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).     

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.     

Correlation spectroscopy of minor fluorescent species: signal purification and distribution analysis

We are performing experiments that use fluorescence resonance energy transfer (FRET) and fluorescence correlation spectroscopy (FCS) to monitor the movement of an individual donor-labeled sliding clamp protein molecule along acceptor-labeled DNA. In addition to the FRET signal sought from the sliding clamp-DNA complexes, the detection channel for FRET contains undesirable signal from free sliding clamp and free DNA. When multiple fluorescent species contribute to a correlation signal, it is difficult or impossible to distinguish between contributions from individual species. As a remedy, we introduce "purified FCS", which uses single molecule burst analysis to select a species of interest and extract the correlation signal for further analysis. We show that by expanding the correlation region around a burst, the correlated signal is retained and the functional forms of FCS fitting equations remain valid. We demonstrate the use of purified FCS in experiments with DNA sliding clamps. We also introduce "single-molecule FCS", which obtains diffusion time estimates for each burst using expanded correlation regions. By monitoring the detachment of weakly-bound 30-mer DNA oligomers from a single-stranded DNA plasmid, we show that single-molecule FCS can distinguish between bursts from species that differ by a factor of 5 in diffusion constant.     

Exploring the Dynamics of Cell Processes through Simulations of Fluorescence Microscopy Experiments

Fluorescence correlation spectroscopy (FCS) methods are powerful tools for unveiling the dynamical organization of cells. For simple cases, such as molecules passively moving in a homogeneous media, FCS analysis yields analytical functions that can be fitted to the experimental data to recover the phenomenological rate parameters. Unfortunately, many dynamical processes in cells do not follow these simple models, and in many instances it is not possible to obtain an analytical function through a theoretical analysis of a more complex model. In such cases, experimental analysis can be combined with Monte Carlo simulations to aid in interpretation of the data. In response to this need, we developed a method called FERNET (Fluorescence Emission Recipes and Numerical routines Toolkit) based on Monte Carlo simulations and the MCell-Blender platform, which was designed to treat the reaction-diffusion problem under realistic scenarios. This method enables us to set complex geometries of the simulation space, distribute molecules among different compartments, and define interspecies reactions with selected kinetic constants, diffusion coefficients, and species brightness. We apply this method to simulate single- and multiple-point FCS, photon-counting histogram analysis, raster image correlation spectroscopy, and two-color fluorescence cross-correlation spectroscopy. We believe that this new program could be very useful for predicting and understanding the output of fluorescence microscopy experiments.     

Probing GFP-actin diffusion in living cells using fluorescence correlation spectroscopy

The cytoskeleton of eukaryotic cells is continuously remodeled by polymerization and depolymerization of actin. Consequently, the relative content of polymerized filamentous actin (F-actin) and monomeric globular actin (G-actin) is subject to temporal and spatial fluctuations. Since fluorescence correlation spectroscopy (FCS) can measure the diffusion of fluorescently labeled actin it seems likely that FCS allows us to determine the dynamics and hence indirectly the structural properties of the cytoskeleton components with high spatial resolution. To this end we investigate the FCS signal of GFP-actin in living Dictyostelium discoideum cells and explore the inherent spatial and temporal signatures of the actin cytoskeleton. Using the free green fluorescent protein (GFP) as a reference, we find that actin diffusion inside cells is dominated by G-actin and slower than diffusion in diluted cell extract. The FCS signal in the dense cortical F-actin network near the cell membrane is probed using the cytoskeleton protein LIM and is found to be slower than cytosolic G-actin diffusion. Furthermore, we show that polymerization of the cytoskeleton induced by Jasplakinolide leads to a substantial decrease of G-actin diffusion. Pronounced fluctuations in the distribution of the FCS correlation curves can be induced by latrunculin, which is known to induce actin waves. Our work suggests that the FCS signal of GFP-actin in combination with scanning or spatial correlation techniques yield valuable information about the local dynamics and concomitant cytoskeletal properties.     

Complexation of lipofectamine and cholesterol-modified DNA sequences studied by single-molecule fluorescence techniques

Lipoplex formation for normal and cholesterol-modified oligonucleotides is investigated by fluorescence correlation spectroscopy (FCS). To overcome the problems related to the fitting of autocorrelation curves when fluorescence bursts are present, the baseline fluorescence levels and the fluorescence bursts in the same trace were separately analyzed. This approach was not previously used in FCS studies of lipoplexes and allowed a more detailed characterization of this heterogeneous system. From the baseline levels, the number of free/bound DNA molecules and the presence of tens to hundreds of nanometer-sized lipoplexes were estimated using various mathematical models. Analysis of the fluorescent bursts provided an indication about the sizes of the lipoplexes, the number of DNA molecules in these aggregates, and the relative amount of lipids in each aggregate. An explanation for the higher transfection efficiency previously reported for one of the cholesterol-modified oligonucleotide compounds was found in relation to the formation of large size lipoplexes.     

