Fluorescence intensity multiple distributions analysis: concurrent determination of diffusion times and molecular brightness

Fluorescence correlation spectroscopy (FCS) has proven to be a powerful technique with single-molecule sensitivity. Recently, it has found a complement in the form of fluorescence intensity distribution analysis (FIDA). Here we introduce a fluorescence fluctuation method that combines the features of both techniques. It is based on the global analysis of a set of photon count number histograms, recorded with multiple widths of counting time intervals simultaneously. This fluorescence intensity multiple distributions analysis (FIMDA) distinguishes fluorescent species on the basis of both the specific molecular brightness and the translational diffusion time. The combined information, extracted from a single measurement, increases the readout effectively by one dimension and thus breaks the individual limits of FCS and FIDA. In this paper a theory is introduced that describes the dependence of photon count number distributions on diffusion coefficients. The theory is applied to a series of photon count number histograms corresponding to different widths of counting time intervals. Although the ability of the method to determine specific brightness values, diffusion times, and concentrations from mixtures is demonstrated on simulated data, its experimental utilization is shown by the determination of the binding constant of a protein-ligand interaction exemplifying its broad applicability in the life sciences.     

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.     

Resolving heterogeneity on the single molecular level with the photon-counting histogram

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.     

Measurement of monomer-oligomer distributions via fluorescence moment image analysis

We present higher-order moment analysis of fluorescence intensity fluctuations from individual laser scanning microscopy images applied to study monomer-oligomer distributions. We demonstrate that the number densities and brightness ratios of a mixed population of monomers and oligomers can be determined by analyzing higher-order moments of the fluorescence intensity fluctuations from individual images for specific ranges of densities and particle brightness ratios. Computer simulations and experiments with fluorescent microspheres and cells were performed to illustrate the detection limits and accuracy of this statistical approach. The simulation results show that the concentration of the dimer or oligomer population should be less than or equal to the monomeric concentration for the method to provide accurate results, and that the upper density detection limit of the population of monomers is one order-of-magnitude higher than the concentration of the oligomers. We implemented this technique to resolve two populations of fluorescent microspheres with different brightness ratios and we also applied the moment-analysis method to examine the distribution of aggregation states of PDGF-beta receptors in human fibroblast cells. The method was able to resolve a tetrameric population of the PDGF-beta receptors relative to the background distribution of nonspecifically bound fluorophore.     

Single-molecule detection technologies in miniaturized high-throughput screening: fluorescence intensity distribution analysis

Single-molecule detection technologies are becoming a powerful readout format to support ultra-high-throughput screening. These methods are based on the analysis of fluorescence intensity fluctuations detected from a small confocal volume element. The fluctuating signal contains information about the mass and brightness of the different species in a mixture. The authors demonstrate a number of applications of fluorescence intensity distribution analysis (FIDA), which discriminates molecules by their specific brightness. Examples for assays based on brightness changes induced by quenching/dequenching of fluorescence, fluorescence energy transfer, and multiple-binding stoichiometry are given for important drug targets such as kinases and proteases. FIDA also provides a powerful method to extract correct biological data in the presence of compound fluorescence.     

Fluorescence intensity and lifetime distribution analysis: toward higher accuracy in fluorescence fluctuation spectroscopy

Fluorescence fluctuation methods such as fluorescence correlation spectroscopy and fluorescence intensity distribution analysis (FIDA) have proven to be versatile tools for studying molecular interactions with single molecule sensitivity. Another well-known fluorescence technique is the measurement of the fluorescence lifetime. Here, we introduce a method that combines the benefits of both FIDA and fluorescence lifetime analysis. It is based on fitting the two-dimensional histogram of the number of photons detected in counting time intervals of given width and the sum of excitation to detection delay times of these photons. Referred to as fluorescence intensity and lifetime distribution analysis (FILDA), the technique distinguishes fluorescence species on the basis of both their specific molecular brightness and the lifetime of the excited state and is also able to determine absolute fluorophore concentrations. The combined information yielded by FILDA results in significantly increased accuracy compared to that of FIDA or fluorescence lifetime analysis alone. In this paper, the theory of FILDA is elaborated and applied to both simulated and experimental data. The outstanding power of this technique in resolving different species is shown by quantifying the binding of calmodulin to a peptide ligand, thus indicating the potential for application of FILDA to similar problems in the life sciences.     

