k-Space image correlation spectroscopy: a method for accurate transport measurements independent of fluorophore photophysics

We present the theory and application of reciprocal space image correlation spectroscopy (kICS). This technique measures the number density, diffusion coefficient, and velocity of fluorescently labeled macromolecules in a cell membrane imaged on a confocal, two-photon, or total internal reflection fluorescence microscope. In contrast to r-space correlation techniques, we show kICS can recover accurate dynamics even in the presence of complex fluorophore photobleaching and/or "blinking". Furthermore, these quantities can be calculated without nonlinear curve fitting, or any knowledge of the beam radius of the exciting laser. The number densities calculated by kICS are less sensitive to spatial inhomogeneity of the fluorophore distribution than densities measured using image correlation spectroscopy. We use simulations as a proof-of-principle to show that number densities and transport coefficients can be extracted using this technique. We present calibration measurements with fluorescent microspheres imaged on a confocal microscope, which recover Stokes-Einstein diffusion coefficients, and flow velocities that agree with single particle tracking measurements. We also show the application of kICS to measurements of the transport dynamics of alpha5-integrin/enhanced green fluorescent protein constructs in a transfected CHO cell imaged on a total internal reflection fluorescence microscope using charge-coupled device area detection.     

Dynamics of fluorescence marker concentration as a probe of mobility.

We have developed an effective experimental system for the characterization of molecular and structural mobility. It incorporates a modified fluorescence microscope geometry and a variety of analytical techniques to measure effective diffusion coefficients ranging over almost six orders of magnitude, from less than 10(-11) cm2/s to greater than 10(-6) cm2/s. Two principal techniques, fluorescence correlation spectroscopy (FCS) and fluorescence photobleaching recovery (FPR), are employed. In the FPR technique, translational transport rates are measured by monitoring the evolution of a spatial inhomogeneity of fluorescence that is produced photochemically in a microscopic volume by a short burst of intense laser radiation. In contrast, FCS uses laser-induced fluorescence to probe the spontaneous concentration fluctuations in microscopic sample volumes. The kinetics are analyzed by computing time-correlation functions of the stochastic fluctuations of the measured fluorescence intensity. The optical system and digital photocount correlator designed around a dedicated minicomputer are described and discussed. The general power of these techniques is demonstrated with examples from studies conducted on bulk solutions, lipid bilayer membranes, and mammalian cell plasma membranes.     

A Generalization of Theory for Two-Dimensional Fluorescence Recovery after Photobleaching Applicable to Confocal Laser Scanning Microscopes

Fluorescence recovery after photobleaching (FRAP) using confocal laser scanning microscopes (confocal FRAP) has become a valuable technique for studying the diffusion of biomolecules in cells. However, two-dimensional confocal FRAP sometimes yields results that vary with experimental setups, such as different bleaching protocols and bleaching spot sizes. In addition, when confocal FRAP is used to measure diffusion coefficients (D) for fast diffusing molecules, it often yields D-values that are one or two orders-of-magnitude smaller than that predicted theoretically or measured by alternative methods such as fluorescence correlation spectroscopy. Recently, it was demonstrated that this underestimation of D can be corrected by taking diffusion during photobleaching into consideration. However, there is currently no consensus on confocal FRAP theory, and no efforts have been made to unify theories on conventional and confocal FRAP. To this end, we generalized conventional FRAP theory to incorporate diffusion during photobleaching so that analysis by conventional FRAP theory for a circular region of interest is easily applicable to confocal FRAP. Finally, we demonstrate the accuracy of these new (to our knowledge) formulae by measuring D for soluble enhanced green fluorescent protein in aqueous glycerol solution and in the cytoplasm and nucleus of COS7 cells.     

