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General electromagnetic theory of total internal reflection fluorescence: the quantitative basis for mapping cell-substratum topography D. GINGELL 1 , 0. S. HEAVENS2 and J. S. MELLOR' 1 2 Department of Anatomy and Biology as applied to Medicine, The Middlesex Hospital Medical School, Cleveland Street, London 117, UK Department of Physics, University of York, York, UK Summary Total internal reflection fluorescence (TlKF) has recently been used to look at the contacts made between cells and a glass surface on -which they are spread. Our method utilizes the fluorescence of a water-soluble dye that acts as an extracellular aqueous volume marker. Fluorescence is stimulated by the short-range electric field near the glass surface that exists under conditions of total internal reflection. Since fluorescence is normally generated beneath a spread cell and not beyond it, the fluorescence of the image is related to the size of the cell-glass water gap. The images obtained are remarkable for their detail, contrast and the absence of confusing granularity due to cytoplasmic heterogeneity, which is commonly seen in interference reflection (IRM) images. We here develop a rigorous electromagnetic theory of total internal reflection in layered structures appropriate for cell contacts and apply it to quantitative TIRF. We show that: (1) TIRF, unlike IRM, can report cell-glass gaps in a way that is practically independent of the detailed physical properties of the cell; (2) TIRF is also far more sensitive than IRM for measuring cellglass water gaps up to =100 nm. These striking results explain the image quality seen by TIRF. As the initial step towards verifying our theory we show that measurement of the fluorescence stimulated by total internal reflection at a simple glass-water interface matches theoretical predictions. Introduction (Axelrod, 1981; Weiss et al. 1982). Here we present a quantitative basis for its use and show that it is far superior to IRM for studying cell contacts. We realize that not all who are interested in the application of TIRF will wish to do battle with the mathematics, so our paper is organized so that the results are fully understandable without reference to the theoretical section (pp. 2-8). The basis of TIRF is as follows. Consider a collimated beam of light in glass (refractive index H\), incident at an angle <p on a planar boundary with a transparent medium of lower index n2, where (p exceeds the critical angle </>c(«2, «i). In this case total internal reflection occurs; all the energy is reflected back into the glass and no transmitted wave propagates through «2- F ° r the interface between a microscope coverslip and water (for example), Snell's Law gives: Knowledge of the pattern of contacts between a cell and the surface on which it is spread is basic to understanding cell attachment and movement on solid substrata. A decade ago the re-introduction of interference reflection microscopy (IRM) heralded a major advance in the understanding of cell contacts and their relationship to the cytoskeleton. Nevertheless IRM has very serious drawbacks and although image interpretation has been placed on a quantitative basis (Gingell & Todd, 1979; Gingell et al. 1982) insufficient knowledge of dimensions and refractile properties of the cell periphery is still a substantial practical limitation. Even qualitative misinterpretations of IRM images are easily made (Gingell, 1981). An alternative procedure to IRM employs total internal reflection fluorescence (TIRF). This powerful light-microscopic tool was first used in cell biology only recently 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 Key words: electromagnetic theory, total internal reflection fluorescence, evanescent wave, cell-substratum contact. = arcsin(n z /«i). 677 Although there is no net energy flow into medium n-i there is a very short-range electromagnetic disturbance in the second medium near the interface, called an evanescent wave. This will often have a complicated waveform but its amplitude falls exponentially into medium n-i normal to the interface, and dies out in less than a wavelength. This phenomenon has a long history and was anticipated by Newton. It forms the basis of a type of beam-splitting prism and, most importantly, occurs in fibre optic transmission lines. The relatively recent interest shown by chemists in this seemingly rather arcane phenomenon stems from the fact that if a fluid medium contains dissolved fluorescent molecules, emission can be stimulated by the evanescent wave in a very restricted zone within one wavelength of the glass surface. This has been used for several decades to study the adsorption of fluorescent macromolecules at optical interfaces (see Hlady et al. 1985) but it is only in the past few years that cell biologists have become aware of the subject and have used it to look at cells spread on glass. Axelrod (1981) reported the use of the fluorescent lipid analogue Dil to label cell surfaces and he was the first to demonstrate strictly localized fluorescence where cells come close to glass. Gingell et al. (1985) demonstrated that striking images showing the topography of the cell-glass apposition zone can be obtained using a fluorescent extracellular water-soluble dye acting as an aqueous volume marker. This produces dark contacts against a bright background by virtue of exclusion of the extracellular aqueous volume at contacts. The essential point of this technique is that no fluorescence is normally stimulated from the aqueous medium beyond the cell, since the evanescent wave does not penetrate the several micrometres necessary to cross the cytoplasm. It is for precisely this reason that the volume marker technique is able to provide a unique map of the cell-glass contact zone by reporting variations in the thickness of the aqueous region between a living cell and its transparent substratum. In the following analysis we develop rigorous expressions for the electrical energy in the cell-glass gap under conditions of TIR illumination, by solving Maxwell's equations for all the conditions likely to arise at cell contacts. From these equations we predict the variation in the stimulated fluorescence with cell-glass separation and discuss several factors that may influence the results. A critical comparison of T I R F and IRM is made. Finally, we compare the experimentally measured fluorescence at a simple glass-water interface with our theoretical predictions. (b) (a) \E \E \ V E \ V D 7fc n, *C(»4.