Fluorescence Correlation Spectroscopy to determine diffusion laws: application to live cell membranes
Laure Wawrezinieck1,2, Pierre-Francois Lenne1,*, Didier Marguet2, Herve Rigneault1
1 Institut Fresnel (CNRS - univ. Aix-Marseille III) Domaine Universitaire de Saint Jerome - 13397 Marseille cedex 20 - France 2 Centre Immunologie Marseille Luminy (CNRS - INSERM - univ. Aix-Marseille II) Parc scientifique de Luminy - 13009 Marseille cedex 9 - France
ABSTRACT
Fluorescence correlation spectroscopy (FCS) is a mature and powerful technique for measuring diffusion coefficients. In a standard experiment, it measures the spontaneous fluorescence fluctuations arising from a single observation volume defined by confocal optics. However, the study becomes uneasy as soon as the diffusion is impeded by obstacles or specific mechanisms, as it is the case for the cell membrane components in live cells. In this paper, we show that doing FCS measurements at different sizes of observation volumes gives access to the diffusion laws without a priori knowledge of the landscape in which molecules are diffusing. Using this strategy, a measurement of diffusion laws of lipids in monophasic Giant Unilamellar Vesicles and in the plasma membrane of live cells is carried out.
Keywords: diffusion, anomalous diffusion, diffusion law, fluorescence correlation spectroscopy, giant unilamellar vesicle, live cell, cell membrane.
1. INTRODUCTION
Fluorescence correlation spectroscopy (FCS) was introduced by Elson and Magde1 in 1974 as a performing tool for determining chemical kinetic constants and diffusion coefficients by measuring spontaneous fluorescence fluctuations at thermodynamic equilibrium. FCS is now commonly used to measure low concentrations and diffusion coefficients of fluorescent molecules both in vivo and in vitro. In this case, the fluorescence fluctuations around the equilibrium value are due to random variations of the number of molecules in the observation volume: since this volume is open, molecules can enter or leave it by diffusion. Assuming that the studied molecules move freely in this known volume, a single FCS measurement enables to deduce the diffusion coefficient from the measured diffusion time. When free diffusion can no longer be assumed, as in live cell membranes2-4, the standard FCS treatment becomes uneasy, and a lot less information can be obtained. Without further care on the treatment of FCS data, wrong diffusion coefficients can even be calculated5. Here, we propose to carry out several FCS experiments for different sizes of the observation volume, in order to obtain the diffusion law, which has then to be explained by a diffusion model. With this method, the assumed diffusion model will not intervene in the treatment of experimental data as in a standard FCS treatment, but will only be used for the final interpretation of the results. In this paper, we give details about the method used to change the observation volume sizes. We then apply this method on lipids in Giant Unilamellar Vesicles (GUVs) and on the components of live cell membranes.
* Email: [email protected] 2. STANDARD FCS TREATMENT: MEASUREMENT AT A SINGLE WAIST
2.1. FCS experimental realization
Fluorescence correlation spectroscopy1 is a versatile technique for in vivo and in vitro investigation of biochemical interactions. It is based on the statistical analysis of spontaneous fluorescence fluctuations in an open volume, which is defined by a focused laser and confocal optics. This method is sensitive to fluorescence fluctuations at the single molecule level: when there are very few molecules in the observation volume, each molecule contributes significantly to the measured signal. As a consequence, FCS experiments will aim at reducing concentrations and observation volumes and at the same time increasing the fluorescence photon yield per molecule, in order to have high signal-to-noise ratios.
