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Technical University of Dresden, Dresden, Germany
Correspondence: Address reprint requests to P. Schwille, Tel.: 49-351-4634-0328, E-mail: petra.schwille{at}biotec.tu-dresden.de.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHEORYMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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–3) is an established method for the determination of local concentrations, molecular weights, translational and rotational diffusion coefficients, chemical rate constants, association and dissociation constants, and photodynamics. First applied on molecules in solution, the use of FCS was then extended to the study of two-dimensional diffusion in artificial, supported lipid bilayers (4). Later, FCS was applied to native cell membranes and free-standing artificial lipid bilayers (5,6). The detection volume is usually positioned on a horizontal membrane, which can induce serious photobleaching: the slower the diffusion, the higher the residence time of the molecule in the detection volume. To avoid significant photobleaching of the fluorophores, which would lead to a distortion of the corresponding correlation curve, the excitation power has to be reduced. However, for reduced excitation powers, the dark counts of the detector will introduce additional noise in the correlation curve and the acquisition time has to be increased. To achieve a good signal/noise ratio, but also to avoid systematic distortions of the correlation curve due to short measurement times, continuous acquisition for time periods of several orders-of-magnitude larger than the diffusion times are required. But the long measurement times are limited by the stability of the setup. Changes of the position of the detection volume with respect to the membrane give rise to a distortion of the correlation curve and a poorly defined detection volume.
Various FCS-related methods with a scanning detection volume have been developed to circumvent some of the above-mentioned problems: Scanning FCS in solution (7–10) or on surfaces (11) can be used to study static and dynamic parameters of the system. Image correlation spectroscopy, first introduced by Petersen et al. (12), measures very slow dynamic parameters. Raster image correlation spectroscopy extends the application of this method to a wide range of diffusion times (13). Ruan et al. (14) introduced a new type of scanning FCS on membranes, which accesses the intermediate temporal regime. With this approach, the detection volume is scanned in a circular way through the equator of a giant unilamellar vesicle (GUV), which results in a set of correlation curves from all points along the scanned circle, permitting the study of binding and membrane dynamics which would otherwise be obscured by an excess of fluorophores in solution. Compared to FCS with a fixed detection volume at the top of the cell or vesicle, the alignment of the detection volume along the membrane in scanning fluorescence correlation spectroscopy (SFCS) allows for a better separation of the signal from fluorescent background in the solution. However, the use of two-photon excitation bears several risks due to the high photobleaching in membranes limiting the counts per particle and therefore, for a given acquisition time, the statistical accuracy of the correlation curve.
Here we discuss the use of one-photon scanning FCS as commonly applied in laser scanning microscopes and focus on studying membrane dynamics with high accuracy in challenging biological systems. The detection volume is scanned in a linear fashion (Fig. 1 a) rather than in the circular scan pattern employed in Ruan et al. (14). Furthermore, correlation curves were not calculated for all points along the scan path, but membrane movements are corrected for, and only the contributions of the membrane are taken into account to calculate the correlation curve. In this way we achieve a reproducible and well-defined detection volume even in an unstable system.
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) is the use of continuous wave excitation instead of two-photon excitation, which results in higher achievable counts per particle and reduced photobleaching. The improved signal not only permits shorter measurement times but also facilitates accurate measurements of very slow diffusion, encountered, for example, in yeast cell membranes. In addition, the enhanced signal allows for parameter-free determination of diffusion constants with two-foci cross-correlation spectroscopy (TFCCS) and binding studies using dual-color fluorescence cross-correlation spectroscopy (dcFCCS) with continuous and pulsed interleaved excitation. Continuous wave SFCS can be easily implemented in a commercial laser scanning microscope and readily used with a modern FCS instrument like the Zeiss Confocor 3 (Carl Zeiss, Jena, Germany).
