Fluorescence Fluctuation Experiments Research Articles

Protein oligomerization and mobility within the nuclear envelope evaluated by the time-shifted mean-segmented Q factor

Analysis of fluorescence fluctuation experiments by the mean-segmented Q (MSQ) method was recently used to successfully characterize the oligomeric state and mobility of proteins within the nuclear envelope (NE) of living cells. However, two significant shortcomings of MSQ were recognized. Non-ideal detector behavior due to dead-time and afterpulsing as well as the lack of error analysis currently limit the potential of MSQ. This paper presents time-shifted MSQ (tsMSQ), a new formulation of MSQ that is robust with respect to dead-time and afterpulsing. In addition, a protocol for performing error analysis on tsMSQ data is introduced to assess the quality of fit models and estimate the uncertainties of fit parameters. Together, these developments significantly simplify and improve the analysis of fluorescence fluctuation data taken within the NE. To demonstrate these new developments, tsMSQ was used to characterize the oligomeric state and mobility of the luminal domains of two inner nuclear membrane SUN proteins. The results for the luminal domain of SUN2 obtained through tsMSQ without correction for non-ideal detector effects agree with a recent study that was conducted using the original MSQ formulation. Finally, tsMSQ was applied to characterize the oligomeric state and mobility of the luminal domain of the germline-restricted SUN3.

Quantitative Brightness Analysis of Protein Oligomerization in the Nuclear Envelope

Brightness analysis of fluorescence fluctuation experiments has been used to successfully measure the oligomeric state of proteins at the plasma membrane, in the nucleoplasm, and in the cytoplasm of living cells. Here we extend brightness analysis to the nuclear envelope (NE), a double membrane barrier separating the cytoplasm from the nucleoplasm. Results obtained by applying conventional brightness analysis to fluorescently tagged proteins within the NE exhibited an unusual concentration dependence. Similarly, the autocorrelation function of the fluorescence fluctuations exhibited unexpected changes with protein concentration. These observations motivated the application of mean-segmented Q analysis, which identified the existence of a fluctuation process distinct from molecular diffusion in the NE. We propose that small changes in the separation of the inner and outer nuclear membrane are responsible for the additional fluctuation process, as suggested by results obtained for luminal and nuclear membrane-associated EGFP-tagged proteins. Finally, we applied these insights to study the oligomerization of the luminal domains of two nuclear membrane proteins, nesprin-2 and SUN2, which interact transluminally to form a nuclear envelope-spanning linker molecular bridge known as the linker of the nucleoskeleton and cytoskeleton complex.

Characterization of Ternary Protein Systems In Vivo with Tricolor Heterospecies Partition Analysis

Tools and assays that characterize protein-protein interactions are of fundamental importance to biology, because protein assemblies play a critical role in the control and regulation of nearly every cellular process. The availability of fluorescent proteins has facilitated the direct and real-time observation of protein-protein interactions inside living cells, but existing methods are mostly limited to binary interactions between two proteins. Because of the scarcity of techniques capable of identifying ternary interactions, we developed tricolor heterospecies partition analysis. The technique is based on brightness analysis of fluorescence fluctuations from three fluorescent proteins that serve as protein labels. We identified three fluorescent proteins suitable for tricolor brightness experiments. In addition, we developed the theory of identifying interactions in a ternary protein system using tricolor heterospecies partition analysis. The theory was verified by experiments on well-characterized protein systems. A graphical representation of the heterospecies partition data was introduced to visualize interactions in ternary protein systems. Lastly, we performed fluorescence fluctuation experiments on cells expressing a coactivator and two nuclear receptors and applied heterospecies partition analysis to explore the interactions of this ternary protein system.

The statistics of protein expression ratios for cellular fluorescence studies

Fluorescence studies of cellular protein-protein interactions commonly employ transient cotransfection to express two proteins carrying distinct fluorescent labels. Because transiently transfected cells differ significantly in their expression level, the concentration ratio of the two expressed proteins varies, which in turn influences the measured fluorescence signal. Knowledge of the statistics of protein expression ratios is of considerable interest both from a fundamental point of view and for cellular fluorescence studies. Despite the perceived randomness of transient transfection, we were able to develop a quantitative model that describes the average and distribution of the protein expression ratio from a cell population. We show that the expression ratio is proportional to the molar plasmid ratio and relate the distribution to the finite number of active plasmids in the cell. The process of cationic lipid-mediated transfection is explored in more detail. Specifically, the influence of lipoplexes on the statistics of the expression ratio is examined. We further demonstrate that the transfection model provides a quantitative description of fluorescence fluctuation experiments, where only a fraction of the proteins are labeled.

Quantifying Ternary Protein Expression Fractions using Three-Channel Fluorescence Fluctuation Spectroscopy

Fluorescence studies of cellular protein-protein interactions commonly employ transient transfection to express proteins carrying distinct fluorescent labels. Because transiently transfected cells differ significantly in their expression level, the concentration ratio of the expressed proteins varies, which in turn influences the measured fluorescence signal. Knowledge of the statistics of protein expression ratios, which currently is not well understood, is of considerable interest both from a fundamental point of view and for cellular fluorescence studies. Despite the perceived randomness of transient transfection, we recently succeeded in developing a model that describes the distribution and the average of the protein expression ratio for the coexpression of two proteins. Here we extend our previous work to the simultaneous coexpression of three proteins, where each protein species is labeled with a distinctly colored fluorescent protein. All protein species are simultaneously excited using two-photon absorption. The fluorescence of the protein mixture is split according to color into three detection channels. Brightness measurements of the individual proteins combined with intensity ratio data between detection channels is used to identify the protein expression ratios of all three proteins. We examine the relationship between DNA-plasmid fractions and protein expression fractions. In addition, we quantify the cell-to-cell scatter in the protein expression ratios for different transfection protocols in order to identify the best conditions for three-color fluorescence fluctuation experiments. This work was supported by grants from the National Institutes of Health (GM64589) and the National Science Foundation (PHY 0346782).

