Fluorescence Correlation Spectroscopy Data Research Articles

Analytical Form of the Fluorescence Correlation Spectroscopy Autocorrelation Function in Chemically Reactive Systems.

Fluorescence correlation spectroscopy (FCS) applied to chemically reactive systems provides information about chemical reaction equilibrium constants and diffusion coefficients of reactants. These physical quantities are determined from the FCS-measured autocorrelation function, G(t), as a function of time, t. In most of the studied cases, the analytical form of G(t) is well-known for reactions that are much faster than the diffusion time of reactants across the focal volume probed by FCS or when they are much slower than the diffusion time. Here, we develop an analytical form of G(t) for reactions occurring at an intermediate time scale comparable to the diffusion time. G(t) depends on the reaction rates in such reactions. We focus on reversibly binding a fluorescently labeled small molecule to a macromolecule in a diluted solution in thermodynamic equilibrium. Our approach allows the analysis of FCS data over a wide range of diffusion coefficients, reaction rate constants, and brightness levels of fluorescent labels. Our G(t) is valid even when the fluorescent label changes its brightness upon binding. The easy-to-implement analytical form of the autocorrelation function greatly helps experimentalists study chemical reactions, determining the equilibrium constants of reactions and the reaction rates.

Statistical analysis of the autocorrelation function in fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is a powerful method to measure concentration, mobility, and stoichiometry in solution and in living cells, but quantitative analysis of FCS data remains challenging due to the correlated noise in the autocorrelation function (ACF) of FCS. We demonstrate here that least-squares fitting of the conventional ACF is incompatible with the χ2 goodness-of-fit test and systematically underestimates the true fit parameter uncertainty. To overcome this challenge, a simple method to fit the ACF is introduced that allows proper calculation of goodness-of-fit statistics and that provides more tightly constrained parameter estimates than the conventional least-squares fitting method, achieving the theoretical minimum uncertainty. Because this method requires significantly more data than the standard method, we further introduce an approximate method that requires fewer data. We demonstrate both these new methods using experiments and simulations of diffusion. Finally, we apply our method to FCS data of the peripheral membrane protein HRas, which has a slow-diffusing membrane-bound population and a fast-diffusing cytoplasmic population. Despite the order-of-magnitude difference of the diffusion times, conventional FCS fails to reliably resolve the two species, whereas the new method identifies the correct model and provides robust estimates of the fit parameters for both species.

FCSNet and ImFCSNet, convolutional neural network approaches to FCS data analysis.

Fluorescence Correlation Spectroscopy (FCS) is a widely used tool to analyse molecular dynamics in biological samples. It analyses the correlation function of the fluorescence fluctuations in a defined observation volume to extract information about the underlying molecular processes. However, FCS faces a number of challenges. First, it requires the use of theoretical fit models that often cannot be solved exactly and thus require approximations. Second, the measurement times for FCS are comparatively long, on the order of a minute, to obtain accurate parameter estimates. Third, the data analysis can be computationally quite time consuming. We therefore explore deep learning approaches to address these issues. For this purpose, we focus on Imaging FCS, a camera-based FCS modality, that provides correlation functions at or between any pixels on a camera, without loss of generality. We developed two convolutional neural networks (CNNs). FCSNet and ImFCSNet use either correlation functions or raw intensity traces as input, respectively. Both networks are trained on simulated, synthetic data, as it is difficult to obtain ground truth data for FCS over wide parameter ranges. More importantly, it allows us to use arbitrary experimental geometries and molecular processes, even when analytic models are not available for conventional fitting, thus solving the first problem. We demonstrate that the two CNNs perform well on synthetic and experimental data and outperform conventional nonlinear least squares (NLS) fits by a) requiring about one order of magnitude less data, b) providing higher precision for parameter estimates, and c) being two orders of magnitude faster. To demonstrate the power of CNNs we present comparisons of data evaluations by conventional NLS fitting on lipid bilayers and cells and on data recorded on total internal reflection and light sheet microscopes.

Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking.

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated N2atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. These results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

Size and Fluorescence Properties of Algal Photosynthetic Antenna Proteins Estimated by Microscopy.

