Cumulant analysis in fluorescence fluctuation spectroscopy

Quantifying biomolecular organisation in membranes with brightness-transit statistics

Cells crucially rely on the interactions of biomolecules at their plasma membrane to maintain homeostasis. Yet, a methodology to systematically quantify biomolecular organisation, measuring diffusion dynamics and oligomerisation, represents an unmet need. Here, we introduce the brightness-transit statistics (BTS) method based on fluorescence fluctuation spectroscopy and combine information from brightness and transit times to elucidate biomolecular diffusion and oligomerisation in both cell-free in vitro and in vitro systems incorporating living cells. We validate our approach in silico with computer simulations and experimentally using oligomerisation of EGFP tethered to supported lipid bilayers. We apply our pipeline to study the oligomerisation of CD40 ectodomain in vitro and endogenous CD40 on primary B cells. While we find a potential for CD40 to oligomerize in a concentration or ligand depended manner, we do not observe mobile oligomers on B cells. The BTS method combines sensitive analysis, quantification, and intuitive visualisation of dynamic biomolecular organisation.

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.

Autocorrelation function of finite-length data in fluorescence correlation spectroscopy

The experimental autocorrelation function of fluorescence correlation spectroscopy calculated from finite-length data is a biased estimator of the theoretical correlation function. This study presents a new theoretical framework that explicitly accounts for the data length to allow for unbiased analysis of experimental autocorrelation functions. To validate our theory, we applied it to experiments and simulations of diffusion and characterized the accuracy and precision of the resulting parameter estimates. Because measurements in living cells are often affected by instabilities of the fluorescence signal, autocorrelation functions are typically calculated on segmented data to improve their robustness. Our reformulated theory extends the range of usable segment times down to timescales approaching the diffusion time. This flexibility confers unique advantages for live-cell data that contain intensity variations and instabilities. We describe several applications of short segmentation to analyze data contaminated with unwanted fluctuations, drifts, or spikes in the intensity that are not suited for conventional fluorescence correlation analysis. These results demonstrate the potential of our theoretical framework to significantly expand the experimental systems accessible to fluorescence correlation spectroscopy.

Radial pair correlation of molecular brightness fluctuations maps protein diffusion as a function of oligomeric state within live-cell nuclear architecture

Nuclear proteins can modulate their DNA binding activity and the exploration volume available during DNA target search by self-associating into higher-order oligomers. Directly tracking this process in the nucleoplasm of a living cell is, however, a complex task. Thus, here we present a microscopy method based on radial pair correlation of molecular brightness fluctuations (radial pCOMB) that can extract the mobility of a fluorescently tagged nuclear protein as a function of its oligomeric state and spatiotemporally map the anisotropy of this parameter with respect to nuclear architecture. By simply performing a rapid frame scan acquisition, radial pCOMB has the capacity to detect, within each pixel, protein oligomer formation and the size-dependent obstruction nuclear architecture imparts on this complex's transport across sub-micrometer distances. From application of radial pCOMB to an oligomeric transcription factor and DNA repair protein, we demonstrate that homo-oligomer formation differentially regulates chromatin accessibility and interaction with the DNA template.

Combining Fluorescence Fluctuations and Photobleaching to Quantify Surface Density

We have established a self-calibrated method, called pbFFS for photobleaching fluctuation fluorescence spectroscopy, which aims to characterize molecules or particles labeled with an unknown distribution of fluorophores. Using photobleaching as a control parameter, pbFFS provides information on the distribution of fluorescent labels and a reliable estimation of the absolute density or concentration of these molecules. We present a complete theoretical derivation of the pbFFS approach and experimentally apply it to measure the surface density of a monolayer of fluorescently tagged streptavidin molecules, which can be used as a base platform for biomimetic systems. The surface density measured by pbFFS is consistent with the results of spectroscopic ellipsometry, a standard surface technique. However, pbFFS has two main advantages: it enables in situ characterization (no dedicated substrates are required) and can be applied to low masses of adsorbed molecules, which we demonstrate here by quantifying the density of biotin-Atto molecules that bind to the streptavidin layer. In addition to molecules immobilized on a surface, we also applied pbFFS to molecules diffusing in solution, to confirm the distribution of fluorescent labels found on a surface. Hence, pbFFS provides a set of tools for investigating the molecules labeled with a variable number of fluorophores, with the aim of quantifying either the number of molecules or the distribution of fluorescent labels, the latter case being especially relevant for oligomerization studies.

