Simultaneous diffusion and brightness measurements and brightness profile visualization from single fluorescence fluctuation traces of GFP in living cells

Fluorescence correlation spectroscopy (FCS) and photon-counting histogram (PCH) analysis use the same experimental fluorescence intensity fluctuations, but each analytical method focuses on a different property of the signal. The time-dependent decay of the correlation of fluorescence fluctuations is measured in FCS yielding, for instance, molecular diffusion coefficients. The amplitude distribution of these fluctuations is calculated by PCH analysis yielding information about the molecular brightness of fluorescent species. Analysis of both FCS and PCH results in the molecular concentration of the sample. Using a previously described global analysis procedure we report here precise, simultaneous measurements of diffusion constants and brightness values from single fluorescence fluctuation traces of green-fluorescent protein (GFP, S65T) in the cytoplasm of Dictyostelium cells. The use of a polynomial profile in PCH analysis, describing the detected three-dimensional shape of the confocal volume, enabled us to obtain well fitting results for GFP in cells. We could visualize the polynomial profile and show its deviation from a Gaussian profile.     

Fluorescence correlation spectroscopy and quantitative cell biology

Fluorescence correlation spectroscopy (FCS) analyzes fluctuations in fluorescence within a small observation volume. Autocorrelation analysis of FCS fluctuation data can be used to measure concentrations, diffusion properties, and kinetic constants for individual fluorescent molecules. Photon count histogram analysis of fluorescence fluctuation data can be used to study oligomerization of individual fluorescent molecules. If the FCS observation volume is positioned inside a living cell, these parameters can be measured in vivo. FCS can provide the requisite quantitative data for analysis of molecular interaction networks underlying complex cell biological processes.     

Fluorescence correlation spectroscopy: past, present, future

In recent years fluorescence correlation spectroscopy (FCS) has become a routine method for determining diffusion coefficients, chemical rate constants, molecular concentrations, fluorescence brightness, triplet state lifetimes, and other molecular parameters. FCS measures the spatial and temporal correlation of individual molecules with themselves and so provides a bridge between classical ensemble and contemporary single-molecule measurements. It also provides information on concentration and molecular number fluctuations for nonlinear reaction systems that complement single-molecule measurements. Typically implemented on a fluorescence microscope, FCS samples femtoliter volumes and so is especially useful for characterizing small dynamic systems such as biological cells. In addition to its practical utility, however, FCS provides a window on mesoscopic systems in which fluctuations from steady states not only provide the basis for the measurement but also can have important consequences for the behavior and evolution of the system. For example, a new and potentially interesting field for FCS studies could be the study of nonequilibrium steady states, especially in living cells.     

High-pressure fluorescence correlation spectroscopy

We demonstrate that a novel high-pressure cell is suitable for fluorescence correlation spectroscopy (FCS). The pressure cell consists of a single fused silica microcapillary. The cylindrical shape of the capillary leads to refraction of the excitation light, which affects the point spread function of the system. We characterize the influence of these beam distortions by FCS and photon-counting histogram (PCH) analysis and identify the optimal position for fluorescence fluctuation experiments in the capillary. At this position within the capillary, FCS and photon-counting histogram experiments are described by the same equations as used in standard FCS experiments. We report the first experimental realization of fluorescence fluctuation spectroscopy under high pressure. A fluorescent dye was used as a model system for evaluating the properties of the capillary under pressure. The autocorrelation function and the photon count distribution were measured in the pressure range from 0 to 300 MPa. The fluctuation amplitude and the diffusion coefficient show a small pressure dependence. The changes of these parameters, which are on the order of 10%, are due to the pressure changes of the viscosity and the density of the aqueous medium.     

Fluorescence correlation spectroscopy in living cells

Fluorescence correlation spectroscopy (FCS) is an ideal analytical tool for studying concentrations, propagation, interactions and internal dynamics of molecules at nanomolar concentrations in living cells. FCS analyzes minute fluorescence-intensity fluctuations about the equilibrium of a small ensemble (<10(3)) of molecules. These fluctuations act like a 'fingerprint' of a molecular species detected when entering and leaving a femtoliter-sized optically defined observation volume created by a focused laser beam. In FCS the fluorescence fluctuations are recorded as a function of time and then statistically analyzed by autocorrelation analysis. The resulting autocorrelation curve yields a measure of self-similarity of the system after a certain time delay, and its amplitude describes the normalized variance of the fluorescence fluctuations. By fitting the curves to an appropriate physical model, this method provides precise information about a multitude of measurement parameters, including diffusion coefficients, local concentration, states of aggregation and molecular interactions. FCS operates in real time with diffraction-limited spatial and sub-microsecond temporal resolution. Assessing diverse molecular dynamics within the living cell is a challenge well met by FCS because of its single-molecule sensitivity and high dynamic resolution. For these same reasons, however, intracellular FCS measurements also harbor the large risk of collecting artifacts and thus producing erroneous data. Here we provide a step-by-step guide to the application of FCS to cellular systems, including methods for minimizing artifacts, optimizing measurement conditions and obtaining parameter values in the face of diverse and complex conditions of the living cell. A discussion of advantages and disadvantages of one-photon versus two-photon excitation for FCS is available in Supplementary Methods online.     