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THEORY |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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D of the fluorophores. During data analysis, the emission, which can be attributed to the membrane-bound fluorophores, is integrated for each scan. These intensity values form the discrete time-trace Fi, which is used to calculate the correlation curve G(i), where i represents integer multiples of the scanning period T (Fig. 1).
For a fluorophore confined to the membrane (x = 0) at the position (y, z) and a scan in x-direction with a constant velocity v through all of the membrane, the average emitted light intensity is
 | (1) |
= 
QI0 is the product of the setup efficiency , the fluorescence yield per fluorophore Q, and the excitation amplitude I0. The value 
is the molecule detection function of the setup, which is the product of excitation intensity distribution and the collection efficiency function of the objective-pinhole combination. Most commonly, a three-dimensional Gaussian is assumed for :
 | (2) |
 | (3) |
This gives rise to the following autocorrelation function, describing two-dimensional diffusion of one component in a Gaussian elliptical detection volume:
 | (4) |
 | (5) |
is the number density autocorrelation function for two-dimensional diffusion for an average concentration c, N = c
w0z0 is the mean number of molecules in the effective detection area, 
is the diffusion time, and the structure parameter 
describes the ellipticity of the detection area. The triplet contribution has been neglected since triplet times are in the range of microseconds and cannot be resolved with SFCS.
Two-foci cross correlation (TFCCS)
By alternately scanning along two lines at a distance d parallel to each other, two effective foci in the membrane with a displacement d along the y-direction can be realized (Fig. 2 a). The photons in the two foci are not collected within the same time window, but with a delay td, which is usually given by the scan period. If td is much smaller than the diffusion time D, it can be neglected. The cross correlation of the intensity traces corresponding to the two intersections results in the correlation curve (15,16)
 | (6) |
 | (7) |
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Because of the alternating data collection in the two foci, the resulting cross-correlation curve is shifted by the delay time td, as can be seen by looking at the definition of the cross-correlation curve Gx for intensity traces F(t) and H(t) and the cross-correlation curve 
for intensity traces F(t) and H(t + td):
 | (8) |
D, this shift needs to be taken into consideration in performing the fit.
Two-foci cross correlation on planar membranes
The same setup also permits TFCCS on planar membranes with the additional advantage of simultaneous determination of diffusion coefficients in different parts of the sample. As depicted in Fig. 2 b, two parallel lines are scanned within the membrane and the contributions from corresponding parts of the sample (denoted by a box) of the length s belonging to the equivalent time window tm = s/v are summed up for each scan. Depending on the length of the time window, the effective detection area can be practically circular (very short time window) or a line (long time window).
The unnormalized molecule detection function (x, y) is given by the convolution of the Gaussian detection area of waist radius w0 with a step function of length s, describing the scanning in x direction:
 | (9) |
 | (10) |
 | (11) |
An elongated detection volume offers the advantage of a high signal/noise ratio in the correlation curve, since one out of two fluorophores that originates in one detection area will finally reach the second one.
Dual-color cross correlation
In dual-color cross correlation (dcFCCS) the auto- and cross-correlation curves for two spectral channels are calculated. In case of an ideal setup with completely overlapping detection volumes Veff and negligible spectral cross talk, the concentrations of the unbound molecules ca and cb and of the bound molecules cab can be determined from the amplitudes of the correlation functions (17):
 | (12) |
In case of a nonperfect overlap of the detection volumes, Eq. 6 describes the cross-correlation function. Yet, for small imperfections, Eq. 5 can be used to fit the data and Eq. 12 can be used approximately if one compares the measured cross-correlation amplitude to the maximally achievable cross-correlation amplitude. The maximally achievable cross-correlation amplitude corresponds to a complete binding of the species involved and can be estimated using a sample with known high cross correlation (16). Often a double-labeled molecule (i.e., DNA) with a high labeling efficiency is used.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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The movement of the detection volume was controlled directly with the Zeiss LSM operation software. The line mode was used for one-focus measurements and the frame mode with N x 2 pixels for two-foci measurements. For pulsed interleaved excitation (PIE) the multitrack mode was applied. In this mode the excitation lasers are alternately used for every other line scan by blocking the undesired laser line with an acousto-optical tunable filter. Bidirectional scanning was employed whenever useful to increase the acquisition speed.