«|) < 4» 0C (d) (c) \E A v /i i.}-,.£,., Fig. 1. Layered dielectric model of cell-glass apposition. Light is incident at an angle (f> (which exceeds the critical angle) on the interface between glass (>i\) and a film of aqueous medium (« 2 ) of thickness t\. The cell membrane is represented by an isotropic dielectric film of thickness tz~h and refractive index n3. The average cytoplasmic index is W4. Complex waves (£1 ...E4) have complex amplitudes in the positive .v direction (A...Z5) and negative .v direction (A' ... C'). Quantities /3 r , yr are defined in the text. 678 D. Gingell et al. Fig. 2. The four situations that can arise when an evanescent wave E exists in medium n2 are: in case (a) the waves in media 3 and 4 are also evanescent; in (b) a continuous wave C exists in medium 3; whereas in (c) it exists in medium 4. In case (d) the media 3 and 4 support continuous waves. The relationships between the incident angle <p and critical angles <pc(nr,)i\) are explained in the text. Theoretical We confine the analysis to the case of a plane s-polarized wave with electric vector perpendicular to the plane of incidence (i.e. parallel to the reflecting interface), incident at angle <p>(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 thinfilmsof thickness t2 — t\ and *i, respectively. The symbol" represents a complex quantity. A diagram of the layered system is shown in Fig. 1 in which the y direction is perpendicular to the plane of the paper. The amplitudes EVT will in general be complex. The incident wave has components Ey in the y direction but Ex = E~ = 0. Amplitudes Evr and refractive indices nr are referred to media r = 1... 4. The quantities yr, /Jr are defined below. A ...D are complex amplitude coefficients (phasors) of waves in the ±x direction. In all that follows, ti\ > n2, but distinct and interesting cases for the different relative magnitudes of n\, «3 and na, will emerge. In region r, the appropriate form of Maxwell's equations for plane waves of amplitude Ey are: -nrkl)Ey dxl (1) (2) o • ax • where , „ /. When the waves in media 2, 3 and 4 are evanescent, the solutions for the second-order differential equation take the forms: Y < 0 tz>x>tx F i = A e~'Y ~ Ey3 = C e~p'x + €' ftA " ' x>tz where 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 -A'y, -B +iB~p2 -B' 0 0 0 + 1=0 -iB'Pz 0 0 0 + y. = o 0 -C'e -C'p3 0 eft'' 0 0 + C ' e ft'2 0 0 + C'p3 eft'2 0 0=0 0 0=0 -Df + Dp4 e -ft'z (7) 0=0 0 =0. These are solved using determinants to give the complex coefficients A', B, B', C, C', D. Substitution into equations (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 adjacent layers, but quite a lot of algebra is needed to obtain the explicit solutions considered in this paper.) In a two-film system, 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 in Fig. 2A-D. Consider the behaviour of the function fiT-»z as the angle of incidence <p> <pc(ti2,>i\) varies: (8) when ti\ sin <p>nr the root is positive and /3r is real. However, when n\ sin <p<.nr, (9) where j3r is purely imaginary and yr is real. Consequently, when this occurs the wave in medium r becomes continuous. The significance of this switch is easily understood since Snell's Law requires that the angle of refraction in a medium adjacent to a dielectric film is independent of the refractive index of the film and depends only on the indices of the two bounding media. Therefore, we can define a critical angle between ti\ and « r : n\ sin0! = « r «? sin 2 0, - n 2 = 0. The relations: c <t> {nr,nx)><p><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 an evanescent wave is called frustrated total internal reflection (FTIR). While the relationships between nT and <p that we have described do indeed solely determine whether FTIR can occur, the power of the transmitted wave will fall exponentially with the width of the gap containing the evanescent wave. It falls to around zero for a gap in the order of A. We shall return later to the subject of FTIR in relation to cell contacts. For a cell surface, medium 3 represents lipid ( t t 3 ~ l - 4 ; Ninham & Parsegian (1970)) and medium 4 represents cytoplasm (1-36 Sjn 4 ^ 1-37 from refractometry; Bailey & Gingell (unpublished); Izzard & Lochner (1976)). Since W3 will exceed ;?4 situation c should not arise in observation on cells. Having calculated the squared amplitude |i?v2(.v)|2, which is proportional to electrical energy at a particular depth (JC) in the water gap, we make use of the fact that stimulated fluorescence is proportional to the local electric field energy (see Appendix 1). The coefficient of proportionality linking emission with stimulation will include quantum efficiency (Q) and fluorochrome concentration (M). The proportion of the emitted photons detected by a 680 D. Gingell et al. counting instrument will depend on several factors that are a constant (S) for a given system. Thus detected fluorescence (Fc) for an area beneath a cell where the water gap is t\ will be: Fc = QMS Jo \EvZ{x) | 2 dx = (10) QMSI(tx). The background fluorescence (F^) at a nearby area without a cell will be: F b = QMS f" \Ev2(x) \2dx = QMSI(»). Jo (11) Therefore, relative fluorescence is given by: )• (12) The coefficient QMS drops out and the ratio F, obtained from experimental measurements of fluorescence beneath the 