A usual FCS setup is described in fig. 1. Fluorophores such as Rhodamine 6G (Rh6G), Green Fluorescent Protein (GFP) or Bodipy are excited by the 488 nm line of an Ar+ ion laser. The excitation beam is focused by a high numerical aperture (N.A. = 1.2) microscope objective to a diffraction limited spot. Only the fluorophores within the illuminated region are excited. The fluorescence light is collected through the same microscope objective. Because of the Stokes shift, the emitted fluorescence occurs at a longer wavelength than the excitation: it can be separated from the excitation light by the dichroic mirror before it is directed into the detectors. The chosen detectors are silicon avalanche photodiodes, which have high photon-counting detection efficiencies, and low dark count rates: they have single photon sensitivity. In order to limit the detection volume, a confocal setup is used: a pinhole (20 or 50 µm) is placed in the image plane of the microscope objective, which blocks all light not coming from the focal region. To get a better signal-to-noise ratio, the excitation light has to be blocked. The dichroic mirror deflects the excitation light and transmits the red-shifted emission light. Emission bandpass filters are introduced in front of the detectors to improve the suppression of the scattered laser light. The fluorescence intensity signal is processed by a multiple-tau hardware correlator. This correlator has multiple sampling and delay times6: it measures the autocorrelation function (ACF) with high precision for delays ranging from less than a microsecond to a few minutes.
Ar+ ion laser (488 nm) Confocal volume
beam correlator expander
pinhole emission filter
dichroic sample microscope mirror objective APD
Fig. 1. FCS setup
2.2. Autocorrelation function calculation and free Brownian motion
Fluorescence fluctuations are quantified by calculating the temporal autocorrelation function g(2)(τ) of the recorded intensity signal:
()2 I ()t I (t +τ ) g ()τ = , (1) I ()t 2 where stands for a temporal average. The shape of the autocorrelation function can be predicted from the nature of the underlying molecular process. For a single diffusing species, in the absence of chemical kinetics, concentration fluctuations in the open observation volume are caused by the diffusion of molecules through this volume. In the confocal microscope configuration exposed in 2.1., the observation volume is defined by the convolution of the excitation volume due to the tightly focused laser and the detection volume determined by confocal optics. This observation volume is assumed to be a prolate ellipsoidal Gaussian volume, with an axial waist wz and a lateral waist wxy. In the cases where the diffusion of molecules occurs in 3D or 2D, the autocorrelation functions have respectively the following analytical forms1:
()2 1 1 1 g3D ()τ = 1+ , (2a) N τ 2 1+ w τ τ 1+ z D wxy τ D 1 1 g ()2 ()τ = 1+ , (2b) 2D N τ 1+ τ D w2 where τ = xy , (2c) D 4D and D is the diffusion coefficient.
1.5 experimental ACF 3D free diffusion fit 1.4
1.3
1.2
1.1 autocorrelation function autocorrelation 1.0
0.001 0.01 0.1 1 10 100 1000 time (ms)
Fig. 2. Autocorrelation function corresponding to the 3D free diffusion of Rhodamine 6G fluorophores
When the results of FCS measurements are compared to the theoretical free Brownian diffusion ACF (fig. 2), three types of information can be obtained. First, the shape of the curve enables to detect the mode of motion of the molecules. In particular, non-Brownian motion, such as directed, confined or anomalous diffusion cannot be fitted by (2a) or (2b). Second, the mean number of molecules in the observation volume can be calculated from the initial correlation amplitude, g(2)(0) = 1+1/
3. STANDARD FCS TREATMENT APPLIED TO LIVE CELL MEMBRANES
It has been seen that FCS can be easily used when studying free diffusing molecules. Nevertheless, the ideal case of free Brownian motion does not always apply. For example, the diffusion of molecules in cell membranes or cell organelles is often hindered or even confined by local cellular structures or specific mechanisms (fig. 3): macroscopic diffusion coefficients of proteins and lipids in cell membranes are 5 to 100 times smaller than those in artificial bilayers.
free diffusion
free diffusion?
confined diffusion
Fig. 3. Hindered diffusion by domains; the determination of diffusion coefficients depends critically on the confinement.
