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.     

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.     

Cumulant analysis in fluorescence fluctuation spectroscopy

A novel technique for the analysis of fluorescence fluctuation experiments is introduced. Fluorescence cumulant analysis (FCA) exploits the factorial cumulants of the photon counts and resolves heterogeneous samples based on differences in brightness. A simple analytical model connects the cumulants of the photon counts with the brightness epsilon and the number of molecules N in the optical observation volume for each fluorescent species. To provide the tools for a rigorous error analysis of FCA, expressions for the variance of factorial cumulants are developed and tested. We compare theory with experiment by analyzing dye mixtures and simple fluorophore solutions with FCA. A comparison of FCA with photon-counting histogram (PCH) analysis, a related technique, shows that both methods give identical results within experimental uncertainty. Both FCA and PCH are restricted to data sampling times that are short compared to the diffusion time of molecules through the observation volume of the instrument. But FCA theory, in contrast to PCH, can be extended to treat arbitrary sampling times. Here, we derive analytical expressions for the second factorial cumulant as a function of the sampling time and demonstrate that the theory successfully models fluorescence fluctuation data.     

Visualization of synaptic vesicle movement in intact synaptic boutons using fluorescence fluctuation spectroscopy

Not much is known about the mobility of synaptic vesicles inside small synapses of the central nervous system, reflecting a lack of methods for visualizing these dynamics. We adapted confocal spot detection with fluctuation analysis to monitor the mobility of fluorescently labeled synaptic vesicles inside individual boutons of cultured hippocampal neurons. Using Monte Carlo simulations we were able to propose a simple quantitative model that can describe vesicle mobility in small hippocampal boutons under resting conditions and different pharmacological treatments. We find that vesicle mobility in a time window of 20 s can be well described by caged diffusion (D approximately 5 x 10(-5) microm(2)/s, cage sizes of approximately 50 nm). Mobility can be upregulated by phosphatase blockage and increased further by actin disruption in a dose-dependent manner. Inhibition of the myosin light chain kinase slows down vesicle mobility 10-fold, whereas other kinases like protein kinase C (PKC), A (PKA), and calmodulin kinase II (caMKII) do not affect mobility in unstimulated boutons.     

In vivo quantitative studies of dynamic intracellular processes using fluorescence correlation spectroscopy

It has been a significant challenge to quantitatively study the dynamic intracellular processes in live cells. These studies are essential for a thorough understanding of the underlying mechanisms regulating the signaling pathways and the transitions between cell cycle stages. Our studies of Cdc20, an important mitotic checkpoint protein, throughout the cell cycle demonstrate that fluorescence correlation spectroscopy is a powerful tool for in vivo quantitative studies of dynamic intracellular processes. In this study, Cdc20 is found to be present primarily in a large complex (>1 Mda) during interphase with a diffusion constant of 1.8+/-0.1 microm2/s and a concentration of 76+/-24 nM, consistent with its association with the APC/C. During mitosis, however, a proportion of Cdc20 dissociates from APC/C at a rate of 12 pM/s into a soluble pool with a diffusion constant of 19.5+/-5.0 microm2/s, whose size is most consistent with free Cdc20. This free pool accumulates to 50% of total Cdc20 (approximately 40 nM) during chronic activation of the mitotic checkpoint but disappears during mitotic exit at a rate of 31 pM/s. The observed changes in the biochemical assembly states of Cdc20 closely correlate to the known temporal pattern of the activity of APC/CCdc20 in mitosis. Photon counting histograms reveal that both complexes contain only a single molecule of Cdc20. The underlying mechanisms of the activities of APC/CCdc20 throughout the cell cycle are discussed in light of our experimental observations.     

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.     

Probing ligand protein binding equilibria with fluorescence fluctuation spectroscopy

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.     

Structure and dynamics of lipoplex formation examined using two-photon fluorescence cross-correlation spectroscopy

The conditions required to form transfectable lipoplexes have been extensively studied [Zuhorn, I. S., and Hoekstra, D. (2002) J. Membr. Biol. 189, 167-179]. However, to date, experiments have not addressed either the order of events of lipoplex formation in solution or the maximum number of DNA molecules per vesicle in stable single-vesicle lipoplexes. In this study, we have employed two-photon excitation fluorescence correlation spectroscopy (TPE-FCS) and two-photon fluorescence cross-correlation spectroscopy (TPE-XCS) to examine both fluorescence-labeled DNA and cationic vesicle structure and dynamics simultaneously. The dependence of large aggregated lipoplex formation on DNA-to-cationic lipid charge ratio was determined, as was the maximum number of 40 bp double-stranded DNA oligonucleotides able to bind to a single vesicle.     

Stochastic fractal behavior in concentration fluctuation and fluorescence correlation spectroscopy.

