigning the cytoplasmic refractive index

1-On

0-8-

0-6-

0-4-

0-2-

IRM

10 20 30 40 50Water gap (| (nm)

60

Fig. 7. Curves ( i)-( iv) as Fig. 6 except substratummodelled as glass of high refractive index ii\ = 1 8 5 . Curve(v) as for (ii) except n^ = n+, i.e. cell membrane opticallydeleted.

becomes unimportant when high-index glass is used.But first, consider the situation of TIRF on normalglass shown in Fig. 8. Fluorescence beneath a lamella,as a function of the water gap, is shown in theascending curves. Fluorescence stimulated beyond thelamella, due to partial penetration of the thin cytoplas-mic layer by the evanescent wave, is shown in thedescending curves. For a given lamella thickness,increasing the water gap (i.e. moving the lamellafurther away from the glass) reduces the fluorescenceoriginating beyond it while increasing that beneath it,up to the bright background value where relativefluorescence approaches unity. Results are given forlamellae of 100 and 200nm. Obviously, much lessfluorescence is generated beyond a thick lamella than athin one.

When the same modelling is done with glass of highrefractive index (Fig. 9) it is immediately clear thatvery little fluorescence originates beyond the cell, evenwith no water gap. When (p = 78° a 100 nm lamella iseffectively infinitely thick. This offers an unambiguousway of analysing the contacts of cells where suchlamellae form, and this will be expanded in a sub-sequent paper.

50 100Water gap r, (nm)

150

Fig. 8. Evanescent wave can penetrate a thin cytoplasmiclamella and stimulate fluorescence beyond it. Inset sketchshows details. Ascending curves: relative fluorescencegenerated beneath cell approaches unity as aqueous gap t\

increases. Descending curves: relative fluorescencegenerated beyond lamella falls to zero as l\ increases.Continuous curves, 100nm lamella; broken curves, 200 nmlamella. Angle of incidence either 76° or 64° as shown.A = 488nm.


Under what conditions does frustrated total internalreflection fluorescence (FTIRF) occur and what canbe learned from this effect?

In the results given so far, no reference has been madeto the different possible electromagnetic waveforms inthe cell periphery (Fig. 2). In most situations case (a)is appropriate, but at sufficiently small (p values, not farabove the critical angle <pc{nz,n\), case (b) and ulti-mately at <f) values just above </>c(«2.«i) case (d) willoccur. As <p is reduced that part of the cell peripherywith the highest refractive index will be the first totransmit a continuous wave. We would expect this to bethe plasma membrane bilayer and the conditions for acontinuous wave in n^ but not «4 are:

When these criteria are satisfied, the plasma membranewill behave like a parallel wafer guide, and a wave willbe propagated along it, totally internally reflected fromthe lipid-water and lipid-cytoplasm boundaries. Ata slightly smaller incident angle a continuous wavewill be transmitted through the cytoplasm as well(case (a)). This will happen when:

0c(«2i«i) <(P <arcs in(« 4 /«i ) .

We have in fact seen fluorescence stimulated by laserlight transmitted by FTIR from cells that have regionsvery close to glass, when illuminated at incident angleswell above 0 c (n 2 ,n i ) . These fluorescent beams look

like comet tails, originating at cells and pointing awayfrom the light source. This phenomenon will bediscussed further in a later paper. The fact that FTIRFfirst appears near 69° in the case of chick heartfibroblasts shows that the part of the cell peripherywith the highest refractive index has an index of 1-40.This is presumably the mean refractive index of thelipid bilayer.

To what extent is gap measurement influenced byabsorption of the stimulating evanescent wave byaqueous fluorochrome molecules?

Fig. 10 illustrates the degree to which perturbation ofthe evanescent wave, due to its absorption by thefluorochrome, affects fluorescence. It can be seen thatrelative fluorescence decays more rapidly as the absorp-tion coefficient Kz increases, so that increasing Kz issimilar to increasing the refractive index of glass. Thisincidentally suggests that a suitable absorber in themedium could attenuate the evanescent wave, withoutrecourse to a substratum of high refractive index.However, our reason for modelling absorption was tosee whether it was likely to 'bleed off sufficientevanescent wave energy to cause a significant errorin quantitative work. Since our maximum measuredextinction coefficient for fluorescein isothiocyanate(6850OM~'cm~') gives an evanescent wave absorptioncoefficient of only 5X 10~5 there should be no measur-able error from this source (see next section).