Fluorescence fluctuation spectroscopy: ushering in a new age of enlightenment for cellular dynamics

Originally developed for applications in physics and physical chemistry, fluorescence fluctuation spectroscopy is becoming widely used in cell biology. This review traces the development of the method and describes some of the more important applications. Specifically, the methods discussed include fluorescence correlation spectroscopy (FCS), scanning FCS, dual color cross-correlation FCS, the photon counting histogram and fluorescence intensity distribution analysis approaches, the raster scanning image correlation spectroscopy method, and the Number and Brightness technique. The physical principles underlying these approaches will be delineated, and each of the methods will be illustrated using examples from the literature.     

On the statistics of fluorescence correlation spectroscopy

I present a detailed statistical analysis of fluorescence correlation spectroscopy (FCS) which is a natural extension of an early work. This analysis more realistically takes account of the following issues. (1) A spatial Gaussian laser excitation of fluorescence, (2) the effect of a small number of fluorescent molecules in the observation volume, (3) the shot noise effect due to random emission of fluorescent photons, and (4) a hyperbolic form for the fluorescence autocorrelation function obtained in the case of diffusion. Based on these assumptions, the results differ from the earlier work in several respects, in particular, the dependence of the signal-to-noise ratio on sample concentration and the understanding of shot noise in fluorescence fluctuation moments.     

Global analysis of fluorescence fluctuation data

Over the last decade the number of applications of fluorescence correlation spectroscopy (FCS) has grown rapidly. Here we describe the development and application of a software package, FCS Data Processor, to analyse the acquired correlation curves. The algorithms combine strong analytical power with flexibility in use. It is possible to generate initial guesses, link and constrain fit parameters to improve the accuracy and speed of analysis. A global analysis approach, which is most effective in analysing autocorrelation curves determined from fluorescence fluctuations of complex biophysical systems, can also be implemented. The software contains a library of frequently used models that can be easily extended to include user-defined models. The use of the software is illustrated by analysis of different experimental fluorescence fluctuation data sets obtained with Rhodamine Green in aqueous solution and enhanced green fluorescent protein in vitro and in vivo.An erratum to this article can be found at Victor V. Skakun, Mark A. Hink and Anatoli V. Digris contributed equally to this work.     

荧光相关谱测量技术研究

荧光相关谱(fluorescence correlation spectroscopy,FCS)是对处于热平衡态条件下的荧光分子发出的荧光强度涨落进行时间相关处理的一种单分子检测方法,能够直接测量分子在溶液里的扩散系数和浓度.影响FCS测量扩散系数准确性的因素有分子量子效率,测量时间,样本折射率和温度偏差等.用FCS分别测量溶有荧光染料罗丹明6G(rhodamine 6G,Rh.6G)和青色素Cy5甘油水溶液的粘滞系数,实验结果表明:荧光分子的量子效率是影响测量准确性的重要因素,要求其每秒发射的光子数目(photon counts per second,cps)至少达到1 000(photons/s).     

Spatial-temporal studies of membrane dynamics: scanning fluorescence correlation spectroscopy (SFCS)

Giant unilamellar vesicles (GUVs) have been widely used as a model membrane system to study membrane organization, dynamics, and protein-membrane interactions. Most recent studies have relied on imaging methods, which require good contrast for image resolution. Multiple sequential image processing only detects slow components of membrane dynamics. We have developed a new fluorescence correlation spectroscopy (FCS) technique, termed scanning FCS (i.e., SFCS), which performs multiple FCS measurements simultaneously by rapidly directing the excitation laser beam in a uniform (circular) scan across the bilayer of the GUVs in a repetitive fashion. The scan rate is fast compared to the diffusion of the membrane proteins and even small molecules in the GUVs. Scanning FCS outputs a "carpet" of timed fluorescence intensity fluctuations at specific points along the scan. In this study, GUVs were assembled from rat kidney brush border membranes, which included the integral membrane proteins. Scanning FCS measurements on GUVs allowed for a straightforward detection of spatial-temporal interactions between the protein and the membrane based on the diffusion rate of the protein. To test for protein incorporation into the bilayers of the GUVs, antibodies against one specific membrane protein (NaPi II cotransporter) were labeled with ALEXA-488. Fluorescence images of the GUVs in the presence of the labeled antibody showed marginal fluorescence enhancement on the GUV membrane bilayers (poor image contrast and resolution). With the application of scanning FCS, the binding of the antibody to the GUVs was detected directly from the analysis of diffusion rates of the fluorescent antibody. The diffusion coefficient of the antibody bound to NaPi II in the GUVs was approximately 200-fold smaller than that in solution. Scanning FCS provided a simple, quantitative, yet highly sensitive method to study protein-membrane interactions.     

