A computational neuron model based on Poisson-Nernst-Planck theory

Abstract

Modelling of the nerve impulse is often simplified to one spatial dimension, for example by using cable theory. In reality signals propagate in a complex three dimensional environment, and neurons may electrostatically affect cells in close proximity. To investigate this, the electrochemistry of the neuron environment is modelled using the Poisson--Nernst--Planck theory of electrodiffusion. An accurate numerical solver for the Poisson--Nernst--Planck equations in three dimensions is developed. The solver, integrated with a simple computational model of ion channels, is capable of simulating the dynamics of multiple electrical charge species for an arbitrary configuration of membranes and ion channels. Preliminary simulations of simplified neurons show resting membrane potentials broadly consistent with the Goldman equation of electrochemistry, but with interesting differences in some cases. The model can be applied to the detailed study of the nerve impulse. References

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