Approximations of stationary calcium nanodomains in the presence of buffers with two binding sites

Calcium ion (Ca2+) elevations near open Ca2+ channels, termed Ca2+ nanodomains, trigger secretory vesicle fusion, myocyte contraction, and other fundamental physiological processes. Ca2+ nanodomains are shaped by the interplay between Ca2+ influx, diffusion, and binding to Ca2+ buffers and sensors, which absorb most of the Ca2+ entering the cell. The dependence of Ca2+ concentration on the distance from the Ca2+ channel can be modeled with reasonable accuracy using closed-form approximations of quasi-stationary solutions of the corresponding reaction-diffusion equations. Such stationary approximations help to reveal the qualitative characteristics of Ca2+ nanodomains without resorting to computationally expensive numerical simulations. Although a variety of nanodomain approximations are known when Ca2+ is diffusing in the presence of Ca2+ buffers with a single Ca2+ binding site, most biological buffers have more complex Ca2+-binding stoichiometry. We present several closed-form approximations of Ca2+ nanodomains in the presence of buffers with two binding sites, extending prior work on stationary Ca2+ nanodomains. Our approximants interpolate between the short-range and long-range distance-dependence of Ca2+ concentration using a combination of rational and exponential functions. We shows that this method achieves significant accuracy for a very wide range of Ca2+ buffering parameter values. Supported by NSF DMS-1517085 (V.M)