The photon counting histogram in fluorescence fluctuation spectroscopy.

Fluorescence correlation spectroscopy (FCS) is generally used to obtain information about the number of fluorescent particles in a small volume and the diffusion coefficient from the autocorrelation function of the fluorescence signal. Here we demonstrate that photon counting histogram (PCH) analysis constitutes a novel tool for extracting quantities from fluorescence fluctuation data, i.e., the measured photon counts per molecule and the average number of molecules within the observation volume. The photon counting histogram of fluorescence fluctuation experiments, in which few molecules are present in the excitation volume, exhibits a super-Poissonian behavior. The additional broadening of the PCH compared to a Poisson distribution is due to fluorescence intensity fluctuations. For diffusing particles these intensity fluctuations are caused by an inhomogeneous excitation profile and the fluctuations in the number of particles in the observation volume. The quantitative relationship between the detected photon counts and the fluorescence intensity reaching the detector is given by Mandel's formula. Based on this equation and considering the fluorescence intensity distribution in the two-photon excitation volume, a theoretical expression for the PCH as a function of the number of molecules in the excitation volume is derived. For a single molecular species two parameters are sufficient to characterize the histogram completely, namely the average number of molecules within the observation volume and the detected photon counts per molecule per sampling time epsilon. The PCH for multiple molecular species, on the other hand, is generated by successively convoluting the photon counting distribution of each species with the others. The influence of the excitation profile upon the photon counting statistics for two relevant point spread functions (PSFs), the three-dimensional Gaussian PSF conventionally employed in confocal detection and the square of the Gaussian-Lorentzian PSF for two photon excitation, is explicitly treated. Measured photon counting distributions obtained with a two-photon excitation source agree, within experimental error with the theoretical PCHs calculated for the square of a Gaussian-Lorentzian beam profile. We demonstrate and discuss the influence of the average number of particles within the observation volume and the detected photon counts per molecule per sampling interval upon the super-Poissonian character of the photon counting distribution.     

Fluorescence Correlation Spectroscopy Measures Molecular Transport in Cells

Fluorescence correlation spectroscopy (FCS) can measure dynamics of fluorescent molecules in cells. FCS measures the fluctuations in the number of fluorescent molecules in a small volume illuminated by a thin beam of excitation light. These fluctuations are processed statistically to yield an autocorrelation function from which rates of diffusion, convection, chemical reaction, and other processes can be extracted. The advantages of this approach include the ability to measure the mobility of a very small number of molecules, even down to the single molecule level, over a wide range of rates in very small regions of a cell. In addition to rates of diffusion and convection, FCS also provides unique information about the local concentration, states of aggregation and molecular interaction using fluctuation amplitude and cross-correlation methods. Recent advances in technology have rendered these once difficult measurements accessible to routine use in cell biology and biochemistry. This review provides a summary of the FCS method and describes current areas in which the FCS approach is being extended beyond its original scope.     

Sensitivity enhancement in fluorescence correlation spectroscopy of multiple species using time-gated detection

Fluorescence correlation spectroscopy (FCS) is a powerful technique to measure chemical reaction rates and diffusion coefficients of molecules in thermal equilibrium. The capabilities of FCS can be enhanced by measuring the energy, polarization, or delay time between absorption and emission of the collected fluorescence photons in addition to their arrival times. This information can be used to change the relative intensities of multiple fluorescent species in FCS measurements and, thus, the amplitude of the intensity autocorrelation function. Here we demonstrate this strategy using lifetime gating in FCS experiments. Using pulsed laser excitation and laser-synchronized gating in the detection channel, we suppress photons emitted within a certain time interval after excitation. Three applications of the gating technique are presented: suppression of background fluorescence, simplification of FCS reaction studies, and investigation of lifetime heterogeneity of fluorescently labeled biomolecules. The usefulness of this technique for measuring forward and backward rates of protein fluctuations in equilibrium and for distinguishing between static and dynamic heterogeneity makes it a promising tool in the investigation of chemical reactions and conformational fluctuations in biomolecules.     

Fluorescence fluctuation spectroscopy.