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) where a, = (Pi + 0 2 a2 = - ( $ a s 3 /M/^4si ) sinh(5i + fizifiz + p*4) cosh(5i 34) sinhSi — ^ 3 ()3 4 — Pi) coshS] (14a) (14b) 2 ^zh + P sinh/?2/]) sinh<5i (14c) coshd] + (y32p4 sinhp 2 t) + p3 cosh/32J 1) sinhS] (14d) and Whence: |2 — (15) and (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 and 2 2yf i [ - ^ ^ + /3i(/3 /3i 2 sinhj82/, s m h 2 p V , + p i 3 ( c o s h 2 p ^ 1 - l ) + <1(p-2--l (19) sinh/32/, ) 2 For the case £)—»°° (or ^ ^ 0 ; W3—»n2) we obtain the expression for I^Vl2 for an evanescent wave at a single interface between two bulk media: 1 4n 1 cos (p f exp 4^x (20) Setting the exponent equal to unity we obtain x, the characteristic wave penetration depth, namely the distance into medium 2 at which the squared amplitude has fallen to l/e of its value at x = 0. Thus: vac x = (21) sin2<p Mapping cell-substratum topography 681 A compact expression for / is obtained as usual by integrating the squared amplitude from .v = 0 to infinity. (22) jMwy The form of the evanescent wave Ev{x,z) shown to be: Ev(x,z) at an unbounded interface is relatively straightforward and it can be *nx sin0 - 8, | e~ f c v , = 2«i cos(p • cos( cot \ where the phase angle ^vac (23a) / / 8 \ Pz a.^tan-'/, ). \k0nicos<pj (23b) The final consideration of case (a) involves solving for the field in the fourth medium: where a3 and a4 are given in equation (14c,d). Integration between x = t and infinity gives: 2 lit t \tffePi '' -/B 4 (y?.§+ /&*)• 7(11 2) If the cytoplasm contained a fluorescent volume marker this expression would give fluorescence versus cytoplasm-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 the glass by an aqueous gap t\. Case (b) If there is a continuous wave in the third medium (Fig. 2(b)) we replace P\ by — y 3 and obtain: |£2l 22 2 fl2,2 , 2 b + p 22 bb4 = - ( y ! - j82j84) sind, + y3(/32 + j84) cosd where = (26) > (27a) (27b) b 3 = y3 (/34 sinh/32f, + /32 coshj32r,) cosd, + (^264 cosh^2«, - yf si sinSi (27c) b 4 s y3 (/34 cosh/32/, + B2 sinh/32^ 1) cos61 + (/32/34 sinS) (27d) s i ^ When the fourth medium supports a continuous wave /3 4 becomes — y\ leading to: |2 4y?[{cicosh/32(<1 -.v) + c 2 sinh^ 2 (t 1 - ,v)}2 + {c4 co8h/32(ti - JC) + c3 - P2) sinhj62t\ 'cosh^i + PZ(Y\ y4 - Pl)coshB2t\ •'.3 inh6,} 2 2 1 + 74) COShB2t\ cosh6i + (Yip '3 • PzY*) sinnp2^i •sinh6,} where CI = /3 2 y 4 sinh6] (30a) C2 = /33y4COSh5, (30b) c3=#sinh6, (30c) c 4 = /3 2 /3 3 cosh<5 1 (30d) and 8\ = Pi{tz—1\) as defined earlier. Setting the denominator of equation (29) to^i and integrating with respect to x: |(C' 682 + °2 D. Cn/^e// e< a/. ° 3 + ° 4 ) sinh2j3t, + 2(cf - c2 - c2 + c2)^, + j - (c,c 2 -fc 3 c 4 )(cosh2)3 2 / l - 1 ) | . (31) P22 J 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: - ., = ty2\ 4rf[73(73 sin6 2 • sinh/32(<i - x) - fi2 cos<52 • cosh02(*, - x)}1 +y5{y 3 cos<52-sinhj82(f, -x)+/3 2 sin<5 2 • cosh/32(*i ~ x)}2] . (32) 2 [73(71X4 — y3l)sinhyS2fi •cos6 2 + /3 2 (yiy 4 + yf)cosh/32ti -sin<52] [(7i73 - £ 2 y 4 ) sinhj82t, • sin<52 - y 3 £ 2 (yi + y4) cosh£2«i • cos<52]2 d, = Y$ sin2<52 + 74-73 cos 2 6 2 2 z (33a) 2 d 2 s yf/31 cos 6 2 + yip 2 sin <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: - ' and {(7i73-/3l)sinhyS 2 f 1 } 2 +{y3 2 (y 1 + y 3 ) c o s h e r , } 2 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 absorbs the 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 field equations and obtain a complex fi2 (eqn (4)): ]}2 = ko{a-ib), where (38a) 2 • 2_L 2 a = 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 define ^{^2} - s, so that ^ ^2 = 5 ] + J52 . (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 obtain: \E 12 = 1 y2] where jV jV, tiftf finally + Np (NY+XS+NSrf+iNSAUYN^)2' '<''= ess'<''-*>fe, sinS2(t, - * i ( v) + e- ' "- te3sinS2(<1-x)+^cos52(i1-x)}. s we V ' (41a) x) N2 = t '^~ {gl cosS2(t, -x) -g2smS2(tl -x)} + e - s . d , - * ) ^ ^ CosS2(*, _ x ) + f t s i n 5 2 ( f ] _ x)y . (41b) JV 3 = y33(/34cosa2 • sinhCT! + Si coscr2 • cosher — 5 2 sina 2 • sinhaj) cosh^i • cosher — 5 2 ^4 sin0 2 • sinhCTi + /3f cosa 2 • sinhCTi) sinhdj . oshai + 5 j sina 2 • sinha] +5 2 COSCT 2 • cosha^coshSi + (5i/3 4 sin0 2 • sinh<7i + 5 2 /3 4 cosa 2 • coshai + /3f sina 2 • coshai) sinh6) . Ns = /33()34 cosa 2 • coshCT] + Si COSCT2 • (41c) (41d) sinhcrj - S 2 sina 2 • cosha^ coshdi + (S1P4 COSCT2 • sinh<7i — S2^34 sina 2 • coshai + /33 COSCT2 • cosh<7i) sinh^i . Nf, = j33(j34 sina 2 • sinhCTi + Si sina 2 • coshCT] + S 2 cosa 2 • sinhai) coshoj + (Si/3 4 sina 2 • cosher + S2y34 COSCT2 • sinhCT] +^33 sina 2 • sinhCTi) sinhoj . (41e) (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) Jo which gives the fluorescence at an unbounded interface in the presence of absorption, can be obtained from our results by reducing equation (40) for the case t\ —* °o; tz^* t\. After much algebra all terms in /33 and /34 disappear and we obtain: giving the characteristic decay depth x = 1/2S. Integration gives the background electric energy in the absorbing medium: 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 when K2 = 0 (implying S 2 = 0, whereupon Si = fi2). 