Fluorescence correlation spectroscopy experiments to quantify free diffusion coefficients in reaction-diffusion systems: The case of Ca2+ and its dyes

Many cell signaling pathways involve the diffusion of messengers that bind/unbind to intracellular components. Quantifying their net transport rate under different conditions, then requires having separate estimates of their free diffusion coefficient and binding/unbinding rates. In this paper, we show how performing sets of Fluorescence Correlation Spectroscopy (FCS) experiments under different conditions, it is possible to quantify free diffusion coefficients and on and off rates of reaction-diffusion systems. We develop the theory and present a practical implementation for the case of the universal second messenger, calcium (Ca$^{2+}$) and single-wavelength dyes that increase their fluorescence upon Ca$^{2+}$ binding. We validate the approach with experiments performed in aqueous solutions containing Ca$^{2+}$ and Fluo4 dextran (both in its High and Low Affinity versions). Performing FCS experiments with tetramethylrhodamine-dextran in Xenopus laevis oocytes, we infer the corresponding free diffusion coefficients in the cytosol of these cells. Our approach can be extended to other physiologically relevant reaction-diffusion systems to quantify biophysical parameters that determine the dynamics of various variables of interest.