Brownian dynamics simulations of fluorescence fluctuation spectroscopy

We have developed a program for the simulation of the fluorescence fluctuations as detected from highly diluted samples of (bio)molecules. The model is applied to translational diffusion and takes into account the hydrodynamic interactions. The solution concentration is kept constant by assuming periodic boundary conditions and spans here the range 0.5< C < 10 nM. We show that the fluorescence correlation functions can be accurately computed on systems of limited size (a few molecules per simulation box) by simulating for a total time approximately 100-300 times the diffusion relaxation time of the fluorescence autocorrelation function. The model is applied also to the simulation of the scanning fluorescence correlation spectroscopy (FCS) and of the photon counting histograms for the confocal collection configuration. Scanning FCS simulations of highly diluted samples (C approximately equals 0.5 nM) show anticorrelation effects in the autocorrelation functions of the fluorescence signal that are less evident for higher concentrations. We suggest here that this effect may be due to the non-uniform occupancy of the scanning area by the fluorophores.     

Perceptual dominance time distributions in multistable visual perception

Perceptual multistability, alternative perceptions of an unchanging stimulus, gives important clues to neural dynamics. The present study examined 56 perceptual dominance time series for a Necker cube stimulus, for ambiguous motion, and for binocular rivalry. We made histograms of the perceptual dominance times, based on from 307 to 2478 responses per time series (median=612), and compared these histograms to gamma, lognormal and Weibull fitted distributions using the Kolmogorov–Smirnov goodness-of-fit test. In 40 of the 56 tested cases a lognormal distribution provided an acceptable fit to the histogram (in 24 cases it was the only fit). In 16 cases a gamma distribution, and in 11 cases a Weibull distribution, were acceptable but never as the only fit in either case. Any of the three distributions were acceptable in three cases and none provided acceptable fits in 12 cases. Considering only the 16 cases in which a lognormal distribution was rejected (p<0.05) revealed that minor adjustments to the fourth-moment term of the lognormal characteristic function restored good fits. These findings suggest that random fractal theory might provide insight into the underlying mechanisms of multistable perceptions.     

Isolation of bright aggregate fluctuations in a multipopulation image correlation spectroscopy system using intensity subtraction

Image correlation spectroscopy allows sensitive measurement of the spatial distribution and aggregation state of fluorescent membrane macro molecules. When studying a single population system (i.e., aggregates of similar brightness), an accurate measure can be made of the aggregate number per observation area, but this measurement becomes much more complex in a distributed population system (i.e., bright and faint aggregates). This article describes an alternate solution that involves extraction of the bright aggregate population information. This novel development for image correlation spectroscopy, termed intensity subtraction analysis, uses sequential uniform intensity subtraction from raw confocal images. Sequential intensity subtraction results in loss of faint aggregate fluctuations that are smaller in magnitude than fluctuations due to the brightest aggregates. The resulting image has correlatable fluctuations originating from only the brightest population, permitting quantification of this population's distribution and further cross-correlation measurements. The feasibility of this technique is demonstrated using fluorescent microsphere images and biological samples. The technique is further used to examine the spatial distribution of a plasma-membrane-labeled fluorescent synthetic ganglioside, and to cross-correlate this probe with various membrane markers. The evidence provided demonstrates that bright aggregates of the fluorescent ganglioside are associated with clathrin-coated pits, membrane microvilli, and detergent-resistant membranes.     

Nanosecond time-resolved emission spectroscopy of a fluorescence probe adsorbed to L-alpha-egg lecithin vesicles.