Studying slow membrane dynamics with continuous wave scanning fluorescence correlation spectroscopy

Here we discuss the application of scanning fluorescence correlation spectroscopy (SFCS) using continuous wave excitation to analyze membrane dynamics. The high count rate per molecule enables the study of very slow diffusion in model and cell membranes, as well as the application of two-foci fluorescence cross-correlation spectroscopy for parameter-free determination of diffusion constants. The combination with dual-color fluorescence cross-correlation spectroscopy with continuous or pulsed interleaved excitation allows binding studies on membranes. Reduction of photobleaching, higher reproducibility, and stability compared to traditional FCS on membranes, and the simple implementation in a commercial microscopy setup make SFCS a valuable addition to the pool of fluorescence fluctuation techniques.     

Self-Calibrated Line-Scan STED-FCS to Quantify Lipid Dynamics in Model and Cell Membranes

Only a limited number of noninvasive techniques are available to directly measure the dynamic behavior of lipids in model and cell membranes. Here, we explored whether a commercial instrument could be used for fluorescence correlation spectroscopy (FCS) under pulsed stimulated emission depletion (STED). To overcome issues with photobleaching and poor distinction between confocal and STED signals, we implemented resonant line-scan STED with filtered FCS, which has the additional benefit of autocalibrating the dimensions of the point-spread function and obtaining spatially resolved molecular mobility at subdiffraction resolution. With supported lipid bilayers, we achieved a detection spot radius of 40 nm, although at the expense of decreased molecular brightness. We also used this approach to map the dynamics of Atto646N-labeled sphingomyelin and phosphatidylethanolamine in the plasma membrane. Despite the reliability of the method and the demonstration that photobleaching and the photophysical properties of the dye did not influence diffusion measurements, we found great heterogeneities even within one cell. For both lipids, regions of high local density correlated with slow molecular diffusion, indicating trapping of Atto646N-labeled lipids. Future studies with new dyes are needed to reveal the origin of the trapping.     

Fluorescence correlation spectroscopy for the study of membrane dynamics and protein/lipid interactions

Fluorescence correlation spectroscopy (FCS) is a powerful technique to study dynamic biomolecular processes. It allows the estimation of concentrations, diffusion coefficients, molecular interactions, and other processes causing fluctuations in the fluorescence intensity, thus yielding information about aggregation processes, enzymatic reactions, or partition coefficients. During the last years, FCS has been successfully applied to model and cellular membranes, proving to be a promising tool for the study of membrane dynamics and protein/lipid interactions. Here we describe the theoretical basis of FCS and some practical implications for its application in membrane studies. We discuss sources of potential artifacts, such as membrane undulations, positioning of the detection volume, and photobleaching. Special attention is paid to aspects related to instrumentation and sample preparation as well as data acquisition and analysis. Finally, we comment on some strategies recently developed for the specific improvement of FCS measurements on membranes.     

Improved Model of Fluorescence Recovery Expands the Application of Multiphoton Fluorescence Recovery after Photobleaching in Vivo

Multiphoton fluorescence recovery after photobleaching is a well-established microscopy technique used to measure the diffusion of macromolecules in biological systems. We have developed an improved model of the fluorescence recovery that includes the effects of convective flows within a system. We demonstrate the validity of this two-component diffusion-convection model through in vitro experimentation in systems with known diffusion coefficients and known flow speeds, and show that the diffusion-convection model broadens the applicability of the multiphoton fluorescence recovery after photobleaching technique by enabling accurate determination of the diffusion coefficient, even when significant flows are present. Additionally, we find that this model allows for simultaneous measurement of the flow speed in certain regimes. Finally, we demonstrate the effectiveness of the diffusion-convection model in vivo by measuring the diffusion coefficient and flow speed within tumor vessels of 4T1 murine mammary adenocarcinomas implanted in the dorsal skinfold chamber.     

Spatial Fourier analysis of video photobleaching measurements. Principles and optimization.

