A Poisson--Nernst--Planck Model for Biological Ion Channels---An Asymptotic Analysis in a Three-Dimensional Narrow Funnel

@article{Singer2009APM,
  title={A Poisson--Nernst--Planck Model for Biological Ion Channels---An Asymptotic Analysis in a Three-Dimensional Narrow Funnel},
  author={Amit Singer and John Norbury},
  journal={SIAM Journal of Applied Mathematics},
  year={2009},
  volume={70},
  pages={949-968}
}
We wish to predict ionic currents that flow through narrow protein channels of biological membranes in response to applied potential and concentration differences across the channel when some features of channel structure are known. We propose to apply singular perturbation analysis to the coupled Poisson–Nernst–Planck equations, which are the basic continuum model of ionic permeation and semiconductor physics. In semiconductor physics the problem is a singular perturbation, because the ratio… CONTINUE READING