Nanosecond time-resolved emission spectra (TRES) are fluorescence emission spectra obtained at discrete times during the fluorescence decay. The complete data-set obtainable is a surface representing the intensity at all wavelengths and times during the emission decay time. When 2-p-toluidinonaphthalene-6-sulfonate (2,6 p-TNS) is adsorbed to egg lecithin vesicles, an excited-state reaction associated with energetic changes of the emitting species occurs on the nanosecond time scale. Convolution of the fluorescence decay with the excitation response introduces an artifact in the time-dependent spectra. A precedure is described by which this artifact can be eliminated. The data for the generation of time-resolved emission spectra are obtained with a computer-interfaced instrument based on the single-photon counting method.     

Time-integrated fluorescence cumulant analysis in fluorescence fluctuation spectroscopy

We introduce a new analysis technique for fluorescence fluctuation data. Time-integrated fluorescence cumulant analysis (TIFCA) extracts information from the cumulants of the integrated fluorescence intensity. TIFCA builds on our earlier FCA theory, but in contrast to FCA or photon counting histogram (PCH) analysis is valid for arbitrary sampling times. The motivation for long sampling times lies in the improvement of the signal/noise ratio of the data. Because FCA and PCH theory are not valid in this regime, we first derive a theoretical model of cumulant functions for arbitrary sampling times. TIFCA is the first exact theory that describes the effects of sampling time on fluorescence fluctuation experiments. We calculate factorial cumulants of the photon counts for various sampling times by rebinning of the original data. Fits of the data to models determine the brightness, the occupation number, and the diffusion time of each species. To provide the tools for a rigorous error analysis of TIFCA, expressions for the variance of cumulants are developed and tested. We demonstrate that over a limited range rebinning reduces the relative error of higher order cumulants, and therefore improves the signal/noise ratio. The first four cumulant functions are explicitly calculated and are applied to simple dye systems to test the validity of TIFCA and demonstrate its ability to resolve species.     

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.     

Mapping the number of molecules and brightness in the laser scanning microscope

We describe a technique based on moment-analysis for the measurement of the average number of molecules and brightness in each pixel in fluorescence microscopy images. The average brightness of the particle is obtained from the ratio of the variance to the average intensity at each pixel. To obtain the average number of fluctuating particles, we divide the average intensity at one pixel by the brightness. This analysis can be used in a wide range of concentrations. In cells, the intensity at any given pixel may be due to bright immobile structures, dim fast diffusing particles, and to autofluorescence or scattering. The total variance is given by the variance of each of the above components in addition to the variance due to detector noise. Assuming that all sources of variance are independent, the total variance is the sum of the variances of the individual components. The variance due to the particles fluctuating in the observation volume is proportional to the square of the particle brightness while the variance of the immobile fraction, the autofluorescence, scattering, and that of the detector is proportional to the intensity of these components. Only the fluctuations that depend on the square of the brightness (the mobile particles) will have a ratio of the variance to the intensity >1. Furthermore, changing the fluorescence intensity by increasing the illumination power, distinguishes between these possible contributions. We show maps of molecular brightness and number of cell migration proteins obtained using a two-photon scanning microscope operating with a photon-counting detector. These brightness maps reveal binding dynamics at the focal adhesions with pixel resolution and provide a picture of the binding and unbinding process in which dim molecules attach to the adhesions or large molecular aggregates dissociate from adhesion.     

A retrieval algorithm to evaluate the Photosystem I and Photosystem II spectral contributions to leaf chlorophyll fluorescence at physiological temperatures