The Mean Single Molecule Rate (mSMR) in the Analysis of Fluorescence Fluctuations: Measurements on DNA Mixtures of Defined Composition

We present a method for the evaluation of fluorescence fluctuations on the basis of Mandel’s Q parameter, using sampling time-dependent factorial cumulants. By relating the Q parameter to the sampling time, we obtain the mean single molecule rate (mSMR), an easy to interpret expression that provides both brightness and diffusion information. The model is suitable for the widely used confocal setups with single photon excitation and a single detection channel. We present a way to correct the mSMR for afterpulsing, dead time and background noise. To account for photokinetic effects at short sampling times, we expand the model by a simple on/off isomerization term, which is similar to the well-known triplet model. The functionality of the mSMR is shown using Monte Carlo simulations. The correction mechanisms and the experimental applicability of the model are then demonstrated by DNA measurements of defined composition. By systematically analyzing DNA mixtures, we can show that at large sampling times, the mSMR correctly describes the single molecule brightness rates and the diffusive properties of DNA molecules. At short sampling times, the photokinetic effects of isomerization are accurately described by the mSMR model. Since additionally the mSMR can easily be corrected for measurement artefacts such as detector dead time, afterpulsing and background noise, this is a valuable advantage over the standard method of fluorescence correlation spectroscopy.

Enhanced temporal and spatial resolution in super-resolution covariance imaging algorithm with deconvolution optimization

Based on the numerical analysis that covariance exhibits superior statistical precision than cumulant and variance, a new SOFI algorithm by calculating the n orders covariance for each pixel is presented with an almost 2n -fold resolution improvement, which can be enhanced to 2ⁿ via deconvolution. An optimized deconvolution is also proposed by calculating the (n + 1) order SD associated with each n order covariance pixel, and introducing the results into the deconvolution as a damping factor to suppress noise generation. Moreover, a re-deconvolution of the covariance image with the covariance-equivalent point spread function is used to further increase the final resolution by above 2-fold. Simulated and experimental results show that this algorithm can significantly increase the temporal-spatial resolution of SOFI, meanwhile, preserve the sample's structure. Thus, a resolution of 58 nm is achieved for 20 experimental images, and the corresponding acquisition time is 0.8 seconds.

Resolving fluorescent species by their brightness and diffusion using correlated photon-counting histograms

Fluorescence fluctuation spectroscopy (FFS) refers to techniques that analyze fluctuations in the fluorescence emitted by fluorophores diffusing in a small volume and can be used to distinguish between populations of molecules that exhibit differences in brightness or diffusion. For example, fluorescence correlation spectroscopy (FCS) resolves species through their diffusion by analyzing correlations in the fluorescence over time; photon counting histograms (PCH) and related methods based on moment analysis resolve species through their brightness by analyzing fluctuations in the photon counts. Here we introduce correlated photon counting histograms (cPCH), which uses both types of information to simultaneously resolve fluorescent species by their brightness and diffusion. We define the cPCH distribution by the probability to detect both a particular number of photons at the current time and another number at a later time. FCS and moment analysis are special cases of the moments of the cPCH distribution, and PCH is obtained by summing over the photon counts in either channel. cPCH is inherently a dual channel technique, and the expressions we develop apply to the dual colour case. Using simulations, we demonstrate that two species differing in both their diffusion and brightness can be better resolved with cPCH than with either FCS or PCH. Further, we show that cPCH can be extended both to longer dwell times to improve the signal-to-noise and to the analysis of images. By better exploiting the information available in fluorescence fluctuation spectroscopy, cPCH will be an enabling methodology for quantitative biology.

Identifying Heteroprotein Complexes in the Nuclear Envelope

The nucleus is delineated by the nuclear envelope (NE), which is a double membrane barrier composed of the inner and outer nuclear membranes as well as a ∼40-nm wide lumen. In addition to its barrier function, the NE acts as a critical signaling node for a variety of cellular processes, which are mediated by protein complexes within this subcellular compartment. Although fluorescence fluctuation spectroscopy is a powerful tool for characterizing protein complexes in living cells, it was recently demonstrated that conventional fluorescence fluctuation spectroscopy methods are not suitable for applications in the NE because of the presence of slow nuclear membrane undulations. We previously addressed this challenge by developing time-shifted mean-segmented Q (tsMSQ) analysis and applied it to successfully characterize protein homo-oligomerization in the NE. However, many NE complexes, such as the linker of the nucleoskeleton and cytoskeleton complex, are formed by heterotypic interactions, which single-color tsMSQ is unable to characterize. Here, we describe the development of dual-color (DC) tsMSQ to analyze NE heteroprotein complexes built from proteins that carry two spectrally distinct fluorescent labels. Experiments performed on model systems demonstrate that DC tsMSQ properly identifies heteroprotein complexes and their stoichiometry in the NE by accounting for spectral cross talk and local volume fluctuations. Finally, we applied DC tsMSQ to study the assembly of the linker of the nucleoskeleton and cytoskeleton complex, a heteroprotein complex composed of Klarsicht/ANC-1/SYNE homology and Sad1/UNC-84 (SUN) proteins, in the NE of living cells. Using DC tsMSQ, we demonstrate the ability of the SUN protein SUN2 and the Klarsicht/ANC-1/SYNE homology protein nesprin-2 to form a heterocomplex in vivo. Our results are consistent with previously published in vitro studies and demonstrate the utility of the DC tsMSQ technique for characterizing NE heteroprotein complexes.

