- Poster presentation
- Open Access
A novel method for approximating equilibrium single-channel Ca2+ domains
© Matveev 2015
- Published: 18 December 2015
- Synaptic Transmission
- Equilibrium Concentration
- Numerical Approximation
- Parameter Range
- Analytic Approximation
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) [1–4]. 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 , 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.
- Neher E: Usefulness and limitations of linear approximations to the understanding of Ca2+ signals. Cell Calcium. 1998, 24 (5-6): 345-357.PubMedView ArticleGoogle Scholar
- Smith GD, Wagner J, Keizer J: Validity of the rapid buffering approximation near a point source of calcium ions. Biophys J. 1996, 70 (6): 2527-2539.PubMedPubMed CentralView ArticleGoogle Scholar
- Bertram R, Smith GD, Sherman A: Modeling study of the effects of overlapping Ca2+ microdomains on neurotransmitter release. Biophys J. 1999, 76 (2): 735-750.PubMedPubMed CentralView ArticleGoogle Scholar
- Smith GD, Dai LX, Miura RM, Sherman A: Asymptotic analysis of buffered calcium diffusion near a point source. Siam J Appl Math. 2001, 61 (5): 1816-1838.View ArticleGoogle Scholar
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.