Antenna proteins play a major role in the regulation of light-harvesting in photosynthesis. However, less is known about a possible link between their sizes (oligomerization state) and fluorescence intensity (number of photons emitted). Here, we used a microscopy-based method, Fluorescence Correlation Spectroscopy (FCS), to analyze different antenna proteins at the particle level. The direct comparison indicated that Chromera Light Harvesting (CLH) antenna particles (isolated from Chromera velia) behaved as the monomeric Light Harvesting Complex II (LHCII) (from higher plants), in terms of their radius (based on the diffusion time) and fluorescence yields. FCS data thus indicated a monomeric oligomerization state of algal CLH antenna (at our experimental conditions) that was later confirmed also by biochemical experiments. Additionally, our data provide a proof of concept that the FCS method is well suited to measure proteins sizes (oligomerization state) and fluorescence intensities (photon counts) of antenna proteins per single particle (monomers and oligomers). We proved that antenna monomers (CLH and LHCIIm) are more “quenched” than the corresponding trimers. The FCS measurement thus represents a useful experimental approach that allows studying the role of antenna oligomerization in the mechanism of photoprotection.

Picosecond to Second Fluorescence Correlation Spectroscopy for Studying Solute Exchange and Quenching Dynamics in Micellar Media.

Numerous studies have been devoted to understand the reaction kinetics in micelles, where the accessible kinetic time window is often limited by the dynamic range of the employed spectroscopic technique. This is usually accompanied by a selection of probes that comfortably explore time scales where slow solute exchange kinetics is negligible, as compared to the fast excited state reactions. This has led to an undervaluation of the role played by dynamic partitioning of hydrophilic solutes in microheterogeneous media. Here, we employ fluorescence correlation spectroscopy (FCS) and the zwitterionic dye Rhodamine 110 to quantitatively explore the impact of solute exchange on the photoinduced electron transfer between this dye and N,N-dimethylaniline in micellar media. Our study elucidates the coupling and interplay between the kinetics of photophysics, quenching, and solute exchange through a quantitative unified molecular-state quenching-kinetic model that describes the steady-state ensemble and FCS data from subnanosecond photon antibunching to millisecond diffusions.

Particle Diffusivity and Free-Energy Profiles in Hydrogels from Time-Resolved Penetration Data

A combined experimental and theoretical method to simultaneously determine diffusivity and free-energy profiles of particles that penetrate into inhomogeneous hydrogel systems is presented. As the only input, arbitrarily normalized concentration profiles from fluorescence intensity data of labeled tracer particles for different penetration times are needed. The method is applied to dextran molecules of varying size that penetrate into hydrogels of polyethylene-glycol chains with different lengths that are covalently cross-linked by hyperbranched polyglycerol hubs. Extracted dextran bulk diffusivities agree well with fluorescence correlation spectroscopy data obtained separately. Empirical scaling laws for dextran diffusivities and free energies inside the hydrogel are identified as a function of the dextran mass. An elastic free-volume model that includes dextran as well as polyethylene-glycol linker flexibility quantitively describes the repulsive dextran-hydrogel interaction free energy, which is of steric origin, and furthermore suggests that the hydrogel mesh-size distribution is rather broad and particle penetration is dominated by large hydrogel pores. Particle penetration into hydrogels for steric particle-hydrogel interactions is thus suggested to be governed by an elastic size-filtering mechanism that involves the tail of the hydrogel pore-size distribution.

Variations in Plasma Membrane Topography Can Explain Heterogenous Diffusion Coefficients Obtained by Fluorescence Correlation Spectroscopy.

Fluorescence correlation spectroscopy (FCS) is frequently used to study diffusion in cell membranes, primarily the plasma membrane. The diffusion coefficients reported in the plasma membrane of the same cell type and even within single cells typically display a large spread. We have investigated whether this spread can be explained by variations in membrane topography throughout the cell surface, that changes the amount of membrane in the FCS focal volume at different locations. Using FCS, we found that diffusion of the membrane dye DiI in the apical plasma membrane was consistently faster above the nucleus than above the cytoplasm. Using live cell scanning ion conductance microscopy (SICM) to obtain a topography map of the cell surface, we demonstrate that cell surface roughness is unevenly distributed with the plasma membrane above the nucleus being the smoothest, suggesting that the difference in diffusion observed in FCS is related to membrane topography. FCS modeled on simulated diffusion in cell surfaces obtained by SICM was consistent with the FCS data from live cells and demonstrated that topography variations can cause the appearance of anomalous diffusion in FCS measurements. Furthermore, we found that variations in the amount of the membrane marker DiD, a proxy for the membrane, but not the transmembrane protein TCRζ or the lipid-anchored protein Lck, in the FCS focal volume were related to variations in diffusion times at different positions in the plasma membrane. This relationship was seen at different positions both at the apical cell and basal cell sides. We conclude that it is crucial to consider variations in topography in the interpretation of FCS results from membranes.

