Fluorescence correlation spectroscopy. I. Conceptual basis and theory

We describe a method for determining chemical kinetic constants and diffusion coefficients by measuring the rates of decay of spontaneous concentration fluctuations. The equilibrium of the system is not disturbed during the measurement. We measure the number of molecules of a specified type in a defined open volume as a function of time and compute the time course of the deviations from the thermodynamic mean concentration. The method is based on the principle that the rates of decay of spontaneous microscopic fluctuations are determined by the same phenomenological rate coefficients as those of macroscopic departures from equilibrium which result from external perturbations. Hence, an analysis of fluctuations yields the same chemical rate constants and diffusion coefficients as are measured by conventional procedures. In practice the number of the specified molecules is measured by a property such as absorbance or fluorescence which is specific and sensitive to chemical change. The sample volume is defined by a light beam which traverses the cell. As the molecules appear in or disappear from the light beam, either due to diffusion or chemical reaction, their concentration fluctuations give rise to corresponding fluctuations of the intensity of absorbed or emitted light. This paper presents the theory needed to derive chemical rate constants and diffusion coefficients from these fluctuations in light intensity. The theory is applied to three examples of general interest: pure diffusion in the absence of chemical reaction; the binding of a small rapidly diffusing ligand to a larger slowly diffusing macromolecule; and a unimolecular isomerization. The method should be especially useful in studying highly cooperative systems, relatively noncooperative systems with intermediate states closely spaced in free energy, small systems, and systems not readily subject to perturbations of state.     

Motion of myosin fragments during actin-activated ATPase: fluorescence correlation spectroscopy study.

The rates of the translational motion of myosin fragments, heavy meromyosin (HMM), and heavy meromyosin subfragment-1 (HMM S-1) were measured during actin-activated ATPase reaction by the method of fluorescence correlation spectroscopy. This technique monitors the random fluctuations in the concentration of fluorescent molecules in an open volume which result from the translational diffusion of the molecular species under observation. The statistical behavior of the fluctuations is represented in the form of the autocorrelation function, which is related to the translational diffusion coefficient of the fluorescent molecules. The translational motion of fluorescently labeled myosin fragments was progressively slowed down after additions of increasing amounts of actin in the presence of excess MgATP. When these results are interpreted according to a simple binding scheme, the extent of the retardation can be used to obtain the apparent association constant for binding of S-1 and HMM to actin in the presence of MgATP. In 0.1M KCl and at 23°C, the apparent association constants were determined as K_app^HMM = 2.2 × 10⁴M^?1 and K_app^S-1 = 8.8 × 10³ for HMM and S-1, respectively.     

Total internal reflection with fluorescence correlation spectroscopy: nonfluorescent competitors

Total internal reflection with fluorescence correlation spectroscopy is a method for measuring the surface association/dissociation rate constants and absolute densities of fluorescent molecules at the interface of a planar substrate and solution. This method can also report the apparent diffusion coefficient and absolute concentration of fluorescent molecules very close to the surface. Theoretical expressions for the fluorescence fluctuation autocorrelation function when both surface association/dissociation kinetics and diffusion through the evanescent wave, in solution, contribute to the fluorescence fluctuations have been published previously. In the work described here, the nature of the autocorrelation function when both surface association/dissociation kinetics and diffusion through the evanescent wave contribute to the fluorescence fluctuations, and when fluorescent and nonfluorescent molecules compete for surface binding sites, is described. The autocorrelation function depends in general on the kinetic association and dissociation rate constants of the fluorescent and nonfluorescent molecules, the surface site density, the concentrations of fluorescent and nonfluorescent molecules in solution, the solution diffusion coefficients of the two chemical species, the depth of the evanescent field, and the size of the observed area on the surface. Both general and approximate expressions are presented.     

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.     

Total internal reflection with fluorescence correlation spectroscopy: combined surface reaction and solution diffusion

Total internal reflection with fluorescence correlation spectroscopy (TIR-FCS) is a method for measuring the surface association/dissociation rates and absolute densities of fluorescent molecules at the interface of solution and a planar substrate. This method can also report the apparent diffusion coefficient and absolute concentration of fluorescent molecules very close to the surface. An expression for the fluorescence fluctuation autocorrelation function in the absence of contributions from diffusion through the evanescent wave, in solution, has been published previously (N. L. Thompson, T. P. Burghardt, and D. Axelrod. 1981, Biophys. J. 33:435-454). This work describes the nature of the TIR-FCS autocorrelation function when both surface association/dissociation kinetics and diffusion through the evanescent wave contribute to the fluorescence fluctuations. The fluorescence fluctuation autocorrelation function depends in general on the kinetic association and dissociation rate constants, the surface site density, the concentration of fluorescent molecules in solution, the solution diffusion coefficient, and the depth of the evanescent field. Both general and approximate expressions are presented.     