The major use of the fluorescence recovery after photobleaching (FRAP) technique is to measure the translational motion of the molecular components in various condensed media. In a conventional laser spot photobleaching experiment, a photomultiplier is used to measure the total brightness levels of the bleached region in the sample, so no spatial information can be directly obtained. In video-FRAP, a series of images after photobleaching is acquired, allowing the spatial character of the recovery to be determined; this permits direct detection of both anisotropic diffusion and flow. To utilize all of the available image data to determine the transport coefficients, a two-dimensional spatial Fourier transform analysis of the images after photobleaching was employed. The change in the transform between two time points reflects the action of diffusion during the interim. An important advantage of this method, which involves taking the ratio of image transforms at different time points, is that it does not require a specific initial condition to be created by laser photobleaching. The ability of the analysis to extract transport coefficients from computer-simulated diffusional recovery is assessed in the presence of increasing amounts of noise. Experimental data analysis from the diffusion of proteins in viscous solutions and from the diffusion of protein receptors on cell surfaces demonstrate the feasibility of the Fourier analysis to obtain transport coefficients from the video FRAP measurement.     

Micrometer-scale domains in fibroblast plasma membranes

We have used the technique of fluorescence photobleaching recovery to measure the lateral diffusion coefficients and the mobile fractions of a fluorescent lipid probe, 1-acyl-2-(12-[(7-nitro-2-1, 3-benzoxadiazol-4-yl)aminododecanoyl]) phosphatidylcholine (NBD-PC), and of labeled membrane proteins of human fibroblasts. Values for mobile fractions decrease monotonically with increasing size of the laser spot used for the measurements, over a range of 0.35-5.0 microns. Values for NBD-PC diffusion coefficients increase in part of this range to reach a plateau at larger laser spots. This variation is not an artifact of the measuring system, since the effects are not seen if diffusion of the probe is measured in liposomes. We also find that the distribution of diffusion coefficients measured with small laser spots is heterogeneous indicating that these small spots can sample different regions of the membrane. These regions appear to differ in protein concentration. Our data strongly indicate that fibroblast surface membranes consist of protein-rich domains approximately 1 micron in diameter, embedded in a relatively protein-poor lipid continuum. These features appear in photographs of labeled cell surfaces illuminated by the expanded laser beam.     

Characterization of Cell Boundary and Confocal Effects Improves Quantitative FRAP Analysis

Fluorescence recovery after photobleaching (FRAP) is an important tool used by cell biologists to study the diffusion and binding kinetics of vesicles, proteins, and other molecules in the cytoplasm, nucleus, or cell membrane. Although many FRAP models have been developed over the past decades, the influence of the complex boundaries of 3D cellular geometries on the recovery curves, in conjunction with regions of interest and optical effects (imaging, photobleaching, photoswitching, and scanning), has not been well studied. Here, we developed a 3D computational model of the FRAP process that incorporates particle diffusion, cell boundary effects, and the optical properties of the scanning confocal microscope, and validated this model using the tip-growing cells of Physcomitrella patens. We then show how these cell boundary and optical effects confound the interpretation of FRAP recovery curves, including the number of dynamic states of a given fluorophore, in a wide range of cellular geometries—both in two and three dimensions—namely nuclei, filopodia, and lamellipodia of mammalian cells, and in cell types such as the budding yeast, Saccharomyces pombe, and tip-growing plant cells. We explored the performance of existing analytical and algorithmic FRAP models in these various cellular geometries, and determined that the VCell VirtualFRAP tool provides the best accuracy to measure diffusion coefficients. Our computational model is not limited only to these cells types, but can easily be extended to other cellular geometries via the graphical Java-based application we also provide. This particle-based simulation—called the Digital Confocal Microscopy Suite or DCMS—can also perform fluorescence dynamics assays, such as number and brightness, fluorescence correlation spectroscopy, and raster image correlation spectroscopy, and could help shape the way these techniques are interpreted.     

