Autocorrelation function of finite-length data in fluorescence correlation spectroscopy

Statistical analysis of fluorescence intensity transients with Bayesian methods

Molecular movement and interactions at the single-molecule level, particularly in live cells, are often studied using fluorescence correlation spectroscopy (FCS). While powerful, FCS has notable drawbacks: It requires high laser intensities and long acquisition times, increasing phototoxicity, and often relies on problematic statistical assumptions in data fitting. We introduce fluorescence intensity trace statistical analysis (FITSA), a Bayesian method that directly analyzes fluorescence intensity traces. FITSA offers faster, more stable convergence than previous approaches and provides robust parameter estimation from far shorter measurements than conventional FCS. Our results demonstrate that FITSA achieves comparable precision to FCS while requiring substantially fewer photons. This advantage becomes even more pronounced when accounting for statistical dependencies in FCS analysis, which are often overlooked but necessary for accurate error estimation. By reducing laser exposure, FITSA minimizes phototoxicity effects, representing a major advancement in the quantitative analysis of molecular processes across fields.

Nanoscale domains govern local diffusion and aging within FUS condensates

Biomolecular condensates regulate cellular physiology by sequestering and processing RNAs and proteins, yet how these processes are locally tuned within condensates remains unclear. Moreover, in neurodegenerative diseases such as amyotrophic lateral sclerosis (ALS), condensates undergo liquid-to-solid phase transitions, but capturing early intermediates in this process has been challenging. Here, we present a surface multi-tethering approach to achieve intra-condensate single-molecule tracking of fluorescently labeled RNA and protein molecules within liquid-like condensates. Using RNA-binding protein Fused in Sarcoma (FUS) as a model for condensates implicated in ALS, we discover that RNA and protein diffusion is confined within distinct nanometer-scale domains, or nanodomains, which exhibit unique connectivity and chemical environments. During condensate aging, these nanodomains reposition, facilitating FUS fibrilization at the condensate surface, a transition enhanced by FDA-approved ALS drugs. Our findings demonstrate that nanodomain formation governs condensate function by modulating biomolecule sequestration and percolation, offering insights into condensate aging and disease-related transitions.

Nanoscale domains govern local diffusion and aging within FUS condensates

Biomolecular condensates regulate cellular physiology by sequestering and processing RNAs and proteins, yet how these processes are locally tuned within condensates remains unclear. Moreover, in neurodegenerative diseases such as amyotrophic lateral sclerosis (ALS), condensates undergo liquid-to-solid phase transitions, but capturing early intermediates in this process has been challenging. Here, we present a surface multi-tethering approach to achieve intra-condensate single-molecule tracking of fluorescently labeled RNA and protein molecules within liquid-like condensates. Using RNA-binding protein Fused in Sarcoma (FUS) as a model for condensates implicated in ALS, we discover that RNA and protein diffusion is confined within distinct nanometer-scale domains, or nanodomains, which exhibit unique connectivity and chemical environments. During condensate aging, these nanodomains reposition, facilitating FUS fibrilization at the condensate surface, a transition enhanced by FDA-approved ALS drugs. Our findings demonstrate that nanodomain formation governs condensate function by modulating biomolecule sequestration and percolation, offering insights into condensate aging and disease-related transitions.

Super-resolution algorithms for imaging FCS enhancement: A comparative study

Understanding the structure and dynamics of biological systems is often limited by the trade-off between spatial and temporal resolution. Imaging fluorescence correlation spectroscopy (ImFCS) is a powerful technique for capturing molecular dynamics with high temporal precision but remains diffraction limited. This constraint poses challenges for quantifying dynamics of subcellular structures like membrane-proximal cortical actin fibers. Computational super-resolution microscopy (CSRM) presents an accessible strategy for enhancing spatial resolution without specialized instrumentation, enabling compatibility with ImFCS. In this study, we evaluated various CSRM techniques, including super-resolution radial fluctuations, mean-shift super-resolution, and multiple signal classification imaging, using total internal reflection fluorescence datasets of actin fibers labeled with F-tractin-mApple. By combining structural masks from total internal reflection fluorescence and CSRM, we distinguished off-fiber, mixed, and on-fiber regions for region-specific diffusion analyses. Although all CSRM algorithms improve ImFCS data analysis, super-resolution radial fluctuations demonstrated superior performance in identifying cortical actin fibers, showing minimal variance in on-fiber diffusion coefficients. These findings establish a framework for integrating CSRM with ImFCS to achieve high-resolution spatial and dynamic characterization of subcellular structures from single measurements.

FCS videos: Fluorescence correlation spectroscopy in space and time

Fluorescence Correlation Spectroscopy (FCS), invented more than 50 years ago is a widely used tool providing information on molecular processes in a variety of samples from materials to life sciences. In the last two decades FCS was multiplexed and ultimately made into an imaging technique that provided maps of molecular parameters over whole sample cross-section. However, it was still limited by a measurement time on the order of minutes. With the improvement of FCS time resolution to seconds using deep learning, we extend here FCS to so-called FCS videos that can provide information how the molecular parameters determined by Imaging FCS change in space and time. This opens up new possibilities for the investigation of molecular processes. Here, we demonstrate the feasibility of the approach and show FCS video applications to lipid bilayers and cell membranes.