Despite an increasing interest in the architecture of the plasma membrane, a comprehensive view is still lacking. The fluid mosaic model of the membrane was proposed by Singer and Nicolson in 19727, in which the membrane contains no heterogeneities. For the past decades, there has been growing evidence for a lateral organization, in which cholesterol- and sphingolipid-rich domains coexist with more fluid domains enriched in phospholipids with unsaturated hydrocarbon chains8, 9. The data leading to this postulate of membrane microdomains come mainly from biochemical studies: unlike the rest of the membrane, lipid microdomains are resistant to cold detergents such as Triton- X100 and can be extracted10. However, it has been recently shown that Triton-X100 itself may promote the formation of domains in artificial membranes11. A more reliable and dynamic study of the structure of the membrane is necessary: FCS can help drawing a picture of the landscape in which molecules are diffusing.
3.1. Insertion of fluorescent lipids and fluorescent proteins in the plasma membrane of live cells
All experiments are carried out on COS-7 cells. We study the dynamics of diffusion of a couple of proteins and lipids, which are thought to partition differently in lipid microdomains. Fluorescently conjugated lipid probes BODIPY-C12-sphingomyelin (BODIPY-C12-SM) are incorporated in the plasma membrane by a lipid exchange procedure12: they are added at low concentrations in the form of complexes with BSA. We also use the glycosylphosphatidylinositol (GPI)-linked GFP protein as a fluorescent probe of the membrane. Cells are transiently transfected with the plasmid coding for the fusion protein GFP-GPI, previously mixed with ExGen 500 reagent. Because of charge interaction, the transfection reagent and DNA form complexes which are absorbed by endocytosis. As a result, the cell is made to produce itself the fluorescent proteins that are then addressed to the plasma membrane.
3.2. Positioning the confocal volume on the plasma membrane
Next, the membrane has to be placed in the plane of symmetry xy of the confocal volume (fig. 4a). It is easier to run a measurement on a single membrane when the two sides of the membrane are separated by the nucleus. The cells adhere on a chambered coverglass mounted on a xyz piezo nanopositioning/scanning stage. A first xy scan is carried out in order to visualize the cell nucleus, which is not stained (fig. 4b). A z scan is then performed in the middle of the nucleus to distinguish the two sides of the membrane. We choose to localize the confocal volume on the upper membrane, which has no contact with the coverglass, to avoid interactions between the diffusing lipids and the borosilicate.
20 a b c confocal volume 15 m)
µ 10 nucleus
5 position ( z 0 coverglass 20 40 60 80 100x103 detected intensity (cps) 20 µm
Fig. 4. Positioning of the confocal volume on the plasma membrane: a. schematic view of the position of the confocal volume in the cell; b. xy scan of the cell; the white cross corresponds to the xy position chosen for the z scan; c. z scan of the cell; the arrow shows the z position chosen for the FCS measurement.
3.3. Results of FCS measurements on live cell membranes
A measurement of an experimental ACF is carried out for the GFP-linked GPI proteins, which are diffusing in the plasma membrane of COS-7 cells (fig. 5). It has to be noted that a model of diffusion is needed to get information from an ACF.