Two-Color Spatial Cumulant Analysis Detects Heteromeric Interactions between Membrane Proteins

Fluorescence fluctuation spectroscopy can be used to measure the aggregation of fluorescently labeled molecules and is typically performed using time series data. Spatial intensity distribution analysis and fluorescence moment image analysis are established tools for measuring molecular brightnesses from single-color images collected with laser scanning microscopes. We have extended these tools for analysis of two-color images to resolve heteromeric interactions between molecules labeled with spectrally distinct chromophores. We call these new methods two-color spatial intensity distribution analysis and two-color spatial cumulant analysis (2c-SpCA). To implement these techniques on a hyperspectral imaging system, we developed a spectral shift filtering technique to remove artifacts due to intrinsic cross talk between detector bins. We determined that 2c-SpCA provides better resolution from samples containing multiple fluorescent species; hence, this technique was carried forward to study images of living cells. We used fluorescent heterodimers labeled with enhanced green fluorescent protein and mApple to quantify the effects of resonance energy transfer and incomplete maturation of mApple on brightness measurements. We show that 2c-SpCA can detect the interaction between two components of trimeric G-protein complexes. Thus, 2c-SpCA presents a robust and computationally expedient means of measuring heteromeric interactions in cellular environments.

Recent progress in single-molecule studies of mRNA localization in vivo

From biogenesis to degradation, mRNA goes through diverse types of regulation and interaction with other biomolecules. Uneven distribution of mRNA transcripts and the diverse isoforms and modifications of mRNA make us wonder how cells manage the complexity and keep the functional integrity for the normal development of cells and organisms. Single-molecule microscopy tools have expanded the scope of RNA research with unprecedented spatiotemporal resolution. In this review, we highlight the recent progress in the methods for labeling mRNA targets and analyzing the quantitative information from fluorescence images of single mRNA molecules. In particular, the MS2 system and its various applications are the main focus of this article. We also review how recent studies have addressed biological questions related to the significance of mRNA localization in vivo. Efforts to visualize the dynamics of single mRNA molecules in live cells will push forward our knowledge on the nature of heterogeneity in RNA sequence, structure, and distribution as well as their molecular function and coordinated interaction with RNA binding proteins.

Number and brightness analysis reveals that NCAM and FGF2 elicit different assembly and dynamics of FGFR1 in live cells

Both fibroblast growth factor-2 (FGF2) and neural cell adhesion molecule (NCAM) trigger FGF receptor 1 (FGFR1) signaling; however, they induce remarkably distinct receptor trafficking and cellular responses. The molecular basis of such a dichotomy and the role of distinct types of ligand-receptor interaction remain elusive. Number of molecules and brightness (N&B) analysis revealed that FGF2 and NCAM promote different FGFR1 assembly and dynamics at the plasma membrane. NCAM stimulation elicits long-lasting cycles of short-lived FGFR1 monomers and multimers, a behavior that might reflect a rapid FGFR1 internalization and recycling. FGF2, instead, induces stable dimerization at the dose that stimulates cell proliferation. Reducing the occupancy of FGFR1 in response to low FGF2 doses causes a switch towards cyclically exposed and unstable receptor dimers, consistently with previously reported biphasic response to FGF2 and with the divergent signaling elicited by different ligand concentrations. Similar instability was observed upon altering the endocytic pathway. Thus, FGF2 and NCAM induce differential FGFR1 clustering at the cell surface, which might account for the distinct intracellular fate of the receptor and, hence, for the different signaling cascades and cellular responses.

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.

Optimizing the metric in sensorless adaptive optical microscopy with fluorescence fluctuations

Adaptive optics (AO) strategies using optimization-based, sensorless approaches are widely used, especially for microscopy applications. To converge rapidly to the best correction, such approaches require that a quality metric and a set of modes be chosen optimally. Fluorescence fluctuations microscopy, a family of methods that provides quantitative measurements of molecular concentration and mobility in living specimen, is in particular need of adaptive optics, since its results can be strongly biased by optical aberrations. We examined two possible metrics for sensorless AO, measured in a solution of fluorophores diffusing in 3D: the fluorescence count rate and the molecular brightness (or number of photons detected per molecule in the observation volume). We studied their respective measurement noise and sensitivity to aberrations. Then, AO correction accuracy was experimentally assessed by measuring the residual aberration after correcting a known wavefront. We proposed a theoretical framework to predict the correction accuracy, knowing the metric measurement noise and sensitivity. In the small aberration range, the brightness allows more accurate corrections when fluorophores are few but bright, whereas the count rate performs better in more concentrated solutions. When correcting large aberrations, the count rate is expected to be a more reliable metric.

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.