684 D. Gingell et al. Numerical results The objective of this work is to show how the water gap between a cell and its substratum can be measured by the TI R-induced fluorescence of a water-soluble dye in the gap. Thus we compute curves of fluorescence versus gap width. Since the electric field of the evanescent wave in the gap stimulates fluorescence, the curves are strongly dependent on factors that affect field energy, namely the angle of incidence <p of the laser beam on the glass-water interface, and the refractive index ti\ of the glass. These two factors also govern how far the evanescent wave penetrates not only into the gap but also into the adjacent cell. If the cell is very thin the wave may even penetrate right through it and stimulate fluorescent molecules on the far side. We shall present the results of calculations, using the theory developed above, which show to what extent measurement of the water gap by T I R F depends on <p and 77] as well as on the physical properties of the cell and its shape. We shall also discuss other factors that may influence the results and give a numerical comparison of the sensitivities of T I R F and IRM. Dependence of fluorescence on the width of the water gap for various incident angles (p and refractive indices of the glass n/ Fig. 3 shows fluorescence (in arbitrary units) stimulated by light (A = 488 nm) incident at angles between 70° and 85°. The curves show how fluorescence depends on the thickness (t\) of the water layer in which the evanescent wave develops. Fig. 4 shows curves of relative fluorescence (F) (fluorescence expressed as a fraction of the bright background value, as defined in equation (12)) versus t\ for <p values between 65° and 85° for both normal glass (wj = 1-539) and high-index glass (ii\ = 1-85). The optical properties of the cell are as shown in Fig. 3. The significant feature of these curves is the short range of T I R F : in all these cases 90% of background fluorescence is reached before the water gap reaches 160 nm. Penetration of the evanescent wave falls as <p increases. On high-index glass at high incident angle 90 % of background fluorescence is reached before the water gap reaches 80 nm, giving an appropriate range for measuring cell-substratum gaps without the evanescent wave passing right through the cytoplasm of thinly spread cells (see below). Relationship between fluorescence and gap width for various assumptions about the nature of the cell surface An important result is shown in Fig. 5. Whereas on normal glass ((p = 75°; n\ = 1-539) setting the cytoplas* mic refractive index to either 1-37 or 1-40 makes a significant 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 less than 2-5nm, right through the useful range from 0 to 70 nm or more. At t\ = 10nm the error is 10%, falling to 5 % at 30 nm. Furthermore, the presence or absence of a membrane in the model makes even less difference than the cytoplasmic variation discussed. We conclude that gap measurement on a high-index substratum is virtually independent of assumptions about the refractive index of the cytoplasm and the ce.ll membrane. Comparison of TIRF with IRM for measuring cellsubstratum topography Figs 6 and 7 show comparisons of quantitative interference reflection theory (Gingell & Todd, 1979) with the present TIRF theory. In comparing the merits of these two techniques we define sensitivity as the change in signal/background with water gap, dR/dti. In the case of TIRF, R = F (eqn (12)). The IRM theory has been experimentally validated and is capable of high accuracy (Gingell et al. 1982) provided the optical properties of the components are adequately known. This, however, can be a serious practical limitation for measuring cell contacts. IRM is best on low-index 40 30- 20- 10- (iY) 50 100 Water gap /| (nm) 150 Fig. 3. Calculated fluorescence Fc (arbitrary units) generated by the evanescent wave in the aqueous gap beneath a model cell (see Fig. 1) plotted as a function of gap thickness t\. Curves are shown for several angles of incidence <p= (i) 70°, (ii) 75°, (iii) 80°, (iv) 85°. Refractive indices are as follows: glass n\ = 1-539; aqueous medium /?2 = 1-337; cell membrane n^ = 1-45 (thickness t2~t\ = 4nm); cytoplasm «.» = 1-37. Wavelength of incident light A = 488 nm. Mapping cell-substratum topography 685 glass, where the differences in amplitudes reflected from glass and the cell surface are minimized. In this situation (Fig. 6) it is clear that the IRM image only begins to give useful information about the cell-glass gap when it exceeds 30nm or so; at smaller distances sensitivity is very poor. Furthermore, the result is dependent on the cytoplasmic refractive index because IRM image formation depends on phase retardation due to the refraction of light through the cytoplasm as well as reflection at the cell periphery. The reflected amplitude is a function of the refractive indices of the various layers of the cell surface and the interpretation of IRM images depends on the details of the assumed properties of this region. Even under optimal conditions of high illuminating numerical aperture where the contribution of cell thickness to image formation is minimized, this contribution still depends critically on the cytoplasmic refractive index (Bailey & Gingell, unpublished), and it is for this reason that cytoplasmic inhomogeneities give IRM images a characteristic granularity. 80 100 Water gap (, Fig. 4. Calculated relative fluorescence F developed in a variable aqueous gap /|. Upper three curves, refractive index of glass n\ = 1-85; lower three curves, n\ = 1-539. Incident angles (<p) 65°, 75°, 85° as shown. Other parameters as in Fig. 3. IRM TIRF 10 10 20 30 40 50 Water gap f, (nm) 60 70 Fig. 5. Calculated relative fluorescence F developed in a variable aqueous gap t\ showing the limited dependence of fluorescence 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 the membrane is (optically) absent. 686 D. Gingell et al. 20 30 40 50 Water gap I, (nm) 60 70 F i g . 