Addressing spatiotemporal signal variations in pair correlation function analysis

Fluorescence correlation spectroscopy (FCS) is a cornerstone technique in optical microscopy to measure, for example, the concentration and diffusivity of fluorescent emitters and biomolecules in solution. The application of FCS to complex biological systems, however, is fraught with inherent intricacies that impair the interpretation of correlation patterns. Critical among these intricacies are temporal variations beyond diffusion in the quantity, intensity, and spatial distribution of fluorescent emitters. These variations introduce distortions into correlated intensity data, thus compromising the accuracy and reproducibility of the analysis. This issue is accentuated in imaging-based approaches such as pair correlation function (pCF) analysis due to their broader regions of interest compared with point-detector-based approaches. Despite ongoing developments in FCS, attention to systems characterized by a spatiotemporal-dependent probability distribution function (ST-PDF) has been lacking. To address this knowledge gap, we developed a new analytical framework for ST-PDF systems that introduces a dual-timescale model function within the conventional pCF analysis. Our approach selectively differentiates the signals associated with rapid processes, such as particle diffusion, from signals stemming from spatiotemporal variations in the distribution of fluorescent emitters occurring at extended delay timescales. To corroborate our approach, we conducted proof-of-concept experiments on an ST-PDF system, wherein the, initially, uniform distribution of fluorescent microspheres within a microfluidic channel changes into a localized accumulation of microspheres over time. Our framework is offering a comprehensive solution for investigating various phenomena such as biomolecular binding, sedimentation, and particle accumulation.

Segmented fluorescence correlation spectroscopy (FCS) on a commercial laser scanning microscope

Performing accurate Fluorescence Correlation Spectroscopy (FCS) measurements in cells can be challenging due to cellular motion or other intracellular processes. In this respect, it has recently been shown that analysis of FCS data in short temporal segments (segmented FCS) can be very useful to increase the accuracy of FCS measurements inside cells. Here, we demonstrate that segmented FCS can be performed on a commercial laser scanning microscope (LSM), even in the absence of the dedicated FCS module. We show how data can be acquired on a Leica SP8 confocal microscope and then exported and processed with a custom software in MATLAB. The software performs segmentation of the data to extract an average ACF and measure the diffusion coefficient in specific subcellular regions. First of all, we measure the diffusion of fluorophores of different size in solution, to show that good-quality ACFs can be obtained in a commercial LSM. Next, we validate the method by measuring the diffusion coefficient of GFP in the nucleus of HeLa cells, exploiting variations of the intensity to distinguish between nucleoplasm and nucleolus. As expected, the measured diffusion coefficient of GFP is slower in the nucleolus relative to nucleoplasm. Finally, we apply the method to HeLa cells expressing a PARP1 chromobody to measure the diffusion coefficient of PARP1 in different subcellular regions. We find that PARP1 diffusion is slower in the nucleolus compared to the nucleoplasm.

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.

Deep learning reduces data requirements and allows real-time measurements in imaging FCS

Imaging fluorescence correlation spectroscopy (FCS) is a powerful tool to extract information on molecular mobilities, actions, and interactions in live cells, tissues, and organisms. Nevertheless, several limitations restrict its applicability. First, FCS is data hungry, requiring 50,000 frames at 1-ms time resolution to obtain accurate parameter estimates. Second, the data size makes evaluation slow. Third, as FCS evaluation is model dependent, data evaluation is significantly slowed unless analytic models are available. Here, we introduce two convolutional neural networks-FCSNet and ImFCSNet-for correlation and intensity trace analysis, respectively. FCSNet robustly predicts parameters in 2D and 3D live samples. ImFCSNet reduces the amount of data required for accurate parameter retrieval by at least one order of magnitude and makes correct estimates even in moderately defocused samples. Both convolutional neural networks are trained on simulated data, are model agnostic, and allow autonomous, real-time evaluation of imaging FCS measurements.

Current capabilities and future perspectives of FCS: super-resolution microscopy, machine learning, and in vivo applications

Fluorescence correlation spectroscopy (FCS) is a single molecule sensitive tool for the quantitative measurement of biomolecular dynamics and interactions. Improvements in biology, computation, and detection technology enable real-time FCS experiments with multiplexed detection even in vivo. These new imaging modalities of FCS generate data at the rate of hundreds of MB/s requiring efficient data processing tools to extract information. Here, we briefly review FCS's capabilities and limitations before discussing recent directions that address these limitations with a focus on imaging modalities of FCS, their combinations with super-resolution microscopy, new evaluation strategies, especially machine learning, and applications in vivo.