2017/10/06 by Jérôme Cartailler, David Holcman, Cartailler, J. +1
Biochemistry, Genetics and Molecular Biology · #35B25 #35B44 #35J66 #92C05 #92C37 #Analysis of PDEs (math.AP) #Biological Physics (physics.bio-ph) #Diffusion and Search Dynamics #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Neurons and Cognition (q-bio.NC) #Protein Structure and Dynamics #RNA Research and Splicing #Subcellular Processes (q-bio.SC)
paper · pdf · doi:10.48550/arxiv.1710.02423
openalex publication_date 2017/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.