Conventional Fluorescence Correlation Spectroscopy Research Articles

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.

Objective scanning-based fluorescence cross-correlation spectroscopy (Scan-FCCS) for studying the fusion dynamics of protein phase separation.

Protein phase separation plays a very important role in many biological processes and is closely related to the occurrence and development of some serious diseases. So far, the fluorescence imaging method and fluorescence correlation spectroscopy (FCS) have been frequently used to study the phase separation behavior of proteins. Due to the wide size distribution of protein condensates in phase separation from nano-scale to micro-scale in solution and living cells, it is difficult for the fluorescence imaging method and conventional FCS to fully reflect the real state of protein phase separation in the solution due to the low spatio-temporal resolution of the conventional fluorescence imaging method and the limited detection area of FCS. Here, we proposed a novel method for studying the protein phase separation process by objective scanning-based fluorescence cross-correlation spectroscopy (Scan-FCCS). In this study, CRDBP proteins were used as a model and respectively fused with fluorescent proteins (EGFP and mCherry). We first compared conventional FCS and Scan-FCS methods for characterizing the CRDBP protein phase separation behaviors and found that the reproducibility of Scan-FCS is significantly improved by the scanning mode. We studied the self-fusion process of mCherry-CRDBP and EGFP-CRDBP and observed that the phase change concentration of CRDBP was 25 nM and the fusion of mCherry-CRDBP and EGFP-CRDBP at 500 nM was completed within 70 min. We studied the effects of salt concentration and molecular crowding agents on the phase separation of CRDBP and found that salt can prevent the self-fusion of CRDBP and molecular crowding agents can improve the self-fusion of CRDBP. Furthermore, we found the recruitment behavior of CRDBP to β-catenin proteins and studied their recruitment dynamics. Compared to conventional FCS, Scan-FCCS can significantly improve the reproducibility of measurements due to the dramatic increase of detection zone, and more importantly, this method can provide information about self-fusion and recruitment dynamics in protein phase separation.

CRDBP Protein Phase Separation and Its Recruitment to β-Catenin Protein in a Single Living Cell.

The Coding Region Determinant-Binding Protein (CRDBP) is a carcinoembryonic protein, and it is overexpressed in various cancer cells in the form of granules. We speculated the formation of CRDBP granules possibly through liquid-liquid phase separation (LLPS) processes due to the existence of intrinsically disordered regions (IDRs) in CRDBP. So far, we did not know whether or how phase separation processes of CRDBP occur in single living cells due to the lack of in vivo methods for studying intracellular protein phase separation. Therefore, to develop an in situ method for studying protein phase separation in living cells is a very urgent task. In this work, we proposed an efficient method for studying phase separation behavior of CRDBP in a single living cell by combining in situ fluorescence correlation spectroscopy (FCS) and fluorescence cross-correlation spectroscopy (FCCS) with a fluorescence protein fusion technique. We first predicted and confirmed that CRDBP has phase separation in solution by conventional fluorescence imaging and FCS methods. And then, we in situ studied the phase separation behaviors of CRDBP in living cells and observed three states of CRDBP phase separation such as monomer state, cluster state, and granule state. We studied the effects of CRDBP truncated forms and its inhibitor on the CRDBP phase separation. Furthermore, we discovered the recruitment of CRDBP to β-catenin protein in living cells and investigated the effects of CRDBP structures and inhibitor on CRDBP recruitment behavior. This finding may help us to further understand the mechanism of CRDBP protein for regulating Wnt signaling pathway. Additionally, our results documented that FCS/FCCS is an efficient and alternative method for studying protein phase separation in situ in living cells.

Nanowaveguide-illuminated fluorescence correlation spectroscopy for single molecule studies.

