Capturing membrane structure and function in lattice Boltzmann models

TL;DR

This paper presents a novel lattice Boltzmann modeling approach for simulating membrane behavior at the cellular level, capturing complex transport phenomena and membrane dynamics from first principles.

Contribution

It introduces a new mesoscopic lattice Boltzmann method that models membrane transport and reproduces key equations like the Goldman equation from fundamental physics.

Findings

Successfully recovers the Goldman equation from first principles.

Demonstrates hyper-polarization due to multiple relaxation timescales.

Provides a framework for realistic 3D cell membrane simulations.

Abstract

We develop a mesoscopic approach to model the non-equilibrium behavior of membranes at the cellular scale. Relying on lattice Boltzmann methods, we develop a solution procedure to recover the Nernst-Planck equations and Gauss's law. A general closure rule is developed to describe mass transport across the membrane, which is able to account for protein-mediated diffusion based on a coarse-grained representation. We demonstrate that our model is able to recover the Goldman equation from first principles and show that hyper-polarization occurs when membrane charging dynamics are controlled by multiple relaxation timescales. The approach provides a promising way to characterize non-equilibrium behaviors that arise due to the role of membranes in mediating transport based on realistic three-dimensional cell geometries.