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A novel method for approximating equilibrium single-channel Ca2+ domains

Localized calcium (Ca2+) signals control some of the most fundamental physiological processes, including synaptic transmission as well as its activity-dependent plasticity. Computational and mathematical modeling played a crucial role in the understanding of spatio-temporal Ca2+ dynamics that drives these processes, and showed that Ca2+ concentration around a single Ca2+ channel reaches a quasi-stationary distribution (known as the Ca2+ "nanodomain") within tens of microseconds after the opening of the channel, and collapses as rapidly after the closing of the channel. Such localization of Ca2+ in time and space is achieved by its rapid diffusion as well as its binding to its multiple interaction partners collectively called Ca2+ buffers and Ca2+ sensors. One of the successes of mathematical modeling was the development of several analytic approximations describing the equilibrium concentration of Ca2+ as a function of distance from the open Ca2+ channel, such as the Rapid Buffering Approximation (RBA), the Linear Approximation (LA) and the Excess Buffering Approximation (EBA) [14]. Each of these approximations has a particular applicability parameter regime created by the interplay between the properties of Ca2+ buffers, in particular their mobility and Ca2+ binding rates, and the strength of the Ca2+ current. Here we present a novel approximation method which does not rely on a specific range of the relevant Ca2+ and buffer parameters, and is based on matching the low-distance and large-distance asymptotic behavior of the concentration function. Even at low orders, the resulting approximation is as accurate as the second-order RBA and EBA approximations [4], but its validity extends far beyond the parameter range of applicability of RBA and EBA. The usefulness of the resulting approximation is two-fold: first, together with the previously developed approximations, the novel method could provide a deeper intuition into the dependence of Ca2+ nanodomain properties on the relevant buffering parameters, and second, it constitutes an efficient numerical approximation tool in the modeling of the Ca2+ signals underlying presynaptic and postsynaptic phenomena.

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Correspondence to Victor Matveev.

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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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Keywords

  • Synaptic Transmission
  • Equilibrium Concentration
  • Numerical Approximation
  • Parameter Range
  • Analytic Approximation