Anomalous Diffusion in Inverted Variable-Lengthscale Fluorescence Correlation Spectroscopy

Using fluorescence correlation spectroscopy (FCS) to distinguish between different types of diffusion processes is often a perilous undertaking because the analysis of the resulting autocorrelation data is model dependant. Two recently introduced strategies, however, can help move toward a model-independent interpretation of FCS experiments: 1) the obtention of correlation data at different length scales and 2) their inversion to retrieve the mean-squared displacement associated with the process under study. We use computer simulations to examine the signature of several biologically relevant diffusion processes (simple diffusion, continuous-time random walk, caged diffusion, obstructed diffusion, two-state diffusion, and diffusing diffusivity) in variable-length-scale FCS. We show that, when used in concert, length-scale variation and data inversion permit us to identify non-Gaussian processes and, regardless of Gaussianity, to retrieve their mean-squared displacement over several orders of magnitude in time. This makes unbiased discrimination between different classes of diffusion models possible.     

On the analysis of high order moments of fluorescence fluctuations.

A simple, straightforward analysis to characterize the distribution of aggregate sizes in a reversible aggregation system at equilibrium is presented. The method, an extension of fluorescence correlation spectroscopy (FCS), is based on measurements of higher order moments of spontaneous fluctuations of fluorescence intensity emitted from a defined open region of the sample. These fluctuations indicate fluctuations of the numbers of the fluorescent molecules in the observation region. Shot noise resulting from the random character of fluorescence emission and from the photoelectric detection system is modeled as a Poisson distribution and is subtracted from the measured photon count fluctuation moments to yield the desired fluorescence fluctuation moments. This analysis can also be used to estimate the fraction of immobile fluorophores in FCS measurements.     

Confined detection volume of fluorescence correlation spectroscopy by bare fiber probes

A fiber-tip-based near-field fluorescence correlation spectroscopy (FCS) has been developed for confining the detection volume to sub-diffraction-limited dimensions. This near-field FCS is based on near-field illumination by coupling a scanning near-field optical microscope (SNOM) to a conventional confocal FCS. Single-molecule FCS analysis at 100 nM Rhodamine 6G has been achieved by using bare chemically etched, tapered fiber tips. The detection volume under control of the SNOM system has been reduced over one order of magnitude compared to that of the conventional confocal FCS. Related factors influencing the near-field FCS performance are investigated and discussed in detail. In this proof-of-principle study, the preliminary experimental results suggest that the fiber-tip-based near-field FCS might be a good alternative to realize localized analysis at the single-molecule level.     

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.     

The standard deviation in fluorescence correlation spectroscopy

The standard deviation (SD) in fluorescence correlation spectroscopy (FCS) has been mostly neglected in applications. However, the knowledge of the correct SD is necessary for an accurate data evaluation, especially when fitting theoretical models to experimental data. In this work, an algorithm is presented that considers the essential features of FCS. It allows prediction of the performance of FCS measurements in various cases, which is important for finding optimal experimental conditions. The program calculates the SD of the experimental autocorrelation function online. This procedure leads to improved parameter estimation, compared to currently used theoretical approximations for the SD. Three methods for the calculation of the SD are presented and compared to earlier analytical solutions (D. E. Koppel. 1974. Phys. Rev. A. 10:1938-1945.), calculation directly from fluorescence intensity values, by averaging several FCS measurements, or by dividing one measurement into a set of shorter data packages. Although the averaging over several measurements yields accurate estimates for the SD, the other two methods are considerably less time consuming, can be run online, and yield comparable results.     

Statistical analysis of fluorescence correlation spectroscopy: the standard deviation and bias

We present a detailed statistical analysis of fluorescence correlation spectroscopy for a wide range of timescales. The derivation is completely analytical and can provide an excellent tool for planning and analysis of FCS experiments. The dependence of the signal-to-noise ratio on different measurement conditions is extensively studied. We find that in addition to the shot noise and the noise associated with correlated molecular dynamics there is another source of noise that appears at very large lag times. We call this the "particle noise," as its behavior is governed by the number of particles that have entered and left the laser beam sample volume during large dwell times. The standard deviations of all the points on the correlation function are calculated analytically and shown to be in good agreement with experiments. We have also investigated the bias associated with experimental correlation function measurements. A "phase diagram" for FCS experiments is constructed that demonstrates the significance of the bias for any given experiment. We demonstrate that the value of the bias can be calculated and added back as a first-order correction to the experimental correlation function.     

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: molecular recognition at the single molecule level

Fluorescence correlation spectroscopy (FCS) is a fluorescence microscopy technique that allows the study of molecular interactions in extremely low volumes, at nanomolar concentrations, even when binding is not accompanied by a fluorescence change. It can be applied directly in living cells. FCS clearly considerably extends the possibilities of the classical techniques used in molecular recognition studies and can be considered to belong to a growing group of techniques that allow detection at the single molecule level. In this review, several applications of FCS, both in vitro and in vivo, will be discussed.     