Computational design and interpretation of single-RNA translation experiments.

Advances in fluorescence microscopy have introduced new assays to quantify live-cell translation dynamics at single-RNA resolution. We introduce a detailed, yet efficient sequence-based stochastic model that generates realistic synthetic data for several such assays, including Fluorescence Correlation Spectroscopy (FCS), ribosome Run-Off Assays (ROA) after Harringtonine application, and Fluorescence Recovery After Photobleaching (FRAP). We simulate these experiments under multiple imaging conditions and for thousands of human genes, and we evaluate through simulations which experiments are most likely to provide accurate estimates of elongation kinetics. Finding that FCS analyses are optimal for both short and long length genes, we integrate our model with experimental FCS data to capture the nascent protein statistics and temporal dynamics for three human genes: KDM5B, β-actin, and H2B. Finally, we introduce a new open-source software package, RNA Sequence to NAscent Protein Simulator (rSNAPsim), to easily simulate the single-molecule translation dynamics of any gene sequence for any of these assays and for different assumptions regarding synonymous codon usage, tRNA level modifications, or ribosome pauses. rSNAPsim is implemented in Python and is available at: https://github.com/MunskyGroup/rSNAPsim.git.

Structural diffusion properties of two atypical Dps from the cyanobacterium Nostoc punctiforme disclose interactions with ferredoxins and DNA

Ferritin-like proteins, Dps (DNA-binding protein from starved cells), store iron and play a key role in the iron homeostasis in bacteria, yet their iron releasing machinery remains largely unexplored. The electron donor proteins that may interact with Dps and promote the mobilization of the stored iron have hitherto not been identified. Here, we investigate the binding capacity of the two atypical Dps proteins NpDps4 and NpDps5 from Nostoc punctiforme to isolated ferredoxins. We report NpDps-ferredoxin interactions by fluorescence correlation spectroscopy (FCS) and fluorescence resonance energy transfer (FRET) methods. Dynamic light scattering, size exclusion chromatography and native gel electrophoresis results show that NpDps4 forms a dodecamer at both pH 6.0 and pH 8.0, while NpDps5 forms a dodecamer only at pH 6.0. In addition, FCS data clearly reveal that the non-canonical NpDps5 interacts with DNA at pH 6.0. Our spectroscopic analysis shows that [FeS] centers of the three recombinantly expressed and isolated ferredoxins are properly incorporated and are consistent with their respective native states. The results support our hypothesis that ferredoxins could be involved in cellular iron homeostasis by interacting with Dps and assisting the release of stored iron.

Bayesian Approach to Fluorescence Correlation Spectroscopy Data Analysis - The Danger of Least-Square Fitting

Bayesian Approach to Fluorescence Correlation Spectroscopy Data Analysis - The Danger of Least-Square Fitting

Statistical Analysis of Scanning Fluorescence Correlation Spectroscopy Data Differentiates Free from Hindered Diffusion.

Cells rely on versatile diffusion dynamics in their plasma membrane. Quantification of this often heterogeneous diffusion is essential to the understanding of cell regulation and function. Yet such measurements remain a major challenge in cell biology, usually due to low sampling throughput, a necessity for dedicated equipment, sophisticated fluorescent label strategies, and limited sensitivity. Here, we introduce a robust, broadly applicable statistical analysis pipeline for large scanning fluorescence correlation spectroscopy data sets, which uncovers the nanoscale heterogeneity of the plasma membrane in living cells by differentiating free from hindered diffusion modes of fluorescent lipid and protein analogues.

Enhanced Luminescent Properties of Photo-Stable Copper Nanoclusters through Formation of "Protein-Corona"-Like Assemblies.