-3 40x10 -3 -3 20x10 20x10 20 0 0
residuals 0 2-species free diffusion 1-species free diffusion anomalous diffusion τanomalous = 34.9 ms τD 1 = 0.8 ms (48%) 1.08 τD = 10.6 ms 1.08 1.08 α = 0.62 τD 2 = 24.5 ms (52%)
1.06 1.06 1.06
1.04 1.04 1.04
1.02 1.02 1.02 autocorrelation function autocorrelation
1.00 1.00 1.00
0.001 0.1 10 1000 0.001 0.1 10 1000 0.001 0.1 10 1000 a time (ms) b time (ms) c time (ms)
Fig. 5. Experimental ACF (grey line) corresponding to the diffusion of GFP-GPI in the plasma membrane of live cells fitted with different functions (black lines): a. one species diffusing freely in 2D; b. one species diffusing anomaly in 2D; c. two species diffusing freely, one in 2D, the other in 3D
Three types of functions have been tried to fit this experimental ACF. First, a free 2D diffusion fit, as defined in equation (2b), is used in fig. 5a. As it can be seen from the residuals versus time curve, this fitting function is not appropriate. Two other functions can improve drastically the quality of the fit: an anomalous 2D diffusion fit (fig. 5b), as well as a 2-species free diffusion fit (fig. 5c). The 2-species diffusion fit is obtained from the multiplication of the two functions (2a) and (2b): one species is supposed to diffuse freely in 2D, while the other diffuses freely in 3D. In the case of anomalous diffusion13, the mean square displacement is no longer proportional to time t, but rather to tα, with α < 1. α The ACF is also changed: in formula (2a) and (2b), (τ/τD) has to be replaced by (τ/τanomalous) . Anomalous diffusion is a specific diffusion mode corresponding to the presence of multiple energy potential traps with binding energies that vary over wide ranges of time and space. Unfortunately, this fitting function applies to lots of diffusion modes which are not anomalous diffusion, as it was defined by Bouchaud and Georges. Furthermore, the new parameter α lacks physical meaning. In particular, the landscape in which the molecules are diffusing cannot be described with this single parameter. In the case of the ACF measured for GFP-GPI, it is difficult to choose between the 1-species anomalous diffusion fit and the 2-species free diffusion fit, just from the quality of the two fits. Indeed, the residuals versus time curves do not enable to discriminate between the two fitting functions. A basic knowledge of the biological process is hence needed to choose the appropriate fitting function for the experimental ACF curve. A measurement of the ACF for the BODIPY-C12-SM lipids is then carried out (fig. 6), in order to help discriminating between these two diffusion modes. In the case of this lipid, the 2D free diffusion fit is sufficient to describe the ACF. The two other fits which have been tried do have smaller residuals, but only because they use more fitting parameters, not because these diffusion modes are more appropriate for the description of the lipid motion. In particular, the anomalous coefficient α has a value very close to 1 (α = 0.99), contrary to the one found for GFP-GPI (α = 0.62); moreover, the fast diffusing fraction is on the order of 10%, which has to be compared to the one for GFP- GPI (48%).
0.1 0.1 0.1
0.0 0.0 0.0 residuals 1.20 1.20 1.20 1-species free diffusion anomalous diffusion 2-species free diffusion τanomalous = 37.9 ms τD 1 = 0.5 ms (10%) τD = 38.2 ms α = 0.99 τ = 40.5 ms (90%) 1.15 1.15 1.15 D 2
1.10 1.10 1.10
1.05 1.05 1.05 autocorrelation function
1.00 1.00 1.00
0.001 0.1 10 1000 0.001 0.1 10 1000 0.001 0.1 10 1000 a time (ms) b time (ms) c time (ms)
Fig. 6. Experimental ACF (grey line) corresponding to the diffusion of BODIPY-C12-SM in the plasma membrane of live cells fitted with different functions (black lines): a. one species diffusing freely in 2D; b. one species diffusing anomaly in 2D; c. two species diffusing freely, one in 2D, the other in 3D
Since BODIPY-C12-SM diffuse freely in 2D, the 2-species free diffusion fit should be used to describe the GFP-GPI motion. Furthermore, the smaller diffusion time is compatible with a 3D diffusion time of GFP-GPI in the Golgi apparatus, which has been previously measured. The larger one would then correspond to the diffusion time of GFP-GPI in the cell plasma membrane. The fraction of fast diffusing molecules is on the order of 48%, which is compatible with confocal cell images (fig. 4b): they show comparable intracellular and membrane staining. It was shown that even more complex model ACFs are needed in the case of local confinement of the diffusion in small organelles of sizes comparable to the size of the observation volume. Gennerich and Schild2 have proposed a non-analytical solution for the ACF to describe the diffusion of fluorophores in dendrites of cultured neurons. However, this method is based on the a priori knowledge of the confinement geometry.
