Quarterly Reviews of Biophysics 9, I (1976), pp. 49-68 Printed in Great Britain
Applications of Fluorescence Correlation Spectroscopyf WATT W.WEBB School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, U.S.A.
INTRODUCTION
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LATERAL DIFFUSION IN L I P I D BILAYERS
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SOME INNOVATIONS IN FCS METHODOLOGY
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D I S C U S S I O N OF DIFFUSION IN MEMBRANES
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REFERENCES
67 INTRODUCTION
The preceding paper by Douglas Magde has recounted the basic principles of Fluorescence Correlation Spectroscopy (FCS) as originally described (see Magde, Elson & Webb, 1972; Elson & Magde, 1974; Magde, Elson & Webb, 1974; Elson & Webb, 1975; referred to collectively as MEW), and has described the first application to chemical kinetics. In this paper I shall first illustrate the same principles of FCS with a simple graphical demonstration model based on the scheme for application to lateral diffusion in membranes as it was developed in our laboratory by Dr T.J.Herbert; I shall then proceed to discuss some current research in our group organized jointly with Professor E. L. Elson at Cornell. To indicate the current capability of FCS, I shall describe some recent instrumentation developments by Dr D. E. Koppel and show some illustrative data provided by Dr Koppel and Dr J. Schlessinger on transport in solutions selected for this symposium, 'Dynamics of Macromolecules in Solution'. Finally I shall present t This paper was presented at the symposium on Dynamics of Macromolecules in Solution at the 5th International Biophysics Congress in Copenhagen, Denmark, 4-9 August 1975. [49]
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graphically some ideas about lateral transport in and on cell membranes that have evolved from our thinking about our current experiments on transport in both lipid bilayers and mammalian cell membranes. Experiments being carried out by Dr Koppel, Dr Schlessinger, Dr D. Axelrod, L. Barak, P. Dragsten, J. Reidler and D. Wolf with E. L. Elson and myself will be reported elsewhere.
LATERAL DIFFUSION I N L I P I D BILAYERS
In preparation for measurements of lateral diffusion in lipid bilayers we form a black lipid membrane by conventional techniques (Mueller et al. 1962) in a wire loop mounted on a hypodermic syringe. The loop is Filters P.M. tube
Syringe tube To infusion pump
LArgon
7------^--/ n
laser -
+ Diff. amp.
Correlator
(b)
Bilayer Laser beam
Fig. 1. (a) Schematic diagram of apparatus for Fluorescence Correlation Spectroscopy. (6) Lipid bilayer formed by Mueller-Rudin technique using hypodermic syringe to supply and meter droplet of lipid solution. Laser beam is focused on bilayer.
Applications of fluorescence correlation spectroscopy
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Lecithin
Fluorophore
Fig. 2. Schematic representation of a section of lipid bilayer showing dissolved carbocyanine fluorophore in expected configuration within the bilayer.
positioned in a spectrometer cell within an optical cavity arranged for efficient collection of thefluorescentlight excited by a laser beam focused on the membrane (see Fig. 1 a, b). To form the membrane, a solution of lipids and fluorophore in hexane or octane is injected into the plane of the wire loop using the hypodermic syringe. There it forms a meniscus; then the excess solution is drawn off with the syringe and the remaining droplet thins down to form a black lipid membrane suspended in the loop. The laser beam illuminates and excites thefluorophoresin a circular spot on the membrane. Precise temperature regulation is available and the technique was sufficiently tractable for Dr T. J. Herbert to form black lipid membranes from a broad composition range of mixtures of cholesterol and egg lecithin that were labelled with small additions, say io~3 mole fraction, of lipid soluble fluorophore, dioctadecyl oxycarbocyanine. This molecule is thought to enter the molecular structure of the bilayer with its head group lying parallel to the surface of the membrane and the hydrocarbon tails parallel to the hydrocarbon tails of the phospholipids that form the membrane. The orientation of the polar head group parallel to the surface of the bilayer was demonstrated by Yguerabide & Stryer (1971) and confirmed by Badley, Martin & Schneider (1973). We can visualize the molecular structure of the bilayer as shown in Fig. 2. We think that the carbocyanine molecule mimics the phospholipid rather well and that its diffusion is quite similar to that of the phospholipids. The carbocyanine molecules, here shaded black, are induced to fluoresce
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Fig. 3. Topographical map of bilayer containing dissolved fluorophore molecules (small circles) randomly distributed within it. Large circles represent areas illuminated by the laser beam. Only the illuminated fluorophore molecules fluoresce (solid circles). The four illuminated circles may be regarded as examples of configurations found at various times. The time scale of the changes due to diffusion in and out of an illuminated area is a characteristic diffusion time from which the diffusion coefficient is deduced. Note that the numbers of illuminated molecules N = 10, 5, 8, 4 are actually much smaller than the actual numbers which are typically io 3 -10 6 .
by the laser beam. Thus topographical maps of illuminated spots on the membrane might look something like Fig. 3. The small circles indicate the random positions of the fluorescent molecules in the membrane. However, only those within the illuminated areas actuallyfluoresce;they are shown as solid circles. Four of the many possible configurations of molecules within the laser beam are illustrated by the four beam circles of Fig. 3. In this illustration we show only about ten fluorophore molecules within the beam, although in actual practice we use concentrations of fluorophores that yield IO 3 -IO 6 fluorescent molecules in a beam spot of about 3 /tm radius.
Applications offluorescencecorrelation spectroscopy 53
Now the fluorescence intensity is proportional to the number of illuminated fluorophores and to the intensity of the illumination. Although the intensity within the laser beam is not uniform, we shall pretend in this simple discussion that it is. (The correct equations for the actual case of non-uniform light beams with gaussian intensity profiles are discussed by MEW.) For a uniform beam, the fluorescence intensity is thus precisely proportional to the number of illuminated fluorophores. Because the membrane resembles a viscous fluid layer, we expect the lipid molecule to diffuse laterally in the membrane and in the course of this motion to pass in and out of the illuminated spot. Similarly we expect the dissolved fluorophore molecules to diffuse in and out of the beam. Since our fluorophore does not dissolve noticeably in the surrounding aqueous phase, the only available mechanism for change of the number of illuminated fluorophores is lateral diffusion within the membrane. (Photolysis of the fluorophore by the bright laser beam may also destroy the fluorophore but this perturbation can be kept negligible.) As the fluorophore molecules diffuse the number N* within the beam fluctuates with time. The configurations at various times would look something like the four examples of Fig. 3. The variance of the number N* within the beam obtained by many independent observations is simply the variance of a random variable
\(u.i\ ) ) — yv ) so
(Kj*y
~ (N*y
Because thefluorescenceintensity / i s proportional to N*, its fluctuations are proportional and the variance is similarly as has b een shown by MEW. We should recall that in typical experiments (N*) > io 4 so £/ < 1 % rather than the much larger variations implied by the small values of N* in our schematics. In any case the value of the variance of the intensity fluctuations provides an accurate assay of the number, and thus the concentration, of independent mobile fluorophore molecules. Now the essential information for measurement of diffusion is derived from the time scale of the fluctuations of the fluorescence intensity. This time scale is determined by the characteristic time required for a molecule
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80
90
Fig. 4. Diffusion in aqueous solution of the free dye molecule rhodamine 6G (A) and bovine serum albumen (BSA) labelled with rhodamine 6G, pH 7, o-i M phosphate buffer (•). Several data sets indicate reproducibility of the time dependence of the normalized correlation functions £(j)lft.
to diffuse out of the illuminated circle. Recall that the diffusion coefficient D is defined in terms of the spatial correlation function by where f is the position vector, d is the dimensionality of the diffusion space (we suppose d = 2, for a membrane) and T the diffusion time. This equation suggests that the characteristic time scale TD of intensity fluctuations due to two-dimensional diffusion of molecules in and out of a spot of radius w as in our problem should be approximately TD = w2I^D.