Statistical precision in super-resolution optical fluctuation imaging

The super-resolution optical fluctuation imaging (SOFI) technique enhances image spatial resolution by calculating the spatiotemporal cross-cumulants of independent stochastic intensity fluctuations of emitters. Ideally, SOFI eliminates any noise that is not correlated over time, but in practice, due to limited data lengths, the statistical uncertainty of cumulants will affect the continuities and homogeneities of SOFI images. Since the variance and signal-to-noise ratio (SNR) characterize cumulant statistical uncertainty, we determined theoretical expressions for these based on a single dataset. From a simulation of temporal fluctuations of blinking fluorescent emitters, we calculated the quantitative relation between the SNR of cumulants and multiple parameters of the blinking signal, such as the on-time ratio, acquisition frame to average blinking rate ratio, sequence length, and photon amplitude, which not only provides a physical interpretation for SOFI phenomena but also theoretical guidance to achieve optimal practical outcomes.

Quantifying the dynamics of the oligomeric transcription factor STAT3 by pair correlation of molecular brightness

Oligomerization of transcription factors controls their translocation into the nucleus and DNA-binding activity. Here we present a fluorescence microscopy analysis termed pCOMB (pair correlation of molecular brightness) that tracks the mobility of different oligomeric species within live cell nuclear architecture. pCOMB amplifies the signal from the brightest species present and filters the dynamics of the extracted oligomeric population based on arrival time between two locations. We use this method to demonstrate a dependence of signal transducer and activator of transcription 3 (STAT3) mobility on oligomeric state. We find that on entering the nucleus STAT3 dimers must first bind DNA to form STAT3 tetramers, which are also DNA-bound but exhibit a different mobility signature. Examining the dimer-to-tetramer transition by a cross-pair correlation analysis (cpCOMB) reveals that chromatin accessibility modulates STAT3 tetramer formation. Thus, the pCOMB approach is suitable for mapping the impact oligomerization on transcription factor dynamics.

Fluorescence cumulants analysis with non-ideal observation profiles

One of the challenges of fluorescence fluctuation fpectroscopy (FFS) is an adequate approximation of a brightness profile. The key feature of fluorescence intensity distribution analysis (FIDA) is a polynomial approximation of a brightness profile. A broad range of brightness profile shapes can be well described by this approximation. A different approach consisting of the introduction of additional fitting parameters, defined as a relative difference between integrals of the actual brightness profile and its Gaussian approximation, is used in photon counting histogram (PCH) analysis. It is sufficient to introduce only one additional fitting parameter (first-order correction) to get an adequate fit to the experimental data in many practical applications. In the current study, we apply these approaches to the theory of time integrated fluorescence cumulants analysis. We demonstrate that developed corrections improve results of FFS analysis applied to simulated and experimental data. The use of different brightness profile approximations and normalizations in PCH and FIDA leads to different estimates of brightness and the number of molecules, even though they represent the same physical quantities. Based on the developed theory, we derive equations that relate brightness and the number of molecules in PCH and FIDA.

Advanced fluorescence microscopy methods for the real-time study of transcription and chromatin dynamics

In this contribution we provide an overview of the recent advances allowed by the use of fluorescence microscopy methods in the study of transcriptional processes and their interplay with the chromatin architecture in living cells. Although the use of fluorophores to label nucleic acids dates back at least to about half a century ago,¹ two recent breakthroughs have effectively opened the way to use fluorescence routinely for specific and quantitative probing of chromatin organization and transcriptional activity in living cells: namely, the possibility of labeling first the chromatin loci and then the mRNA synthesized from a gene using fluorescent proteins. In this contribution we focus on methods that can probe rapid dynamic processes by analyzing fast fluorescence fluctuations.

Quantifying protein-protein interactions of peripheral membrane proteins by fluorescence brightness analysis

Fluorescently labeled proteins that are found both in the cytoplasm and at the plasma membrane, such as peripheral membrane proteins, create stratified fluorescent layers that present a challenging environment for brightness studies with fluorescence fluctuation spectroscopy. The geometry of each layer along with fluorescence and brightness contributions from adjacent layers generates a convoluted raw brightness that conceals the underlying brightness of each individual layer. Because the brightness at a layer establishes the oligomeric state of the fluorescently labeled protein at said layer, we developed a method that connects the experimental raw brightness with the physical brightness at each layered compartment. The technique determines the oligomerization in each compartment from an axial intensity scan through the sample, followed by a fluorescence fluctuation spectroscopy measurement at each layer. We experimentally verify the technique with H-Ras-EGFP as a model system and determine its oligomeric state at both the plasma membrane and in the cytoplasm. Furthermore, we study the oligomerization of the Gag matrix domain of Human T-lymphotropic virus Type 1. The matrix domain targets the Gag polyprotein to the plasma membrane where, subsequently, viral assembly occurs. We determine the oligomerization of matrix in the cytoplasm and observe the onset of protein-protein interactions at the membrane. These observations shed light on the early assembly steps of the retrovirus.

