Geometrical Effects on Nonlinear Electrodiffusion in Cell Physiology

J. Cartailler, Z. Schuss, D. Holcman

Research output: Contribution to journalArticlepeer-review


We report here new electrical laws, derived from nonlinear electrodiffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson–Nernst–Planck equations for charge concentration and electric potential as a model of electrodiffusion. In the case at hand, the entire boundary is impermeable to ions and the electric field satisfies the compatibility condition of Poisson’s equation. We construct an asymptotic approximation for certain singular limits to the steady-state solution in a ball with an attached cusp-shaped funnel on its surface. As the number of charge increases, they concentrate at the end of cusp-shaped funnel. These results can be used in the design of nanopipettes and help to understand the local voltage changes inside dendrites and axons with heterogeneous local geometry.

Original languageEnglish
Pages (from-to)1971-2000
Number of pages30
JournalJournal of Nonlinear Science
Issue number6
StatePublished - 1 Dec 2017


  • Asymptotics
  • Curvature
  • Cusp–shaped funnel
  • Electro-diffusion
  • Electrolytes
  • Mobius conformal map
  • Neurobiology
  • Nonelectroneutrality
  • Nonlinear partial differential equation
  • Poisson–Nernst–Planck


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