Solution Poisson-Boltzmann equation: Application in the Human Neuron Membrane

TL;DR

This paper models the electric potential across human neuron membranes using the Poisson-Boltzmann equation, considering electrolyte distribution, glycocalyx, and lipid bilayer effects in a simplified one-dimensional framework.

Contribution

It applies the Poisson-Boltzmann equation to neuron membranes with a simplified model including electrolytes, glycocalyx, and lipid bilayer effects, providing insights into membrane potential distribution.

Findings

Derived solutions for membrane potential considering electrolyte distribution.

Highlighted the influence of glycocalyx and lipid bilayer on potential.

Provided a simplified one-dimensional model for neuron membrane potential.

Abstract

With already demonstrated in previous work the equations that describe the space dependence of the electric potential are determined by the solution of the equation of Poisson-Boltzmann. In this work we consider these solutions for the membrane of the human neuron, using a model simplified for this structure considering the distribution of electrolytes in each side of the membrane, as well as the effect of glycocalyx and the lipidic bilayer. It was assumed that on both sides of the membrane the charges are homogeneously distributed and that the potential depends only on coordinate z.