A new computational procedure to resolve the contribution of Photosystem I (PSI) and Photosystem II (PSII) to the leaf chlorophyll fluorescence emission spectra at room temperature has been developed. It is based on the Principal Component Analysis (PCA) of the leaf fluorescence emission spectra measured during the OI photochemical phase of fluorescence induction kinetics. During this phase, we can assume that only two spectral components are present, one of which is constant (PSI) and the other variable in intensity (PSII). Application of the PCA method to the measured fluorescence emission spectra of Ficus benjamina L. evidences that the temporal variation in the spectra can be ascribed to a single spectral component (the first principal component extracted by PCA), which can be considered to be a good approximation of the PSII fluorescence emission spectrum. The PSI fluorescence emission spectrum was deduced by difference between measured spectra and the first principal component. A single-band spectrum for the PSI fluorescence emission, peaked at about 735?nm, and a 2-band spectrum with maxima at 685 and 740?nm for the PSII were obtained. A linear combination of only these two spectral shapes produced a good fit for any measured emission spectrum of the leaf under investigation and can be used to obtain the fluorescence emission contributions of photosystems under different conditions. With the use of our approach, the dynamics of energy distribution between the two photosystems, such as state transition, can be monitored in vivo, directly at physiological temperatures. Separation of the PSI and PSII emission components can improve the understanding of the fluorescence signal changes induced by environmental factors or stress conditions on plants.     

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.     

Deconvolving single-molecule intensity distributions for quantitative microscopy measurements

In fluorescence microscopy, images often contain puncta in which the fluorescent molecules are spatially clustered. This article describes a method that uses single-molecule intensity distributions to deconvolve the number of fluorophores present in fluorescent puncta as a way to "count" protein number. This method requires a determination of the correct statistical relationship between the single-molecule and single-puncta intensity distributions. Once the correct relationship has been determined, basis histograms can be generated from the single-molecule intensity distribution to fit the puncta distribution. Simulated data were used to demonstrate procedures to determine this relationship, and to test the methodology. This method has the advantages of single-molecule measurements, providing both the mean and variation in molecules per puncta. This methodology has been tested with the avidin-biocytin binding system for which the best-fit distribution of biocytins in the sample puncta was in good agreement with a bulk determination of the avidin-biocytin binding ratio.     

Molecular Brightness Characterization of EGFP In Vivo by Fluorescence Fluctuation Spectroscopy

We characterize the molecular properties of autofluorescence and transiently expressed EGFP in the nucleus and in the cytoplasm of HeLa cells by fluorescence correlation spectroscopy (FCS) and by photon counting histogram (PCH) analysis. PCH has been characterized and applied in vitro, but its potential for in vivo studies needs to be explored. Thus, this study mainly focuses on the characterization of PCH analysis in vivo. The strength of PCH lies in its ability to distinguish biomolecules by their molecular brightness value. Because the concept of molecular brightness is crucial for PCH analysis, we study the molecular brightness of EGFP and determine the statistical accuracy of its measurement under in vivo conditions. We started by characterizing the influence of autofluorescence on EGFP measurements. We found a molecular brightness of EGFP that is a factor of 10 higher than the brightness of the autofluorescence. Moment analysis demonstrates that the contribution of autofluorescence to fluorescence fluctuation experiments is negligible at EGFP concentrations of one protein per excitation volume. The molecular brightness of EGFP measured in the nucleus, the cytoplasm, and in vitro are identical and our study demonstrates that molecular brightness is a very stable and predictable quantity for cellular measurements. In addition to PCH, we also analyzed the autocorrelation function of EGFP. The diffusion coefficient of EGFP is a factor of 3 lower in vivo than compared to in vitro, and a simple diffusion process describes the autocorrelation function. We found that in the nucleus the fluorescence intensity is stable as a function of time, while measurements in the cytoplasm display fluorescence intensity drifts that complicate the data analysis. We introduce and discuss an analysis method that minimizes the influence of the intensity drifts on PCH analysis. This method allows us to recover the correct molecular brightness of EGFP even in the presence of drifts of the fluorescence intensity signal. We found the molecular brightness of EGFP to be a very robust parameter, and anticipate the use of PCH analysis for the study of oligomerization processes in vivo.     

The use of fractal image statistics in the estimation of lateral spatial extent

It has been argued that the characteristics of many commonly occurring surface textures are such that the resulting luminance distributions have the statistical properties of fractals, over a wide range of spatial scales. We show that, when fractal luminance distributions are spatially filtered, the spatial density of zero-crossings obtained is inversely proportional to the scale of filtering, and is not strongly dependent on the fractal dimension of the pattern used. We propose that this predictable property of natural images could provide a basis for the estimation of lateral spatial extent by counting zero-crossings within an interval at a variety of spatial scales, and averaging over spatial scale. We carried out experiments to compare the relative apparent lateral extents of fractal patterns and patterns of equally spaced bars, as a function of the number of bars. The results are in good agreement with theory.     

