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.

The diffusion of fluorescent particles through a small, illuminated observation volume gives rise to intensity fluctuations caused by particle number fluctuations in the open observation volume and the inhomogeneous excitation-beam profile. The intensity distribution of these fluorescence fluctuations is experimentally captured by the photon-counting histogram (PCH). We recently introduced the theory of the PCH for diffusing particles (Chen et al., Biophys. J., 77:553-567), where we showed that we can uniquely describe the distribution of photon counts with only two parameters for each species: the molecular brightness of the particle and the average number of particles within the observation volume. The PCH is sensitive to the molecular brightness and thus offers the possibility to separate a mixture of fluorescent species into its constituents, based on a difference in their molecular brightness alone. This analysis is complementary to the autocorrelation function, traditionally used in fluorescence fluctuation spectroscopy, which separates a mixture of species by a difference in their diffusion coefficient. The PCH of each individual species is convoluted successively to yield the PCH of the mixture. Successful resolution of the histogram into its components is largely a matter of the signal statistics. Here, we discuss the case of two species in detail and show that a concentration for each species exists, where the signal statistics is optimal. We also discuss the influence of the absolute molecular brightness and the brightness contrast between two species on the resolvability of two species. A binary dye mixture serves as a model system to demonstrate that the molecular brightness and the concentration of each species can be resolved experimentally from a single or from several histograms. We extend our study to biomolecules, where we label proteins with a fluorescent dye and show that a brightness ratio of two can be resolved. The ability to resolve a brightness ratio of two is very important for biological applications.

Typically, fluctuation correlation spectroscopy (FCS) data acquisition cards measure the number of photon events per time interval (i.e., bin) - time mode. Commercial FCS cards combine the bins through hardware in order to calculate the autocorrelation function. Such a design therefore does not yield the time resolved photon sequence, but only the autocorrelation of that sequence. A different acquisition method which measures the number of time intervals between photon events has been implemented - photon mode. This method takes advantage of the fact that in FCS the rate of photon counts is much less than the frequency of the clock that is used to determine the temporal location of the photons. By using this new mode of data acquisition, the current card design allows for 25 ns time resolution. The data acquisition card can operate in both time and photon mode and yields the time resolved sequence of photon arrivals in both cases. Therefore, the data is available for analysis by any method(s), such as but not limited to, autocorrelation, photon counting histogram, and higher order autocorrelation. © 2000 American Institute of Physics.

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 (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.

We examine the binding of fluorescent ligands to proteins by analyzing the fluctuation amplitude g(0) of fluorescence fluctuation experiments. The normalized variance g(0) depends on the molecular brightness and the concentration of each species in the sample. Thus a single g(0) measurement is not sufficient to resolve individual species. Titration of the ligand with protein establishes the link between molecular brightness and concentration by fitting g(0) to a binding model and allows the separation of species. We first apply g(0) analysis to binary dye mixtures with brightness ratios of 2 and 4 to demonstrate the feasibility of this technique. Next we consider the influence of binding on the fluctuation amplitude g(0). The dissociation coefficient, the molecular brightness ratio, and the stochiometry of binding strongly influence the fluctuation amplitude. We show that proteins with a single binding site can be clearly differentiated from proteins with two independent binding sites. The binding of fluorescein-labeled digoxigenin to a high-affinity anti-digoxin antibody was studied experimentally. A global analysis of the fluctuation amplitude and the fluorescence intensity not only recovered the dissociation coefficient and the number of binding sites, but also revealed the molecular heterogeneity of the hapten-antibody complex. Two species were used to model the molecular heterogeneity. We confirmed the molecular heterogeneity independently by fluorescence lifetime experiments, which gave fractional populations and molecular brightness values that were virtually identical to those of the g(0) analysis. The identification and characterization of molecular heterogeneity have far-reaching consequences for many biomolecular systems. We point out the important role fluctuation experiments may have in this area of research.

We report direct measurement of the center-of-mass diffusion coefficient, D, of uncharged flexible linear chains adsorbed at the solid-liquid interface at dilute surface coverage. We find D ∼ N-3/2 (N is degree of polymerization) when N was varied by more than an order of magnitude (N = 48, 113, 244, 456, and 693) and the scatter of the data was low. The experimental system was poly(ethylene glycol), PEG, adsorbed from dilute aqueous solution onto a self-assembled hydrophobic monolayer, condensed octadecyltriethoxysilane. The method of measurement was fluorescence correlation spectroscopy of a rhodamine green derivative dye that was end-attached to one sole end of the adsorbed PEG chains. The observed scaling implies the diffusion time τ ∼ N3 if Rg ∼ N3/4 as expected for a chain in good solvent in two dimensions (Rg is the radius of gyration), but a variety of other theoretical approaches to describe the dynamical scaling are also plausible. The multiplicity of plausible dynamical transport scenarios is compounded by the fact that polymer diffusion is sensitive to chain conformation on the surface which is not directly observable. Various theoretical scenarios are explored, and the need for new experiments, theory, and computer simulation studies to allow definitive interpretation of this observation of simple and clean fractional power law scaling is emphasized.

The dimeric Crotalus atrox venom PLA2 is part of the secreted phospholipase A2 (PLA2) enzyme family that interacts at the lipid-solution interface to hydrolyze the sn-2 acyl ester bond of phospholipids. We have employed fluorescence correlation spectroscopy (FCS) to study the monomer-dimer equilibrium of the C. atrox venom PLA2 in solution, in the presence of urea, and in the presence of monomeric and micellar n-dodecylphosphocholine (C12-PN), a phosphatidylcholine analogue. Dilution experiments show that PLA2 is an extremely tight dimer, Kd < or = 0.01 nM, in solution. Urea was introduced to weaken the subunit's association, and an estimate for the PLA(2) dimer dissociation constant in buffer was obtained by linear extrapolation. The derived dissociation constant was at least several orders of magnitude greater than that suggested from the dilution experiments, indicating a complex interaction between urea and the PLA2 dimer. FCS data indicate that the PLA2 dimer begins to dissociate at 10 mM C12-PN in 10 mM Ca2+ and at 5 mM C12-PN in 1 mM EDTA. The PLA2 tryptophan fluorescence displayed spectral shifts and intensity changes upon interacting with C12-PN. On the basis of the FCS and tryptophan fluorescence results, we postulate an intermediate state where the two monomers are in loose interaction within a protein-lipid comicelle. As the concentration of C12-PN was increased, complete dissociation of the dimer was observed, inferred from the doubling of the particle number, and the average diffusion constant decreased to approximately 60 microm2/s, consistent with PLA2 associated with a C12-PN micelle. The presence of Ca2+ makes the comicelle intermediate more stable, retarding the separation of the monomers in the micellar suspension. Our data clearly indicate that PLA2, though a strong dimer in the absence of lipids, is dissociated by micellar C12-PN and supports the monomer hypothesis for PLA2 action.