Approximate analytical time-dependent solutions to describe large-amplitude local calcium transients in the presence of buffers

Local Ca²⁺ signaling controls many neuronal functions, which is often achieved through spatial localization of Ca²⁺ signals. These nanodomains are formed due to combined effects of Ca²⁺ diffusion and binding to the cytoplasmic buffers. In this article we derived simple analytical expressions to describe Ca²⁺ diffusion in the presence of mobile and immobile buffers. A nonlinear character of the reaction-diffusion problem was circumvented by introducing a logarithmic approximation of the concentration term. The obtained formulas reproduce free Ca²⁺ levels up to 50 μM and their changes in the millisecond range. Derived equations can be useful to predict spatiotemporal profiles of large-amplitude [Ca²⁺] transients, which participate in various physiological processes.