Oligomer size of the serotonin 5-hydroxytryptamine 2C (5-HT2C) receptor revealed by fluorescence correlation spectroscopy with photon counting histogram analysis: evidence for homodimers without monomers or tetramers

Fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) are techniques with single molecule sensitivity that are well suited for examining the biophysical properties of protein complexes in living cells. In the present study, FCS and PCH were applied to determine the diffusion coefficient and oligomeric size of G-protein-coupled receptors. FCS was used to record fluctuations in fluorescence intensity arising from fluorescence-tagged 5-hydroxytryptamine 2C (5-HT(2C)) receptors diffusing within the plasma membrane of HEK293 cells and rat hippocampal neurons. Autocorrelation analysis yielded diffusion coefficients ranging from 0.8 to 1.2 μm(2)/s for fluorescence-tagged receptors. Because the molecular brightness of a fluorescent protein is directly proportional to the number of fluorescent proteins traveling together within a protein complex, it can be used to determine the oligomeric size of the protein complex. FCS and PCH analysis of fluorescence-tagged 5-HT(2C) receptors provided molecular brightness values that were twice that of GFP and YFP monomeric controls, similar to a dimeric GFP control, and unaltered by 5-HT. Bimolecular fluorescence complementation of the N- and C-terminal halves of YFP attached to 5-HT(2C) receptors was observed in endoplasmic reticulum/Golgi and plasma membranes with a brightness equal to monomeric YFP. When GFP-tagged 5-HT(2C) receptors were co-expressed with a large excess of untagged, non-fluorescent 5-HT(2C) receptors, the molecular brightness was reduced by half. PCH analysis of the FCS data were best described by a one-component dimer model without monomers or tetramers. Therefore, it is concluded that 5-HT(2C) receptors freely diffusing within the plasma membrane are dimeric.     

Ultra-high resolution imaging by fluorescence photoactivation localization microscopy

Biological structures span many orders of magnitude in size, but far-field visible light microscopy suffers from limited resolution. A new method for fluorescence imaging has been developed that can obtain spatial distributions of large numbers of fluorescent molecules on length scales shorter than the classical diffraction limit. Fluorescence photoactivation localization microscopy (FPALM) analyzes thousands of single fluorophores per acquisition, localizing small numbers of them at a time, at low excitation intensity. To control the number of visible fluorophores in the field of view and ensure that optically active molecules are separated by much more than the width of the point spread function, photoactivatable fluorescent molecules are used, in this case the photoactivatable green fluorescent protein (PA-GFP). For these photoactivatable molecules, the activation rate is controlled by the activation illumination intensity; nonfluorescent inactive molecules are activated by a high-frequency (405-nm) laser and are then fluorescent when excited at a lower frequency. The fluorescence is imaged by a CCD camera, and then the molecules are either reversibly inactivated or irreversibly photobleached to remove them from the field of view. The rate of photobleaching is controlled by the intensity of the laser used to excite the fluorescence, in this case an Ar+ ion laser. Because only a small number of molecules are visible at a given time, their positions can be determined precisely; with only approximately 100 detected photons per molecule, the localization precision can be as much as 10-fold better than the resolution, depending on background levels. Heterogeneities on length scales of the order of tens of nanometers are observed by FPALM of PA-GFP on glass. FPALM images are compared with images of the same molecules by widefield fluorescence. FPALM images of PA-GFP on a terraced sapphire crystal surface were compared with atomic force microscopy and show that the full width at half-maximum of features approximately 86 +/- 4 nm is significantly better than the expected diffraction-limited optical resolution. The number of fluorescent molecules and their brightness distribution have also been determined using FPALM. This new method suggests a means to address a significant number of biological questions that had previously been limited by microscope resolution.