Exploring the Dynamics of Cell Processes through Simulations of Fluorescence Microscopy Experiments

Fluorescence correlation spectroscopy (FCS) methods are powerful tools for unveiling the dynamical organization of cells. For simple cases, such as molecules passively moving in a homogeneous media, FCS analysis yields analytical functions that can be fitted to the experimental data to recover the phenomenological rate parameters. Unfortunately, many dynamical processes in cells do not follow these simple models, and in many instances it is not possible to obtain an analytical function through a theoretical analysis of a more complex model. In such cases, experimental analysis can be combined with Monte Carlo simulations to aid in interpretation of the data. In response to this need, we developed a method called FERNET (Fluorescence Emission Recipes and Numerical routines Toolkit) based on Monte Carlo simulations and the MCell-Blender platform, which was designed to treat the reaction-diffusion problem under realistic scenarios. This method enables us to set complex geometries of the simulation space, distribute molecules among different compartments, and define interspecies reactions with selected kinetic constants, diffusion coefficients, and species brightness. We apply this method to simulate single- and multiple-point FCS, photon-counting histogram analysis, raster image correlation spectroscopy, and two-color fluorescence cross-correlation spectroscopy. We believe that this new program could be very useful for predicting and understanding the output of fluorescence microscopy experiments.     

Simultaneous diffusion and brightness measurements and brightness profile visualization from single fluorescence fluctuation traces of GFP in living cells

Fluorescence correlation spectroscopy (FCS) and photon-counting histogram (PCH) analysis use the same experimental fluorescence intensity fluctuations, but each analytical method focuses on a different property of the signal. The time-dependent decay of the correlation of fluorescence fluctuations is measured in FCS yielding, for instance, molecular diffusion coefficients. The amplitude distribution of these fluctuations is calculated by PCH analysis yielding information about the molecular brightness of fluorescent species. Analysis of both FCS and PCH results in the molecular concentration of the sample. Using a previously described global analysis procedure we report here precise, simultaneous measurements of diffusion constants and brightness values from single fluorescence fluctuation traces of green-fluorescent protein (GFP, S65T) in the cytoplasm of Dictyostelium cells. The use of a polynomial profile in PCH analysis, describing the detected three-dimensional shape of the confocal volume, enabled us to obtain well fitting results for GFP in cells. We could visualize the polynomial profile and show its deviation from a Gaussian profile.     

Fluorescence correlation spectroscopy and quantitative cell biology

Fluorescence correlation spectroscopy (FCS) analyzes fluctuations in fluorescence within a small observation volume. Autocorrelation analysis of FCS fluctuation data can be used to measure concentrations, diffusion properties, and kinetic constants for individual fluorescent molecules. Photon count histogram analysis of fluorescence fluctuation data can be used to study oligomerization of individual fluorescent molecules. If the FCS observation volume is positioned inside a living cell, these parameters can be measured in vivo. FCS can provide the requisite quantitative data for analysis of molecular interaction networks underlying complex cell biological processes.     

Fluorescence fluctuation spectroscopy: ushering in a new age of enlightenment for cellular dynamics

Originally developed for applications in physics and physical chemistry, fluorescence fluctuation spectroscopy is becoming widely used in cell biology. This review traces the development of the method and describes some of the more important applications. Specifically, the methods discussed include fluorescence correlation spectroscopy (FCS), scanning FCS, dual color cross-correlation FCS, the photon counting histogram and fluorescence intensity distribution analysis approaches, the raster scanning image correlation spectroscopy method, and the Number and Brightness technique. The physical principles underlying these approaches will be delineated, and each of the methods will be illustrated using examples from the literature.     