Fluctuations in the concentration of Brownian particles in one and two dimensions, or any reasonable measurement of the concentration such as in fluorescence correlation spectroscopy, is shown to be a stochastic fractal with a long tail. Being singular at omega = 0, the power spectrum of the fluctuation S(omega) approximately omega-1/2 for diffusion in one dimension, approximately log omega in two dimensions, but non-singular in three dimensions. This discovery provides one simple physical mechanism for possible long-memory fractal behavior, and its implications to various biological processes are discussed.     

DNA-induced polymerization of HIV-1 integrase analyzed with fluorescence fluctuation spectroscopy

Human immunodeficiency virus type 1 (HIV-1) integrase is essential for viral replication. Integrase inserts the viral DNA into the host DNA. We studied the association of integrase to fluorescently labeled oligonucleotides using fluorescence correlation spectroscopy. The binding of integrase to the fluorescent oligonucleotides resulted in the appearance of bright spikes during fluorescence correlation spectroscopy measurements. These spikes arise from the formation of high molecular mass protein-DNA complexes. The fluorescence of the free DNA was separated from the spikes with a statistical method. From the decrease of the concentration of free oligonucleotides, a site association constant was determined. The DNA-protein complexes were formed rapidly in a salt-dependent manner with site association constants ranging between 5 and 40 microm(-1) under different conditions. We also analyzed the kinetics of the DNA-protein complex assembly and the effect of different buffer components. The formation of the fluorescent protein-DNA complex was inhibited by guanosine quartets, and the inhibition constant was determined at 1.8 +/- 0.6 x 10(8) m(-1). Displacement of bound DNA with G-quartets allowed the determination of the dissociation rate constant and proves the reversibility of the association process.     

Molecular heterogeneity of O-acetylserine sulfhydrylase by two-photon excited fluorescence fluctuation spectroscopy

O-acetylserine sulfhydrylase, a homo-dimeric enzyme from Salmonella typhimurium, covalently binds one pyridoxal 5'-phosphate molecule per subunit as a fluorescent coenzyme. Different tautomers of the Schiff base between the coenzyme and lysine 41 generate structured absorption and fluorescence spectra upon one-photon excitation. We investigated the protein population heterogeneity by fluorescence correlation spectroscopy and lifetime techniques upon two-photon excitation. We sampled the fluorescence intensity from a small number of molecules (approximately 10) and analyzed the distribution of photon counts to separately determine the number and the fluorescence brightness of excited protein molecules. The changes in the average number of molecules and in the fluorescence brightness with the excitation wavelength indicate the presence of at least two fluorescent species, with two-photon excitation maxima at 660 and 800 nm. These species have been identified as the enolimine and ketoenamine tautomers of the protein-coenzyme internal aldimine. Their relative abundance is estimated to be 4:1, whereas the ratio of their two-photon cross sections is reversed with respect to the single-photon excitation case. Consistent results are obtained from the measurement of the lifetime decays, which are sensitive to the excited-state heterogeneity. At least two components were detected, with lifetimes of approximately 2.5 and 0.5 ns. The lifetimes are very close to the values measured in bulk solutions upon one-photon excitation and attributed to the ketoenamine tautomer and to a dipolar species formed upon proton dissociation in the excited state.     

Characterization of cytoplasmic Gag-gag interactions by dual-color z-scan fluorescence fluctuation spectroscopy

Fluorescence fluctuation spectroscopy (FFS) quantifies the interactions of fluorescently-labeled proteins inside living cells by brightness analysis. However, the study of cytoplasmic proteins that interact with the plasma membrane is challenging with FFS. If the cytoplasmic section is thinner than the axial size of the observation volume, cytoplasmic and membrane-bound proteins are coexcited, which leads to brightness artifacts. This brightness bias, if not recognized, leads to erroneous interpretation of the data. We have overcome this challenge by introducing dual-color z-scan FFS and the addition of a distinctly colored reference protein. Here, we apply this technique to study the cytoplasmic interactions of the Gag proteins from human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type 1 (HTLV-1). The Gag protein plays a crucial role in the assembly of retroviruses and is found in both membrane and cytoplasm. Dual-color z-scans demonstrate that brightness artifacts are caused by a dim nonpunctate membrane-bound fraction of Gag. We perform an unbiased brightness characterization of cytoplasmic Gag by avoiding the membrane-bound fraction and reveal previously unknown differences in the behavior of the two retroviral Gag species. HIV-1 Gag exhibits concentration-dependent oligomerization in the cytoplasm, whereas HTLV-1 Gag lacks significant cytoplasmic Gag-Gag interactions.     

The photon counting histogram in fluorescence fluctuation spectroscopy with non-ideal photodetectors

Fluorescence fluctuation spectroscopy utilizes the signal fluctuations of single molecules for studying biological processes. Information about the biological system is extracted from the raw data by statistical methods such as used in fluctuation correlation spectroscopy or photon counting histogram (PCH) analysis. Since detectors are never ideal, it is crucial to understand the influence of photodetectors on signal statistics to correctly interpret the experimental data. Here we focus on the effects of afterpulsing and detector dead-time on PCH statistics. We determine the dead-time and afterpulse probability for our detectors experimentally and show that afterpulsing can be neglected for most experiments. Dead-time effects on the PCH are concentration-dependent and become significant when more than one molecule is present in the excitation volume. We develop a new PCH theory that includes dead-time effects and verify it experimentally. Additionally, we derive a simple analytical expression that accurately predicts the effect of dead-time on the molecular brightness. Corrections for non-ideal detector effects extend the useful concentration range of PCH experiments and are crucial for the interpretation of titration and dilution experiments.     