6. Comparison of (i), (ii) I R M with (iii), (iv) T I R F . Relative signal (i.e. signal/background) appropriate to each method is plotted against the aqueous gap t\. For IRM the parameters used are glass n\ = 1-539; medium n2 = 1 3 3 7 , t\ variable; lower lipid membrane iij = 1 4 5 , 4 n m ; cytoplasm « 4 = 1-40 (i) or 1-37 (ii), 1000 n m ; upper membrane (as lower); upper medium (as lower). For T 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 = 4 8 8 n m ; angle of incidence tf> = 75°only. Although TIRF developed on low-index glass depends to a limited extent on the cytoplasmic refractive index (lower curves, Fig. 6) the sensitivity of the method is very high. On high-index glass (Fig. 7) IRM is useless below 50 nm but on the other hand TIRF is seen to be a very sensitive function of the width of the water gap, rising to almost half the background value in 30 nm. Even 2nrn is probably measurable (see Appendix 2). Dependence of fluorescence on gap width for the special case where the cytoplasm is very thin Evidence from quantitative IRM and supported by electron microscopy shows that cells can make ultrathin peripheral cytoplasmic lamellae, of ~100nm (Gingell & Vince, 1982; Mellor & Gingell, unpublished). These appear as dark areas in IRM, similar to intimate cell-glass contacts. When such lamellae have formed it is difficult if not impossible to measure their separation from the substratum by IRM when their thickness is unknown. If lamellae have a refractive index different from bulk cytoplasm the matter is even more uncertain. In contrast, TIRF offers a way of measuring cell-glass gaps beneath thin lamellae, utilizing the low wave penetration available with- glass of high refractive index. In addition there is the advantage that uncertainty in assigning the cytoplasmic refractive index becomes unimportant when high-index glass is used. But first, consider the situation of T I R F on normal glass shown in Fig. 8. Fluorescence beneath a lamella, as a function of the water gap, is shown in the ascending curves. Fluorescence stimulated beyond the lamella, due to partial penetration of the thin cytoplasmic layer by the evanescent wave, is shown in the descending curves. For a given lamella thickness, increasing the water gap (i.e. moving the lamella further away from the glass) reduces the fluorescence originating beyond it while increasing that beneath it, up to the bright background value where relative fluorescence approaches unity. Results are given for lamellae of 100 and 200nm. Obviously, much less fluorescence is generated beyond a thick lamella than a thin one. When the same modelling is done with glass of high refractive index (Fig. 9) it is immediately clear that very little fluorescence originates beyond the cell, even with no water gap. When (p = 78° a 100 nm lamella is effectively infinitely thick. This offers an unambiguous way of analysing the contacts of cells where such lamellae form, and this will be expanded in a subsequent paper. IRM 1-On 0-8- 0-6- 0-4- 50 100 Water gap r, (nm) 0-2- 10 20 30 40 50 Water gap (| (nm) 60 F i g . 7. Curves (i)-(iv) as Fig. 6 except substratum modelled as glass of high refractive index ii\ = 1 8 5 . Curve (v) as for (ii) except n^ = n+, i.e. cell membrane optically deleted. 150 F i g . 8. Evanescent wave can penetrate a thin cytoplasmic lamella and stimulate fluorescence beyond it. Inset sketch shows details. Ascending curves: relative fluorescence generated beneath cell approaches unity as aqueous gap t\ increases. Descending curves: relative fluorescence generated beyond lamella falls to zero as l\ increases. Continuous curves, 100nm lamella; broken curves, 200 nm lamella. Angle of incidence either 76° or 64° as shown. A = 488nm. Mapping cell—substratum topography 687 Under what conditions does frustrated total internal reflection fluorescence (FTIRF) occur and what can be learned from this effect? In the results given so far, no reference has been made to the different possible electromagnetic waveforms in the cell periphery (Fig. 2). In most situations case (a) is appropriate, but at sufficiently small (p values, not far above the critical angle <pc{nz,n\), case (b) and ultimately at <f) values just above </>c(«2.«i) case (d) will occur. As <p is reduced that part of the cell periphery with the highest refractive index will be the first to transmit a continuous wave. We would expect this to be the plasma membrane bilayer and the conditions for a continuous wave in n^ but not « 4 are: When these criteria are satisfied, the plasma membrane will behave like a parallel wafer guide, and a wave will be propagated along it, totally internally reflected from the lipid-water and lipid-cytoplasm boundaries. At a slightly smaller incident angle a continuous wave will be transmitted through the cytoplasm as well (case (a)). This will happen when: 0 c («2i«i) <( P <arcsin(«4/«i). We have in fact seen fluorescence stimulated by laser light transmitted by FTIR from cells that have regions very close to glass, when illuminated at incident angles well above 0 c ( n 2 , n i ) . These fluorescent beams look Fluorescence beneath cell like comet tails, originating at cells and pointing away from the light source. This phenomenon will be discussed further in a later paper. The fact that FTIRF first appears near 69° in the case of chick heart fibroblasts shows that the part of the cell periphery with the highest refractive index has an index of 1-40. This is presumably the mean refractive index of the lipid bilayer. To what extent is gap measurement influenced by absorption of the stimulating evanescent wave by aqueous fluorochrome molecules? Fig. 10 illustrates the degree to which perturbation of the evanescent wave, due to its absorption by the fluorochrome, affects fluorescence. It can be seen that relative fluorescence decays more rapidly as the absorption coefficient Kz increases, so that increasing Kz is similar to increasing the refractive index of glass. This incidentally suggests that a suitable absorber in the medium could attenuate the evanescent wave, without recourse to a substratum of high refractive index. However, our reason for modelling absorption was to see whether it was likely to 'bleed off sufficient evanescent wave energy to cause a significant error in quantitative work. Since our maximum measured extinction coefficient for fluorescein isothiocyanate (6850OM~'cm~') gives an evanescent wave absorption coefficient of only 5X 10~5 there should be no measurable error from this source (see next section). 1-25 1-20- 115- 110- 105- 50 100 Water gap (| (nm) Fluorescence beyond lamella 150 F i g . 