Fluorescencebeneath cell

50 100Water gap (| (nm)

Fluorescencebeyond lamella

150

Fig. 9. As Fig. 8 except glass nx = 1-85. Results for100nm lamella only given. Curves (i), (iii), <p = 78";

curves (ii), (iv), $ = 64°.

1-25

1-20-

115-

110-

105-

1-00

Fig. 10. Ratio of fluorescence in the absence Ft, andpresence F{, of absorption of the stimulating wave, at anunbounded interface, plotted versus angle of incidence <p.

Coefficient of absorption: (i) A'2 = 0-05; (ii) K2 = 0-005.

Measurement of TIRF at a simple interface

We measured the fluorescence developed by solutionsof fluoresceinated dextran (FD-4; mean Mr = 4100;Sigma, Southampton, UK) at different concen-trations, as a function of the angle of incidence exceed-ing the critical angle, at an unbounded glass-waterinterface. The solutions were made by serial dilution ofa stock containing 5mgml~ FD-4 plus 5mgml~unlabelled dextran (Mr = 6000; Fluka, Buchs, Switzer-land) and 25 mM-Hepes buffer, pH 7-2. Dilution with asimilarly buffered lOmgmP 1 solution of unlabelled6000 Mr dextran obviated small variations in refractiveindex, which otherwise arise due to variable dextrancontent. All solutions were passed through a sterile0-2 nm pore size 'Acrodisc' filter (Gelman SciencesLtd, Northampton, UK) before use. The refractiveindex of the solutions (w2= 1-339) was determinedwith an Abbe refractometer (model 60/ED Mkl;Bellingham & Stanley Ltd, Tunbridge Wells, UK)illuminated with a low-power beam from an argon ionlaser at A = 488 nm.

The equipment used for photon counting has beendescribed in detail elsewhere (Gingell et al. 1985). Forfluorescence measurements, several drops of the dex-tran solutions were placed on the upper surface of aglass prism (n = 1525) and illuminated by means of anargon ion laser (A = 488 nm) at angles above the criticalangle (pc(ri2, «i) = arcsin (1-339/1-525). The beam wasspatially filtered and refocused onto the interface with ahalf-angle convergence of 0-5°. The error in incidentangle at the centre of the optical field was found to beless than ±0-05°. The laser used in light control modegave a constant power output of 100 raW, and the beamwas attenuated with a neutral density filter (O.D. = 1;Melles Griot, Aldershot, UK) to prevent significantphotobleaching. Rotation of the laser beam to givetransverse polarized light (i.e. s-polarization, perpen-dicular to the plane of incidence, to within ±1°) wasobtained with a double Fresnel rhomb (Lexel, LamdaPhotometries, Batford Mill, UK), which screwed tothe front of the laser. Emitted fluorescence was col-lected using a 63 X water immersion objective (Zeiss,Oberkochen, Welwyn Garden City, UK) focused onthe interface, using a photomultiplier aperture of2-5 mm. The laser beam was centred to the optic axis ofthe objective by small adjustments to the angle ofincidence and a lateral micrometer movement, to peakthe photon count rate over 100 s. This was repeatedfor each solution and for every angle of incidence.Although there was no evidence of dextran adsorptionto glass (a 10-20 s rinse in deionized water returned thephoton content to background; see also Hlady et al.1985) the upper surface of the block was rinsedbetween dextran solutions with dilute Teepol, thenwater and finally acetone. This had no effect on

measured fluorescence but gave very reproduciblevalues of laser light scattered by imperfections in theinterface. Scatter was measured at each angle ofincidence using lOmgml"1 unfluoresceinated dextranin place of FD-4, after removing the Schott OG515barrier filter. The extinction coefficient e of each FD-4solution was measured using an LKB Ultrospec 4050spectrophotometer and the absorption coefficient Ki(eqn (38)) was calculated according to the relationshipK2 = 2-303ehM/4jl, where M is the fluorescein (flu-orochrome) concentration. All optical measurementswere made at 22°C.

Fig. 11 A,B shows that, over the entire range of FD-4solutions, fluorescence is linearly proportional to flu-orochrome concentration. Thus quenching is absent,even at the highest concentration used. Comparison oftheory with measured fluorescence over a range ofincident angles was performed in two ways. In the first,experimental values of fluorescence versus (f> are nor-malized to the fluorescence measured at 62° and it canbe seen that they follow closely the correspondingtheoretical curve, shown as a continuous line inFig. 12. The second method involves linear transform-ation of the curves and permits calculation of theconstant QS defined in equation (11). This equationgives the background fluorescence Fb at an unboundedinterface for the case of unit incident amplitude. Weintroduce a factor of cos<p to take account of the factthat the proportion of the incident flux falling withinthe fixed measuring area, viewed by the photomulti-plier, falls with increasing <p. Furthermore, althoughthe total laser beam power is constant during measure-ments, the incident amplitude depends on previousreflections, which change with <p. Setting the angle-independent factors QMS = C and recalling the angulardependence of / we write:

A((p) is the amplitude of the wave in the glass, whichdepends on previous reflections. Substituting for /from equation (22) and expressing Y\ and fiz fromequations (8) and (9) gives:

C = Fb(<f>)/G(<P), (47)

where

G(<P) =

Thus a plot of the experimental values Fb((p) versusthe denominator of equation (47), [D(<j>)], should givea straight line of slope C for a given concentration M.Fig. 13 shows that a most satisfactory linear relation-ship is indeed found between Fb((p) and D((f)) for allconcentrations used. From C we obtain the systemconstant QS, which relates measured photon count rate

2-2x10*-

1-5X103-

lxH)5

5XK)4

64-2°

66-4°

0 1-0 2-0 3-0 4-0 5-0 0 0-5 1-0 2-0Concentration of fluoresceinated dextran (mgnil"1)

3-0 4-0

Fig. 11. A,B- Measured fluorescence as a function of the concentration of FD-4 for a range of incident angles. Curves forthe three low incident angles shown in A are partially included as broken lines in B. The latter has an expanded scalesuitable for larger values of (p. The slopes of the regression lines shown (expressed as the ratio of the slope for 62°) aregiven with the corresponding theoretical values ( ): 1, (1); 0-39, (0-40); 0-25, (0-24); 0-14, (0-15); 0-09, (0-10); 0-06,(0-06); 0-04, (0-03); 0-02, (0-02); 0-01, (0-01). Repeat readings (X) taken 9h later, after the full range of measurementswas completed.

to the integral I(4>, °°) for a given value of M. Thestrictly linear curves that pass through the originindicate: (1) the correctness of the physical theory for asimple interface; (2) the measuring system is highlyaccurate; (3) excitation of fluorescence by scatteredlaser light in our system is negligible; (4) adsorption ofFD-4 onto glass is negligible; (5) photobleaching isnegligible under our experimental conditions; (6) ab-sorption of laser light by the fluorochrome is negligible,as deduced in the previous section. The last pointmeans that the energy absorbed from the evanescentelectromagnetic wave, which drives fluorescence, is anegligible fraction of the electric field energy. The factthat scatter cannot be a major determinant of fluor-escence was shown by direct measurement at 488 nmwithout FD-4. Whereas the photon count from fluor-escence changes 100-fold from lowest to highest inci-dent angle, the count from scatter changed only10-fold. It is therefore related to <p by a completelydifferent functional relationship from that linking flu-orescence with (p. Thus any significant contribution to

the total fluorescence stemming from scattered lightwould bend the straight lines in Fig. 12.

We should stress that the relatively simple situationof an evanescent wave at an unbounded dielectricinterface, which is a limiting case of our general theory,is well known (Born & Wolf, 1975) and has beeninvestigated using fluorescent monolayers (Carniglia etal. 1972). However, we are not aware of any previouscomparison of fluorescence generated over the entireevanescent wave with theoretical values of !{<p, °°) as afunction of incident angle. The results show that ourexperimental system is eminently suited to the task ofmaking reliable accurate quantitative measurements ofcell to glass contacts using the multilayer theory.

Conclusions

The theory of total internal reflection in multilayersthat we have presented is complete insofar as Maxwell's

3X105

2-25X105

l-5xlOs-

62 64 66 68 70 72 74 76 78 80 82

Fig. 12. Fluorescence versus (p normalized to that at<(> = 62°. Experimental points and theoretical curve shown.

equations provide a complete description of the proper-ties of light. The equations give closed form solutionsfor a plane parallel wavefront incident on plane parallellayers. This is a reasonable description of a collimatedlaser beam 'illuminating' cell-glass contacts by TIR.Provided refractive indices at the appropriate wave-length are known, the problem is solved. However, atheory of TIRF, relating fluorescence to the electro-magnetic stimulating energy, is less straightforward.Since the probability of photon emission by a fluor-escent molecule is proportional to the squared ampli-tude of the local electromagnetic field (Appendix 1),the total emission in the evanescent field is proportionalto the integral of the squared amplitude from theglass—water interface to 'infinity', effectively a fewhundred nanometres. When emission is expressed asrelative fluorescence (eqn (12)) the proportionalityfactors QMS cancel out. In a brief discussion ofquantitative TIRF based on cytoplasmic fluorescence,Lanni et al. (1985) used the theory developed byLukosz & Kunz (1977a,b) to compensate for the factthat the proximity of a dielectric interface perturbs theemission of fluorescence. However, they conclude thatthe effect is likely to be small. Since we get precisecorrespondence between the theory for a simple inter-face and experiment without taking this into account,either the correction is negligible or other errorscompensate for it.