Fluorescence Correlation Spectroscopy (FCS) is a method of investigating concentration fluctuations of fluorescent particles typically in the nM range as a result of its femtoliter-sized sample volume. However, biological processes on cell membranes that involve molecules in the μM concentration range require sample volumes well below the conventional FCS limit as well as nanoscale confinement in the longitudinal direction. In this study, we show that an effective measurement volume down to the zeptoliter range can be achieved via the introduction of a nanowire waveguide, resulting in an illumination spot of about 50 nm in lateral dimensions and a longitudinal confinement of around 20 nm just above the waveguide exit surface. Using illumination profiles obtained from finite element method simulations of dielectric nanowaveguides, we perform Monte Carlo simulations of fluorescence fluctuations for two scenarios of fluorophore movement: fluorophores freely diffusing in the three-dimensional (3D) space above the nanowaveguide and fluorophores moving in a two-dimensional (2D) membrane situated directly above the nanowaveguide exit surface. We have developed analytical functions to fit the simulation results and found that an effective illumination size of about 150 zl and 4 × 10−3 µm2 can be obtained for the 3D and 2D scenarios, respectively. Given the flat surface geometry and the deep-subwavelength confinement of its illumination spot, this nanowaveguide-illuminated fluorescence correlation spectroscopy technique may be well suited for studying the concentration and dynamics of densely distributed protein molecules on cell membranes.

A Novel Cuvette-FCS Setup for Single Molecule Measurements of Protein Unfolding and Early Stages of Protein Aggregation

Fluorescence correlation spectroscopy (FCS) is a single molecule technique with wide spread applications in measurements of biophysical properties, e.g., hydrodynamic size and conformational dynamics of biomolecules. However, conventional FCS setups that use high numerical aperture objectives have limitations in performing certain experiments such as those requiring agitations such as stirring or heating, and those involving measurements in solvents with mismatch of refractive indices. Recently using an extra-long working distance objective (ELWD) we have developed an FCS setup that is suitable for performing measurements inside regular cuvettes. The radial resolution and the confocal volume achieved in this setup are approximately 340 nm and 1.8 fL respectively. The signal to noise ratio in the autocorrelation data and counts per molecule obtained from an aqueous solution of rhodamine B are greater than 150 and 60 kHz respectively. We demonstrate that cuvette-FCS can be coupled to accessories such as autotitrators and magnetic stirrers for fully automated measurements of unfolding of proteins mediated by chemical denaturants such as urea. Furthermore, scanning-FCS measurements in this setup allows measurements of time evolution of the size distribution of the early stage aggregates of amyloid proteins. Hence, cuvette-FCS is a suitable technique for performing single molecule measurements in the experiments that are regularly performed in spectrofluorometers but are generally avoided in microscope-based FCS.

Three-State DNA Hairpin Conformational Dynamics Revealed by Higher-Order Fluorescence Correlation Spectroscopy.

Previous fluorescence correlation spectroscopy (FCS) measurements of DNA hairpin folding dynamics revealed at least three conformational states of the DNA are present, distinguished by the brightness of fluorescent dye-quencher labels. Rapid fluctuations between two of the states occurred on time scales observable by FCS. A third state that was static on the FCS time scale was also observed. In this study, we investigate these conformational states using newly developed higher-order FCS techniques. It is shown that conventional FCS alone cannot uniquely distinguish the conformational states or assign their roles in the observed mechanism. The additional information offered by higher-order FCS makes it possible (i) to uniquely identify the static and rapidly fluctuating states and (ii) to directly measure the brightnesses and populations of all three observed states. The rapid fluctuations occurring on the FCS time scale are due to a reversible reaction between the two lowest brightness levels, attributed to the folded and random-coil conformations of the DNA. Evidence is presented that the third state, which is the brightest, may be associated with spatially extended unfolded conformations that are isolated from the more compact conformations by a substantial barrier. These conformations attain a maximum equilibrium population of nearly 10% near physiological temperatures and salt concentrations.

In situ study of RSK2 kinase activity in a single living cell by combining single molecule spectroscopy with activity-based probes.