Quantifying the Diffusion of Membrane Proteins and Peptides in Black Lipid Membranes with 2-Focus Fluorescence Correlation Spectroscopy

Protein diffusion in lipid membranes is a key aspect of many cellular signaling processes. To quantitatively describe protein diffusion in membranes, several competing theoretical models have been proposed. Among these, the Saffman-Delbrück model is the most famous. This model predicts a logarithmic dependence of a protein’s diffusion coefficient on its inverse hydrodynamic radius (D ∝ ln 1/R) for small radius values. For large radius values, it converges toward a D ∝ 1/R scaling. Recently, however, experimental data indicate a Stokes-Einstein-like behavior (D ∝ 1/R) of membrane protein diffusion at small protein radii. In this study, we investigate protein diffusion in black lipid membranes using dual-focus fluorescence correlation spectroscopy. This technique yields highly accurate diffusion coefficients for lipid and protein diffusion in membranes. We find that despite its simplicity, the Saffman-Delbrück model is able to describe protein diffusion extremely well and a Stokes-Einstein-like behavior can be ruled out.     

Measuring surface dynamics of biomolecules by total internal reflection fluorescence with photobleaching recovery or correlation spectroscopy.

The theoretical basis of a new technique for measuring equilibrium adsorption/desorption kinetics and surface diffusion of fluorescent-labeled solute molecules at solid surfaces has been developed. The technique combines total internal reflection fluorescence (TIR) with either fluorescence photobleaching recovery (FPR) or fluorescence correlation spectroscopy (FCS). A laser beam totally internally reflects at a solid/liquid interface; the shallow evanescent field in the liquid excites the fluorescence of surface adsorbed molecules. In TIR/FPR, adsorbed molecules are bleaching by a flash of the focused laser beam; subsequent fluorescence recovery is monitored as bleached molecules exchange with unbleached ones from the solution or surrounding nonilluminated regions of the surface. In TIR/FCS, spontaneous fluorescence fluctuations due to individual molecules entering and leaving a well-defined portion of the evanescent field are autocorrelated. Under appropriate experimental conditions, the rate constants and surface diffusion coefficient can be readily obtained from the TIR/FPR and TIR/FCS curves. In general, the shape of the theoretical TIR/FPR and TIR/FCS curves depends in a complex manner upon the bulk and surface diffusion coefficients, the size of the iluminated or observed region, and the adsorption/desorption/kinetic rate constants. The theory can be applied both to specific binding between immobilized receptors and soluble ligands, and to nonspecific adsorption processes. A discussion of experimental considerations and the application of this technique to the adsorption of serum proteins on quartz may be found in the accompanying paper (Burghardt and Axelrod. 1981. Biophys. J. 33:455).     

A new FRAP/FRAPa method for three-dimensional diffusion measurements based on multiphoton excitation microscopy

We present a new convenient method for quantitative three-dimensionally resolved diffusion measurements based on the photobleaching (FRAP) or photoactivation (FRAPa) of a disk-shaped area by the scanning laser beam of a multiphoton microscope. Contrary to previously reported spot-photobleaching protocols, this method has the advantage of full scalability of the size of the photobleached area and thus the range of diffusion coefficients, which can be measured conveniently. The method is compatible with low as well as high numerical aperture objective lenses, allowing us to perform quantitative diffusion measurements in three-dimensional extended samples as well as in very small volumes, such as cell nuclei. Furthermore, by photobleaching/photoactivating a large area, diffusion along the optical axis can be measured separately, which is convenient when studying anisotropic diffusion. First, we show the rigorous mathematical derivation of the model, leading to a closed-form formula describing the fluorescence recovery/redistribution phase. Next, the ability of the multiphoton FRAP method to correctly measure absolute diffusion coefficients is tested thoroughly on many test solutions of FITC-dextrans covering a wide range of diffusion coefficients. The same is done for the FRAPa method on a series of photoactivatable green fluorescent protein solutions with different viscosities. Finally, we apply the method to photoactivatable green fluorescent protein diffusing freely in the nucleus of living NIH-3T3 mouse embryo fibroblasts.     

FCS cell surface measurements--photophysical limitations and consequences on molecular ensembles with heterogenic mobilities.