In this study, interactions of synthesized copper nanoclusters (CuNCs) with a model transport protein, human serum albumin (HSA), have been systematically investigated by using various spectroscopic approaches. The interactions give rise to the formation of "protein-corona" like assemblies and the luminescence properties (both steady-state and time-resolved) are enhanced due to gradual adsorption of the protein on the surface of the NCs. The associated thermodynamics and binding parameters have been estimated resorting to luminescent experimental techniques as well as isothermal titration calorimetry (ITC) studies, indicating that every NC is surrounded by (4±1) protein molecules. The adsorption of HSA on the surface of the NCs has been characterized by dynamic light scattering (DLS) and time-resolved anisotropy measurements. Finally, fluorescence correlation spectroscopy (FCS) data substantiate the emergence of new "protein-corona" like assemblies resulting in slower translational diffusion motions and concomitant rise of the hydrodynamic diameters.

Single-molecule photobleaching: Instrumentation and applications

Single-molecule photobleaching (smPB) technique is a powerful tool for characterizing molecular assemblies. It can provide a direct measure of the number of monomers constituting a given oligomeric particle and generate the oligomer size distribution in a specimen. A major current application of this technique is in understanding protein aggregation, which is linked to many incurable diseases. Quantitative measurement of the size distribution of an aggregating protein in a physiological solution remains a difficult task, since techniques such as dynamic light scattering or fluorescence correlation spectroscopy (FCS) can provide an average size, but cannot accurately resolve the underlying size distribution. Here we describe the smPB method as implemented on a home-built total internal reflection fluorescence microscope (TIRF). We first describe the construction of a TIRF microscope, and then demonstrate the power of smPB by characterizing a solution of Amylin (hIAPP) oligomers, a 37-residue peptide whose aggregation is associated with Type II diabetes. We compare our results with FCS data obtained from the same specimen, and discuss the advantages and disadvantages of the two techniques.

Quantitative mapping of fluorescently tagged cellular proteins using FCS-calibrated four-dimensional imaging.

The ability to tag a protein at its endogenous locus with a fluorescent protein (FP) enables quantitative understanding of protein dynamics at the physiological level. Genome-editing technology has now made this powerful approach routinely applicable to mammalian cells and many other model systems, thereby opening up the possibility to systematically and quantitatively map the cellular proteome in four dimensions. 3D time-lapse confocal microscopy (4D imaging) is an essential tool for investigating spatial and temporal protein dynamics; however, it lacks the required quantitative power to make the kind of absolute and comparable measurements required for systems analysis. In contrast, fluorescence correlation spectroscopy (FCS) provides quantitative proteomic and biophysical parameters such as protein concentration, hydrodynamic radius, and oligomerization but lacks the capability for high-throughput application in 4D spatial and temporal imaging. Here we present an automated experimental and computational workflow that integrates both methods and delivers quantitative 4D imaging data in high throughput. These data are processed to yield a calibration curve relating the fluorescence intensities (FIs) of image voxels to the absolute protein abundance. The calibration curve allows the conversion of the arbitrary FIs to protein amounts for all voxels of 4D imaging stacks. Using our workflow, users can acquire and analyze hundreds of FCS-calibrated image series to map their proteins of interest in four dimensions. Compared with other protocols, the current protocol does not require additional calibration standards and provides an automated acquisition pipeline for FCS and imaging data. The protocol can be completed in 1 d.

Fluorescence Correlation Spectroscopy on Genomic DNA in Living Cells.

Fluorescence correlation spectroscopy (FCS) is a powerful technique used to measure diffusion, fluctuations, and other transport processes in biomolecular systems. It is, however, prone to artifacts and subject to considerable experimental difficulties when applied to living cells. In this chapter, we provide protocols to conduct quantitative FCS measurements on DNA inside living eukaryotic and prokaryotic cells. We discuss sample preparation, dye selection and characterization, FCS data acquisition, and data analysis, including a method to com pensate for photobleaching to obtain quantitatively meaningful spectra.

Mapping the dynamical organization of the cell nucleus through fluorescence correlation spectroscopy.

The hierarchical organization of the cell nucleus into specialized open reservoirs and the nucleoplasm overcrowding impose restrictions to the mobility of biomolecules and their interactions with nuclear targets. These properties determine that many nuclear functions such as transcription, replication, splicing or DNA repair are regulated by complex, dynamical processes that do not follow simple rules. Advanced fluorescence microscopy tools and, in particular, fluorescence correlation spectroscopy (FCS) provide complementary and exquisite information on the dynamics of fluorescent labeled molecules moving through the nuclear space and are helping us to comprehend the complexity of the nuclear structure. Here, we describe how FCS methods can be applied to reveal the dynamical organization of the nucleus in live cells. Specifically, we provide instructions for the preparation of cellular samples with fluorescent tagged proteins and detail how FCS can be easily instrumented in commercial confocal microscopes. In addition, we describe general rules to set the parameters for one and two-color experiments and the required controls for these experiments. Finally, we review the statistical analysis of the FCS data and summarize the use of numerical simulations as a complementary approach that helps us to understand the complex matrix of molecular interactions network within the nucleus.

