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.

Time-shifted mean-segmented Q data of a luminal protein measured at the nuclear envelope by fluorescence fluctuation microscopy

Fluorescence fluctuation microscopy is a widely used method to determine the mobility and oligomeric state of proteins in the live cell environment. Existing analysis methods rely on statistical evaluation of data segments with the implicit assumption that no significant signal fluctuations occur on the time scale of a data segment. Recent work on extending fluorescence fluctuation methods to the nuclear envelope of living cells identified a slow fluctuation process that is associated with the undulations of the nuclear membranes, which lead to intensity fluctuations due to local volume changes at the nuclear envelope. This environment violates the above-mentioned assumption and is associated with biased evaluation of fluorescence fluctuation data by traditional analysis methods, such as the autocorrelation function. This challenge was overcome by the introduction of the time-shifted mean-segmented Q function, which relies on a sliding scale of data segment lengths. Here, we share experimental fluorescence fluctuation data taken at the nuclear envelope and demonstrate the calculation of the time-shifted mean-segmented Q function from the raw data. The data and analysis should be valuable for researchers interested in fluorescence fluctuation techniques and provides an opportunity to examine the influence of slow fluctuations on existing data analysis methods. The data is related to the research article titled "Protein oligomerization and mobility within the nuclear envelope evaluated by the time-shifted mean-segmented Q factor" [1].

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.

Quantitative modeling of self-oligomerization of proteins in the nuclear envelope by fluorescence fluctuation analysis

Analysis of fluorescence fluctuation data through the time-shifted mean-segmented Q (tsMSQ) analysis method has recently been shown to successfully identify protein oligomerization and mobility in the nuclear envelope by properly accounting for local volume fluctuations of the nuclear envelope within living cells. However, by its nature, tsMSQ produces correlated data which poses unique challenges for applying goodness of fit tests and obtaining parameter uncertainties from individual measurements. In this paper, we overcome these challenges by introducing bootstrap tsMSQ which involves randomly resampling the fluorescence intensity data to eliminate the correlations in the tsMSQ data. This analysis technique was verified in both the cytoplasm and the lumen of the nuclear envelope with well-characterized proteins that served as model systems. Uncertainties and goodness of fit tests of individual measurements were compared to estimates obtained from sampling multiple experiments. We further applied bootstrapping to fluorescence fluctuation data of the luminal domain of the SUN domain-containing protein 2 in order to characterize its self-oligomerization within the nuclear envelope. Analysis of the concentration-dependent brightness suggests a monomer-trimer transition of the protein.

Investigating LINC Complex Protein Homo-oligomerization in the Nuclear Envelopes of Living Cells Using Fluorescence Fluctuation Spectroscopy

Linkers of nucleoskeleton and cytoskeleton (LINC) complexes are conserved nuclear envelope (NE) spanning molecular bridges which mechanically integrate the nucleus with the cytoskeleton and mediate force transmission into the nucleoplasm. Despite their critical roles in fundamental cellular processes such as meiotic chromosome and nuclear positioning, the mechanism of LINC complex assembly in cells remains unclear. To begin to address this deficit, we recently developed z-scan fluorescence fluctuation spectroscopy (FFS) and brightness analysis as a method for quantifying the oligomeric states of fluorescent protein-tagged NE proteins including nesprins and SUN proteins. Since the homo-oligomerization of SUN2 is critical for its ability to interact with nesprins within the perinuclear space, the knowledge obtained through quantitative brightness experiments reveals important insights into the in vivo mechanisms of LINC complex assembly. Here we describe the procedure we use to determine the brightness of proteins in the NE of living cells. In addition to the measurement procedure, we discuss the instrumentation requirements and present the results of applying this procedure to measure the brightness of nesprin-2 and SUN2.

Quantitative Brightness Analysis of Protein Oligomerization in the Nuclear Envelope

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

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

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

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.

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.