The distance d between the two lines for two-foci FCS was measured by repeatedly scanning over a film of dried fluorophores and measuring the distance between the bleached traces in a high resolution LSM-Image.
All measurements were performed at room temperature (22°C).
Materials
1,2-dioleoyl-sn-glycero-3-phosphocholine (dioleoylphosphatidylcholine; DOPC), n-stearoyl-d-erythrosphingosylphosphorylcholine (sphingomyelin), and cholesterol were purchased from Avanti Polar Lipids (Alabaster, AL) and used without further purification. Lissamine rhodamine B 1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine triethylammonium salt (Rhodamine DHPE), BODIPY FL C5-ganglioside GM1 (GM1-BODIPY-FL), cholera toxin subunit B (recombinant), Alexa Fluor 488 conjugate (ctxB-Alexa488), 1,1'-dioctadecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate (DiIC18, DiI), and 3,3'-dioctadecyloxacarbocyanine perchlorate (DiOC18, DiO) were purchased from Molecular Probes (Eugene, OR). Ganglioside GM1, Bovine Brain, was purchased from Merck KGaA (Darmstadt, Germany). Cholera toxin subunit B, labeled with Cy5 (ctxB-Cy5), was produced according to Bacia et al. (18).
Yeast cells expressing Fus-Mid-GFP from a centromeric plasmid pTPQ55 were a kind gift of Kai Simons (MPI-CBG, Dresden, Germany). To reduce intracellular staining we used a vps1
mutant (for details see (19)).
Preparation of model membranes
Giant unilamellar vesicles were produced by a modified electroformation method as described previously (20), using a custom-made closed perfusion chamber heated to 65°C and indium-tin-oxide coated coverslips as electrodes. Briefly, a 5-µL lipid mixture, as indicated in Results, was deposited on indium-tin-oxide-coated coverslips. After evaporation of the solvent, the chamber was assembled and filled with water. A voltage of 1.2 V at 10 Hz was applied for 
2 h. Where applicable, labeled ctxB was added at a saturating concentration to the flow chamber after GUV formation and incubated for 10 min at room temperature. The optical setup was adjusted to the labeled ctxB in solution in the chamber. Residual ctxB was removed by applying a slow flow of water through the perfusion chamber.
Planar supported bilayers were prepared as follows (21): DOPC (molar concentration 80%), Cholesterol (20%), and Rhodamine DHPE (0.001%) were dissolved in chloroform and evaporated under nitrogen flux and then under vacuum for 1 h. The lipids were then rehydrated with 150 mM NaCl, 10 mM HEPES buffer (pH 7.4) and resuspended by vigorous vortexing. The suspension was bath-sonicated at 60°C for 1 h to obtain small unilamellar vesicles. Ten microliters were then placed on a freshly cleaved mica substrate glued to a glass coverslip, for 30 min at room temperature. After that, the sample was rinsed several times to remove unfused vesicles.
Data analysis
Data analysis was performed with software written in MatLab (The MathWorks, Natick, MA). The photon stream was binned in bins of 100 ns to 5 µs depending on the scan speed and arranged as a matrix such that every row corresponded to one line scan (Fig. 1 b). Movements of the membrane were corrected-for by calculating the position of the maximum of a running average over several hundred line scans and shifting it to the same column. An average over all rows was fitted with a Gaussian and only the elements of each row between –2.5 
and 2.5 were added to construct the intensity trace. The correlation function of the resulting intensity trace Fi was computed with a multiple-tau correlation algorithm (22). The correlation curves were fitted with a weighted nonlinear least-squares fitting algorithm. Errors given in the figures are the 95% confidence intervals on the nonlinear least-squares parameter estimates; errors indicated in the text take into account the uncertainties of additional parameters, such as the waist radius w0 or the distance between foci d.