In fact MEW found exactly this result for the characteristic time scale of fluorescence intensity fluctuations from a spot illuminated by a gaussian beam of effective half width w. The correlation function of the intensity fluctuations that provides a complete statistical description of the intensity in this case is
Applications offluorescencecorrelation spectroscopy 55 1001
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
00 10
20
30
40
50
60
70
80
90
r (msec)
Fig. 5. Plots of the reciprocal of the normalized diffusion coefficient show reasonable fits to the expected linear form [(^T)//?]- 1 = 1 + TlTv- •> Rhodamine 6G-labelled BSA, pH 7, o-i M phosphate buffer. A, Rhodamine (sG in water. , Straight line fits.
where /? = i/(iV*>. The amplitude ^(o) = /? = (N*)-1 is determined by the effective number of illuminated, independent fluorophores and provides a useful concentration assay. The time-dependent factor depends on the dimensionality of the diffusion problem as (1 + rJTD)~^d. In all of our experiments the diffusion remains two-dimensional even for solutions in a spectroscopic cell because only the diffusion component perpendicular to the laser beam can change the illumination of a molecule (see MEW). Dr Koppel and Dr Schlessinger have provided a set of FCS correlation functions recorded on fluorophores in solution to illustrate effects of concentration, solution viscosity, molecular weight and formation of micelles on solute diffusion in solution. Fig. 4 compares the normalized correlation functions £(T)//? of free rhodamine 6G, D* ~ io-6cm2/sec. with rhodamine 6G labelled obvine serum albumen, D ~ io~7cm2/sec, in water. Several sets of data are presented by copying the printer output just as the correlation computer presents them. Duplicate curves show
00
50
100 150 ti (msec/cp)
200
Fig. 6. (a) Plots of the normalized correlation functions for rhodamine 6G (5-6 x io~8 M) in water-glycerol mixtures show the slowing by increasing viscosity. (6) Normalization of the data of (a) using tabulated viscosity data shows the expected magnitude of the effect. Percentage (vol./vol.) glycerol: D, o; O, 20; x , 40; A, 60.
240
w
W
3"
Applications offluorescencecorrelation spectroscopy 57
D~IO~S cm2/sec, Af*~500 micelles
D ~ 1 0 " 6 cm2/sec, N*~ 104 molecules 00
J
40
1
I
80
I
1
120
1
1 1 i 160 200
I L 240 280
(msec)
Fig. 7. The correlation function for large micelles of carbocyanine dye in ethanol—water mixtures is compared with the free molecules in ethanol. Note the large amplitude of the correlation function generated by the small illuminated number of micelles. Each micelle contains many fluorophore molecules so is brightly fluorescent. 8xio" 6 mg/ml di-I-C18(3). D, 20% ethanol in water; A, 100% ethanol.
the excellent reproducibility. In Fig. 5 the reciprocal of the normalized correlation function is plotted for two sets of data to demonstrate conformity to the expected (1 +7"/rJr,)~1 form for the correlation function due to diffusion through the gaussian laser beam. The normalized correlation functions shown in Fig. 6 (a) demonstrate the dependence of the diffusion constant on viscosity in water-glycerol mixtures. Dividing the time scale by the known viscosities superimposes the correlation functions, Fig. 6 (b). Diffusion of fluorescent supramolecular objects is illustrated in Fig. 7. One of the lipophilic fluorescent molecules, 3,3'dioctadecylindocarbocyanine (Sims et al. 1974), that we have adopted as a probe of diffusion in lipid membranes, is virtually insoluble in water, has a strong tendency to form large micelles in water-ethanol mixtures and is soluble in ethanol. The non-normalized FCS correlation functions for diffusion of dye micelles in water-ethanol mixtures, so large that D ~ io~8 cm2/sec
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at a concentration such that only about 500 independent micelles are present in a laser beam, is shown in Fig. 7. For comparison the FCS correlation function of free dye molecules in ethanol, shown on the same scale, is the tiny curve near the origin. Actually free dye diffusion is readily measured as is shown in the preceding figures. However the large relative intensity fluctuations, and therefore the large value of |(o), produced by the small number of illuminated, independent diffusing micelles is strikingly illustrated by this example. SOME INNOVATIONS I N FCS
METHODOLOGY
Recognizing the need for measurements of lateral diffusion and kinetics on and in individual biological cells, we decided several years ago to adapt FCS techniques to fluorescence microscopy. Dr Koppel has developed a successful procedure based on a standard Zeiss microscope. A schematic diagram of one version is shown in Fig. 8. Notice that the illuminating laser beam enters through a vertical illuminator using a dichroic mirror as a beam splitter. The plane of focus in the sample is projected as a real image on an adjustable diaphragm in front of the photomultiplier to facilitate collection of the fluorescence from a limited volume in the specimen. Of course the efficiency of collection of fluorescence varies with height above and below the plane of focus but, to our delight, this feature has caused little difficulty. Potentially as problematic is our inability to reduce vibration amplitudes much below 10 nm. In inhomogeneous specimens with sharp segregation of fluorophore the vibration contributions to the FCS correlation function could become a problem but have in practice also caused little difficulty so far. The most serious basic limitation of the microscope geometry for FCS experiments, as compared with our earlier configuration using a reflecting photometric cavity, is the severe loss offluorescencecollection efficiency. In the reflective cavity geometry collection efficiencies can easily exceed 50 % while practical values in the microscope geometry may be as much as an order of magnitude lower. However, there is an important compensating advantage in the microscopy geometry since background fluorescence from cell windows, attached tissue, supporting structures, etc., are effectively rejected. We have even found the microscope geometry to be preferable for lipid bilayer specimens. Of major importance in improving the convenience and efficiency of FCS experiments is the development of an optimized correlator
Applications offluorescencecorrelation spectroscopy 59 M
ND1 ND2'
SF —
7M Fig. 8. Schematic arrangement of fluorescence microscope geometry for Fluorescence Correlation Spectroscopy. The laser beam is aimed by mirrors M through attenuating neutral density filters ND1 and ND 2 into lens L1 in the vertical illuminator of a Zeiss research microscope. The beam is deflected by the dichroic mirror into the objective lens L2 which focuses it on the sample through which it may pass to an intensity monitor (Mon.). The fluorescence excited in the sample is collected by the objective lens L2 passes through the dichroic mirror DM with little attentuation and into the beam filter BF which removes residual scattered laser light and transmits the fluorescence into a focal plane diaphragm FD which is positioned to select the desired area on the sample with the help of the removable mirror M and horizontal viewing eyepiece. Finally the fluorescence radiation intensity is measured by the photomultiplier tube PMT. The photocurrent fluctuations are then analysed by a digital correlator.
^corporating photon counting, internal direct compensation for laser fluctuations, real time display of correlation functions, and rapid display of normalized functions and preprogrammed fits to anticipated forms. The convenience of this arrangement should be suggested by the illustrative data which are worked up with this system. A general purpose DEC-11-20 minicomputer with 16000 core memory is used on line for the correlation and subsequently for analysis. Details of the microscope and correlation system will be published elsewhere by Dr Koppel. He has already analysed the signal-to-noise problems of FCS (Koppel, 1974). With the presently available beam
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diameters < i /tm, and instrumental stability and beam diameters < i /im, measurements of diffusion coefficients as small as io~9cm2/sec are feasible. To measure D < io~9 cm2/sec a method based on the fluorescence bleaching technique described by Poo & Cone (1974) are more convenient and may be carried out in the same apparatus.