Protein phosphorylation is a very important regulatory mechanism in a majority of biological processes, and the determination of protein kinase activity plays a key role in the pathological study and drug development of kinase-related diseases. However, it is very challenging to in situ study endogenous protein kinase activity in a single living cell due to the shortage of in vivo efficient methods. Here, we propose a new strategy for direct determination of protein kinase activity in a single living cell by combining single molecule fluorescence correlation spectroscopy (FCS) with activity-based probes (ABPs). Ribosomal S6 kinase-2 (RSK2) was used as a model, and the ABPs were synthesized on the basis of RSK2 inhibitor FMK to specially label active RSK2 in living cells. Conventional FCS and MEMFCS (maximum entropy method) single molecule techniques were used to in situ determine RSK2 activity in living cells based on the difference in molecular weight between free probes and probe-RSK2 complexes. Furthermore, wild-type and mutated RSK2 were fused with enhanced green fluorescent protein (EGFP) using lentivirus infection, and fluorescence cross-correlation spectroscopy (FCCS) was used to verify the selective binding of ABPs to RSK2-EGFP fusion protein in living cells. Finally, FCS with ABPs was applied for in situ monitoring of the activation of endogenous RSK2 in the stimulation of serum, epidermal growth factor, kinase inhibitors and ultraviolet irradiation; we observed that endogenous RSK2 showed different behaviors in the cytoplasm and the nucleus in some stimulation. Our results document that FCS with ABPs is a very promising method for studying endogenous protein kinases in living cells.

Fluorescence Correlation Spectroscopy with Nanowire Waveguide Illumination for High Concentration Conditions

Fluorescence correlation spectroscopy (FCS), a technique based on correlating the fluorescence signal from a small sample volume, has been commonly used to study biological processes such as photophysical phenomena, binding kinetics, and intracellular dynamics. In a conventional FCS setup, the sample volume is defined by a focused laser beam for excitation and a confocal pin hole for collection resulting in a size of about one femtoliter. Evanescent waves from total internal reflection have been used to obtain a smaller sample volume, as a result of the improved confinement along the longitudinal axis for the illumination. However, applying FCS under physiological conditions where the molecule concentration is typically in the µM range requires an even smaller sample volume. Here we propose to apply FCS with nanowire waveguide illumination with nanometer-sized lateral and longitudinal confinement. Nanowire waveguides, made of a dielectric nanowire with a diameter of ∼50 nm embedded inside a metal film, allow for the efficient transmission of visible light by exploiting surface waves traveling along the dielectric-metal boundary. Such waveguides can generate a lateral illumination area of about 50 nanometers in diameter. In addition, a longitudinal confinement of around 20 nanometers is achieved with the rapidly-attenuating near fields exiting from the waveguide. The strong confinement in both lateral and longitudinal directions thus lead to a sample volume on the order of one zeptoliter, allowing for FCS measurements in the µM concentration range. By combining Brownian dynamics simulations with the illumination profile obtained from finite element method simulations of a zinc oxide nanowire waveguide in a silver metal film, we numerically calculate the correlation function to demonstrate the use of this method in the study of molecular dynamics under high concentration conditions.

Building, Characterization, and Applications of Cuvette-FCS in Denaturant-Induced Expansion of Globular and Disordered Proteins.

Fluorescence correlation spectroscopy (FCS) is a single-molecule sensitive technique with widespread applications in biophysics. However, conventional microscope-based FCS setups have limitations in performing certain experiments such as those requiring agitations such as stirring or heating, and those involving measurements in solvents with the mismatch of refractive indices. We have recently developed an FCS setup that is suitable for performing measurements inside regular cuvettes. The cuvette-FCS is suitable for performing single-molecule measurements in experiments that are regularly performed in spectrofluorometers but are generally avoided in microscope-based FCS. Here we describe building and characterization of the performance of the cuvette-FCS setup in detail. Finally, we have used a natively folded protein and an intrinsically disordered protein to demonstrate and describe how cuvette-FCS can be applied conveniently to measure urea-dependent expansion of hydrodynamic size of proteins.

Correction to "Artifact-Free and Detection-Profile-Independent Higher-Order Fluorescence Correlation Spectroscopy for Microsecond-Resolved Kinetics. 2. Mixtures and Reactions".

