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.