D I S C U S S I O N OF DIFFUSION IN MEMBRANES
The focus of current applications of FCS in our laboratory is lateral transport in and on membranes. We are measuring transport in lipid bilayers and in and on mammalian cell membranes of inactive lipophilic fluorophore molecules,fluorescentlabelled phospholipids and fluorescent labelled protein ligands. These experiments are still mostly in a preliminary stage. However, as so often happens when a new experimental method is applied to an old problem, we have been stimulated to think about some alternative concepts of transport in cell membranes. Our first application of FCS to transport on membranes consisted of measurements by Dr T. J. Herbert of the transport of the lipophilic dye dioctadecyl oxycarbocyanine in black lipid membranes prepared by the Mueller-Rudin technique (Mueller et al. 1962). These experiments provided the model for the graphic description of diffusion measurements that introduced this paper and established our original techniques for membrane diffusion experiments. The methods are now improved as has been indicated by incorporation of microscope optics to reduce background and full photon counting digital correlation to increase collection efficiency. Dr Herbert's results on egg lecithin plus 7-dehydrocholesterol cover a wide range of compositions and temperatures. He observed diffusion coefficients from a maximum of 2 x icr 8 cm2/sec down to his measurable < io~9 cm2/sec. His systematic variation with composition is suggestive of an enhanced viscosity below 12°C at around 2:1 lecithin: cholesterol in just the region of ordering anomalies observed by Rand & Pangborn (1973). Although informally quoted, these data have not been published because we had not had the opportunity to complete controls, determine the effects of solvent in the membrane, and duplicate the original data - as we believe essential with any new techniques. Now, additional, quite precise diffusion experiments on various black lipid membranes with a similar carbocyanine dye are underway in the hands of Dr Koppel, L. Barak and Professor P. Fahey.
Applications of fluorescence correlation spectroscopy
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We have anticipated that residual solvent would have a profound effect on diffusion in black lipid membranes so we have assimilated in our laboratory the Mueller-Montal techniques for preparation of lipid bilayers by combination of surface monolayers (Montal & Mueller, 1972). With the help of these methods, Mr David Wolf is measuring solvent effects in lipid bilayers in preparation for diffusion experiments on lipid bilayers that are essentially free of solvent. These experiments on lipid bilayers have two objectives: to determine the characteristics of diffusive lateral transport in the two-dimensional lipid bilayer system and to provide a simple model system on which to develop further techniques for observations of transport on cell membranes. In developing the physical techniques for transport experiments we have been more successful than we had anticipated. However, the basic problem of two-dimensional diffusion in lipid bilayers has raised more questions than we had expected. There are fundamental difficulties in connecting the diffusion coefficient in a strictly two-dimensional system with an effective twodimensional viscosity. One problem arises in coupling the diffusion coefficient D defined in terms of the macroscopic transport equation Z)V2C = dcjdt with the coefficient D defined through a two-dimensional Stokes-Einstein relation. The difficulty can be viewed in several ways, for example: (1) as a long-time tail in the particle velocity-velocity correlation that appears in analysing the fluctuations that describe twodimensional Brownian motion and eventually define a diffusion coefficient ; (2) as a consequence of the singular properties of the continuum hydrodynamics of viscous drag in two-dimensional calculations. Several recent papers summarize this problem in simple terms and provide references; see particularly Alder & Wainwright (1970), Lewis (1973) and Keyes & Oppenheim (1973). Razi-Naqvi (1974) has also pointed out an associated difficulty in two dimensions that enters into the interpretation transients in chemical kinetics and the spin-spin interactions involved in deducing microviscosity by EPR and NMR methods. For analysis of macroscopic diffusive transport in lipid bilayer membranes, these problems may be without consequence since it is quite likely that the molecular level diffusion in lipid bilayers is not closely approximated by a strictly two-dimensional model (Jones, Felderhof & Deutch, private communication). However, in this case we appear to lack a reliable relation between the viscosity of a membrane and the macroscopic diffusion coefficient for a molecule dissolved in it. Furthermore, the
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connexion between the values of translational diffusion coefficients deduced from NMR and EPR techniques and the appropriate viscosity for macroscopic transport in lipid bilayers is subject to comparable problems of analysis. Transport on biological cell membranes is being studied in our laboratory with some success using FCS and other fluorescence techniques. In the fluorescence microscope geometry a variety of chromophores including dansyl and rhodamine labelled phosphatidylethanolamine, rhodamine labelled concanavalin A, and various carbocyanine and merocyanine dyes are being applied in experiments on erythrocytes, cultured mammalian cells including neuroblastoma and lymphocytes. Consideration of preliminary experiments has led some of us to infer that many molecules including membrane lipids may not be capable of significant lateral diffusion on some mammalian cell membranes over distances greater than about i ftm. Nevertheless, it is well known from ESR, NMR andfluorescencedepolarization measurements that the lipid molecules are capable of rotational diffusion rates consistent with the microviscosity of fluid lipids, say a few poise. That microviscosity implies translational diffusion coefficients of ~ io^cir^/sec for free lipids and ~ io~9cm2/sec for free proteins. Some of our preliminary translational diffusion experiments suggest much smaller lateral diffusion rates. Several magnificent experiments have been reported in the literature that do demonstrate the possibility of macroscopic transport in some cell membranes. Although no diffusion of labelled proteins was seen on erythrocytes by Peters et al. (1974), Frye & Edidin (1970) found that labelled antibodies are gradually mixed on the surface of cells following fusion, and Poo & Cone (1974) found that rhodopsin diffuses in the visual disk membrane at rates consistent with rhodopsin molecules in a fluid lipid bilayer. Lee (1975), Cherry (1975) and Edidin (1974) have recently reviewed the available data. The popular model of a cell membrane, described in the famous review by Singer & Nicolson (1972), implies that lateral diffusion of both lipids and proteins should proceed at a rate consistent with the expected liquidlipid viscosity. This model is beautifully illustrated in the Scientific American article by Capaldi (1974). The proteins appear as isolated islands inserted in the two-dimensional sea of lipid bilayers and thus should diffuse independently. The membrane proteins, external proteincarbohydrate coating and the microtubule apparatus are conventionally pictured as discontinuous insertions intersecting a continuous multiply-
Applications offluorescencecorrelation spectroscopy 63
Fig. 9. Topographical map of a lipid membrane with dissolved fluorophore and embedded, isolated proteins. Compare with Fig. 3. Here isolated proteins do not significantly inhibit diffusion of lipid or lipid-like fluorophore.
connected lipid bilayer. No substantial barriers for macroscopic lateral diffusion of lipids or lipoproteins in the cell membrane are implied. Now we can easily visualize and illustrate the effects of varying the geometry of the non-lipid components of a cell membrane on lateral diffusion by returning to the schematic diagram introduced in Fig. 3 to show the fluorophore labelled lipid bilayer. On this diagram we can superimpose sketches to describe various topologies of the cell membrane and consider their effects on lateral diffusive transport. Fig. 9 depicts isolated particles immersed in the fluorescent labelled lipid bilayer as suggested by Capaldi's illustrations of the SingerNicolson model. Lipid lateral diffusion is not inhibited. This model probably describes accurately the diffusion of rhodopsin in visual disks. The figure suggests that the isolated macromolecules and particles would have mobility as floating islands. However, as was pointed out to me by F. Fox (private communication), the proteins might well be coupled rigidly together by a three dimensional network above and/or below the 5
QRB 9
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Fig. 10. Compartmentalization by lipid-protein interaction. Topographical map of lipid membrane with dissolved fluorophore with embedded, isolated proteins surrounded by fixed lipid layers that are sufficiently thick to subdivide the membrane into compartments comparable in size to illuminated areas. Diffusion appears somewhat inhibited in FCS experiments. Note that fluorophase in this particular case is supposed to have segregated into fluid lipid phase.
lipid bilayer. In this case the proteins are immobilized, yet the lipids would be mobile. The frequent occurrence of a rather tightly bound lipid layer attached to proteins immersed in the lipid bilayer seems to be established. If the bound layers overlap as in Fig. 10, the lipid bilayer is divided into isolated regions and lateral transport of both lipid and protein is inhibited in spite of the fact that the proteins are isolated. This model, or one in which spectrin forms the bound network, may apply to erythrocytes and account for the results of Peters et al. (1974). Similarly, if the proteins form a closed network in the plane of the bilayer, as in Fig. 11, macroscopic lateral transport of both protein and lipid is inhibited. However, a new possibility for macroscopic lateral transport arises wherever we have a continuous network. Weak binding or absorption of amphophilic molecules at lipid-protein or lipid-water interfaces or on the surface diffusion of
Applications offluorescencecorrelation spectroscopy 65
Fig. 11. Topographical map of lipid membrane with one configuration of a closed protein network compartmentalizing the lipid into isolated pockets comparable in size to the illuminated areas. Lipid diffusion is inhibited to a degree dependent on compartment size; protein diffusion is negligible.