For two-foci measurements, two intensity traces Fi and Hi were extracted from the photon stream and processed in an analogous way. Equations 4 and 7 were fitted globally to obtain one set of fit parameters.
For dcFCCS with continuous excitation, one intensity trace was extracted from each channel as described above and auto- and cross-correlation curves were calculated and fitted to Eq. 5 to determine relative cross-correlation amplitudes. For dcFCCS with PIE, two intensity traces were extracted from the orange channel and one from the green channel (cross excitation of the green dye with the orange laser and cross talk of the orange dye into the green channel were negligible).
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RESULTS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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D = 524 ± 54 ms corresponds to a diffusion coefficient of D = 0.019 ± 0.006 µm2/s.
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D exhibit a higher degree of correlation. The distance d between the two lines was determined to be 300 ± 15 nm as described in Materials and Methods. A global fit of the measured correlation curves to Eq. 7 resulted in w0 = 199 ± 12 nm and D = 0.23 ± 0.03 µm2/s. Due to the different composition of the GUV, this value is an order-of-magnitude higher than the diffusion coefficient measured in the previous section.
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D = 42 ± 3ms corresponds to a diffusion coefficient of D = 0.24 ± 0.07 µm2/s, based on a waist radius of w0 = 200 ± 20 nm determined from a calibration measurement of Alexa488 in solution.
Two-foci cross correlation on planar membranes
Fig. 5 shows the outcome of scanning TFCCS on a homogeneous supported lipid bilayer, as described in Theory, above, and Fig. 2 b. The bilayer was composed of 80% DOPC and 20% cholesterol and was labeled with 0.001% Rhodamine DHPE. The two lines had a separation of d = 430 ± 20 nm. The length of the part of the line scan used to construct the intensity trace was s = 2.87 µm. The resulting diffusion coefficient D = 3.5 ± 0.3 µm2/s is in good agreement with a value of D = 4.1 ± 0.8 µm2/s obtained with traditional FCS.
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). Usually alternating short laser pulses with a repetition rate of several MHz are required for PIE. In SFCS, PIE can be implemented in a much simpler fashion. By alternating the green and the orange excitation for every other line scan, the contributions from the different fluorophores can be separated. This is due to the fact that the contributions from the green-emitting fluorophores in the orange detection channel upon excitation with the orange laser, and that from the orange-emitting fluorophores in the green detection channel upon excitation with the green laser, are negligible. Fig. 7 a shows auto- and cross-correlation curves obtained on GUVs composed of 50% cholesterol and 50% sphingomyelin and labeled with 0.004% DiO and 0.002% DiI. These two dyes are not supposed to cross-correlate and have partially overlapping excitation and emission spectra. Fig. 7 b shows the auto- and cross-correlation curves obtained on the same sample as Fig. 7 a using PIE.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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Another important advantage of SFCS is its robustness to instabilities which limit the acquisition times in static FCS on membranes. In SFCS, slow movements are corrected-for and the contributions from all of the membrane are summed up. As a result, a reproducible and well-defined detection area is obtained, and the measurement becomes insensitive to membrane undulations, which can otherwise be a severe problem since they mimic an additional diffusing component (24).
To calculate the diffusion coefficient from the diffusion time, the waist w0 of the detection area has to be known. It can be determined by calibration measurements with free dye or with two-foci SFCS. It can also be extracted directly from the line scans (Fig. 1 b) by fitting the line profile to a Gaussian, but nonperpendicular scanning, residual curvature, or faster membrane movements result in an enlarged estimate for this value.
In one-focus measurements, an exact calibration of the detection area is complicated, since varying alignment, temperature, refractive index of the sample, or cover-slide thickness result in a poorly defined detection volume (25). Moreover, calibration measurements performed in solution to determine the two-dimensional detection area on the membrane are only exact for an ideal Gaussian detection volume.
