Novel Approximation of a Stationary Single-Channel Ca2+ Nanodomain

Abstract

We consider the stationary solution for the Ca2+ concentration near a point Ca2+ source describing a single-channel Ca2+ nanodomain, in the presence of a single mobile buffer with one-to-one Ca2+ binding. Previously, a number of Ca2+ nanodomains approximations have been developed, such as the Excess Buffer approximation, the Rapid Buffering approximation, and the Linear approximation, each valid for appropriate buffering conditions. Apart from providing a simple method of estimating Ca2+ and buffer concentrations without resorting to computationally expensive numerical solution of reaction-diffusion equations, such approximations proved useful in revealing the dependence of nanodomain Ca2+ distribution on crucial parameters such as buffer mobility and its Ca2+ binding properties. Here we present a novel form of analytic approximation, which is based on matching the short-range Taylor series of the nanodomain concentration with the long-range asymptotic series expressed in inverse powers of distance from channel location. Namely, we use a “dual” Padé rational function approximation to simultaneously match terms in the short- and the long-range series, and show that this provides an accurate approximation to the nanodomain Ca2+ and buffer concentrations. We compare this approximation with the previously obtained approximations, and show that it yields a better estimate of the free buffer concentration for a wide range of buffering conditions. The drawback of the presented method is that it has a complex algebraic form above the lowest, bilinear order, and cannot be readily extended to multiple Ca2+ channels. However, it may be possible to extend at least some of the features of this method to the case of cooperative Ca2+ buffers with two Ca2+ binding sites (e.g. calretinin), the case which existing analytic methods do not address. This work was supported in part by the National Science Foundation grant DMS-1517085.