Fission yeast Myo2: Molecular organization and diffusion in the cytoplasm.

Myosin-II is required for the assembly and constriction of cytokinetic contractile rings in fungi and animals. We used electron microscopy, fluorescence recovery after photobleaching (FRAP), and fluorescence correlation spectroscopy (FCS) to characterize the physical properties of Myo2 from fission yeast Schizosaccharomyces pombe. By electron microscopy, Myo2 has two heads and a coiled-coiled tail like myosin-II from other species. The first 65 nm of the tail is a stiff rod, followed by a flexible, less-ordered region up to 30 nm long. Myo2 sediments as a 7 S molecule in high salt, but aggregates rather than forming minifilaments at lower salt concentrations; this is unaffected by heavy chain phosphorylation. We used FRAP and FCS to observe the dynamics of Myo2 in live S. pombe cells and in cell extracts at different salt concentrations; both show that Myo2 with an N-terminal mEGFP tag has a diffusion coefficient of ∼ 3 µm2 s-1 in the cytoplasm of live cells during interphase and mitosis. Photon counting histogram analysis of the FCS data confirmed that Myo2 diffuses as doubled-headed molecules in the cytoplasm. FCS measurements on diluted cell extracts showed that mEGFP-Myo2 has a diffusion coefficient of ∼ 30 µm2 s-1 in 50 to 400 mM KCl concentrations.

Determination of Equilibrium Constant and Relative Brightness in FRET-FCS by Including the Third-Order Correlations.

Fluorescence correlation spectroscopy (FCS) encodes the information on the equilibrium constant (K), the relative fluorescence brightness of fluorophore (Q), and the forward and backward reaction rate constants (k+ and k-) on a physical or chemical relaxation. However, it has been a long-standing problem to completely resolve the FCS data to get the thermodynamic and kinetic information. Recently, we have solved the problem for fluorescence autocorrelation spectroscopy (FACS). Here, we extend the method to fluorescence cross-correlation spectroscopy (FCCS), which appears when FCS is coupled with fluorescence resonance energy transfer (FRET). Among 12 total second-order and third-order pre-exponential factors in a relaxation process probed by the FRET-FCS technique, 3 are independent. We presented and discussed 3 sets of explicit solutions to use these pre-exponential factors to calculate K and Q. Together with the relaxation time, the acquired K will allow people to obtain k+ and k-, so that the goal of deciphering the FRET-FCS data will be fully reached. The theory is verified by extensive computer simulations and tested experimentally on a system of oligonucleotide hybridization.

Reconceptualizing Fluorescence Correlation Spectroscopy for Monitoring and Analyzing Periodically Passing Objects.

Fluorescence correlation spectroscopy (FCS) is a sensitive technique commonly applied for studying the dynamics of nanoscale-labeled objects in solution. Current analysis of FCS data is largely based on the assumption that the labeled objects are stochastically displaced due to Brownian motion. However, this assumption is often invalid for microscale objects, since the motion of these objects is dominated by Stokes drag and settling or rising effects, rather than stochastic Brownian motion. To utilize the power of FCS for systems with nonstochastic displacements of objects, the collection and analysis of FCS data have to be reconceptualized. Here, we extended the applicability of FCS for the detection and analysis of periodically passing objects. Toward this end, we implemented droplet-based microfluidics, in which monodispersed droplets containing fluorescent marker are flowing equally spaced within microchannels. We show by simulations and experiments that FCS can sensitively quantify the flow-rates, variability, and content of rapidly passing droplets. This information can be derived at high temporal resolution, based on the intensity fluctuations generated by only 5–10 passing droplets. Moreover, by utilizing the periodicity of the flowing droplets for noise reduction by averaging, FCS can monitor accurately the droplets flow even if their fluorescence intensity is negligible. Hence, extending FCS for periodically passing objects converts it into a powerful analytical tool for high-throughput droplet-based microfluidics. Moreover, based on the principles described here, FCS can be straightforwardly applied for a variety of systems in which the passing of objects is periodic rather than stochastic.