TY - JOUR
T1 - Geometrical Effects on Nonlinear Electrodiffusion in Cell Physiology
AU - Cartailler, J.
AU - Schuss, Z.
AU - Holcman, D.
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media New York.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - 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.
AB - 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.
KW - Asymptotics
KW - Curvature
KW - Cusp–shaped funnel
KW - Electro-diffusion
KW - Electrolytes
KW - Mobius conformal map
KW - Neurobiology
KW - Nonelectroneutrality
KW - Nonlinear partial differential equation
KW - Poisson–Nernst–Planck
UR - http://www.scopus.com/inward/record.url?scp=85019556628&partnerID=8YFLogxK
U2 - 10.1007/s00332-017-9393-2
DO - 10.1007/s00332-017-9393-2
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AN - SCOPUS:85019556628
VL - 27
SP - 1971
EP - 2000
JO - Journal of Nonlinear Science
JF - Journal of Nonlinear Science
SN - 0938-8974
IS - 6
ER -