9. As Fig. 8 except glass nx = 1-85. Results for 100nm lamella only given. Curves (i), (iii), <p = 78"; curves (ii), (iv), $ = 64°. 688 D. Gingell et al. 1-00 F i g . 10. Ratio of fluorescence in the absence Ft, and presence F{, of absorption of the stimulating wave, at an unbounded 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 solutions of fluoresceinated dextran (FD-4; mean M r = 4100; Sigma, Southampton, UK) at different concentrations, as a function of the angle of incidence exceeding the critical angle, at an unbounded glass-water interface. The solutions were made by serial dilution of a stock containing 5mgml~ FD-4 plus 5mgml~ unlabelled dextran (Mr = 6000; Fluka, Buchs, Switzerland) and 25 mM-Hepes buffer, pH 7-2. Dilution with a similarly buffered l O m g m P 1 solution of unlabelled 6000 Mr dextran obviated small variations in refractive index, which otherwise arise due to variable dextran content. All solutions were passed through a sterile 0-2 nm pore size 'Acrodisc' filter (Gelman Sciences Ltd, Northampton, UK) before use. The refractive index of the solutions (w2= 1-339) was determined with an Abbe refractometer (model 60/ED Mkl; Bellingham & Stanley Ltd, Tunbridge Wells, UK) illuminated with a low-power beam from an argon ion laser at A = 488 nm. The equipment used for photon counting has been described in detail elsewhere (Gingell et al. 1985). For fluorescence measurements, several drops of the dextran solutions were placed on the upper surface of a glass prism (n = 1525) and illuminated by means of an argon ion laser (A = 488 nm) at angles above the critical angle (pc(ri2, «i) = arcsin (1-339/1-525). The beam was spatially filtered and refocused onto the interface with a half-angle convergence of 0-5°. The error in incident angle at the centre of the optical field was found to be less than ±0-05°. The laser used in light control mode gave a constant power output of 100 raW, and the beam was attenuated with a neutral density filter (O.D. = 1; Melles Griot, Aldershot, UK) to prevent significant photobleaching. Rotation of the laser beam to give transverse polarized light (i.e. s-polarization, perpendicular to the plane of incidence, to within ±1°) was obtained with a double Fresnel rhomb (Lexel, Lamda Photometries, Batford Mill, UK), which screwed to the front of the laser. Emitted fluorescence was collected using a 63 X water immersion objective (Zeiss, Oberkochen, Welwyn Garden City, UK) focused on the interface, using a photomultiplier aperture of 2-5 mm. The laser beam was centred to the optic axis of the objective by small adjustments to the angle of incidence and a lateral micrometer movement, to peak the photon count rate over 100 s. This was repeated for each solution and for every angle of incidence. Although there was no evidence of dextran adsorption to glass (a 10-20 s rinse in deionized water returned the photon content to background; see also Hlady et al. 1985) the upper surface of the block was rinsed between dextran solutions with dilute Teepol, then water and finally acetone. This had no effect on measured fluorescence but gave very reproducible values of laser light scattered by imperfections in the interface. Scatter was measured at each angle of incidence using lOmgml" 1 unfluoresceinated dextran in place of FD-4, after removing the Schott OG515 barrier filter. The extinction coefficient e of each FD-4 solution was measured using an LKB Ultrospec 4050 spectrophotometer and the absorption coefficient Ki (eqn (38)) was calculated according to the relationship K2 = 2-303ehM/4jl, where M is the fluorescein (fluorochrome) concentration. All optical measurements were made at 22°C. Fig. 11 A,B shows that, over the entire range of FD-4 solutions, fluorescence is linearly proportional to fluorochrome concentration. Thus quenching is absent, even at the highest concentration used. Comparison of theory with measured fluorescence over a range of incident angles was performed in two ways. In the first, experimental values of fluorescence versus (f> are normalized to the fluorescence measured at 62° and it can be seen that they follow closely the corresponding theoretical curve, shown as a continuous line in Fig. 12. The second method involves linear transformation of the curves and permits calculation of the constant QS defined in equation (11). This equation gives the background fluorescence Fb at an unbounded interface for the case of unit incident amplitude. We introduce a factor of cos<p to take account of the fact that the proportion of the incident flux falling within the fixed measuring area, viewed by the photomultiplier, falls with increasing <p. Furthermore, although the total laser beam power is constant during measurements, the incident amplitude depends on previous reflections, which change with <p. Setting the angleindependent factors QMS = C and recalling the angular dependence of / we write: A((p) is the amplitude of the wave in the glass, which depends on previous reflections. Substituting for / from equation (22) and expressing Y\ and fiz from equations (8) and (9) gives: C = Fb(<f>)/G(<P), (47) where G(<P) = Thus a plot of the experimental values Fb((p) versus the denominator of equation (47), [D(<j>)], should give a straight line of slope C for a given concentration M. Fig. 13 shows that a most satisfactory linear relationship is indeed found between Fb((p) and D((f)) for all concentrations used. From C we obtain the system constant QS, which relates measured photon count rate Mapping cell-substratum topography 689 2-2x10*- 1-5X10 3 - 64-2° lxH) 5 66-4° 4 5XK) 0 1-0 2-0 3-0 4-0 5-0 0 0-5 1-0 2-0 Concentration 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 for the three low incident angles shown in A are partially included as broken lines in B. The latter has an expanded scale suitable for larger values of (p. The slopes of the regression lines shown (expressed as the ratio of the slope for 62°) are given 