special molecules but not for lipids. Something of this sort may be involved in the experiments of Frye & Edidin (1970) on antibody transport after cell fusion. How these various barriers affect FCS or bleaching measurements of lateral diffusion depends on the mesh size of the barrier network. If the scale or the net is as fine as the laser beam size in the experiments, say 1-5 fim, the apparent diffusion rate is drastically reduced and the fluorophore appears immobilized. Electron microscopy suggests that the scale of barrier networks on mammalian cells would normally be < 1 /on so they would be recognized as barriers in lateral transport experiments. In all of these cases microviscosities measured by NMR and EPR could still be quite small and the lipids could be quite fluid within each mesh. Recent X-ray diffraction experiments on lipid bilayer and liquid crystals have also suggested rather more complex structures than have been customarily ascribed to either the liquid crystal or the gel state of 5-2
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the bilayer. See, for example, Gulik-Krzywicki (1975) or Tardieu, Luzzati & Reman (1973). They note a feature that I would suggest may enhance lateral diffusion in gel state bilayers. They report the observation of pronounced corregations of the bilayer on a scale of distance > 150 A. These systematic perturbations involve molecular arrangements that may inhibit, promote or channel lateral diffusion by providing liquid-like pathways through the gel phase regions of the membrane. Similarly vestiges of these structures remaining in the liquid crystal phases may also inhibit lateral diffusion significantly. Finally, it is necessary to consider the problem of diffusion in the lipid bilayer in the simple case where two phases coexist as laterally separated patches. In this case the phase that dominates lateral diffusion rates is generally the multiply connected or matrix phase. Thus the macroscopic lateral distribution of the phases is at least as important as the diffusion coefficients themselves. Hui & Parsons (1975) have obtained electron micrographs of phospholipid-cholesterol mixed bilayers with finely divided lateral phase separation that suggests a continuously connected network of one phase that would control lateral diffusion. This speculative discussion of lateral transport on most mammalian cell membranes is obviously far from complete, but it is intended to convey a caution that the connexion between microviscosity of membrane lipids and lateral diffusion in the lipids is highly uncertain. In addition it is intended to suggest that the usual concepts of the cell membrane topology may mislead us into anticipating easy macroscopic lipid transport in the lipid bilayer whereas in fact compartmentalization of the lipid by rigid networks may inhibit its passive motion to highly localized microscopic regions. Instead of visualizing the cell membrane as a bilayer of lipid with protein islands, we probably should visualize it as a relatively rigid mesh of protein with lipid bilayer meniscus structures sealing its pores. The support of the NIH through grant no. GM21661-01, the NSF through grant no. DMR75-04509, a grant from the Research Corporation, and a research fellowship from the John Simon Guggenheim Memorial Foundation are gratefully acknowledged. This research has also been assisted by the facilities of the NSF-supported Materials Science Center at Cornell.
Applications of fluorescence correlation spectroscopy
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REFERENCES
B. J. & WAINWRIGHT, T. E. (1970). Decay of the velocity autocorrelation function. Phys. Rev. A 1, 18-21.
ALDER,
BADLEY, R. A., MARTIN, W. G. & SCHNEIDER, H. (1973). Dynamic behavior
of fluorescent probes in lipid bilayer model membranes. Biochemistry, N.Y. 12,268-75, CAPALDI, R. A. (1974). A dynamic model of cell membranes. Scient. Am. 230, 26-33.
R. J. (1975). Protein mobility in membranes. FEBS Lett. 55, 1-7. M. (1974). Rotational diffusion in membranes. A. Rev. Biophys. Bioeng. 3, 179-201. ELSON, E. L. & MAGDE, D. (1974). Fluorescence correlation spectroscopy. I. Conceptual basis and theory. Biopolymers 13, 1-27. ELSON, E. L. & WEBB, W. W. (1975). Concentration correlation spectroscopy: A new biophysical probe based on occupation number fluctuations. A. Rev. Biophys. Bioeng. 4, 311-34. FRYE, L. D. & EDIDIN, M. (1970). The rapid intermixing of cell surface antigens after formation of mouse-human heterokaryons. J. Cell Set. 7, 3I9~35GULIK-KRZYWICKI, T. (1975). Structural studies of the associations between biological membrane components. Biochim. biophys. Ada 415, 1-28. Hui, S. W. & PARSONS, D. F. (1975). Direct observation of domains wet bilayers. Science, N.Y. 190, 383-4. CHERRY, EDIDIN,
JONES, R. B., FELDERHOF, B. U. & DEUTCH, J. M. Diffusion of polymers
along a fluid-fluid interface. (Unpublished private communication.) KEYES, T. & OPPENHEIM, I. (1973). Bilinear hydrodynamics and the Stokes-
Einstein Law. Phys. Rev. 8, 937. D. E. (1974). Statistical accuracy in fluorescence correlation spectroscopy. Phys. Rev. A io, 1938-45. LEE, A. G. (1975). Functional properties of biological membranes: a physical chemical approach. Prog. Biophys. & molec. Biol. 29, 3-56. LEWIS, J. C. (1973). On the Einstein—Stokes diffusion coefficient for Brownian motion in two dimensions. Phys. Lett. 44 A, 245-6. MAGDE, D., ELSON, E. & WEBB, W. W. (1972). Thermodynamic fluctuations in a reacting system - measurements by fluorescence correlation spectroscopy. Phys. Rev. Lett. 29, 705-8. MAGDE, D., ELSON, E. L. & WEBB, W. W. (1974). Fluorescence correlation spectroscopy. II. An experimental realization. Biopolymers 13, 29-61. MONTAL, M. & MUELLER, P. (1972). Formation of bimolecular membranes from lipid monolayers and a study of their electrical properties. Proc. KOPPEL,
natn. Acad. Sd. U.S.A. 69, 3561-6. P., RUDIN, D. O., TIEN, H. T. & WESCOTT, W. C. (1962). Reconstitution of excitable cell membrane structure in vitro. Circulation 26, 1167-70. PETERS, R., PETERS, J., TEWS, K. H. & BAHR, W. (1974). A microfluorimetric MUELLER,
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study of translational diffusion in erythrocyte membranes. Biochim. biophys. Ada 367, 282-94. Poo, M.-m. & CONE, R. A. (1974). Lateral diffusion of rhodopsin in the photoreceptor membrane. Nature, Lond. z$], 438-41. RAND, R. P. & PANGBORN, W. A. (1973). A structural transition in egg lecithin-cholesterol bilayers at 12 °C. Biochim. biophys. Ada 318, 299-
3°5-
RAZI-NAQVI, K. (1974). Diffusion-controlled reactions in two-dimensional fluids: Discussion of measurements of lateral diffusion of lipids in biological membranes. Chem. Phys. Lett. 28, 280-4. SIMS, P. J., WAGGONER, A. S., WANG, C. H. & HOFFMAN, J. F. (1974). Studies on the mechanism by which cyanine dyes measure membrane potential in red blood cells and phosphatidyl-choline vesicles. Biochemistry, N. Y. J 3> 33IS-3O. SINGER, S. J. & NICOLSON, G. L. (1972). The fluid mosaic model of the structure of cell membranes. Science, N.Y. 175, 720-31. TARDIEU, A., LUZZATI, V. & REMAN, F. C. (1973). Structure and polymorphism of the hydrocarbon chains of lipids: A study of lecithin-water phases.
J.molec.Biol. 75, 711-33. YGUERABIDE, J.
& STRYER, L. (1971). Fluorescence spectroscopy of an oriented model membrane. Proc. natn. Acad. Sci. U.S.A. 68, 1217-21.