In this paper, we show that measuring the diffusion time of fluorophores at different sizes of volume of observations can keep us from using complex ACFs, which may be hard to implement as soon as there are lots of parameters. Furthermore, the measurement of diffusion laws does not need inferences on the diffusion mode. Those are only needed to interpret the measured diffusion laws. 4. DIFFUSION LAW MEASUREMENT BY FCS
4.1. Change of the size of the observation volume
The easiest way to measure the diffusion law of diffusing molecules consists in measuring their diffusion times through observation volumes of different sizes. Microscope objectives with different magnifications can be used in order to change the transversal size of the observation volume, which is diffraction-limited. We have rather chosen to use a single objective: its apparent numerical aperture can be changed by underfilling its back-aperture (fig. 7).
iris
microscope objective
µ2 < µ1 µ1
N.A. = n sin(µ ) N.A. < N.A. focal plane 1 1 2 1
1.0 1.0 0.8 0.8 point spread 0.6 0.6 function 0.4 w1 0.4 w2 > w1 0.2 0.2 0.0 0.0 -400 0 400 -400 0 400
Fig. 7. Change of the size of the observation volume by underfilling the back-aperture of the microscope objective
An iris is introduced between the laser beam expander and the dichroic mirror, in order to select the extension of the laser beam falling on the back-aperture of the microscope objective. The point spread function of this optical setup is a direct function of the iris aperture: the more underfilled the objective is, the larger the point spread function is. As a consequence, the experimentalist can easily change the size of the observation volume.
4.2. Characterization of observation volumes with fluorescent microspheres
Fluorescent microspheres (PS-Speck Microscope Point Source Kit from Molecular Probes) are used to characterize the shape of the observation volume. These microspheres are silicon beads of 175 ± 5 nm in diameter filled with fluorophores. They are deposited on a coverglass mounted on the piezo nanoscanning stage so that they can be moved in the observation volume in the three directions. The volume inferred from the fluorescence signal which is measured by the detectors is the result of the convolution of the observation volume with the bead shape: a deconvolution is needed to obtain the real observation volume. Interestingly, the use of smaller beads would permit to distinguish smaller details in the observation volume. A scan along the axis of symmetry z and a scan in the plane of symmetry xy enable the calculation of wxy and wz. The results for different iris apertures are shown in fig. 8.
Iris aperture
Ifluorescence Ifluorescence Ifluorescence
xy scan
2 2 2 x (µm) 2 x (µm) 2 x (µm) 2 y (µm) y (µm) y (µm) 0 0 0 wxy = 220 nm wxy = 290 nm wxy = 380 nm
Ifluorescence Ifluorescence Ifluorescence
z scan
-8 -4 0 4 8 -8 -4 0 4 8 -8 -4 0 4 8 z (µm) z (µm) z (µm) wz = 1.36 µm wz = 2.52 µm wz = 3.71 µm
Fig. 8. Measurement of the lateral and transversal waist for different lateral extension of the excitation beam falling on the back- aperture of the microscope objective; the xy scans are experimental results (prior to deconvolution), whereas the numerical values of wxy and wz are given after deconvolution
4.3. Measurement of the laser waist wxy and the diffusion time τD
To draw the diffusion law of components of a 2D membrane, one needs to measure the diffusion time τD as a function of the waist wxy of the laser beam: we will assume that the membrane is placed in the plane of symmetry xy of the observation volume.
Fluorescent microspheres can be used as explained in 3.2. to measure the lateral waist wxy of the observation volume, which is also the waist of the excitation laser beam. We prefer a faster method that is based on the measurement of the diffusion time of a fluorophore, which diffusion coefficient is known. Rh6G diffusion coefficient has already been measured14: D = 280 µm2/s at 22°C for a concentration of 0.5 nM. We use Rh6G to calibrate the size of the observation volume.
In the case of non-Brownian diffusion, it has been seen in 3. that fitting functions can be hard to deal with. We rather define the diffusion time τD as the FWHM of the ACF curve. This is compatible with the definition for free diffusion, and permits to have a quick and robust determination of τD.