Fluorescence correlation spectroscopy (FCS) is a primary tool in the time-resolved analysis of nonreacting or reacting molecules in solution, based on fluorescence intensity fluctuations. However, conventional FCS alone is insufficient for a complete determination of reaction or mixture parameters. In an accompanying article, a technique for the computation of artifact-free higher-order correlations with microsecond time resolution was described. Here, we demonstrate the applications of the technique to analyze the systems of fast and slow reactions. As an example of non- or slow-reacting systems, the technique is applied to resolve two-component mixtures of labeled oligonucleotides. Next, the protonation reaction of fluorescein isothiocyanate in phosphate buffer is analyzed as an example of fast reactions (relaxation time <1 μs). By reference to an (apparent) nonreacting system, the simple factorized form of cumulant-based higher-order correlations is exploited to remove the dependence on the molecular d...

Artifact-Free and Detection-Profile-Independent Higher-Order Fluorescence Correlation Spectroscopy for Microsecond-Resolved Kinetics. 2. Mixtures and Reactions.

Fluorescence correlation spectroscopy (FCS) is a primary tool in the time-resolved analysis of nonreacting or reacting molecules in solution, based on fluorescence intensity fluctuations. However, conventional FCS alone is insufficient for a complete determination of reaction or mixture parameters. In an accompanying article, a technique for the computation of artifact-free higher-order correlations with microsecond time resolution was described. Here, we demonstrate the applications of the technique to analyze the systems of fast and slow reactions. As an example of non- or slow-reacting systems, the technique is applied to resolve two-component mixtures of labeled oligonucleotides. Next, the protonation reaction of fluorescein isothiocyanate in phosphate buffer is analyzed as an example of fast reactions <10 μs (actual time scale ∼6 μs). By reference to an (apparent) nonreacting system, the simple factorized form of cumulant-based higher-order correlations is exploited to remove the dependence on the molecular detection function (MDF). Therefore, there is no need to model and characterize the experimental MDF, and the precision and the accuracy of the technique are enhanced. It is verified that the higher-order correlation analysis enables a complete and simultaneous determination of the number and brightness parameters of mixing or reacting molecules, the reaction relaxation time, and forward and reverse reaction rates.

Artifact-Free and Detection-Profile-Independent Higher-Order Fluorescence Correlation Spectroscopy for Microsecond-Resolved Kinetics. 1. Multidetector and Sub-Binning Approach.

Fluorescence correlation spectroscopy (FCS) is a powerful tool in the time-resolved analysis of nonreacting or reacting molecules in solution, based on fluorescence intensity fluctuations. However, conventional (second-order) FCS alone is insufficient to measure all parameters needed to describe a reaction or mixture, including concentrations, fluorescence brightnesses, and forward and reverse rate constants. For this purpose, correlations of higher powers of fluorescence intensity fluctuations can be calculated to yield additional information from the single-photon data stream collected in an FCS experiment. To describe systems of diffusing and reacting molecules, considering cumulants of fluorescence intensity results in simple expressions in which the reaction and diffusion parts factorize. The computation of higher-order correlations in experiments is hindered by shot-noise and common detector artifacts, the effects of which become worse with increasing order. In this article, we introduce a technique to calculate artifact-free higher-order correlation functions with improved time resolution, and without any need for modeling and calibration of detector artifacts. The technique is formulated for general multidetector experiments and verified in both two-detector and single-detector configurations. Good signal-to-noise ratio is achieved down to 1 μs in correlation curves up to order (2, 2). This capability makes possible a variety of new measurements including multicomponent analysis and fast reaction kinetics, as demonstrated in a companion article (10.1021/acs.jpcb.7b00408).