7-5X104-

1000 2000 3000D(<p)

4000 5000

Fig. 13. Measured fluorescence (photon count rate)plotted against [D((p)], the denominator of equation (47).The slope C at each concentration is the coefficient ofproportionality between the measured photon count rateand the stimulating evanescent wave energy. The slopes ofthe regression lines expressed as a ratio of that for5mgml" ' are: 1-0, (1-0); 0-80, (0-80); 0-61, (0-60); 0-38,(0-40); 0-20, (0-20); 0-09, (0-10); 0-05, (0-05), where theratios of the concentrations used are shown in parenthesis.

There remains a problem that is less easy to decide.Our quantitative volume-marker TIRF method as-sumes that the entire volume between the substratumand the plasma membrane is equally accessible to thefluorescent tracer molecules. However, the presence ofglycoproteins external to the bilayer may result in acertain volume fraction being unavailable to tracermolecules. The error will be minimal with a smalltracer such as unconjugated fluorescein or rhodamine.Gingell et al. (1985) showed that 168 000MT dextran isexcluded from certain zones of cell-glass contact, butthat 4000Mr fluoresceinated dextran and free fluor-escein are apparently not. Where a probe is excluded,an increasing error would occur as the separationapproaches and then falls below the thickness of theglycoprotein region. By further measurements on therelative fluorescence at cell contacts using fluorescentprobes of different sizes it should be possible to knowwhen volume exclusion is influencing the results.

Summary of results

(1) T1RF provides an exquisitely sensitive way ofmeasuring cell-glass apposition distances up to 100 nmor so.

(2) The method is incomparably more sensitivethan quantitative interference reflection microscopy(IRM) to small changes in distance, up to 100 nm ormore. At larger separations IRM comes into its ownand TIRF becomes insensitive.

(3) TIRF is relatively insensitive to the opticalproperties of the cell periphery and cortical cytoplasm.On glass of high refractive index this insensitivity isremarkable. This provides TIRF with a second majoradvantage over IRM that is sensitive to the refractiveheterogeneity of cytoplasm (even under optimal con-ditions of high illuminating numerical aperture) andthe assumed refractive index of the bilayer and periph-eral glycoprotein region.

(4) The possibilities of varying evanescent wavepenetration by use of substrata of a range of refractiveindices, and by varying the angle of incidence of thestimulating beam provide a powerful tool for analysingcell contacts. With highly attenuated waves it should bepossible to resolve the otherwise difficult question ofthe size of the cell-glass gap beneath very thin cyto-plasmic extensions.

Despite the drawback of relatively expensive andcomplex equipment, including that for recording cellimages at relatively low levels of light (Gingell et al.1985), we feel that TIRF, even in a qualitative form,will soon be considered an indispensable tool forstudying cell contacts. In following papers we shallpresent an experimental investigation of TIRF usingthin films and a quantitative analysis of the contacts ofspread cells.

D.G. thanks the Science and Engineering ResearchCouncil for supporting this work, and his family for support-ing him while deriving equation (40). We are grateful toDr P. Tatham for his kind assistance with optical densitymeasurements.

Appendix 1

The Poynting vector (5) is defined as the energy fluxdirected normal to unit area per second. In MKS units

01,= i) (Ai)

= Nhv,

where iV = number of quanta passing unit cross-sec-tion per second, e and er are the absolute and relativepermittivities of material r and £o, f.io are the electricand magnetic permittivities of free space, respectively,

h is Planck's constant and v is frequency. E is theamplitude of the electric field. Hence:

(A2)

Suppose photons flow axially along a cylinder of unitcross-sectional area and length c/\/lFr containing Mfluorochrome molecules per unit volume. The numberof molecules in the cylinder is:

Mc/VFT.

The number of excitations per second F' is pro-portional to A' and to the number of moleculesaccessed, so that:

NMc _ MeVer ~Tv (A3)

which gives the required relationship between the fieldand the generated fluorescence.

Appendix 2

We believe that our bulk volume marker method mayhave a vertical resolution better than 2nm, for thereasons given in Numerical Results, third section. Itmight be thought that resolution would be limited bythe dye concentration, since this determines the meanseparation between fluorochrome molecules. Since thelatter greatly exceeds 2nm it is important to show thatit is not a limiting factor.