Circumvention of fluorophore photobleaching in fluorescence fluctuation experiments: a beam scanning approach.

Photobleaching is a fluorophore-damaging process that commonly afflicts single-molecule fluorescence studies. It becomes an especially severe problem in fluorescence fluctuation experiments when studying slowly diffusing particles. One way to circumvent this problem is to use beam scanning to decrease the residence time of the fluorophores in the excitation volume. We report a systematic study of the effects of circular beam scanning on the photobleaching of fluorescent particles as observed in single-photon excitation fluorescence fluctuation experiments. We start by deriving a simple expression relating the average detected fluorescence to the photobleaching cross section of the fluorophores. We then perform numerical calculations of the spatial distribution of fluorescent particles in order to understand under which conditions beam scanning can prevent the formation of a photobleaching hole. To support these predictions, we show experimental results obtained for large unilamellar vesicles containing a small amount of the fluorescent lipophilic tracer DiD. We establish the required scanning radius and frequency range in order to obtain sufficient reduction of the photobleaching effect for that system. From the detected increase in fluorescence upon increase in scanning speed, we estimate the photobleaching cross section of DiD.

Quantitative determination of the single-molecule detection regime in fluorescence fluctuation microscopy by means of photon counting histogram analysis

Fluorescence fluctuation experiments are performed in single-molecule detection regime if the fluorescence of at most one molecule is registered at a time. Although the significance of such experiments for investigations of complex nonergodic systems like those met in the biosciences has been stressed out by many scientists, the quantitative and accurate determination of the single-molecule detection regime received rather little attention. In this work we present a method based on the photon counting histogram (PCH) analysis, which enables the determination of the average number N of molecules within the observation volume, for which only the fluorescence of individual molecules is detected at a time. Thus, the accurate design of fluorescence fluctuation experiments performed in single-molecule detection regime is possible. Demonstrative fluorescence fluctuation experiments based on two-photon excitation are performed on diluted solutions of coumarin 153, in order to verify the potential of the PCH analysis in experiments on the single-molecule detection level. If the mean number N of molecules within the excitation volume is larger than 0.048, the probability to simultaneously detect the fluorescence of two or more molecules is no longer negligible, i.e., no single-molecule detection regime. If the mean number N of molecules is lower than 0.0057, the detection limit of the method is reached, i.e., the fluorescence signal cannot be distinguished from the background. Consequently, the concentration of coumarin 153 characteristic for the single-molecule detection regime lies in the range 13-110 pmol/l for the given experimental conditions. We also investigate the influence of the molecular brightness, i.e., detected photons per fluorophore molecule and sampling time, on the single-molecule detection regime.

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.

Dual-Color Photon-Counting Histogram

We report on the development of dual-color photon-counting histogram (PCH) analysis. Dual-color PCH is an extension of regular PCH and considers the photon counts received in two detection channels instead of one. Because each detection channel records a different color, dual-color PCH distinguishes fluorescent species not only by differences in their brightness, but also according to their color. The additional discrimination by color increases the sensitivity of PCH in resolving a mixture of species considerably. Most dual-color fluorescence fluctuation experiments are performed on fluorophores with overlapping emission spectra. This overlap results in spectral cross talk between the detector channels, which reduces resolvability. Here, we demonstrate that dual-color PCH is able to resolve binary dye mixtures in the presence of cross talk from a single measurement without any additional information about the sample. We discuss the effect of sampling time on the fit parameters of dual-color PCH. Differences between dual-color fluorescence correlation spectroscopy and dual-color PCH will also be addressed. We quantitatively resolve a mixture of the two fluorescent proteins CFP and YFP, which is challenging because of the strong spectral overlap of their emission spectra. Dichroic mirrors are needed to direct the light into the two detection channels. We quantify the influence of these filters on dual-color PCH analysis and determine the optimal transition wavelength of the dichroic mirror for the CFP-YFP pair.

High-pressure cell for fluorescence fluctuation spectroscopy

We introduce a high-pressure cell for fluorescence fluctuation spectroscopy. The pressure cell consists of a cylindrical, fused silica microcapillary and a modified pressure plug, which connects the cell to a pressure generating apparatus. The capillary serves both as the body and the optical window of the cell. The pressure cell is mounted onto the stage of an optical microscope. The small diameter of the capillary allows the use of high numerical aperture objectives, which are required for fluorescence fluctuation experiments. The pressure stability of the cell has been tested up to 4 kbar. We performed two-photon excitation experiments on simple dyes as a function of pressure. The diffusion coefficient was determined by fluorescence correlation spectroscopy. We also used the same cell to measure the pressure dependence of fluorescence lifetimes.

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 ɛ 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.

High-Pressure Fluorescence Correlation Spectroscopy

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 300MPa. 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.

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.

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.

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 N¯. 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 ϵ. 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.

Statistical accuracy in fluorescence fluctuation experiments

The mathematical expression of the signal to noise ratio in fluorescence fluctuation experiments is derived for arbitrary sample profiles and for any mechanism of translational motion, and experimentally verified. The signal to noise ratio depends on the mean count rate per particle per dwell time, the mean number of particles per sample volume, time characteristics of the correlation function, sample profile characteristics, and the data collection time. Statistical accuracy of the third order moment of fluorescence intensity fluctuations is also studied. The optimum concentration for the third order moment analysis is about one particle per sample volume.