Paxillin dynamics measured during adhesion assembly and disassembly by correlation spectroscopy

Paxillin is an adaptor molecule involved in the assembly of focal adhesions. Using different fluorescence fluctuation approaches, we established that paxillin-EGFP is dynamic on many timescales within the cell, ranging from milliseconds to seconds. In the cytoplasmic regions, far from adhesions, paxillin is uniformly distributed and freely diffusing as a monomer, as determined by single-point fluctuation correlation spectroscopy and photon-counting histogram analysis. Near adhesions, paxillin dynamics are reduced drastically, presumably due to binding to protein partners within the adhesions. The photon-counting histogram analysis of the fluctuation amplitudes reveals that this binding equilibrium in new or assembling adhesions is due to paxillin monomers binding to quasi-immobile structures, whereas in disassembling adhesions or regions of adhesions, the equilibrium is due to exchange of large aggregates. Scanning fluctuation correlation spectroscopy and raster-scan image correlation spectroscopy analysis of laser confocal images show that the environments within adhesions are heterogeneous. Relatively large adhesions appear to slide transversally due to a treadmilling mechanism through the addition of monomeric paxillin at one side and removal of relatively large aggregates of proteins from the retracting edge. Total internal reflection microscopy performed with a fast acquisition EM-CCD camera completes the overall dynamic picture and adds details of the heterogeneous dynamics across single adhesions and simultaneous bursts of activity at many adhesions across the cell.     

Characterization of brightness and stoichiometry of bright particles by flow-fluorescence fluctuation spectroscopy

Characterization of bright particles at low concentrations by fluorescence fluctuation spectroscopy (FFS) is challenging, because the event rate of particle detection is low and fluorescence background contributes significantly to the measured signal. It is straightforward to increase the event rate by flow, but the high background continues to be problematic for fluorescence correlation spectroscopy. Here, we characterize the use of photon-counting histogram analysis in the presence of flow. We demonstrate that a photon-counting histogram efficiently separates the particle signal from the background and faithfully determines the brightness and concentration of particles independent of flow speed, as long as undersampling is avoided. Brightness provides a measure of the number of fluorescently labeled proteins within a complex and has been used to determine stoichiometry of protein complexes in vivo and in vitro. We apply flow-FFS to determine the stoichiometry of the group specific antigen protein within viral-like particles of the human immunodeficiency virus type-1 from the brightness. Our results demonstrate that flow-FFS is a sensitive method for the characterization of complex macromolecular particles at low concentrations.     

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.     

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.     

Cellular characterization of adenylate kinase and its isoform: two-photon excitation fluorescence imaging and fluorescence correlation spectroscopy

Adenylate kinase (AK) is a ubiquitous enzyme that regulates the homeostasis of adenine nucleotides in the cell. AK1beta (long form) from murine cells shares the same protein sequence as AK1 (short form) except for the addition of 18 amino acid residues at its N-terminus. It is hypothesized that these residues serve as a signal for protein lipid modification and targeting of the protein to the plasma membrane. To better understand the cellular function of these AK isoforms, we have used several modern fluorescence techniques to characterize these two isoforms of AK enzyme. We fused cytosolic adenylate kinase (AK1) and its isoform (AK1beta) with enhanced green fluorescence protein (EGFP) and expressed the chimera proteins in HeLa cells. Using two-photon excitation scanning fluorescence imaging, we were able to directly visualize the localization of AK1-EGFP and AK1beta-EGFP in live cells. AK1beta-EGFP mainly localized on the plasma membrane, whereas AK1-EGFP distributed throughout the cell except for trace amounts in the nuclear membrane and some vesicles. We performed fluorescence correlation spectroscopy measurements and photon-counting histogram analysis in specific domains of live cells. For AK1-EGFP, we observed only one diffusion component in the cytoplasm. For AK1beta-EGFP, we observed two distinct diffusion components on the plasma membrane. One corresponded to the free diffusing protein, whereas the other represented the membrane-bound AK1beta-EGFP. The diffusion rate of AK1-EGFP was slowed by a factor of 1.8 with respect to that of EGFP, which was 50% more than what we would expect for a free diffusing AK1-EGFP. To rule out the possibility of oligomer formation, we performed photon-counting histogram analysis to direct analyze the brightness difference between AK1-EGFP and EGFP. From our analysis, we concluded that cytoplasmic AK1-EGFP is monomeric. fluorescence correlation spectroscopy proved to be a powerful technique for quantitatively studying the mobility of the target protein in live cells. This technology offers advantages in studying protein interactions and function in the cell.     

