Efficient approximations for stationary single-channel Ca2+ nanodomains across length scales

Abstract

ABSTRACTWe 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 Ca2+ buffer with one-to-one Ca2+ binding. We present computationally efficient approximants that estimate stationary single-channel Ca2+ nanodomains with great accuracy in broad regions of parameter space. The presented approximants have a functional form that combines rational and exponential functions, which is similar to that of the well-known Excess Buffer Approximation and the linear approximation, but with parameters estimated using two novel (to our knowledge) methods. One of the methods involves interpolation between the short-range Taylor series of the buffer concentration and its long-range asymptotic series in inverse powers of distance from the channel. Although this method has already been used to find Padé (rational-function) approximants to single-channel Ca2+ and buffer concentration, extending this method to interpolants combining exponential and rational functions improves accuracy in a significant fraction of the relevant parameter space. A second method is based on the variational approach, and involves a global minimization of an appropriate functional with respect to parameters of the chosen approximations. Extensive parameter sensitivity analysis is presented, comparing these two methods with previously developed approximants. Apart from increased accuracy, the strength of these approximants is that they can be extended to more realistic buffers with multiple binding sites characterized by cooperative Ca2+ binding, such as calmodulin and calretinin.STATEMENT OF SIGNIFICANCEMathematical and computational modeling plays an important role in the study of local Ca2+ signals underlying vesicle exocysosis, muscle contraction and other fundamental physiological processes. Closed-form approximations describing steady-state distribution of Ca2+ in the vicinity of an open Ca2+ channel have proved particularly useful for the qualitative modeling of local Ca2+ signals. We present simple and efficient approximants for the Ca2+ concentration in the presence of a mobile Ca2+ buffer, which achieve great accuracy over a wide range of model parameters. Such approximations provide an efficient method for estimating Ca2+ and buffer concentrations without resorting to numerical simulations, and allow to study the qualitative dependence of nanodomain Ca2+ distribution on the buffer’s Ca2+ binding properties and its diffusivity.