Applications of Fluorescence Correlation Spectroscopyf WATT W.WEBB School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, U.S.A.
INTRODUCTION
49
LATERAL DIFFUSION IN L I P I D BILAYERS
50
SOME INNOVATIONS IN FCS METHODOLOGY
58
D I S C U S S I O N OF DIFFUSION IN MEMBRANES
60
REFERENCES
67 INTRODUCTION
The preceding paper by Douglas Magde has recounted the basic principles of Fluorescence Correlation Spectroscopy (FCS) as originally described (see Magde, Elson & Webb, 1972; Elson & Magde, 1974; Magde, Elson & Webb, 1974; Elson & Webb, 1975; referred to collectively as MEW), and has described the first application to chemical kinetics. In this paper I shall first illustrate the same principles of FCS with a simple graphical demonstration model based on the scheme for application to lateral diffusion in membranes as it was developed in our laboratory by Dr T.J.Herbert; I shall then proceed to discuss some current research in our group organized jointly with Professor E. L. Elson at Cornell. To indicate the current capability of FCS, I shall describe some recent instrumentation developments by Dr D. E. Koppel and show some illustrative data provided by Dr Koppel and Dr J. Schlessinger on transport in solutions selected for this symposium, 'Dynamics of Macromolecules in Solution'. Finally I shall present t This paper was presented at the symposium on Dynamics of Macromolecules in Solution at the 5th International Biophysics Congress in Copenhagen, Denmark, 4-9 August 1975. [49]
4-2
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W. W. WEBB
graphically some ideas about lateral transport in and on cell membranes that have evolved from our thinking about our current experiments on transport in both lipid bilayers and mammalian cell membranes. Experiments being carried out by Dr Koppel, Dr Schlessinger, Dr D. Axelrod, L. Barak, P. Dragsten, J. Reidler and D. Wolf with E. L. Elson and myself will be reported elsewhere.
LATERAL DIFFUSION I N L I P I D BILAYERS
In preparation for measurements of lateral diffusion in lipid bilayers we form a black lipid membrane by conventional techniques (Mueller et al. 1962) in a wire loop mounted on a hypodermic syringe. The loop is Filters P.M. tube
Syringe tube To infusion pump
LArgon
7------^--/ n
laser -
+ Diff. amp.
Correlator
(b)
Bilayer Laser beam
Fig. 1. (a) Schematic diagram of apparatus for Fluorescence Correlation Spectroscopy. (6) Lipid bilayer formed by Mueller-Rudin technique using hypodermic syringe to supply and meter droplet of lipid solution. Laser beam is focused on bilayer.
Applications of fluorescence correlation spectroscopy
51
Lecithin
Fluorophore
Fig. 2. Schematic representation of a section of lipid bilayer showing dissolved carbocyanine fluorophore in expected configuration within the bilayer.
positioned in a spectrometer cell within an optical cavity arranged for efficient collection of thefluorescentlight excited by a laser beam focused on the membrane (see Fig. 1 a, b). To form the membrane, a solution of lipids and fluorophore in hexane or octane is injected into the plane of the wire loop using the hypodermic syringe. There it forms a meniscus; then the excess solution is drawn off with the syringe and the remaining droplet thins down to form a black lipid membrane suspended in the loop. The laser beam illuminates and excites thefluorophoresin a circular spot on the membrane. Precise temperature regulation is available and the technique was sufficiently tractable for Dr T. J. Herbert to form black lipid membranes from a broad composition range of mixtures of cholesterol and egg lecithin that were labelled with small additions, say io~3 mole fraction, of lipid soluble fluorophore, dioctadecyl oxycarbocyanine. This molecule is thought to enter the molecular structure of the bilayer with its head group lying parallel to the surface of the membrane and the hydrocarbon tails parallel to the hydrocarbon tails of the phospholipids that form the membrane. The orientation of the polar head group parallel to the surface of the bilayer was demonstrated by Yguerabide & Stryer (1971) and confirmed by Badley, Martin & Schneider (1973). We can visualize the molecular structure of the bilayer as shown in Fig. 2. We think that the carbocyanine molecule mimics the phospholipid rather well and that its diffusion is quite similar to that of the phospholipids. The carbocyanine molecules, here shaded black, are induced to fluoresce
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Fig. 3. Topographical map of bilayer containing dissolved fluorophore molecules (small circles) randomly distributed within it. Large circles represent areas illuminated by the laser beam. Only the illuminated fluorophore molecules fluoresce (solid circles). The four illuminated circles may be regarded as examples of configurations found at various times. The time scale of the changes due to diffusion in and out of an illuminated area is a characteristic diffusion time from which the diffusion coefficient is deduced. Note that the numbers of illuminated molecules N = 10, 5, 8, 4 are actually much smaller than the actual numbers which are typically io 3 -10 6 .
by the laser beam. Thus topographical maps of illuminated spots on the membrane might look something like Fig. 3. The small circles indicate the random positions of the fluorescent molecules in the membrane. However, only those within the illuminated areas actuallyfluoresce;they are shown as solid circles. Four of the many possible configurations of molecules within the laser beam are illustrated by the four beam circles of Fig. 3. In this illustration we show only about ten fluorophore molecules within the beam, although in actual practice we use concentrations of fluorophores that yield IO 3 -IO 6 fluorescent molecules in a beam spot of about 3 /tm radius.
Applications offluorescencecorrelation spectroscopy 53
Now the fluorescence intensity is proportional to the number of illuminated fluorophores and to the intensity of the illumination. Although the intensity within the laser beam is not uniform, we shall pretend in this simple discussion that it is. (The correct equations for the actual case of non-uniform light beams with gaussian intensity profiles are discussed by MEW.) For a uniform beam, the fluorescence intensity is thus precisely proportional to the number of illuminated fluorophores. Because the membrane resembles a viscous fluid layer, we expect the lipid molecule to diffuse laterally in the membrane and in the course of this motion to pass in and out of the illuminated spot. Similarly we expect the dissolved fluorophore molecules to diffuse in and out of the beam. Since our fluorophore does not dissolve noticeably in the surrounding aqueous phase, the only available mechanism for change of the number of illuminated fluorophores is lateral diffusion within the membrane. (Photolysis of the fluorophore by the bright laser beam may also destroy the fluorophore but this perturbation can be kept negligible.) As the fluorophore molecules diffuse the number N* within the beam fluctuates with time. The configurations at various times would look something like the four examples of Fig. 3. The variance of the number N* within the beam obtained by many independent observations is simply the variance of a random variable
\(u.i\ ) ) — yv ) so
(Kj*y
~ (N*y
Because thefluorescenceintensity / i s proportional to N*, its fluctuations are proportional and the variance is similarly as has b een shown by MEW. We should recall that in typical experiments (N*) > io 4 so £/ < 1 % rather than the much larger variations implied by the small values of N* in our schematics. In any case the value of the variance of the intensity fluctuations provides an accurate assay of the number, and thus the concentration, of independent mobile fluorophore molecules. Now the essential information for measurement of diffusion is derived from the time scale of the fluctuations of the fluorescence intensity. This time scale is determined by the characteristic time required for a molecule
54
W. W. WEBB 10
80
90
Fig. 4. Diffusion in aqueous solution of the free dye molecule rhodamine 6G (A) and bovine serum albumen (BSA) labelled with rhodamine 6G, pH 7, o-i M phosphate buffer (•). Several data sets indicate reproducibility of the time dependence of the normalized correlation functions £(j)lft.
to diffuse out of the illuminated circle. Recall that the diffusion coefficient D is defined in terms of the spatial correlation function by where f is the position vector, d is the dimensionality of the diffusion space (we suppose d = 2, for a membrane) and T the diffusion time. This equation suggests that the characteristic time scale TD of intensity fluctuations due to two-dimensional diffusion of molecules in and out of a spot of radius w as in our problem should be approximately TD = w2I^D.