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 9 h later, after the full range of measurements was completed. to the integral I(4>, °°) for a given value of M. The strictly linear curves that pass through the origin indicate: (1) the correctness of the physical theory for a simple interface; (2) the measuring system is highly accurate; (3) excitation of fluorescence by scattered laser light in our system is negligible; (4) adsorption of FD-4 onto glass is negligible; (5) photobleaching is negligible under our experimental conditions; (6) absorption of laser light by the fluorochrome is negligible, as deduced in the previous section. The last point means that the energy absorbed from the evanescent electromagnetic wave, which drives fluorescence, is a negligible fraction of the electric field energy. The fact that scatter cannot be a major determinant of fluorescence was shown by direct measurement at 488 nm without FD-4. Whereas the photon count from fluorescence changes 100-fold from lowest to highest incident angle, the count from scatter changed only 10-fold. It is therefore related to <p by a completely different functional relationship from that linking fluorescence with (p. Thus any significant contribution to 690 D. Gingell et al. the total fluorescence stemming from scattered light would bend the straight lines in Fig. 12. We should stress that the relatively simple situation of an evanescent wave at an unbounded dielectric interface, which is a limiting case of our general theory, is well known (Born & Wolf, 1975) and has been investigated using fluorescent monolayers (Carniglia et al. 1972). However, we are not aware of any previous comparison of fluorescence generated over the entire evanescent wave with theoretical values of !{<p, °°) as a function of incident angle. The results show that our experimental system is eminently suited to the task of making reliable accurate quantitative measurements of cell to glass contacts using the multilayer theory. Conclusions The theory of total internal reflection in multilayers that we have presented is complete insofar as Maxwell's 3X105 2-25X10 5 l-5xlO s - 7-5X104- 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 properties of light. The equations give closed form solutions for a plane parallel wavefront incident on plane parallel layers. This is a reasonable description of a collimated laser beam 'illuminating' cell-glass contacts by TIR. Provided refractive indices at the appropriate wavelength are known, the problem is solved. However, a theory of TIRF, relating fluorescence to the electromagnetic stimulating energy, is less straightforward. Since the probability of photon emission by a fluorescent molecule is proportional to the squared amplitude of the local electromagnetic field (Appendix 1), the total emission in the evanescent field is proportional to the integral of the squared amplitude from the glass—water interface to 'infinity', effectively a few hundred nanometres. When emission is expressed as relative fluorescence (eqn (12)) the proportionality factors QMS cancel out. In a brief discussion of quantitative T I R F based on cytoplasmic fluorescence, Lanni et al. (1985) used the theory developed by Lukosz & Kunz (1977a,b) to compensate for the fact that the proximity of a dielectric interface perturbs the emission of fluorescence. However, they conclude that the effect is likely to be small. Since we get precise correspondence between the theory for a simple interface and experiment without taking this into account, either the correction is negligible or other errors compensate for it. 1000 2000 3000 4000 5000 D(<p) 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 of proportionality between the measured photon count rate and the stimulating evanescent wave energy. The slopes of the regression lines expressed as a ratio of that for 5mgml"' 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 the ratios of the concentrations used are shown in parenthesis. There remains a problem that is less easy to decide. Our quantitative volume-marker TIRF method assumes that the entire volume between the substratum and the plasma membrane is equally accessible to the fluorescent tracer molecules. However, the presence of glycoproteins external to the bilayer may result in a certain volume fraction being unavailable to tracer molecules. The error will be minimal with a small tracer such as unconjugated fluorescein or rhodamine. Gingell et al. (1985) showed that 168 000MT dextran is excluded from certain zones of cell-glass contact, but that 4000Mr fluoresceinated dextran and free fluorescein are apparently not. Where a probe is excluded, an increasing error would occur as the separation approaches and then falls below the thickness of the glycoprotein region. By further measurements on the relative fluorescence at cell contacts using fluorescent probes of different sizes it should be possible to know when volume exclusion is influencing the results. Mapping cell-substratum topography 691 Summary of results h is Planck's constant and v is frequency. E is the amplitude of the electric field. Hence: (1) T1RF provides an exquisitely sensitive way of measuring cell-glass apposition distances up to 100 nm or so. (2) The method is incomparably more sensitive than quantitative interference reflection microscopy (IRM) to small changes in distance, up to 100 nm or more. At larger separations IRM comes into its own and TIRF becomes insensitive. (3) T I R F is relatively insensitive to the optical properties of the cell periphery and cortical cytoplasm. On glass of high refractive index this insensitivity is remarkable. This provides TIRF with a second major advantage over IRM that is sensitive to the refractive heterogeneity of cytoplasm (even under optimal conditions of high illuminating numerical aperture) and the assumed refractive index of the bilayer and peripheral glycoprotein region. (4) The