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.     

A fluorescence probe of acetylcholine receptor conformation and local anesthetic binding

The fluorescent dye ethidium bromide binds to the acetylcholine receptor with an apparent K_d of $\text{3 μ}\text{M}$ and a stoichiometry of 1 molecule of ethidium per α-bungarotoxin site. Time dependent fluorescent increases were observed upon addition of carbamylcholine, the amplitude and half-time of which were dependent on the Carb¹ concentration. It appeared that these fluorescence increases resulted from a lowering of the K_d for ethidium as the AcChR-Carb complex underwent an isomerization from low to high affinity form(s) for carb, and more ethidium was bound. Titration with the local anesthetic procaine led to ethidium fluorescence increases at low procaine concentrations, followed by a fluorescence decrease at higher procaine concentrations to that level induced by saturating α-bungarotoxin. Thus it appeared that the ethidium binding site either interacted with or was identical with local anesthetic binding site(s).     

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.     

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.     

DNA Bifunctional intercalators. 2. Fluorescence properties and DNA binding interaction of an ethidium homodimer and an acridine ethidium heterodimer

An ethidium homodimer and acridine ethidium heterodimer have been synthesized (Gaugain, B., Barbet, J., Oberlin, R., Roques, B. P., & Le Pecq, J. B. (1978) Biochemistry 17 (preceding paper in this issue)). The binding of these molecules to DNA has been studied. We show that these dimers intercalate only one of their chromophores in DNA. At high salt concentration (Na+ greater than 1 M) only a single type of DNA-binding site exists. Binding affinity constants can then be measured directly using the Mc Ghee & Von Hippel treatment (Mc Ghee, J. D., & Von Hippel, P. H. (1974) J. Mol. Biol. 86, 469). In these conditions the dimers cover four base pairs when bound to DNA. Binding affinities have been deduced from competition experiments in 0.2 M Na+ and are in agreement with the extrapolated values determined from direct DNA-binding measurements at high ionic strength. As expected, the intrinsic binding constant of these dimers is considerably larger than the affinity of the monomer (ethidium dimer K = 2 X 10(8) M-1; ethidium bromide K = 1.5 X 10(5) M-1 in 0.2 M Na+). The fluorescence properties of these molecules have also been studied. The efficiency of the energy transfer from the acridine to the phenanthridinium chromophore, in the acridine ethidium heterodimer when bound to DNA, depends on the square of the AT base pair content. The large increase of fluorescence on binding to DNA combined with a high affinity constant for nucleic acid fluorescent probes. In particular, such molecules can be used in competition experiments to determine the DNA binding constant of ligands of high binding affinity such as bifunctional intercalators.     

Study of 2.5S RNA of 1,4-alpha-glucan branching enzyme by fluorescent methods using ethidium bromide

The fluorescence yield and lifetime of ethidium bromide complexes with 1,4-alpha-glucan branching enzyme and its free nucleic acid component 2.5S RNA were measured. Both fluorescence parameters showed a 10-fold increase in comparison with those characteristics for the free dye. This increase allows to suggest the existence of double-stranded regions in 2.5S RNA both in the free as well as in the protein bound state. The coefficients of fluorescence polarization were also determined for ethidium bromide complexed with free and protein bound 2.5S RNA. They proved to be 13 and 18% respectively. No concentration depolarization was observed in both types of ethidium bromide and ethidium bromide--enzyme--RNA complexes. This proves that the double-stranded regions are rather short and that two ethidium bromide molecules can't be bound to each of them. The binding isotherms were measured for ethidium bromide absorbed on 2.5S RNA and on the holoenzyme. Their parameters napp and rmax are identical in the cases of free and protein bound 2,5S RNA (rmax = 0.046 +/- 0.001). However the binding constants of ethidium bromide complexes with free and protein bound 2.5S RNA differ significantly (Kapp = 2.2 X 10(6) M-1 for free 2.5S RNA and Kapp = 1.6 X 10(6) M-1 for the holoenzyme). The quantity of nucleotides involved in the two double-stranded regions accessible for ethidium binding is estimated to be about 28%. Increasing of Mg2+ ion concentration up to 10(-3) results in a decrease of ethidium bromide binding with double stranded regions. It may be due to a more compact tertiary structure of 2.5S RNA in the presence of Mg2+ in the free as well as in protein bound state.     

Dual-color fluorescence cross-correlation spectroscopy for multicomponent diffusional analysis in solution.