Quantitative Brightness Analysis of Fluorescence Intensity Fluctuations in E. Coli

The brightness measured by fluorescence fluctuation spectroscopy specifies the average stoichiometry of a labeled protein in a sample. Here we extended brightness analysis, which has been mainly applied in eukaryotic cells, to prokaryotic cells with E. coli serving as a model system. The small size of the E. coli cell introduces unique challenges for applying brightness analysis that are addressed in this work. Photobleaching leads to a depletion of fluorophores and a reduction of the brightness of protein complexes. In addition, the E. coli cell and the point spread function of the instrument only partially overlap, which influences intensity fluctuations. To address these challenges we developed MSQ analysis, which is based on the mean Q-value of segmented photon count data, and combined it with the analysis of axial scans through the E. coli cell. The MSQ method recovers brightness, concentration, and diffusion time of soluble proteins in E. coli. We applied MSQ to measure the brightness of EGFP in E. coli and compared it to solution measurements. We further used MSQ analysis to determine the oligomeric state of nuclear transport factor 2 labeled with EGFP expressed in E. coli cells. The results obtained demonstrate the feasibility of quantifying the stoichiometry of proteins by brightness analysis in a prokaryotic cell.

Measuring protein dynamics in live cells: protocols and practical considerations for fluorescence fluctuation microscopy

Quantitative analysis of protein complex stoichiometries and mobilities are critical for elucidating the mechanisms that regulate cellular pathways. Fluorescence fluctuation spectroscopy (FFS) techniques can measure protein dynamics, such as diffusion coefficients and formation of complexes, with extraordinary precision and sensitivity. Complete calibration and characterization of the microscope instrument is necessary in order to avoid artifacts during data acquisition and to capitalize on the full capabilities of FFS techniques. We provide an overview of the theory behind FFS techniques, discuss calibration procedures, provide protocols, and give practical considerations for performing FFS experiments. One important parameter recovered from FFS measurements is the relative molecular brightness that can correlate with oligomerization. Three methods for measuring molecular brightness (fluorescence correlation spectroscopy, photon-counting histogram, and number and brightness analysis) recover similar values when measuring samples under ideal conditions in vitro. However, examples are given illustrating that these different methods used for calculating molecular brightness of fluorescent molecules in cells are not always equivalent. Methods relying on spot measurements are more prone to bleaching and movement artifacts that can lead to underestimation of brightness values. We advocate for the use of multiple FFS techniques to study molecular brightnesses to overcome and compliment limitations of individual techniques.

Quantitative measurement of brightness from living cells in the presence of photodepletion

The brightness of fluorescently labeled proteins provides an excellent marker for identifying protein interactions in living cells. Quantitative interpretation of brightness, however, hinges on a detailed understanding of the processes that affect the signal fluctuation of the fluorescent label. Here, we focus on the cumulative influence of photobleaching on brightness measurements in cells. Photobleaching within the finite volume of the cell leads to a depletion of the population of fluorescently labeled proteins with time. The process of photodepletion reduces the fluorescence signal which biases the analysis of brightness data. Our data show that even small reductions in the signal can introduce significant bias into the analysis of the data. We develop a model that quantifies the bias and introduce an analysis method that accurately determines brightness in the presence of photodepletion as verified by experiments with mammalian and yeast cells. In addition, photodepletion experiments with the fluorescent protein EGFP reveal the presence of a photoconversion process, which leads to a marked decrease in the brightness of the EGFP protein. We also identify conditions where the effect of EGFP's photoconversion on brightness experiments can be safely ignored.

τFCS: multi-method global analysis enhances resolution and sensitivity in fluorescence fluctuation measurements

Fluorescence fluctuation methods have become invaluable research tools for characterizing the molecular-level physical and chemical properties of complex systems, such as molecular concentrations, dynamics, and the stoichiometry of molecular interactions. However, information recovery via curve fitting analysis of fluctuation data is complicated by limited resolution and challenges associated with identifying accurate fit models. We introduce a new approach to fluorescence fluctuation spectroscopy that couples multi-modal fluorescence measurements with multi-modal global curve fitting analysis. This approach yields dramatically enhanced resolution and fitting model discrimination capabilities in fluctuation measurements. The resolution enhancement allows the concentration of a secondary species to be accurately measured even when it constitutes only a few percent of the molecules within a sample mixture, an important new capability that will allow accurate measurements of molecular concentrations and interaction stoichiometry of minor sample species that can be functionally important but difficult to measure experimentally. We demonstrate this capability using τFCS, a new fluctuation method which uses simultaneous global analysis of fluorescence correlation spectroscopy and fluorescence lifetime data, and show that τFCS can accurately recover the concentrations, diffusion coefficients, lifetimes, and molecular brightness values for a two component mixture over a wide range of relative concentrations.