BACKGROUND: Fluorescence Correlation Spectroscopy is a powerful method to analyze densities and diffusive behavior of molecules in membranes, but effects of photodegradation can easily be overlooked. METHOD: Based on experimental photophysical parameters, calculations were performed to analyze the consequences of photobleaching in fluorescence correlation spectroscopy (FCS) cell surface experiments, covering a range of standard measurement conditions. RESULTS: Cumulative effects of photobleaching can be prominent, although an absolute majority of the fluorescent molecules would pass the laser excitation beam without being photo-bleached. Given a distribution of molecules on a cell surface with different diffusive properties, the fraction of molecules that is actually analyzed depends strongly on the excitation intensities and measurement times, as well as on the size of the reservoir of freely diffusing molecules. Both the slower and the faster diffusing molecules can be disfavored. CONCLUSIONS: Apart from quantifying photobleaching effects, the calculations suggest that the effects can be used to extract additional information, for instance about the size of the reservoirs of free diffusion. By certain choices of measurement conditions, it may be possible to more specifically analyze certain species within a population, based on their different diffusive properties, different areas of free diffusion, or different kinetics of possible transient binding.     

How to quantify protein diffusion in the bacterial membrane

Lateral diffusion of proteins in the plane of a biological membrane is important for many vital processes, including energy conversion, signaling, chemotaxis, cell division, protein insertion, and secretion. In bacteria, all these functions are located in a single membrane. Therefore, quantitative measurements of protein diffusion in bacterial membranes can provide insight into many important processes. Diffusion of membrane proteins in eukaryotes has been studied in detail using various experimental techniques, including fluorescence correlation spectroscopy (FCS), fluorescence recovery after photobleaching (FRAP), and particle tracking using single-molecule fluorescence (SMF) microscopy. In case of bacteria, such experiments are intrinsically difficult due to the small size of the cells. Here, we review these experimental approaches to quantify diffusion in general and their strengths and weaknesses when applied to bacteria. In addition, we propose a method to extract multiple diffusion coefficients from trajectories obtained from SMF data, using cumulative probability distributions (CPDs). We demonstrate the power of this approach by quantifying the heterogeneous diffusion of the bacterial membrane protein TatA, which forms a pore for the translocation of folded proteins. Using computer simulations, we study the effect of cell dimensions and membrane curvature on measured CPDs. We find that at least two mobile populations with distinct diffusion coefficients (of 7 and 169 nm(2) ms(-1) , respectively) are necessary to explain the experimental data. The approach described here should be widely applicable for the quantification of membrane-protein diffusion in living bacteria.     

Raster image correlation spectroscopy in live cells

Raster image correlation spectroscopy (RICS) is a noninvasive technique to detect and quantify events in a live cell, including concentration of molecules and diffusion coefficients of molecules; in addition, by measuring changes in diffusion coefficients, RICS can indirectly detect binding. Any specimen containing fluorophores that can be imaged with a laser scanning microscope can be analyzed using RICS. There are other techniques to measure diffusion coefficients and binding; however, RICS fills a unique niche. It provides spatial information and can be performed in live cells using a conventional confocal microscope. It can measure a range of diffusion coefficients that is not accessible with any other single optical correlation-based technique. In this article we describe a protocol to obtain raster scanned images with an Olympus FluoView FV1000 confocal laser scanning microscope using Olympus FluoView software to acquire data and SimFCS software to perform RICS analysis. Each RICS measurement takes several minutes. The entire procedure can be completed in ～2 h. This procedure includes focal volume calibration using a solution of fluorophores with a known diffusion coefficient and measurement of the diffusion coefficients of cytosolic enhanced green fluorescent protein (EGFP) and EGFP-paxillin.     

