Université Abdelmalek Essadi, FST Tanger, Département de Mathématiques, BP 416 Tanger, Morocco.
Math Biosci. 2013 May;243(1):46-56. doi: 10.1016/j.mbs.2013.01.011. Epub 2013 Feb 18.
The Poisson-Boltzmann equation has been increasingly used for the description of biomolecular systems in order to derive their electrostatic properties. We here consider a domain consisting of two living cells which communicate through a system of proteins which assemble at specific membrane areas building microchannels called gap junctions. We describe the asymptotic behavior of the solution of the Poisson-Boltzmann equation posed in this domain. Using Γ-convergence tools, we derive some electrostatic properties of the biological membrane with respect to a vanishing parameter which is simultaneously associated to the membrane thinness, to the diameter of the gap junction microchannels and to the Debye length parameter which characterizes the spatial scale electrostatic interactions between particles within the gap junctions.
泊松-玻尔兹曼方程已被越来越多地用于描述生物分子系统，以推导它们的静电特性。我们在这里考虑一个由两个活细胞组成的区域，它们通过一组蛋白质进行通讯，这些蛋白质在特定的膜区域组装形成微通道，称为间隙连接。我们描述了在这个区域中泊松-玻尔兹曼方程解的渐近行为。使用 Γ 收敛工具，我们推导出了生物膜的一些静电特性，这与一个同时与膜的厚度、间隙连接微通道的直径以及德拜长度参数相关的参数有关，该参数表征了间隙连接内粒子之间的空间尺度静电相互作用。