Simulation of autocorrelation function and photon counting distribution in fluorescence fluctuation spectroscopy

In modern fluorescence fluctuation spectroscopy, the autocorrelation function and photon counting distribution are two widely used statistical characteristics of the measured fluctuating fluorescence intensity signal. Applying special analysis methods such as fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) to these properties, it is possible to recover values of different parameters of fluorescent molecules such as the concentration, diffusion coefficient, molecular brightness, and kinetic rate constants. The development of new analysis methods is senseless without testing their validity, accuracy, and robustness. The most appropriate check of a method is its application to experimental data. However, sometimes it is more convenient and easier to verify a method on simulated data. Simulation is also useful for better understanding the processes that were modeled during the development of analysis methods. Here, we present two simulation models providing an autocorrelation function and photon counting distribution of a sequence of photon arrival times detected in fluorescence fluctuation spectroscopy.

Implementation and application of pulsed interleaved excitation for dual-color FCS and RICS

Pulsed interleaved excitation (PIE) employs pulsed laser sources that are interleaved such that differentially colored fluorophores can be measured or imaged quasi-simultaneously in the absence of spectral crosstalk. PIE improves the robustness and reduces data analysis complexity of many fluorescence techniques, such as fluorescence cross-correlation spectroscopy (FCCS) and raster image cross-correlation spectroscopy (ccRICS), two methods used for quantitative investigation of molecular interactions in vitro and in living cells. However, as PIE is most often used for fluorescence fluctuation spectroscopy and burst analysis experiments and utilizes time-correlated single-photon counting detection and advanced optoelectronics, it has remained a technique that is mostly used by specialized single-molecule research groups. This protocols chapter provides an accessible overview of PIE for anyone considering implementing the method on a homebuilt or commercial microscope. We give details on the instrumentation, data collection and analysis software, on how to properly set up and align a PIE microscope, and finally, on how to perform proper dual-color FCS and RICS experiments.

Imaging fluorescence fluctuation spectroscopy: new tools for quantitative bioimaging

Fluorescence fluctuation spectroscopy (FFS) techniques provide information at the single-molecule level with excellent time resolution. Usually applied at a single spot in a sample, they have been recently extended into imaging formats, referred to as imaging FFS. They provide spatial information at the optical diffraction limit and temporal information in the microsecond to millisecond range. This review provides an overview of the different modalities in which imaging FFS techniques have been implemented and discusses present imaging FFS capabilities and limitations. A combination of imaging FFS and nanoscopy would allow one to record information with the detailed spatial information of nanoscopy, which is ∼20 nm and limited only by fluorophore size and labeling density, and the time resolution of imaging FFS, limited by the fluorescence lifetime. This combination would provide new insights into biological events by providing spatiotemporal resolution at unprecedented levels.

Time-integrated fluorescence cumulant analysis and its application in living cells

Time-integrated fluorescence cumulant analysis (TIFCA) is a data analysis technique for fluorescence fluctuation spectroscopy (FFS) that extracts information from the cumulants of the integrated fluorescence intensity. It is the first exact theory that describes the effect of sampling time on FFS experiment. Rebinning of data to longer sampling times helps to increase the signal/noise ratio of the experimental cumulants of the photon counts. The sampling time dependence of the cumulants encodes both brightness and diffusion information of the sample. TIFCA analysis extracts this information by fitting the cumulants to model functions. Generalization of TIFCA to multicolor FFS experiment is straightforward. Here, we present an overview of the theory, its implementation, as well as the benefits and requirements of TIFCA. The questions of why, when, and how to use TIFCA will be discussed. We give several examples of practical applications of TIFCA, particularly focused on measuring molecular interaction in living cells.

Time-averaged fluorescence intensity analysis in fluorescence fluctuation polarization sensitive experiments

In fluorescence fluctuation polarization sensitive experiments, the limitations associated with detecting the rotational timescale are usually eliminated by applying fluorescence correlation spectroscopy analysis. In this paper, the variance of the time-averaged fluorescence intensity extracted from the second moment of the measured fluorescence intensity is analyzed in the short time limit, before fluctuations resulting from rotational diffusion average out. Since rotational correlation times of fluorescence molecules are typically much lower than the temporal resolution of the system, independently of the time bins used, averaging over an ensemble of time-averaged trajectories was performed in order to construct the time-averaged intensity distribution, thus improving the signal-to-noise ratio. Rotational correlation times of fluorescein molecules in different viscosities of the medium within the range of the anti-bunching time (1-10 ns) were then extracted using this method.

Global analysis in fluorescence correlation spectroscopy and fluorescence lifetime microscopy

Fluorescence correlation spectroscopy (FCS) and related fluctuation spectroscopy and microscopy methods have become important research tools that enable detailed investigations of the chemical and physical properties of molecules and molecular systems in a variety of complex environments. Information recovery via curve fitting of fluctuation data can present complicating challenges due to limited resolution and/or problems with fitting model verification. We discuss a new approach to data analysis called τFCS that couples multiple modes of signal acquisition, here specifically FCS and fluorescence lifetimes, with global analysis. We demonstrate enhanced resolution using τFCS, including the capability to recover the concentration of both molecular species in a two-component mixture even when the species have identical diffusion coefficients and molecular brightness values, provided their fluorescent lifetimes are distinct. We also demonstrate how τFCS provides useful tools for model discrimination in FCS curve fitting.