Quantitative deconvolution of autocorrelations and cross correlations from two-dimensional lifetime decay maps in fluorescence lifetime correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is a widely used method for measuring molecular diffusion and chemical kinetics. However, when a mixture of fluorescent species is taken into account, the conventional FCS method has limitations in extracting autocorrelations for different species and cross correlations between different species. Recently developed fluorescence lifetime correlation spectroscopy (FLCS) based on time-tagged time-resolved (TTTR) photon recording, which can record the global and micro arrival time for each individual photon, has been used to discriminate different species according to fluorescence lifetime. Here, based on two-dimensional lifetime decay maps constructed from TTTR photon stream, we have developed a quantitative lifetime-deconvolution FCS model (LDFCS) to extract precise chemical rates for chemical conversions in multi-species systems. The key point of LDFCS model is separation of different species according to the global distribution of fluorescence lifetime and then deconvolution of autocorrelations and cross-correlations from the two-dimensional lifetime decay maps constructed by the micro arrival times of photon pairs at each delay time.

Determination of Equilibrium Constant and Relative Brightness in Fluorescence Correlation Spectroscopy by Considering Third-Order Correlations.

Fluorescence correlation spectroscopy (FCS) is a powerful tool to investigate molecular diffusion and relaxations, which may be utilized to study many problems such as molecular size and aggregation, chemical reaction, molecular transportation and motion, and various kinds of physical and chemical relaxations. This article focuses on a problem related to using the relaxation term to study a reaction. If two species with different fluorescence photon emission efficiencies are connected by a reaction, the kinetic and equilibrium properties will be manifested in the relaxation term of the FCS curve. However, the conventional FCS alone cannot simultaneously determine the equilibrium constant (K) and the relative fluorescence brightness (Q), both of which are indispensable in the extraction of thermodynamic and kinetic information from the experimental data. To circumvent the problem, an assumption of Q = 0 is often made for the weak fluorescent species, which may lead to numerous errors when the actual situation is not the case. We propose to combine the third-order FCS with the conventional second-order FCS to determine K and Q without invoking other resources. The strategy and formalism are verified by computer simulations and demonstrated in a classical example of the hairpin DNA-folding process.

Super-resolution optical microscopy of lipid plasma membrane dynamics.

Plasma membrane dynamics are an important ruler of cellular activity, particularly through the interaction and diffusion dynamics of membrane-embedded proteins and lipids. FCS (fluorescence correlation spectroscopy) on an optical (confocal) microscope is a popular tool for investigating such dynamics. Unfortunately, its full applicability is constrained by the limited spatial resolution of a conventional optical microscope. The present chapter depicts the combination of optical super-resolution STED (stimulated emission depletion) microscopy with FCS, and why it is an important tool for investigating molecular membrane dynamics in living cells. Compared with conventional FCS, the STED-FCS approach demonstrates an improved possibility to distinguish free from anomalous molecular diffusion, and thus to give new insights into lipid-protein interactions and the traditional lipid 'raft' theory.

Mapping Diffusion in a Living Cell via the Phasor Approach

Diffusion of a fluorescent protein within a cell has been measured using either fluctuation-based techniques (fluorescence correlation spectroscopy (FCS) or raster-scan image correlation spectroscopy) or particle tracking. However, none of these methods enables us to measure the diffusion of the fluorescent particle at each pixel of the image. Measurement using conventional single-point FCS at every individual pixel results in continuous long exposure of the cell to the laser and eventual bleaching of the sample. To overcome this limitation, we have developed what we believe to be a new method of scanning with simultaneous construction of a fluorescent image of the cell. In this believed new method of modified raster scanning, as it acquires the image, the laser scans each individual line multiple times before moving to the next line. This continues until the entire area is scanned. This is different from the original raster-scan image correlation spectroscopy approach, where data are acquired by scanning each frame once and then scanning the image multiple times. The total time of data acquisition needed for this method is much shorter than the time required for traditional FCS analysis at each pixel. However, at a single pixel, the acquired intensity time sequence is short; requiring nonconventional analysis of the correlation function to extract information about the diffusion. These correlation data have been analyzed using the phasor approach, a fit-free method that was originally developed for analysis of FLIM images. Analysis using this method results in an estimation of the average diffusion coefficient of the fluorescent species at each pixel of an image, and thus, a detailed diffusion map of the cell can be created.

Monitoring triplet state dynamics with fluorescence correlation spectroscopy: bias and correction.