Two-foci cross correlation
With scanning two-foci FCS (TFCCS) we measured absolute diffusion coefficients without the need for calibrating the detection area (Fig. 4 a). The one-focus measurement (Fig. 4 b) resulted in a similar value for the diffusion coefficient, but the error was significantly higher due to the difficulties of determining the detection area. The advantage of two-foci SFCS versus one-focus SFCS is even greater for small diffusion times comparable to the scanning period, where meaningful fitting of the autocorrelation curve is limited. By choosing an appropriate distance d, the maximum of the cross-correlation curve can be shifted into the measurement window, rendering accurate fitting possible.
The application of TFCCS is not restricted to spherical membranes. It can also be applied to determine absolute diffusion coefficients on planar membranes (Fig. 5). Since drifts of the setup cannot be corrected-for any longer, SFCS on planar membranes is sensitive to instabilities. However, positioning of the detection volume is no longer crucial, since the waist radius can be determined directly from the fit and does not enter the determination of the diffusion coefficient. Moreover, the length s of the detection area can be easily inferred from the data set, which reduces the number of fit parameters by one, compared to measurements on vertical membranes, rendering the results of the fit more reliable.
Dual-color cross correlation
Scanning dual-color cross correlation (dcFCCS) permits the study of binding and aggregation of labeled molecules on the membrane without the risk of false-positive cross correlation due to membrane movements. Fig. 6 shows auto- and cross-correlation curves of GM1-BODIPY-FL incorporated into a GUV and ctxB-Cy5, which binds to up to five GM1 molecules. Spectral cross talk was negligible. The amplitudes of the autocorrelation curves indicate that the concentration of labeled GM1 molecules is substantially higher than the concentration of ctxB molecules, which could be consistent with unbound GM1 in the inner leaflet of the membrane and GM1 bound to ctxB in the outer leaflet. The relative cross-correlation amplitude is 30%. A calibration measurement on double-labeled DNA molecules in free solution used as a cross-correlation reference showed a cross-correlation amplitude of 55%. For a ratio of bound complexes to unbound GM1 of 1:5 in the absence of quenching or FRET, a relative cross-correlation amplitude of 1.66 x 55% can be expected (16,26). The reduced cross-correlation amplitude could result from a loss of fluorescence of the GM1-BODIPY-FL due to photobleaching or self-quenching, inhomogeneous labeling of the ctxB, and a deteriorated overlap of the detection areas due to the different optical geometry in SFCS.
Dual-color cross correlation with pulsed interleaved excitation
If spectrally closer dyes are used, spectral cross talk, especially from the green dye into the red channel, can lead to a false-positive cross-correlation amplitude. This can be seen in Fig. 7 a, obtained on GUVs labeled with DiO and DiI, which have partially overlapping excitation and emission spectra. Here the relative cross-correlation amplitude due to cross talk was as large as 25%.
Fig. 7 b shows the auto- and cross-correlation curves from the same sample as Fig. 7 a, making use of PIE. The amplitude of the orange autocorrelation curve is significantly higher since it is now free of cross talk. Most importantly, the cross-correlation amplitude completely vanishes, indicating good separation of the dyes.
PIE can be easily applied in scanning dcFCCS without any additional hardware in a confocal microscope by using the multitrack mode. In addition to avoiding cross talk, PIE allows for quantitative analysis of FRET between the two labeled species (27) and an accurate overlap of the detection volumes can more easily be achieved.
SFCS on yeast cell membranes
Due to its high intrinsic stability and optimal separation of membrane and bulk contributions, SFCS permits dynamic measurements even on yeast cell membranes. Previously, it was only possible to assess this kind of extremely slow membrane diffusion using fluorescence recovery after photobleaching (28). Fig. 8 a shows the result of a one-focus SFCS measurement on Fus-Mid-GFP in yeast cell membranes. Because the measurement time was only 100-fold longer than the diffusion time, the correlation curve had to be fit with an offset (29). The resulting diffusion coefficient of D = 0.0028 ± 0.0011 µm2/s is comparable with the results of fluorescence-recovery-after-photobleaching measurements on GFP-Snc1p (28).