Pulsed interleaved excitation: principles and applications

Pulsed interleaved excitation (PIE) is the methodology of interleaved or alternating excitation of different fluorophores on the nanosecond timescale, which allows quasi-simultaneous, yet independent measurements to be performed. PIE simplifies quantification of several fluorescence techniques such as FCCS and FRET experiments. Foremost, it allows to specifically filter out spectral emission bleedthrough (crosstalk) and direct excitation without a decrease in the signal-to-noise ratio (SNR) of the experiment. Next, PIE allows determination of the absolute FRET efficiency from FCCS experiments in the case of nonperfect labeling. In recent years, PIE has been utilized in many different advanced FFS techniques. Combining MFD with PIE allows highly accurate and species-specific spFRET analyses to be performed. The combination of scanning FFS techniques with PIE combines the best of both techniques and allows for false-positive free measurements of molecular interactions in vitro and in living cells. In succession, a comprehensive overview of the principle and versatility of the PIE technique is discussed, the theory for analysis with PIE is outlined by comparing CW- and PIE-FCCS and finally, some of the most important applications of the PIE technique in literature are reviewed.

Direct observation of T4 lysozyme hinge-bending motion by fluorescence correlation spectroscopy

Bacteriophage T4 Lysozyme (T4L) catalyzes the hydrolysis of the peptidoglycan layer of the bacterial cell wall late in the infection cycle. It has long been postulated that equilibrium dynamics enable substrate access to the active site located at the interface between the N- and C-terminal domains. Crystal structures of WT-T4L and point mutants captured a range of conformations that differ by the hinge-bending angle between the two domains. Evidence of equilibrium between open and closed conformations in solution was gleaned from distance measurements between the two domains but the nature of the equilibrium and the timescale of the underlying motion have not been investigated. Here, we used fluorescence fluctuation spectroscopy to directly detect T4L equilibrium conformational fluctuations in solution. For this purpose, Tetramethylrhodamine probes were introduced at pairs of cysteines in regions of the molecule that undergo relative displacement upon transition from open to closed conformations. Correlation analysis of Tetramethylrhodamine intensity fluctuations reveals hinge-bending motion that changes the relative distance and orientation of the N- and C-terminal domains with ≅ 15 μs relaxation time. That this motion involves interconversion between open and closed conformations was further confirmed by the dampening of its amplitude upon covalent substrate trapping. In contrast to the prevalent two-state model of T4L equilibrium, molecular brightness and number of particles obtained from cumulant analysis suggest that T4L populates multiple intermediate states, consistent with the wide range of hinge-bending angles trapped in the crystal structure of T4L mutants.

Determination of membrane protein transporter oligomerization in native tissue using spatial fluorescence intensity fluctuation analysis

Membrane transporter proteins exist in a complex dynamic equilibrium between various oligomeric states that include monomers, dimers, dimer of dimers and higher order oligomers. Given their sub-optical microscopic resolution size, the oligomerization state of membrane transporters is difficult to quantify without requiring tissue disruption and indirect biochemical methods. Here we present the application of a fluorescence measurement technique which combines fluorescence image moment analysis and spatial intensity distribution analysis (SpIDA) to determine the oligomerization state of membrane proteins in situ. As a model system we analyzed the oligomeric state(s) of the electrogenic sodium bicarbonate cotransporter NBCe1-A in cultured cells and in rat kidney. The approaches that we describe offer for the first time the ability to investigate the oligomeric state of membrane transporter proteins in their native state.

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.

Adaptive optics for fluorescence correlation spectroscopy

Fluorescence Correlation Spectroscopy (FCS) yields measurement parameters (number of molecules, diffusion time) that characterize the concentration and kinetics of fluorescent molecules within a supposedly known observation volume. Absolute derivation of concentrations and diffusion constants therefore requires preliminary calibrations of the confocal Point Spread Function with phantom solutions under perfectly controlled environmental conditions. In this paper, we quantify the influence of optical aberrations on single photon FCS and demonstrate a simple Adaptive Optics system for aberration correction. Optical aberrations are gradually introduced by focussing the excitation laser beam at increasing depths in fluorescent solutions with various refractive indices, which leads to drastic depth-dependent bias in the estimated FCS parameters. Aberration correction with a Deformable Mirror stabilizes these parameters within a range of several tens of μm into the solution. We also demonstrate, both theoretically and experimentally, that the molecular brightness scales as the Strehl ratio squared.