The analysis of the intensity fluctuation of a fluorescence signal from a relatively small volume and from a few molecules contains information about the distribution of different species present in the solution and about kinetic parameters of the system. The same information is generally averaged out when the fluorescence experiment is performed in a much larger volume, typically a cuvette experiment. The fundamental reason for this difference is that the fluctuations of the fluorescence signal from a few molecules directly reflect the molecular nature of the matter. Only recently, with the advent of confocal microscopy and two-photon excitation, it has become practical to achieve small excitation volumes in which only a few fluorescent molecules are present. We introduce the concept of fluctuation spectroscopy and highlight some of the technical aspects. We discuss different analysis methods used in fluctuation spectroscopy and evaluate their use for studying protein-protein interactions.     

Fluorescence correlation spectroscopy in small cytosolic compartments depends critically on the diffusion model used

Fluorescence correlation spectroscopy (FCS) is a powerful technique for measuring low concentrations of fluorescent molecules and their diffusion constants. In the standard case, fluorescence fluctuations are measured in an open detection volume defined by the confocal optics. However, if FCS measurements are carried out in cellular processes that confine the detection volume, the standard FCS model leads to erroneous results. In this paper, we derive a modified FCS model that takes into account the confinement of the detection volume. Using this model, we have carried out the first FCS measurements in dendrites of cultured neurons. We further derive, for the case of confined diffusion, the limits within which the standard two- and three-dimensional diffusion models give reliable results.     

Fluorescence correlation spectroscopy and photobleaching recovery of multiple binding reactions. I. Theory and FCS measurements

Fluorescence correlation spectroscopy (FCS) and fluorescence photobleaching recovery (FPR) are two methods that may be used to measure diffusion and chemical reaction kinetics in small, labile systems such as biological cells. These methods are here applied to systems in which a fluorescent ligand can bind to a polyvalent substrate molecule in a multistep reaction sequence. The analytical theory for both FCS and FPR is extended to allow analysis of these kinds of systems. Experimental measurements of the binding of ethidium bromide to DNA by FCS confirm the theoretical analysis. (FPR measurements on the same system are reported in the accompanying paper.) The analysis shows that FCS and FPR perceive multivalent binding reactions differently. This difference results from the selective effect of the photobleaching process in the chemical reaction system. The development and results we report could have useful applications to a wide range of biopolymeric binding and assembly process.     

Fluorescence correlation spectroscopy and photobleaching recovery of multiple binding reactions. II. FPR and FCS measurements at low and high DNA concentrations

The preceding paper develops the theory for the interpretation of fluorescence photobleaching recovery (FPR) measurements of multiple binding of a ligand to a multivalent substrate molecule. Based on a reasonable assumption about the mechanism of the photobleaching process, this analysis shows that the observed behavior of a multivalent system should be practically identical to that of a univalent binding system. This is in contrast to the expected and observed behavior of fluorescence correlation spectroscopy (FCS) measurments. Experimental FPR measurements of multivalent binding of ethidium bromide to DNA confirm these conclusions. The FCS and FPR measurements also reveal an apparently enhanced diffusion of ethidium at high DNA concentration. This enhancement might result from direct transfer of ethidium among DNA molecules.     

Moment expansions in spatial ecological models and moment closure through Gaussian approximation

We describe the dynamics of competing species in terms of interactions between spatial moments. We close the moment hierarchy by employing a Gaussian approximation which assumes that fluctuations are independent and distributed normally about the mean values. The Gaussian approximation provides the lowest-order systematic correction to the mean-field approximation by incorporating the effect of fluctuations. When there are no fluctuations in the system, the mean equations agree with the Gaussian approximation as the fluctuations are weak. As the fluctuations gain strength, they influence the mean quantities and hence the Gaussian approximation departs from the mean-field approximation. At large fluctuation levels, the Gaussian approximation breaks down, as may be explained by the bimodality and skewness of the fluctuation distribution of the partial differential equation.     

Fluorescence correlation spectroscopy close to a fluctuating membrane

Compartmentalization of the cytoplasm by membranes should have a strong influence on the diffusion of macromolecules inside a cell, and we have studied how this could be reflected in fluorescence correlation spectroscopy (FCS) experiments. We derived the autocorrelation function measured by FCS for fluorescent particles diffusing close to a soft membrane, and show it to be the sum of two contributions: short timescale correlations come from the diffusion of the particles (differing from free diffusion because of the presence of an obstacle), whereas long timescale correlations arise from fluctuations of the membrane itself (which create intensity fluctuations by modulating the number of detected particles). In the case of thermal fluctuations this second type of correlation depends on the elasticity of the membrane. To illustrate this calculation, we report the results of FCS experiments carried out close to a vesicle membrane. The measured autocorrelation functions display very distinctly the two expected contributions, and allow both to recover the diffusion coefficient of the fluorophore and to characterize the membrane fluctuations in term of a bending rigidity. Our results show that FCS measurements inside cells can lead to erroneous values of the diffusion coefficient if the influence of membranes is not recognized.