5. EXPERIMENTAL DIFFUSION LAWS IN MEMBRANES
5.1. Diffusion law measurement in monophasic Giant Unilamellar Vesicles
In order to test our setup, the diffusion law has been measured in a model membrane, in which it was already known. A model membrane is a lipid monolayer or bilayer, which composition is chosen and controlled by the experimentalist. Fluorescent lipids are incorporated in this membrane, and have a two-dimension diffusion movement. Giant Unilamellar Vesicles (GUVs) are liposomes made of a single lipid bilayer (fig. 9a). In order to introduce fluorescent lipids in this artificial bilayer, they are prepared by electroformation15 from a pure mixture of dioleoylphosphatidylcholines (DOPC) and fluorescent phosphatidylcholines BODIPY-C5-PC (FL-PC) (1000:1). GUVs of sizes ranging from 10 µm to 100 µm are obtained. Since FL-PC are homogenously dispersed in the whole bilayer, and the composition yields a single phase at ambient temperature, FL-PC have a free 2D motion.
1.08
experimental ACF 1.06 2D free diffusion fit
1.04
1.02 autocorrelation function autocorrelation 1.00
0.001 0.01 0.1 1 10 100 1000 b time (ms)
6 5 4 3 2
diffusion time (ms) time diffusion 1 0
3 0 20 40 60 80 100 120 140x10 2 2 a c waist2 (nm2 ) wxy (nm )
Fig. 9. Measurement of the diffusion law of phospholipids in an artificial membrane: a. confocal image of giant unilamellar vesicles; b. autocorrelation function measured at wxy = 330 nm; c. diffusion law in DOPC GUVs explored by FCS between wxy = 205 nm and wxy = 390 nm.
The fig. 9b shows that a 2D free diffusion curve nicely fits the experimental ACF. This FCS measurement has been carried out at different values of the waist wxy (fig. 9c), which shows that the diffusion time is proportional to the square of the waist. This is compatible with the hypothesis of a free diffusion, and gives access to the diffusion coefficient of the FL-PC in DOPC: D = 6.4 ± 0.5 µm2/s. This value is consistent with the result of another experiment by Kahya et al.16: D = 6.3 ± 0.2 µm2/s.
Once the setup has been tested for known diffusion behaviors, we use it to measure unknown diffusion laws. Instead of working on artificial membrane containing a single phase, we study live cells.
5.2. Diffusion law measurement in live cell membranes
The same protocol as in 3. is followed, but at different sizes of excitation beam waists. The diffusion law of a lipid (BODIPY-C12-SM) in the plasma membrane of live COS-7 cells is measured by FCS (fig. 10). Although the 1- species free 2D diffusion curve seemed to fit nicely the experimental ACF obtained for BODIPY-C12-SM (fig. 6), the diffusion law does not reflect free diffusion. Indeed, the diffusion time is not proportional to the square of the 2 2 transversal waist wxy , but is a linear function of wxy , the intersection of the line with the time axis being strictly positive.
30
25
20
15
10 diffusion time (ms) diffusion
5 BODIPY-C12-SM
0
3 0 20 40 60 80 100 120x10 2 2 wxy (nm )
Fig. 10. diffusion laws measured by FCS of the lipid BODIPY-C12-SM
This diffusion law is neither a free diffusion law, nor an anomalous diffusion law. Although there has to be processes or structures which hinder the diffusion of membrane components in the plane of the membrane, these cannot be described as multiple energy potential traps with binding energies that vary over wide ranges of time and space.
As a consequence, models of diffusion in the cell membrane have to be proposed and tested, until one is found, which can explain the measured diffusion law. The experimentalist should nevertheless keep in mind that several models of diffusion can lead to the same diffusion laws. The chosen model will have to be consistent with the results from other techniques such as biochemical studies, Single Particle Tracking measurements17, 18, etc.