Development of time-integrated multipoint moment analysis for spatially resolved fluctuation spectroscopy with high time resolution

Spatial gradients in the behaviors of soluble proteins are thought to underlie many phenomena in cell and developmental biology, but the nature and even the existence of these gradients are often unclear because few techniques can adequately characterize them. Methods with sufficient temporal resolution to study the dynamics of diffusing molecules can only sample relatively small regions, whereas methods that are capable of imaging larger areas cannot probe fast timescales. To overcome these limitations, we developed and implemented time-integrated multipoint moment analysis (TIMMA), a form of fluorescence fluctuation spectroscopy that is capable of probing timescales down to 20 μs at hundreds of different locations simultaneously in a sample. We show that TIMMA can be used to measure the diffusion of small-molecule dyes and fluorescent colloids, and that it can create spatial maps of the behavior of soluble fluorescent proteins throughout mammalian tissue culture cells. We also demonstrate that TIMMA can characterize internal gradients in the diffusion of freely moving proteins in single cells.

Three-dimensional reconstructions of Arp2/3 complex with bound nucleation promoting factors

Arp2/3 complex initiates the growth of branched actin-filament networks by inducing actin polymerization from the sides of pre-existing filaments. Nucleation promoting factors (NPFs) are essential for the branching reaction through interactions with the Arp2/3 complex prior to branch formation. The modes by which NPFs bind Arp2/3 complex and associated conformational changes have remained elusive. Here, we used electron microscopy to determine three-dimensional structures at ~2 nm resolution of Arp2/3 complex with three different bound NPFs: N-WASp, Scar-VCA and cortactin. All of these structures adopt a conformation with the two actin-related proteins in an actin-filament-like dimer and the NPF bound to the pointed end. Distance constraints derived by fluorescence resonance energy transfer independently verified the NPF location. Furthermore, all bound NPFs partially occlude the actin-filament binding site, suggesting that additional local structural rearrangements are required in the pathway of Arp2/3 complex activation to allow branch formation.

Nuclear physics: quantitative single-cell approaches to nuclear organization and gene expression

The internal workings of the nucleus remain a mystery. A list of component parts exists, and in many cases their functional roles are known for events such as transcription, RNA processing, or nuclear export. Some of these components exhibit structural features in the nucleus, regions of concentration or bodies that have given rise to the concept of functional compartmentalization--that there are underlying organizational principles to be described. In contrast, a picture is emerging in which transcription appears to drive the assembly of the functional components required for gene expression, drawing from pools of excess factors. Unifying this seemingly dual nature requires a more rigorous approach, one in which components are tracked in time and space and correlated with onset of specific nuclear functions. In this chapter, we anticipate tools that will address these questions and provide the missing kinetics of nuclear function. These tools are based on analyzing the fluctuations inherent in the weak signals of endogenous nuclear processes and determining values for them. In this way, it will be possible eventually to provide a computational model describing the functional relationships of essential components.

Determining antibody stoichiometry using time-integrated fluorescence cumulant analysis

We applied fluorescence fluctuation spectroscopy to resolve the binding heterogeneity of fluorescently labeled ligand derived from brain natriuretic peptide (BNP), a widely used diagnostic marker of heart failure, to a corresponding monoclonal antibody. This system includes three species: (1) free ligand molecules, (2) antibody with a single site occupied, and (3) antibody with both sites occupied. The method we used, time-integrated fluorescence cumulant analysis (TIFCA), utilizes cumulants of fluorescence fluctuations to resolve subpopulations of multiple fluorescent species freely diffusing in a solution. The values of the cumulants depend on the concentration, molecular brightness and diffusion time of the fluorescent molecules. The number of molecules in each species reflects the antibody affinity. We apply TIFCA to successfully establish the stoichiometry of the system, estimate affinity, and identify the presence of an inactive fraction of antigen in a single titration experiment.

Fluorescence fluctuation analysis of receptor kinase dimerization

Receptor kinases are essential for the cellular perception of signals. The classical model for activation of the receptor kinase involves dimerization, induced by the binding of the ligand. The mechanisms by which plant receptors transduce signals across the cell surface are largely unknown but plant receptors seem to dimerize as well. In this chapter, we describe two fluorescence fluctuation techniques, fluorescence cross-correlation spectroscopy and photon counting histogram analysis, to study the oligomerization state of receptor kinases in living plant cells in a quantitative manner.

Fluorescence fluctuation spectroscopy and imaging methods for examination of dynamic protein interactions in yeast

Protein interactions are inherently dynamic. In no system is this more true and important than in signaling pathways, where spatial and temporal control of specific protein interactions is key to signaling specificity and timing. While genetic and biochemical interactions form a necessary and important starting point for deciphering interactions among signaling components, they struggle to provide precise information of where and when interactions occur in a live cell setting. In contrast, live cell fluorescence studies such as those outlined below are able to provide quantitative information on the strength, nature, timing, and location of homotypic and heterotypic protein interactions.