Padé Approximation of a Stationary Single-Channel Ca 2+ Nanodomain

Abstract

We consider the stationary solution for the Ca 2þ concentration near a point Ca 2þ source describing a single-channel Ca 2þ nanodomain, in the presence of a single mobile buffer with one-to-one Ca 2þ binding stoichiometry. Previously, a number of Ca 2þ nanodomains approximations have been developed, for instance the excess buffer approximation (EBA), the rapid buffering approximation (RBA), and the linear approximation (LIN), each valid for appropriate buffering conditions. Apart from providing a simple method of estimating Ca 2þ and buffer concentrations without resorting to computationally expensive numerical solution of reaction-diffusion equations, such approximations proved useful in revealing the dependence of nanodomain Ca 2þ distribution on crucial parameters such as buffer mobility and its Ca 2þ binding properties. In this study, we present a different form of analytic approximation, which is based on matching the shortrange 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 we show that this provides an accurate approximation to the nanodomain Ca 2þ 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 our method is that it has a complex algebraic form for any order higher than the lowest bilinear order, and cannot be readily extended to multiple Ca 2þ channels. However, it may be possible to extend the Padé method to estimate Ca 2þ nanodomains in the presence of cooperative Ca 2þ buffers with two Ca 2þ binding sites, the case that existing methods do not address.

Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

“…Another method is based on the Padé approximation, which is usually combined with Laplace transform, see previous studies. [33][34][35][36] We will explore these techniques in detail in our future research.…”

“…For instance, authors in previous studies have proposed multistage ADM, which divides the solution into several small regions. Another method is based on the Padé approximation, which is usually combined with Laplace transform, see previous studies . We will explore these techniques in detail in our future research.…”

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

“…We have presented a significant extension of prior modeling work on equilibrium single-channel Ca 2+ nanodomains, presenting two distinct approaches applied to several types of parametric approximants, which to our knowledge have not been considered previously. In particular, we extend the series interpolation methods recently used to construct rational function (Padé) approximants (32), generalizing it to more accurate and natural parametric forms given by Eqs. [25][26][27], which bear resemblance to the EBA and LIN approximants obtained previously using different methods.…”

Stationary Ca2+nanodomains in the presence of buffers with two binding sites

“…buffers in (38) and generalized in (37), can be extended to buffers with 2:1 Ca 2+ -binding stoichiometry, and we introduced several simple interpolants that combine rational and exponential functions. Several functional forms other than the ones shown in Eqs.…”

“…As noted above, close to the channel location [Ca 2+ ] is dominated by the source term, 1/r, therefore we will modify the buffer error norm, Eq. 27, by taking the logarithm of [Ca 2+ ](37,38,48):…”