5. CONCLUSION
Fluorescence Correlation Spectroscopy is a widely used method for measuring diffusion coefficients, which is well adapted to free diffusing fluorescent molecules. However, the diffusion of molecules in cell substructures is often impeded by physical obstacles or biological mechanisms. To study these complex phenomena, one could try to fit the autocorrelation function with multi-parameter curves. Instead, measuring the diffusion time at different sizes of waists with FCS can permit to have access to diffusion laws, without the implementation of multi-parameter fits. We have shown that the FWHM of the autocorrelation function is not only easy to calculate, but also a robust observable. Using this method, we have measured the diffusion laws of fluorescent molecules in artificial bilayers and in live cell plasma membranes. Whereas lipids have a 2D free diffusion motion in single-phase artificial membranes, the diffusion law of lipids and proteins in live cell membranes is anomalous. At large waists, this diffusion law is indeed a line with a positive intersection with the time axis. It is particularly interesting to note that these two different behaviors cannot be distinguished by the sole study of the shape of ACFs. Furthermore, the measured diffusion law will permit to validate a model of diffusion, and may enable to discriminate between several mechanisms suspected to hinder the diffusion of membrane components. A few mechanisms have already been proposed, such as the role of fences played by the cytoskeleton, or the confining capability of “lipid rafts”, which have yet to be tested and compared to experimental results.
REFERENCES
1. E.L. Elson, D. Magde, "Fluorescence Correlation Spectroscopy. I. Conceptual basis and theory", Biopolymers, 13, 1-27, 1974 2. K. Simons, E. Ikonen, "Functional rafts in cell membranes", Nature, 387, 569-72, 1997 3. D.A. Brown, E. London, "Functions of lipid rafts in biological membranes", Annu. Rev. Cell. Dev. Biol., 14, 111- 36, 1998 4. M. Edidin, "The state of lipid rafts: from model membranes to cells", Annu. Rev. Biophys. Biomol. Struct., 32, 257- 83, 2003 5. A. Gennerich, D. Schild, "Fluorescence Correlation Spectroscopy in small cytosolic compartments depends critically on the diffusion model used", Biophys. J., 79, 3294-306, 2000 6. K. Schatzel, "New concepts in correlator design", Inst. Phys. Conf. Ser., 77, 175-84, 1985 7. S.J. Singer, G.L. Nicolson, "The fluid mosaic model of the structure of cell membranes", Science, 175, 720-31, 1972 8. D.A. Brown, E. London, "Structure and function of sphingolipid- and cholesterol-rich membrane rafts", J. Biol. Chem., 275, 17221-4, 2000 9. K. Simons, E. Ikonen, "Functional rafts in cell membranes", Nature, 387, 569-72, 1997 10. D.A. Brown, J.K. Rose, "Sorting of GPI-anchored proteins to glycolipid-enriched membrane subdomains during transport to the apical cell surface", Cell, 68, 533-44, 2000 11. H. Heerklotz, "Triton promotes domain formation in lipid raft mixtures", Biophys. J., 83, 2693-701, 2002 12. R.E. Pagano, O.C. Martin, Cell biology: a laboratory handbook, vol.2, 507-12, Academic Press, San Diego, 1998 13. J.-P. Bouchaud, A. Georges, "Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications", Phys. Rep., 195, 127-293, 1990 14. D. Magde, E.L. Elson, "Fluorescence Correlation Spectroscopy. II. An experimental realization", Biopolymers, 13, 29-61, 1974 15. L. Mathivet, S. Cribier, P.F. Devaux, "Shape change and physical properties of giant phospholipid vesicles prepared in the presence of an AC electric field", Biophys. J., 70, 1112-21, 1996 16. N. Kahya, D.Scherfeld, K. Bacia, B. Poolman, P. Schwille, "Probing lipid mobility of raft-exhibiting model membranes by fluorescence correlation spectroscopy", J. Biol. Chem., 278, 28109-15, 2003 17. A. Kusumi, Y. Sako, M. Yamamoto, "Confined lateral diffusion of membrane receptors as studied by single particle tracking (nanovid microscopy). Effects of calcium-induced differentiation in cultured epithelial cells". Biophys. J., 65, 2021-40 18. G.J. Schutz, G. Kada, V.P. Pastushenko, H. Schindler, "Properties of lipid microdomains in a muscle cell membrane visualized by single molecule microscopy", EMBO J., 19, 892-901