possibilities of varying evanescent wave penetration by use of substrata of a range of refractive indices, and by varying the angle of incidence of the stimulating beam provide a powerful tool for analysing cell contacts. With highly attenuated waves it should be possible to resolve the otherwise difficult question of the size of the cell-glass gap beneath very thin cytoplasmic extensions. Despite the drawback of relatively expensive and complex equipment, including that for recording cell images 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 for studying cell contacts. In following papers we shall present an experimental investigation of TIRF using thin films and a quantitative analysis of the contacts of spread cells. D.G. thanks the Science and Engineering Research Council for supporting this work, and his family for supporting him while deriving equation (40). We are grateful to Dr P. Tatham for his kind assistance with optical density measurements. Appendix 1 The Poynting vector (5) is defined as the energy flux directed normal to unit area per second. In MKS units 01,= i) (Ai) = Nhv, where iV = number of quanta passing unit cross-section per second, e and e r are the absolute and relative permittivities of material r and £o, f.io are the electric and magnetic permittivities of free space, respectively, 692 D. Gingell et al. (A2) Suppose photons flow axially along a cylinder of unit cross-sectional area and length c/\/lFr containing M fluorochrome molecules per unit volume. The number of molecules in the cylinder is: Mc/VFT. The number of excitations per second F' is proportional to A' and to the number of molecules accessed, so that: NMc _ Me Ver ~Tv (A3) which gives the required relationship between the field and the generated fluorescence. Appendix 2 We believe that our bulk volume marker method may have a vertical resolution better than 2nm, for the reasons given in Numerical Results, third section. It might be thought that resolution would be limited by the dye concentration, since this determines the mean separation between fluorochrome molecules. Since the latter greatly exceeds 2nm it is important to show that it is not a limiting factor. The mean separation of fluorescein molecules / in a l m g m l " 1 solution of fluoresceinated dextran (/V/r = 4000) is =46 nm. Even at our top concentration of 5mgml~' it falls to only 27 nm. Although these distances are certainly not small compared with cellglass gaps or the evanescent decay depth x\ the essential point is thato/ze fluorochrome molecule could give a satisfactory 'report' of a small gap (given a sufficiently sensitive fluorescence detector) as it diffuses in a random walk with components in the A*direction (perpendicular to the walls), radiating at a rate 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 displacement S" in one second is 10 nm. This is far greater than gap dimensions and implies many bounces from the top and bottom walls during one photometric measuring period. Thus: F'(t)dt (A4) Further, even if the fluorescent molecules in the gap were relatively fixed in position during the measuring period, they would occupy random positions on the A--axis, so that the use of a photometric measuring area of much greater diameter than / would give a GINGELL, D., TODD, I. & HEAVENS, O. S. (1982). satisfactory measurement of the gap by generating fluorescence proportional to: Ev2\2dx. The fact that we obtained coincidence between experimental and theoretical curves of fluorescence versus angle of incidence provides a practical proof of the correctness of the above arguments. Although the system is unbounded (no gap) the same principles apply, since/is not small compared with "x. References Quantitative interference microscopy: effect of microscope aperture. Optica Acta 29, 901-908. GINGELL, D. & VINCE, S. (1982). Substratum wettability and charge influence the spreading of Dictvostelium amoebae and the formation of ultrathin cytoplasmic lamellae. 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. In Surface 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-substrate contacts in living fibroblasts: an interference reflection study with an evaluation of the technique. J. Cell Sci. 21, 129-159. LANNI, F., WAGGONER, A. S. & TAYLOR, D. L. (1985). AXELROD, D. (1981). Cell substrate contacts illuminated by total internal reflection fluorescence. J. Cell Biol. 89, 141-145. BORN, M. & WOLF, E. (1975). Principles of Optics, 5th edn. 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 interference reflection images of spread cells: significant contributions from thin peripheral cytoplasm. J. Cell Sa. 49, 237-247. GINGELL, D. & TODD, I. (1979). Interference reflection microscopy. A quantitative theory for image interpretation and its application to cell-substratum separation measurement. Biophys. J. 26, 507-526. GINGELL, D., TODD, I. & BAILEY, J. (1985). Topography of cell-glass apposition revealed by total internal reflection fluorescence of volume markers. J. Cell Biol. 100, 1334-1338. Structural organization of interphase 3T3 fibroblasts studied by total internal reflection fluorescence microscopy. J. Cell Biol. 100, 1091-1102. LUKOSZ, W. & KUNZ, R. E. (1977fl). Light emission by magnetic 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 lifetime of magnetic and electric dipoles near a dielectric interface. Opt. Commun. 20, 195-199. NINHAM, B. W. & PARSEGIAN, V. A. (1970). Van der Waals forces. Special characteristics in lipid-water systems and a general method of calculation based on the Lifshitz theory. Biophys. J. 10, 646-663. WEISS, R. M., BALAKRISHNAN, K., SMITH, B. A. & MCCONNELL, H. M. (1982). Stimulation of fluorescence in a small contact region between rat basophil leukemia cells and planar lipid membrane targets by coherent evanescent radiation. J . biol. Client. 257, 6440-6445. (Received 6 January 1987 - Accepted 4 April 1987) Mapping cell—substratum topography 693