In fact MEW found exactly this result for the characteristic time scale of fluorescence intensity fluctuations from a spot illuminated by a gaussian beam of effective half width w. The correlation function of the intensity fluctuations that provides a complete statistical description of the intensity in this case is
Applications offluorescencecorrelation spectroscopy 55 1001
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
00 10
20
30
40
50
60
70
80
90
r (msec)
Fig. 5. Plots of the reciprocal of the normalized diffusion coefficient show reasonable fits to the expected linear form [(^T)//?]- 1 = 1 + TlTv- •> Rhodamine 6G-labelled BSA, pH 7, o-i M phosphate buffer. A, Rhodamine (sG in water. , Straight line fits.
where /? = i/(iV*>. The amplitude ^(o) = /? = (N*)-1 is determined by the effective number of illuminated, independent fluorophores and provides a useful concentration assay. The time-dependent factor depends on the dimensionality of the diffusion problem as (1 + rJTD)~^d. In all of our experiments the diffusion remains two-dimensional even for solutions in a spectroscopic cell because only the diffusion component perpendicular to the laser beam can change the illumination of a molecule (see MEW). Dr Koppel and Dr Schlessinger have provided a set of FCS correlation functions recorded on fluorophores in solution to illustrate effects of concentration, solution viscosity, molecular weight and formation of micelles on solute diffusion in solution. Fig. 4 compares the normalized correlation functions £(T)//? of free rhodamine 6G, D* ~ io-6cm2/sec. with rhodamine 6G labelled obvine serum albumen, D ~ io~7cm2/sec, in water. Several sets of data are presented by copying the printer output just as the correlation computer presents them. Duplicate curves show
00
50
100 150 ti (msec/cp)
200
Fig. 6. (a) Plots of the normalized correlation functions for rhodamine 6G (5-6 x io~8 M) in water-glycerol mixtures show the slowing by increasing viscosity. (6) Normalization of the data of (a) using tabulated viscosity data shows the expected magnitude of the effect. Percentage (vol./vol.) glycerol: D, o; O, 20; x , 40; A, 60.
240
w
W
3"
Applications offluorescencecorrelation spectroscopy 57
D~IO~S cm2/sec, Af*~500 micelles
D ~ 1 0 " 6 cm2/sec, N*~ 104 molecules 00
J
40
1
I
80
I
1
120
1
1 1 i 160 200
I L 240 280
(msec)
Fig. 7. The correlation function for large micelles of carbocyanine dye in ethanol—water mixtures is compared with the free molecules in ethanol. Note the large amplitude of the correlation function generated by the small illuminated number of micelles. Each micelle contains many fluorophore molecules so is brightly fluorescent. 8xio" 6 mg/ml di-I-C18(3). D, 20% ethanol in water; A, 100% ethanol.
the excellent reproducibility. In Fig. 5 the reciprocal of the normalized correlation function is plotted for two sets of data to demonstrate conformity to the expected (1 +7"/rJr,)~1 form for the correlation function due to diffusion through the gaussian laser beam. The normalized correlation functions shown in Fig. 6 (a) demonstrate the dependence of the diffusion constant on viscosity in water-glycerol mixtures. Dividing the time scale by the known viscosities superimposes the correlation functions, Fig. 6 (b). Diffusion of fluorescent supramolecular objects is illustrated in Fig. 7. One of the lipophilic fluorescent molecules, 3,3'dioctadecylindocarbocyanine (Sims et al. 1974), that we have adopted as a probe of diffusion in lipid membranes, is virtually insoluble in water, has a strong tendency to form large micelles in water-ethanol mixtures and is soluble in ethanol. The non-normalized FCS correlation functions for diffusion of dye micelles in water-ethanol mixtures, so large that D ~ io~8 cm2/sec
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at a concentration such that only about 500 independent micelles are present in a laser beam, is shown in Fig. 7. For comparison the FCS correlation function of free dye molecules in ethanol, shown on the same scale, is the tiny curve near the origin. Actually free dye diffusion is readily measured as is shown in the preceding figures. However the large relative intensity fluctuations, and therefore the large value of |(o), produced by the small number of illuminated, independent diffusing micelles is strikingly illustrated by this example. SOME INNOVATIONS I N FCS
METHODOLOGY
Recognizing the need for measurements of lateral diffusion and kinetics on and in individual biological cells, we decided several years ago to adapt FCS techniques to fluorescence microscopy. Dr Koppel has developed a successful procedure based on a standard Zeiss microscope. A schematic diagram of one version is shown in Fig. 8. Notice that the illuminating laser beam enters through a vertical illuminator using a dichroic mirror as a beam splitter. The plane of focus in the sample is projected as a real image on an adjustable diaphragm in front of the photomultiplier to facilitate collection of the fluorescence from a limited volume in the specimen. Of course the efficiency of collection of fluorescence varies with height above and below the plane of focus but, to our delight, this feature has caused little difficulty. Potentially as problematic is our inability to reduce vibration amplitudes much below 10 nm. In inhomogeneous specimens with sharp segregation of fluorophore the vibration contributions to the FCS correlation function could become a problem but have in practice also caused little difficulty so far. The most serious basic limitation of the microscope geometry for FCS experiments, as compared with our earlier configuration using a reflecting photometric cavity, is the severe loss offluorescencecollection efficiency. In the reflective cavity geometry collection efficiencies can easily exceed 50 % while practical values in the microscope geometry may be as much as an order of magnitude lower. However, there is an important compensating advantage in the microscopy geometry since background fluorescence from cell windows, attached tissue, supporting structures, etc., are effectively rejected. We have even found the microscope geometry to be preferable for lipid bilayer specimens. Of major importance in improving the convenience and efficiency of FCS experiments is the development of an optimized correlator
Applications offluorescencecorrelation spectroscopy 59 M
ND1 ND2'
SF —
7M Fig. 8. Schematic arrangement of fluorescence microscope geometry for Fluorescence Correlation Spectroscopy. The laser beam is aimed by mirrors M through attenuating neutral density filters ND1 and ND 2 into lens L1 in the vertical illuminator of a Zeiss research microscope. The beam is deflected by the dichroic mirror into the objective lens L2 which focuses it on the sample through which it may pass to an intensity monitor (Mon.). The fluorescence excited in the sample is collected by the objective lens L2 passes through the dichroic mirror DM with little attentuation and into the beam filter BF which removes residual scattered laser light and transmits the fluorescence into a focal plane diaphragm FD which is positioned to select the desired area on the sample with the help of the removable mirror M and horizontal viewing eyepiece. Finally the fluorescence radiation intensity is measured by the photomultiplier tube PMT. The photocurrent fluctuations are then analysed by a digital correlator.
^corporating photon counting, internal direct compensation for laser fluctuations, real time display of correlation functions, and rapid display of normalized functions and preprogrammed fits to anticipated forms. The convenience of this arrangement should be suggested by the illustrative data which are worked up with this system. A general purpose DEC-11-20 minicomputer with 16000 core memory is used on line for the correlation and subsequently for analysis. Details of the microscope and correlation system will be published elsewhere by Dr Koppel. He has already analysed the signal-to-noise problems of FCS (Koppel, 1974). With the presently available beam
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diameters < i /tm, and instrumental stability and beam diameters < i /im, measurements of diffusion coefficients as small as io~9cm2/sec are feasible. To measure D < io~9 cm2/sec a method based on the fluorescence bleaching technique described by Poo & Cone (1974) are more convenient and may be carried out in the same apparatus.