Characterization of a fluorophore binding RNA aptamer by fluorescence correlation spectroscopy and small angle X-ray scattering

Using fluorescence correlation spectroscopy (FCS), we have established an in vitro assay to study RNA dynamics by analyzing fluorophore binding RNA aptamers at the single molecule level. The RNA aptamer SRB2m, a minimized variant of the initially selected aptamer SRB-2, has a high affinity to the disulfonated triphenylmethane dye sulforhodamine B. A mobility shift of sulforhodamine B after binding to SRB2m was measured. In contrast, patent blue V (PBV) is visible only if complexed with SRB2m due to increased molecular brightness and minimal background. With small angle X-ray scattering (SAXS), the three-dimensional structure of the RNA aptamer was characterized at low resolution to analyze the effect of fluorophore binding. The aptamer and sulforhodamine B-aptamer complex was found to be predominantly dimeric in solution. Interaction of PBV with SRB2m led to a dissociation of SRB2m dimers into monomers. Radii of gyration and hydrodynamic radii, gained from dynamic light scattering, FCS, and fluorescence cross-correlation experiments, led to comparable conclusions. Our study demonstrates how RNA-aptamer fluorophore complexes can be simultaneously structurally and photophysically characterized by FCS. Furthermore, fluorophore binding RNA aptamers provide a tool for visualizing single RNA molecules.     

Methods to measure the lateral diffusion of membrane lipids and proteins

In this chapter, we discuss methods to measure lateral mobility of membrane lipids and proteins using techniques based on the light microscope. These methods typically sample lateral mobility in very small, micron-sized regions of the membrane so that they can be used to measure diffusion in regions of single cells. The methods are based on fluorescence from the molecules of interest or from light scattered from particles attached to single or small groups of membrane lipids or proteins. Fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS) and Single particle tracking (SPT) are presented in that order. FRAP and FCS methodologies are described for a dedicated wide field microscope although many confocal microscopes now have software permitting these measurement to be made; nevertheless, the principles of the measurement are the same for a wide field or confocal microscope. SPT can be applied to trace the movements of single fluorescent molecules in membranes but this aspect will not be treated in detail.     

Continuous fluorescence microphotolysis and correlation spectroscopy using 4Pi microscopy

Continuous fluorescence microphotolysis (CFM) and fluorescence correlation spectroscopy (FCS) permit measurement of molecular mobility and association reactions in single living cells. CFM and FCS complement each other ideally and can be realized using identical equipment. So far, the spatial resolution of CFM and FCS was restricted by the resolution of the light microscope to the micrometer scale. However, cellular functions generally occur on the nanometer scale. Here, we develop the theoretical and computational framework for CFM and FCS experiments using 4Pi microscopy, which features an axial resolution of ∼100 nm. The framework, taking the actual 4Pi point spread function of the instrument into account, was validated by measurements on model systems, employing 4Pi conditions or normal confocal conditions together with either single- or two-photon excitation. In all cases experimental data could be well fitted by computed curves for expected diffusion coefficients, even when the signal/noise ratio was small due to the small number of fluorophores involved.     

Supercritical angle fluorescence correlation spectroscopy

We explore the potential of a supercritical angle (SA) objective for fluorescence correlation spectroscopy (FCS). This novel microscope objective combines tight focusing by an aspheric lens with strong axial confinement of supercritical angle fluorescence collection by a parabolic mirror lens, resulting in a small detection volume. The tiny axial extent of the detection volume features an excellent surface sensitivity, as is demonstrated by diffusion measurements in model membranes with an excess of free dye in solution. All SA-FCS measurements are directly compared to standard confocal FCS, demonstrating a clear advantage of SA-FCS, especially for diffusion measurements in membranes. We present an extensive theoretical framework that allows for accurate and quantitative evaluation of the SA-FCS correlation curves.     

Using fluorescence correlation spectroscopy to study conformational changes in denatured proteins

Fluorescence correlation spectroscopy (FCS) is a sensitive analytical tool that allows dynamics and hydrodynamics of biomolecules to be studied under a broad range of experimental conditions. One application of FCS of current interest is the determination of the size of protein molecules in the various states they sample along their folding reaction coordinate, which can be accessed through the measurement of diffusion coefficients. It has been pointed out that the analysis of FCS curves is prone to artifacts that may lead to erroneous size determination. To set the stage for FCS studies of unfolded proteins, we first show that the diffusion coefficients of small molecules as well as proteins can be determined accurately even in the presence of high concentrations of co-solutes that change the solution refractive index significantly. Indeed, it is found that the Stokes-Einstein relation between the measured diffusion coefficient and solution viscosity holds even in highly concentrated glycerol or guanidinium hydrochloride (GuHCl) solutions. These measurements form the basis for an investigation of the structure of the denatured state of two proteins, the small protein L and the larger, three-domain protein adenylate kinase (AK). FCS is found useful for probing expansion in the denatured state beyond the unfolding transition. It is shown that the denatured state of protein L expands as the denaturant concentration increases, in a process akin to the transition from a globule to a coil in polymers. This process continues at least up to 5 M GuHCl. On the other hand, the denatured state of AK does not seem to expand much beyond 2 M GuHCl, a result that is in qualitative accord with single-molecule fluorescence histograms. Because both the unfolding transition and the coil-globule transition of AK occur at a much lower denaturant concentration than those of protein L, a possible correlation between the two phenomena is suggested.     

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.