Voltage laws for three-dimensional microdomains with cusp-shaped funnels derived from Poisson-Nernst-Planck equations

Autor:	Cartailler, J., Holcman, D.
Rok vydání:	2017
Předmět:	Quantitative Biology - Neurons and Cognition Mathematics - Analysis of PDEs Physics - Biological Physics Quantitative Biology - Subcellular Processes 35J66 35B44 35B25 92C05 92C37
Druh dokumentu:	Working Paper
Popis:	We study the electro-diffusion properties of a domain containing a cusp-shaped structure in three dimensions when one ionic specie is dominant. The mathematical problem consists in solving the steady-state Poisson-Nernst-Planck (PNP) equation with an integral constraint for the number of charges. A non-homogeneous Neumann boundary condition is imposed on the boundary. We construct an asymptotic approximation for certain singular limits that agree with numerical simulations. Finally, we analyse the consequences of non-homogeneous surface charge density. We conclude that the geometry of cusp-shaped domains influences the voltage profile, specifically inside the cusp structure. The main results are summarized in the form of new three-dimensional electrostatic laws for non-electroneutral electrolytes. We discuss applications to dendritic spines in neuroscience. Comment: 28 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1710.02423 Zobrazit plný text záznamu View this record from Arxiv