D I S C U S S I O N OF DIFFUSION IN MEMBRANES
The focus of current applications of FCS in our laboratory is lateral transport in and on membranes. We are measuring transport in lipid bilayers and in and on mammalian cell membranes of inactive lipophilic fluorophore molecules,fluorescentlabelled phospholipids and fluorescent labelled protein ligands. These experiments are still mostly in a preliminary stage. However, as so often happens when a new experimental method is applied to an old problem, we have been stimulated to think about some alternative concepts of transport in cell membranes. Our first application of FCS to transport on membranes consisted of measurements by Dr T. J. Herbert of the transport of the lipophilic dye dioctadecyl oxycarbocyanine in black lipid membranes prepared by the Mueller-Rudin technique (Mueller et al. 1962). These experiments provided the model for the graphic description of diffusion measurements that introduced this paper and established our original techniques for membrane diffusion experiments. The methods are now improved as has been indicated by incorporation of microscope optics to reduce background and full photon counting digital correlation to increase collection efficiency. Dr Herbert's results on egg lecithin plus 7-dehydrocholesterol cover a wide range of compositions and temperatures. He observed diffusion coefficients from a maximum of 2 x icr 8 cm2/sec down to his measurable < io~9 cm2/sec. His systematic variation with composition is suggestive of an enhanced viscosity below 12°C at around 2:1 lecithin: cholesterol in just the region of ordering anomalies observed by Rand & Pangborn (1973). Although informally quoted, these data have not been published because we had not had the opportunity to complete controls, determine the effects of solvent in the membrane, and duplicate the original data - as we believe essential with any new techniques. Now, additional, quite precise diffusion experiments on various black lipid membranes with a similar carbocyanine dye are underway in the hands of Dr Koppel, L. Barak and Professor P. Fahey.
Applications of fluorescence correlation spectroscopy
61
We have anticipated that residual solvent would have a profound effect on diffusion in black lipid membranes so we have assimilated in our laboratory the Mueller-Montal techniques for preparation of lipid bilayers by combination of surface monolayers (Montal & Mueller, 1972). With the help of these methods, Mr David Wolf is measuring solvent effects in lipid bilayers in preparation for diffusion experiments on lipid bilayers that are essentially free of solvent. These experiments on lipid bilayers have two objectives: to determine the characteristics of diffusive lateral transport in the two-dimensional lipid bilayer system and to provide a simple model system on which to develop further techniques for observations of transport on cell membranes. In developing the physical techniques for transport experiments we have been more successful than we had anticipated. However, the basic problem of two-dimensional diffusion in lipid bilayers has raised more questions than we had expected. There are fundamental difficulties in connecting the diffusion coefficient in a strictly two-dimensional system with an effective twodimensional viscosity. One problem arises in coupling the diffusion coefficient D defined in terms of the macroscopic transport equation Z)V2C = dcjdt with the coefficient D defined through a two-dimensional Stokes-Einstein relation. The difficulty can be viewed in several ways, for example: (1) as a long-time tail in the particle velocity-velocity correlation that appears in analysing the fluctuations that describe twodimensional Brownian motion and eventually define a diffusion coefficient ; (2) as a consequence of the singular properties of the continuum hydrodynamics of viscous drag in two-dimensional calculations. Several recent papers summarize this problem in simple terms and provide references; see particularly Alder & Wainwright (1970), Lewis (1973) and Keyes & Oppenheim (1973). Razi-Naqvi (1974) has also pointed out an associated difficulty in two dimensions that enters into the interpretation transients in chemical kinetics and the spin-spin interactions involved in deducing microviscosity by EPR and NMR methods. For analysis of macroscopic diffusive transport in lipid bilayer membranes, these problems may be without consequence since it is quite likely that the molecular level diffusion in lipid bilayers is not closely approximated by a strictly two-dimensional model (Jones, Felderhof & Deutch, private communication). However, in this case we appear to lack a reliable relation between the viscosity of a membrane and the macroscopic diffusion coefficient for a molecule dissolved in it. Furthermore, the
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connexion between the values of translational diffusion coefficients deduced from NMR and EPR techniques and the appropriate viscosity for macroscopic transport in lipid bilayers is subject to comparable problems of analysis. Transport on biological cell membranes is being studied in our laboratory with some success using FCS and other fluorescence techniques. In the fluorescence microscope geometry a variety of chromophores including dansyl and rhodamine labelled phosphatidylethanolamine, rhodamine labelled concanavalin A, and various carbocyanine and merocyanine dyes are being applied in experiments on erythrocytes, cultured mammalian cells including neuroblastoma and lymphocytes. Consideration of preliminary experiments has led some of us to infer that many molecules including membrane lipids may not be capable of significant lateral diffusion on some mammalian cell membranes over distances greater than about i ftm. Nevertheless, it is well known from ESR, NMR andfluorescencedepolarization measurements that the lipid molecules are capable of rotational diffusion rates consistent with the microviscosity of fluid lipids, say a few poise. That microviscosity implies translational diffusion coefficients of ~ io^cir^/sec for free lipids and ~ io~9cm2/sec for free proteins. Some of our preliminary translational diffusion experiments suggest much smaller lateral diffusion rates. Several magnificent experiments have been reported in the literature that do demonstrate the possibility of macroscopic transport in some cell membranes. Although no diffusion of labelled proteins was seen on erythrocytes by Peters et al. (1974), Frye & Edidin (1970) found that labelled antibodies are gradually mixed on the surface of cells following fusion, and Poo & Cone (1974) found that rhodopsin diffuses in the visual disk membrane at rates consistent with rhodopsin molecules in a fluid lipid bilayer. Lee (1975), Cherry (1975) and Edidin (1974) have recently reviewed the available data. The popular model of a cell membrane, described in the famous review by Singer & Nicolson (1972), implies that lateral diffusion of both lipids and proteins should proceed at a rate consistent with the expected liquidlipid viscosity. This model is beautifully illustrated in the Scientific American article by Capaldi (1974). The proteins appear as isolated islands inserted in the two-dimensional sea of lipid bilayers and thus should diffuse independently. The membrane proteins, external proteincarbohydrate coating and the microtubule apparatus are conventionally pictured as discontinuous insertions intersecting a continuous multiply-
Applications offluorescencecorrelation spectroscopy 63
Fig. 9. Topographical map of a lipid membrane with dissolved fluorophore and embedded, isolated proteins. Compare with Fig. 3. Here isolated proteins do not significantly inhibit diffusion of lipid or lipid-like fluorophore.
connected lipid bilayer. No substantial barriers for macroscopic lateral diffusion of lipids or lipoproteins in the cell membrane are implied. Now we can easily visualize and illustrate the effects of varying the geometry of the non-lipid components of a cell membrane on lateral diffusion by returning to the schematic diagram introduced in Fig. 3 to show the fluorophore labelled lipid bilayer. On this diagram we can superimpose sketches to describe various topologies of the cell membrane and consider their effects on lateral diffusive transport. Fig. 9 depicts isolated particles immersed in the fluorescent labelled lipid bilayer as suggested by Capaldi's illustrations of the SingerNicolson model. Lipid lateral diffusion is not inhibited. This model probably describes accurately the diffusion of rhodopsin in visual disks. The figure suggests that the isolated macromolecules and particles would have mobility as floating islands. However, as was pointed out to me by F. Fox (private communication), the proteins might well be coupled rigidly together by a three dimensional network above and/or below the 5
QRB 9
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W.~W. WEBB
Fig. 10. Compartmentalization by lipid-protein interaction. Topographical map of lipid membrane with dissolved fluorophore with embedded, isolated proteins surrounded by fixed lipid layers that are sufficiently thick to subdivide the membrane into compartments comparable in size to illuminated areas. Diffusion appears somewhat inhibited in FCS experiments. Note that fluorophase in this particular case is supposed to have segregated into fluid lipid phase.
lipid bilayer. In this case the proteins are immobilized, yet the lipids would be mobile. The frequent occurrence of a rather tightly bound lipid layer attached to proteins immersed in the lipid bilayer seems to be established. If the bound layers overlap as in Fig. 10, the lipid bilayer is divided into isolated regions and lateral transport of both lipid and protein is inhibited in spite of the fact that the proteins are isolated. This model, or one in which spectrin forms the bound network, may apply to erythrocytes and account for the results of Peters et al. (1974). Similarly, if the proteins form a closed network in the plane of the bilayer, as in Fig. 11, macroscopic lateral transport of both protein and lipid is inhibited. However, a new possibility for macroscopic lateral transport arises wherever we have a continuous network. Weak binding or absorption of amphophilic molecules at lipid-protein or lipid-water interfaces or on the surface diffusion of
Applications offluorescencecorrelation spectroscopy 65
Fig. 11. Topographical map of lipid membrane with one configuration of a closed protein network compartmentalizing the lipid into isolated pockets comparable in size to the illuminated areas. Lipid diffusion is inhibited to a degree dependent on compartment size; protein diffusion is negligible.