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.     

Fluorescence correlation spectroscopy for the detection and study of single molecules in biology

The recent development of single molecule detection techniques has opened new horizons for the study of individual macromolecules under physiological conditions. Conformational subpopulations, internal dynamics and activity of single biomolecules, parameters that have so far been hidden in large ensemble averages, are now being unveiled. Herein, we review a particular attractive solution-based single molecule technique, fluorescence correlation spectroscopy (FCS). This time-averaging fluctuation analysis which is usually performed in Confocal setups combines maximum sensitivity with high statistical confidence. FCS has proven to be a very versatile and powerful tool for detection and temporal investigation of biomolecules at ultralow concentrations on surfaces, in solution, and in living cells. The introduction of dual-color cross-correlation and two-photon excitation in FCS experiments is currently increasing the number of promising applications of FCS to biological research.     

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.     

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.     

Fluorescence correlation spectroscopy diffusion laws to probe the submicron cell membrane organization

To probe the complexity of the cell membrane organization and dynamics, it is important to obtain simple physical observables from experiments on live cells. Here we show that fluorescence correlation spectroscopy (FCS) measurements at different spatial scales enable distinguishing between different submicron confinement models. By plotting the diffusion time versus the transverse area of the confocal volume, we introduce the so-called FCS diffusion law, which is the key concept throughout this article. First, we report experimental FCS diffusion laws for two membrane constituents, which are respectively a putative raft marker and a cytoskeleton-hindered transmembrane protein. We find that these two constituents exhibit very distinct behaviors. To understand these results, we propose different models, which account for the diffusion of molecules either in a membrane comprising isolated microdomains or in a meshwork. By simulating FCS experiments for these two types of organization, we obtain FCS diffusion laws in agreement with our experimental observations. We also demonstrate that simple observables derived from these FCS diffusion laws are strongly related to confinement parameters such as the partition of molecules in microdomains and the average confinement time of molecules in a microdomain or a single mesh of a meshwork.     

Studying slow membrane dynamics with continuous wave scanning fluorescence correlation spectroscopy

Here we discuss the application of scanning fluorescence correlation spectroscopy (SFCS) using continuous wave excitation to analyze membrane dynamics. The high count rate per molecule enables the study of very slow diffusion in model and cell membranes, as well as the application of two-foci fluorescence cross-correlation spectroscopy for parameter-free determination of diffusion constants. The combination with dual-color fluorescence cross-correlation spectroscopy with continuous or pulsed interleaved excitation allows binding studies on membranes. Reduction of photobleaching, higher reproducibility, and stability compared to traditional FCS on membranes, and the simple implementation in a commercial microscopy setup make SFCS a valuable addition to the pool of fluorescence fluctuation techniques.     

Fluorescence correlation spectroscopy in biology,chemistry, and medicine

This review describes the method of fluorescence correlation spectroscopy (FCS) and its applications. FCS is used for investigating processes associated with changes in the mobility of molecules and complexes and allows researchers to study aggregation of particles, binding of fluorescent molecules with supramolecular complexes, lipid vesicles, etc. The size of objects under study varies from a few angstroms for dye molecules to hundreds of nanometers for nanoparticles. The described applications of FCS comprise various fields from simple chemical systems of solution/micelle to sophisticated regulations on the level of living cells. Both the methodical bases and the theoretical principles of FCS are simple and available. The present review is concentrated preferentially on FCS applications for studies on artificial and natural membranes. At present, in contrast to the related approach of dynamic light scattering, FCS is poorly known in Russia, although it is widely employed in laboratories of other countries. The goal of this review is to promote the development of FCS in Russia so that this technique could occupy the position it deserves in modern Russian science.     