The present paper describes a new experimental scheme for following diffusion and chemical reaction systems of fluorescently labeled molecules in the nanomolar concentration range by fluorescence correlation analysis. In the dual-color fluorescence cross-correlation spectroscopy provided here, the concentration and diffusion characteristics of two fluorescent species in solution as well as their reaction product can be followed in parallel. By using two differently labeled reaction partners, the selectivity to investigate the temporal evolution of reaction product is significantly increased compared to ordinary one-color fluorescence autocorrelation systems. Here we develop the theoretical and experimental basis for carrying out measurements in a confocal dual-beam fluorescence correlation spectroscopy setup and discuss conditions that are favorable for cross-correlation analysis. The measurement principle is explained for carrying out DNA-DNA renaturation kinetics with two differently labeled complementary strands. The concentration of the reaction product can be directly determined from the cross-correlation amplitude.     

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.     

Ethidium bromide resistance in a rat liver epithelial cell line: Association with enhanced drug efflux

Ethidium bromide-resistant cell strains were obtained by continuous selection of an adult rat liver-derived cell line (ARL6T) grown in the continuous presence of 200 ngl ml ethidium bromide. Comparison of resistant strains and parental (sensitive) cells was made for uptake and binding of ethidium bromide, visualized as fluorescent ethidium bromide-nucleic acid complexes. Although uptake of ethidium bromide was similar in parental and resistant cells, efflux kinetics were markedly different. Over a three-hour period, parental (sensitive) cells maintained fluorescence following a short ethidium bromide pulse (100 g/ ml ethidium bromide). In contrast, ethidium bromide-resistant cell lines eliminated photographically detectable fluorescent complexes within three hours following pulse exposure to ethidium bromide. The rapid elimination of ethidium bromide fluorescent complexes in all (5) resistant cell strains examined supports an efflux mechanism as contributing to the resistance of ethidium bromide cytotoxicity in these cells.Abbreviations EtBr ethidium bromide - HBSS Hanks' balanced salt solution     

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.     

Quantitation of DNA and RNA in crude tissue extracts by flow injection analysis.

An automated two-dye flow injection analysis system to quantitate DNA and RNA in crude extracts of tissues is described. The method uses the fluorochrome dyes ethidium bromide and Hoechst 33258. DNA concentration is determined directly from its fluorescence in Hoechst dye. RNA is estimated from fluorescence in ethidium bromide after subtraction of the fluorescence due to DNA. This method has several advantages: a simple extraction procedure, a low detection limit (0.01 micrograms DNA and 0.10 micrograms RNA), automation, and a high sample throughput.     

The binding of polyamines and of ethidium bromide to tRNA.

The binding of spermidine and ethidium bromide to mixed tRNA and phenylalanine tRNA has been studied under equilibrium conditions. The numbers and classes of binding sites obtained have been compared to those found in complexes isolated by gel filtration a low ionic strength. The latter complexes contain 10-11 moles of either spermidine or ethidium per mole of tRNA; either cation is completely displaceable by the other. In ethidium complexes, the first 2-3 moles are bound in fluorescent binding sites; the remaining 7-8 molecules bind in non-fluorescent form. At least one of the binding sites for spermidine appears similar to a binding site for fluorescent ethidium. Similar results are found with E. coli formylmethionine tRNA. Spermine, in excess of 18-20 moles per mole tRNA, causes precipitation of the complex. Putrescine does not form isolable complexes with yeast tRNA and displaces ethidium less readily from preformed ethidium-tRNA complexes. Under equilibrium conditions, in the absence of Mg++, there are 16-17 moles of spermidine bound per mole of tRNA as determined by equilibrium dialysis. Of these, 2-3 bind with a Ksence of 9 mM Mg++, the total number of binding sites is decreased slightly and there appears to be only one class of sites with a Ka = 600 M(-1). Quantitatively similar results are obtained for the binding of spermidine to yeast phenylalanine tRNA. When the interaction between ethidium bromide and mixed tRNA is studied by equilibrium dialysis or spectrophotometric titration, two classes of binding sites are obtained: 2-3 molecules bind with an average Ka = 6.6 x 10(5) M(-1) and 14-15 molecules bind with an average Ka = 4.1 x 10(4) M(-1). Spermidine, spermine, and Mg++ compete effectively for both classes of ethidium sites and have the effect of reducing the apparent binding constants for ethidium. When the binding of ethidium is studied by fluorometry, there are 3-4 highly fluorescent sites per tRNA. These sites are also affected by spermidine, spermine and Mg++. Putrescine has little effect on any of the classes of binding sites. These data are consistent with those found under non-equilibrium conditions. They suggest that polyamines bind to fairly specific regions of tRNA and may be involved in the maintenance of certain structural features of tRNA.     

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: 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.