Sampling effects, noise, and photobleaching in temporal image correlation spectroscopy

We present an extensive investigation of the accuracy and precision of temporal image correlation spectroscopy (TICS). Using simulations of laser scanning microscopy image time series, we investigate the effect of spatiotemporal sampling, particle density, noise, sampling frequency, and photobleaching of fluorophores on the recovery of transport coefficients and number densities by TICS. We show that the recovery of transport coefficients is usually limited by spatial sampling, while the measurement of accurate number densities is restricted by background noise in an image series. We also demonstrate that photobleaching of the fluorophore causes a consistent overestimation of diffusion coefficients and flow rates, and a severe underestimation of number densities. We derive a bleaching correction equation that removes both of these biases when used to fit temporal autocorrelation functions, without increasing the number of fit parameters. Finally, we image the basal membrane of a CHO cell with EGFP/alpha-actinin, using two-photon microscopy, and analyze a subregion of this series using TICS and apply the bleaching correction. We show that the photobleaching correction can be determined simply by using the average image intensities from the time series, and we use the simulations to provide good estimates of the accuracy and precision of the number density and transport coefficients measured with TICS.     

Spatially resolved fluorescence correlation spectroscopy using a spinning disk confocal microscope

We develop an extension of fluorescence correlation spectroscopy (FCS) using a spinning disk confocal microscope. This approach can spatially map diffusion coefficients or flow velocities at up to approximately 10(5) independent locations simultaneously. Commercially available cameras with frame rates of 1000 Hz allow FCS measurements of systems with diffusion coefficients D~10(-7) cm(2)/s or smaller. This speed is adequate to measure small microspheres (200-nm diameter) diffusing in water, or hindered diffusion of macromolecules in complex media (e.g., tumors, cell nuclei, or the extracellular matrix). There have been a number of recent extensions to FCS based on laser scanning microscopy. Spinning disk confocal microscopy, however, has the potential for significantly higher speed at high spatial resolution. We show how to account for a pixel size effect encountered with spinning disk confocal FCS that is not present in standard or scanning FCS, and we introduce a new method to correct for photobleaching. Finally, we apply spinning disk confocal FCS to microspheres diffusing in Type I collagen, which show complex spatially varying diffusion caused by hydrodynamic and steric interactions with the collagen matrix.     

The lack of relationship between fluorescence polarization and lateral diffusion in biological membranes

An investigation has been carried out of the relationship between changes in the fluorescence polarization of 1,6-diphenyl-1,3,5-hexatriene (DPH) and concomittant changes in the lateral diffusion of proteins and lipid probes in membranes. Plasma membranes from lymphocytes and a CH1 mouse lymphoma line were treated with up to 70 mol% (relative to the total membrane phospholipid) of oleic or linoleic fatty acids. Under these conditions the fluorescence polarization of DPH decreased by between 8 and 15% which, in the framework of the microviscosity approach, suggests a membrane fluidity change of between 20 and 50%. The lateral diffusion coefficients of surface immunoglobin and the lipid probes 3,3′-dioctadecylindocarbocyanine and pyrene were also measured in these membranes using the fluorescence photobleaching recovery technique and the rate of pyrene excimer formation. The diffusion rates were found to be unaffected by the presence of free fatty acids. Hence despite large ‘microviscosity’ changes as reported by depolarization of DPH fluorescence, lateral diffusion coefficients are essentially unchanged. This finding is consistent with the idea that perturbing agents such as free fatty acids do not cause a general fluidization of the membrane but act locally to alter, for example, protein function. It is also consistent with the suggestion that lateral mobility of membrane proteins is not modulated by the lipid viscosity.     

High-resolution nonlinear optical imaging of live cells by second harmonic generation

By adapting a laser scanning microscope with a titanium sapphire femtosecond pulsed laser and transmission optics, we are able to produce live cell images based on the nonlinear optical phenomenon of second harmonic generation (SHG). Second harmonic imaging (SHIM) is an ideal method for probing membranes of living cells because it offers the high resolution of nonlinear optical microscopy with the potential for near-total avoidance of photobleaching and phototoxicity. The technique has been implemented on three cell lines labeled with membrane-staining dyes that have large nonlinear optical coefficients. The images can be obtained within physiologically relevant time scales. Both achiral and chiral dyes were used to compare image formation for the case of single- and double-leaflet staining, and it was found that chirality plays a significant role in the mechanism of contrast generation. It is also shown that SHIM is highly sensitive to membrane potential, with a depolarization of 25 mV resulting in an approximately twofold loss of signal intensity.