The diffusion coefficient determined by a two-foci measurement (Fig. 8 b, D = 0.0026 ± 0.0006 µm2/s) is consistent with that value. The measurement time was the same as for Fig. 8 a. Although the curves look slightly more noisy, the diffusion coefficient was actually determined with a higher accuracy, thanks to the additional information from the spatial cross correlation.
SFCS versus traditional FCS
SFCS expands the application of FCS to larger diffusion times. For fast diffusion in membranes, traditional FCS can be superior once the detection volume has been carefully calibrated: It allows for shorter measurement times, easy data analysis, minimized out-of-focus photobleaching, and submicrosecond time resolution. In SFCS, the time resolution is limited by the scanning frequency to approximately a millisecond. Yet in this regime scanning two-foci measurements can lead to far more accurate determination of absolute diffusion constants.
The lower limit for diffusion coefficients measurable with SFCS is determined by the measurement time. The maximum measurement time is limited by drifts of the vesicle perpendicular to the scan direction, which will lead to a scan path nonperpendicular to the membrane and therefore to a distortion of the detection area. In addition, the drift will contribute to the correlation curves as an additional flow term. For large vesicles we found measurement times of up to 1 h to be practical, resulting in a smallest measurable diffusion coefficient being on the order of 10–3 µm2/s.
One important drawback of SFCS with a scan path perpendicular to the membrane is the requirement of a vertical membrane, which precludes its use on flat substrate-adherent cells. However, if stability is not a limiting factor, SFCS can be readily applied on horizontal membranes.
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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The extension to two-foci spatial cross correlation enabled us to perform direct and accurate measurements of diffusion coefficients without the need for calibrating the detection volume. Two-foci scanning cross-correlation spectroscopy was also successfully applied on planar membranes enabling simultaneous, calibration-free measurements of diffusion times in different parts of the sample. The extension to study slow three-dimensional diffusion in solution or inside cells is straightforward.
Scanning dual-color cross-correlation spectroscopy permits quantitative binding and aggregation studies on membranes without the risk of false-positive cross correlation due to membrane movements. The implementation of PIE was shown to successfully eliminate spectral cross talk, permitting the choice of spectrally close fluorophores and providing the prospect of quantitative FRET measurements on membranes using FCS (27).
The high intrinsic stability, the excellent signal/noise ratio, and the good separation of membrane and bulk contributions of SFCS enabled the study of diffusion on yeast cell membranes, which was previously impossible with FCS due to extremely slow diffusion in the range of 10–3 µm2/s.
The various approaches to continuous wave scanning FCS demonstrated here allow the study of different aspects of membrane dynamics on a variety of systems with an accuracy unprecedented in traditional FCS. The simple implementation in a commercial setup should help SFCS to become a standard technique for membrane studies.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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This work was supported by Europaeischer Fond fuer Regionale Entwicklung grant No. 4212/04-02.
Submitted on January 30, 2006; accepted for publication May 12, 2006.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONACKNOWLEDGEMENTSREFERENCES |
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A. Arkhipov, J. Huve, M. Kahms, R. Peters, and K. Schulten Continuous Fluorescence Microphotolysis and Correlation Spectroscopy Using 4Pi Microscopy Biophys. J., December 1, 2007; 93(11): 4006 - 4017. [Abstract] [Full Text] [PDF]
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) of ctxB-Alexa488 bound to a GUV composed of 25% cholesterol, 75% sphingomyelin, and 0.005% GM1 with corresponding fit to 
Fi
= 0.42. Emission filter is HQ525/60 M; pinhole is 60 µm.
,
) and cross-correlation curves (