special molecules but not for lipids. Something of this sort may be involved in the experiments of Frye & Edidin (1970) on antibody transport after cell fusion. How these various barriers affect FCS or bleaching measurements of lateral diffusion depends on the mesh size of the barrier network. If the scale or the net is as fine as the laser beam size in the experiments, say 1-5 fim, the apparent diffusion rate is drastically reduced and the fluorophore appears immobilized. Electron microscopy suggests that the scale of barrier networks on mammalian cells would normally be < 1 /on so they would be recognized as barriers in lateral transport experiments. In all of these cases microviscosities measured by NMR and EPR could still be quite small and the lipids could be quite fluid within each mesh. Recent X-ray diffraction experiments on lipid bilayer and liquid crystals have also suggested rather more complex structures than have been customarily ascribed to either the liquid crystal or the gel state of 5-2
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the bilayer. See, for example, Gulik-Krzywicki (1975) or Tardieu, Luzzati & Reman (1973). They note a feature that I would suggest may enhance lateral diffusion in gel state bilayers. They report the observation of pronounced corregations of the bilayer on a scale of distance > 150 A. These systematic perturbations involve molecular arrangements that may inhibit, promote or channel lateral diffusion by providing liquid-like pathways through the gel phase regions of the membrane. Similarly vestiges of these structures remaining in the liquid crystal phases may also inhibit lateral diffusion significantly. Finally, it is necessary to consider the problem of diffusion in the lipid bilayer in the simple case where two phases coexist as laterally separated patches. In this case the phase that dominates lateral diffusion rates is generally the multiply connected or matrix phase. Thus the macroscopic lateral distribution of the phases is at least as important as the diffusion coefficients themselves. Hui & Parsons (1975) have obtained electron micrographs of phospholipid-cholesterol mixed bilayers with finely divided lateral phase separation that suggests a continuously connected network of one phase that would control lateral diffusion. This speculative discussion of lateral transport on most mammalian cell membranes is obviously far from complete, but it is intended to convey a caution that the connexion between microviscosity of membrane lipids and lateral diffusion in the lipids is highly uncertain. In addition it is intended to suggest that the usual concepts of the cell membrane topology may mislead us into anticipating easy macroscopic lipid transport in the lipid bilayer whereas in fact compartmentalization of the lipid by rigid networks may inhibit its passive motion to highly localized microscopic regions. Instead of visualizing the cell membrane as a bilayer of lipid with protein islands, we probably should visualize it as a relatively rigid mesh of protein with lipid bilayer meniscus structures sealing its pores. The support of the NIH through grant no. GM21661-01, the NSF through grant no. DMR75-04509, a grant from the Research Corporation, and a research fellowship from the John Simon Guggenheim Memorial Foundation are gratefully acknowledged. This research has also been assisted by the facilities of the NSF-supported Materials Science Center at Cornell.
Applications of fluorescence correlation spectroscopy
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ALDER,
BADLEY, R. A., MARTIN, W. G. & SCHNEIDER, H. (1973). Dynamic behavior
of fluorescent probes in lipid bilayer model membranes. Biochemistry, N.Y. 12,268-75, CAPALDI, R. A. (1974). A dynamic model of cell membranes. Scient. Am. 230, 26-33.
R. J. (1975). Protein mobility in membranes. FEBS Lett. 55, 1-7. M. (1974). Rotational diffusion in membranes. A. Rev. Biophys. Bioeng. 3, 179-201. ELSON, E. L. & MAGDE, D. (1974). Fluorescence correlation spectroscopy. I. Conceptual basis and theory. Biopolymers 13, 1-27. ELSON, E. L. & WEBB, W. W. (1975). Concentration correlation spectroscopy: A new biophysical probe based on occupation number fluctuations. A. Rev. Biophys. Bioeng. 4, 311-34. FRYE, L. D. & EDIDIN, M. (1970). The rapid intermixing of cell surface antigens after formation of mouse-human heterokaryons. J. Cell Set. 7, 3I9~35GULIK-KRZYWICKI, T. (1975). Structural studies of the associations between biological membrane components. Biochim. biophys. Ada 415, 1-28. Hui, S. W. & PARSONS, D. F. (1975). Direct observation of domains wet bilayers. Science, N.Y. 190, 383-4. CHERRY, EDIDIN,
JONES, R. B., FELDERHOF, B. U. & DEUTCH, J. M. Diffusion of polymers
along a fluid-fluid interface. (Unpublished private communication.) KEYES, T. & OPPENHEIM, I. (1973). Bilinear hydrodynamics and the Stokes-
Einstein Law. Phys. Rev. 8, 937. D. E. (1974). Statistical accuracy in fluorescence correlation spectroscopy. Phys. Rev. A io, 1938-45. LEE, A. G. (1975). Functional properties of biological membranes: a physical chemical approach. Prog. Biophys. & molec. Biol. 29, 3-56. LEWIS, J. C. (1973). On the Einstein—Stokes diffusion coefficient for Brownian motion in two dimensions. Phys. Lett. 44 A, 245-6. MAGDE, D., ELSON, E. & WEBB, W. W. (1972). Thermodynamic fluctuations in a reacting system - measurements by fluorescence correlation spectroscopy. Phys. Rev. Lett. 29, 705-8. MAGDE, D., ELSON, E. L. & WEBB, W. W. (1974). Fluorescence correlation spectroscopy. II. An experimental realization. Biopolymers 13, 29-61. MONTAL, M. & MUELLER, P. (1972). Formation of bimolecular membranes from lipid monolayers and a study of their electrical properties. Proc. KOPPEL,
natn. Acad. Sd. U.S.A. 69, 3561-6. P., RUDIN, D. O., TIEN, H. T. & WESCOTT, W. C. (1962). Reconstitution of excitable cell membrane structure in vitro. Circulation 26, 1167-70. PETERS, R., PETERS, J., TEWS, K. H. & BAHR, W. (1974). A microfluorimetric MUELLER,
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study of translational diffusion in erythrocyte membranes. Biochim. biophys. Ada 367, 282-94. Poo, M.-m. & CONE, R. A. (1974). Lateral diffusion of rhodopsin in the photoreceptor membrane. Nature, Lond. z$], 438-41. RAND, R. P. & PANGBORN, W. A. (1973). A structural transition in egg lecithin-cholesterol bilayers at 12 °C. Biochim. biophys. Ada 318, 299-
3°5-
RAZI-NAQVI, K. (1974). Diffusion-controlled reactions in two-dimensional fluids: Discussion of measurements of lateral diffusion of lipids in biological membranes. Chem. Phys. Lett. 28, 280-4. SIMS, P. J., WAGGONER, A. S., WANG, C. H. & HOFFMAN, J. F. (1974). Studies on the mechanism by which cyanine dyes measure membrane potential in red blood cells and phosphatidyl-choline vesicles. Biochemistry, N. Y. J 3> 33IS-3O. SINGER, S. J. & NICOLSON, G. L. (1972). The fluid mosaic model of the structure of cell membranes. Science, N.Y. 175, 720-31. TARDIEU, A., LUZZATI, V. & REMAN, F. C. (1973). Structure and polymorphism of the hydrocarbon chains of lipids: A study of lecithin-water phases.
J.molec.Biol. 75, 711-33. YGUERABIDE, J.
& STRYER, L. (1971). Fluorescence spectroscopy of an oriented model membrane. Proc. natn. Acad. Sci. U.S.A. 68, 1217-21.