A marker's dark triplet state is of great importance in fluorescence microscopy: It serves as a means to switch off fluorescent markers and is thus the enabling element for several super-resolution methods. On the other hand, intersystem-crossing to the electronic dark triplet state strongly reduces the fluorescence yield in conventional fluorescence microscopy. The ability to determine the kinetic parameters of transitions into the triplet state is thus of great importance and because fluorescence correlation spectroscopy (FCS) can be applied without disturbing the system under study, it is one of the preferred methods to do so. However, conventional FCS observations of triplet dynamics suffer from bias due to the spatially inhomogeneous irradiance profile of the excitation laser. Herein, we present a novel method to correct this bias and verify it by analyzing both Monte Carlo simulated and experimental data of the organic dye Rhodamine 110 in aqueous solution for both continuous-wave and pulsed excitation. Importantly, our approach can be readily generalized to most other FCS experiments that determine intensity dependent kinetic parameters.

Fluorescence correlation spectroscopy (IUPAC Technical Report)

We present an overview on the applicability of fluorescence correlation spectroscopy (FCS) for the accurate determination of translational diffusion coefficients and thus, via the Stokes–Einstein relation, of molecular size. We consider several of the most common sources of optical aberrations and their impact on the outcome of conventional FCS measurements. We describe also a new variant of FCS, dual-focus FCS, which is robust against most of the considered aberrations, and we report reference values of diffusion coefficients for several fluorescent dyes across the visible spectrum.

Study of Nanoscopic Phase Separation in Membranes using Inverse FCS

Fluorescence correlation spectroscopy (FCS) has been used to study the diffusion of lipid and protein molecules in both synthetic and natural membranes. Recently, a new version of FCS, inverse FCS, has been developed (Wennmalm et al., 2009). For inverse FCS fluorescent probes are present at very high concentration as opposed to low concentration for conventional FCS. The particle of interest in the inverse FCS experiment is non-fluorescent. Fluorescence fluctuations due to the exclusion of fluorescent probes from the excitation spot by the non-fluorescent particles are detected and correlated. In the study of membrane nanodomains by conventional FCS, both domains and probe diffusion contribute to the correlation fluctuation. However, for inverse FCS, the diffusion of fluorescent probes contributes little to the fluctuation due to the high concentration of fluorescent probes. Therefore, inverse FCS provides an opportunity to study the properties of dark nanodomains that exclude the fluorescent probe when the fraction of nanodomains in the membrane is small. Here, we demonstrate by simulation that in these situations inverse FCS can give information about membrane nanoscopic phase separation that is inaccessible to conventional FCS. We also used inverse FCS to experimentally study early phase separation in DLPC/DSPC model membranes. Two different domain evolution pathways have been observed. In one of these two pathways, nanoscopic domains appear at first and then gradually grow to micron size. In the other pathway, the domains reach micron size quickly and their number gradually increases.Inverse-Fluorescence Correlation Spectroscopy, Stefan Wennmalm, Per Thyberg, Lei Xu, and Jerker Widengren. Anal. Chem. 2009, 81, 9209-9215

Early Amyloidogenic Oligomerization Studied through Fluorescence Lifetime Correlation Spectroscopy

Amyloidogenic protein aggregation is a persistent biomedical problem. Despite active research in disease-related aggregation, the need for multidisciplinary approaches to the problem is evident. Recent advances in single-molecule fluorescence spectroscopy are valuable for examining heterogenic biomolecular systems. In this work, we have explored the initial stages of amyloidogenic aggregation by employing fluorescence lifetime correlation spectroscopy (FLCS), an advanced modification of conventional fluorescence correlation spectroscopy (FCS) that utilizes time-resolved information. FLCS provides size distributions and kinetics for the oligomer growth of the SH3 domain of α-spectrin, whose N47A mutant forms amyloid fibrils at pH 3.2 and 37 °C in the presence of salt. The combination of FCS with additional fluorescence lifetime information provides an exciting approach to focus on the initial aggregation stages, allowing a better understanding of the fibrillization process, by providing multidimensional information, valuable in combination with other conventional methodologies.