Observation volumes and {gamma}-factors in two-photon fluorescence fluctuation spectroscopy

Fluorescence fluctuation spectroscopy has become an important measurement tool for investigating molecular dynamics, molecular interactions, and chemical kinetics in biological systems. Although the basic theory of fluctuation spectroscopy is well established, it is not widely recognized that saturation of the fluorescence excitation can dramatically alter the size and profile of the fluorescence observation volume from which fluorescence fluctuations are measured, even at relatively modest excitation levels. A precise model for these changes is needed for accurate analysis and interpretation of fluctuation spectroscopy data. We here introduce a combined analytical and computational approach to characterize the observation volume under saturating conditions and demonstrate how the variation in the volume is important in two-photon fluorescence correlation spectroscopy. We introduce a simple approach for analysis of fluorescence correlation spectroscopy data that can fully account for the effects of saturation, and demonstrate its success for characterizing the observed changes in both the amplitude and relaxation timescale of measured correlation curves. We also discuss how a quantitative model for the observed phenomena may be of broader importance in fluorescence fluctuation spectroscopy.     

Accessing molecular dynamics in cells by fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) analyzes spontaneous fluctuations in the fluorescence emission of small molecular ensembles, thus providing information about a multitude of parameters, such as concentrations, molecular mobility and dynamics of fluorescently labeled molecules. Performed within diffraction-limited confocal volume elements, FCS provides an attractive alternative to photobleaching recovery methods for determining intracellular mobility parameters of very low quantities of fluorophores. Due to its high sensitivity sufficient for single molecule detection, the method is subject to certain artifact hazards that must be carefully controlled, such as photobleaching and intramolecular dynamics, which introduce fluorescence flickering. Furthermore, if molecular mobility is to be probed, nonspecific interactions of the labeling dye with cellular structures can introduce systematic errors. In cytosolic measurements, lipophilic dyes, such as certain rhodamines that bind to intracellular membranes, should be avoided. To study free diffusion, genetically encoded fluorescent labels such as green fluorescent protein (GFP) or DsRed are preferable since they are less likely to nonspecifically interact with cellular substructures.     

Endothelin receptor in virus-like particles: ligand binding observed by fluorescence fluctuation spectroscopy

The functional analysis of transmembrane receptor proteins is frequently hampered by the difficulty to produce sufficiently homogeneous receptor preparations that preserve the physiological biomembrane integration of the receptor protein. To improve the receptor protein density in the lipid bilayer and to maintain the physiological lipid-protein environment, a novel method has been established that enables the selective integration of transmembrane receptors into a virus-like particle (VLiP). Here we have studied the binding of tetramethylrhodamine-labeled endothelin-1 (TMR-ET-1) to VLiP-integrated endothelin A receptor (ET(A)R) by fluorescence fluctuation spectroscopy. The concentration of TMR-ET-1 was determined by fluorescence correlation spectroscopy (FCS). These measurements also confirmed that the free ligand is monomeric in solution in our experiments. Fluorescence intensity distribution analysis (FIDA) was used to quantify the fraction of ligands bound to ET(A)Rs in the VLiPs. For the interaction between ET-1 and VLiP-integrated ET(A)Rs, K(D) values of 0.5 nM and 0.3 nM were determined from ligand and receptor titration experiments, respectively. For comparison, a FIDA analysis was also carried out with ET(A)Rs in membrane fragments derived from an ET(A)R-overexpressing mammalian cell line, which yielded a similar K(D) of 0.2 nM. In addition, we examined the binding competition of a set of reference compounds to VLiP-ET(A)Rs in the presence of ET-1 and obtained K(i) values similar to those reported in the literature. Our results demonstrate that integration into VLiPs does not change the binding properties of the ET(A)Rs. FIDA analysis of VLiP-integrated receptors shows great promise for highly miniaturized and fast compound testing in the pharmaceutical industry.     

Quantifying HTLV-I dynamics

Despite significant advances in our understanding of the immune response to persistent viruses like human T-cell lymphotropic virus type I (HTLV-I), many important questions remain unanswered. Mathematical modelling enables us to interpret and synthesise diverse experimental data in new ways and thus can contribute to our understanding. Here, we review recent advances in mathematical modelling of HTLV-I infection and illustrate how mathematics has enabled us to identify factors that determine an individual's viral burden and risk of developing HTLV-I-associated diseases.     

Fluorescence fluctuation spectroscopy.

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

Fluorescence 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.