Defining the Subcellular Interface of Nanoparticles by Live-Cell Imaging

Understanding of nanoparticle-bio-interactions within living cells requires knowledge about the dynamic behavior of nanomaterials during their cellular uptake, intracellular traffic and mutual reactions with cell organelles. Here, we introduce a protocol of combined kinetic imaging techniques that enables investigation of exemplary fluorochrome-labelled nanoparticles concerning their intracellular fate. By time-lapse confocal microscopy we observe fast, dynamin-dependent uptake of polystyrene and silica nanoparticles via the cell membrane within seconds. Fluorescence recovery after photobleaching (FRAP) experiments reveal fast and complete exchange of the investigated nanoparticles at mitochondria, cytoplasmic vesicles or the nuclear envelope. Nuclear translocation is observed within minutes by free diffusion and active transport. Fluorescence correlation spectroscopy (FCS) and raster image correlation spectroscopy (RICS) indicate diffusion coefficients of polystyrene and silica nanoparticles in the nucleus and the cytoplasm that are consistent with particle motion in living cells based on diffusion. Determination of the apparent hydrodynamic radii by FCS and RICS shows that nanoparticles exert their cytoplasmic and nuclear effects mainly as mobile, monodisperse entities. Thus, a complete toolkit of fluorescence fluctuation microscopy is presented for the investigation of nanomaterial biophysics in subcellular microenvironments that contributes to develop a framework of intracellular nanoparticle delivery routes.     

Dynamics of fluorescence marker concentration as a probe of mobility.

We have developed an effective experimental system for the characterization of molecular and structural mobility. It incorporates a modified fluorescence microscope geometry and a variety of analytical techniques to measure effective diffusion coefficients ranging over almost six orders of magnitude, from less than 10(-11) cm2/s to greater than 10(-6) cm2/s. Two principal techniques, fluorescence correlation spectroscopy (FCS) and fluorescence photobleaching recovery (FPR), are employed. In the FPR technique, translational transport rates are measured by monitoring the evolution of a spatial inhomogeneity of fluorescence that is produced photochemically in a microscopic volume by a short burst of intense laser radiation. In contrast, FCS uses laser-induced fluorescence to probe the spontaneous concentration fluctuations in microscopic sample volumes. The kinetics are analyzed by computing time-correlation functions of the stochastic fluctuations of the measured fluorescence intensity. The optical system and digital photocount correlator designed around a dedicated minicomputer are described and discussed. The general power of these techniques is demonstrated with examples from studies conducted on bulk solutions, lipid bilayer membranes, and mammalian cell plasma membranes.     

Fluorescence correlation spectroscopy, combined with bimolecular fluorescence complementation, reveals the effects of β-arrestin complexes and endocytic targeting on the membrane mobility of neuropeptide Y receptors

Fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) analysis are powerful ways to study mobility and stoichiometry of G protein coupled receptor complexes, within microdomains of single living cells. However, relating these properties to molecular mechanisms can be challenging. We investigated the influence of β-arrestin adaptors and endocytosis mechanisms on plasma membrane diffusion and particle brightness of GFP-tagged neuropeptide Y (NPY) receptors. A novel GFP-based bimolecular fluorescence complementation (BiFC) system also identified Y1 receptor-β-arrestin complexes. Diffusion co-efficients (D) for Y1 and Y2-GFP receptors in HEK293 cell plasma membranes were 2.22 and 2.15 × 10(-9)cm(2)s(-1) respectively. At a concentration which promoted only Y1 receptor endocytosis, NPY treatment reduced Y1-GFP motility (D 1.48 × 10(-9)cm(2)s(-1)), but did not alter diffusion characteristics of the Y2-GFP receptor. Agonist induced changes in Y1 receptor motility were inhibited by mutations (6A) which prevented β-arrestin recruitment and internalisation; conversely they became apparent in a Y2 receptor mutant with increased β-arrestin affinity. NPY treatment also increased Y1 receptor-GFP particle brightness, changes which indicated receptor clustering, and which were abolished by the 6A mutation. The importance of β-arrestin recruitment for these effects was illustrated by reduced lateral mobility (D 1.20-1.33 × 10(-9)cm(2)s(-1)) of Y1 receptor-β-arrestin BiFC complexes. Thus NPY-induced changes in Y receptor motility and brightness reflect early events surrounding arrestin dependent endocytosis at the plasma membrane, results supported by a novel combined BiFC/FCS approach to detect the underlying receptor-β-arrestin signalling complex.     

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.