The mean separation of fluorescein molecules /in a lmgml" 1 solution of fluoresceinated dextran(/V/r = 4000) is =46 nm. Even at our top concentrationof 5mgml~' it falls to only 27 nm. Although thesedistances are certainly not small compared with cell-glass gaps or the evanescent decay depth x\ theessential point is thato/ze fluorochrome molecule couldgive a satisfactory 'report' of a small gap (given asufficiently sensitive fluorescence detector) as it dif-fuses in a random walk with components in the A*-direction (perpendicular to the walls), radiating at arate or |.EV2|2. Even for the largest dextran we have used(A/r= 70000; D - 6 X 1 0 " 7 c m 2 s ~ ! ) the mean displace-ment S" in one second is 10 nm. This is far greater thangap dimensions and implies many bounces from the topand bottom walls during one photometric measuringperiod. Thus:

F'(t)dt (A4)

Further, even if the fluorescent molecules in the gapwere relatively fixed in position during the measuringperiod, they would occupy random positions on theA--axis, so that the use of a photometric measuringarea of much greater diameter than / would give a


satisfactory measurement of the gap by generatingfluorescence proportional to:

Ev2\2dx.

The fact that we obtained coincidence between exper-imental and theoretical curves of fluorescence versusangle of incidence provides a practical proof of thecorrectness of the above arguments. Although thesystem is unbounded (no gap) the same principlesapply, since/is not small compared with "x.

References

AXELROD, D. (1981). Cell substrate contacts illuminated bytotal internal reflection fluorescence. J. Cell Biol. 89,141-145.

BORN, M. & WOLF, E. (1975). Principles of Optics, 5thedn. London: Pergamon.

CARNIGLIA, C. K., MANDEL, L. & DREXHAGE, K. H.

(1972). Absorption and emission of evanescent photons.J. opt. Soc. Am. 62, 479-486.

GINGELL, D. (1981). The interpretation of interferencereflection images of spread cells: significant contributionsfrom thin peripheral cytoplasm. J. Cell Sa. 49, 237-247.

GINGELL, D. & TODD, I. (1979). Interference reflectionmicroscopy. A quantitative theory for imageinterpretation and its application to cell-substratumseparation measurement. Biophys. J. 26, 507-526.

GINGELL, D., TODD, I. & BAILEY, J. (1985). Topography

of cell-glass apposition revealed by total internalreflection fluorescence of volume markers. J. Cell Biol.100, 1334-1338.

GINGELL, D., TODD, I. & HEAVENS, O. S. (1982).

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GINGELL, D. & VINCE, S. (1982). Substratum wettabilityand charge influence the spreading of Dictvosteliumamoebae and the formation of ultrathin cytoplasmiclamellae. J. Cell Sci. 54, 255-285.

HLADY, V., VAN WAGENEN, R. A. & ANDRADE, J. D.

(1985). Total internal reflection intrinsic fluorescence(TIRIF) spectroscopy applied to protein adsorption. InSurface and lnterfacial Aspects of Biomedical Polymers,vol. 2, Protein Adsorption (ed. J. A. Andrade), pp.81-119. London: Plenum Press.

IZZARD, C. A. & LOCHNER, L. R. (1976). Cell-to-substratecontacts in living fibroblasts: an interference reflectionstudy with an evaluation of the technique. J. Cell Sci.21, 129-159.

LANNI, F., WAGGONER, A. S. & TAYLOR, D. L. (1985).

Structural organization of interphase 3T3 fibroblastsstudied by total internal reflection fluorescencemicroscopy. J. Cell Biol. 100, 1091-1102.

LUKOSZ, W. & KUNZ, R. E. (1977fl). Light emission bymagnetic and electric dipoles close to a plane interface. I.Total radiated power. J . opt. Soc. Aw. 67, 1607-1614.

LUKOSZ, W. & KUNZ, R. E. (19776). Fluorescence lifetimeof magnetic and electric dipoles near a dielectricinterface. Opt. Commun. 20, 195-199.

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Waals forces. Special characteristics in lipid-watersystems and a general method of calculation based on theLifshitz theory. Biophys. J. 10, 646-663.

WEISS, R. M., BALAKRISHNAN, K., SMITH, B. A. &

MCCONNELL, H. M. (1982). Stimulation of fluorescencein a small contact region between rat basophil leukemiacells and planar lipid membrane targets by coherentevanescent radiation. J . biol. Client. 257, 6440-6445.

(Received 6 January 1987 - Accepted 4 April 1987)


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