The lipid bilayer at the mesoscale: a physical continuum model

TL;DR

This paper develops a refined continuum model of lipid bilayers that better captures physical interactions and parameter estimation, enabling more accurate multiscale blood flow simulations.

Contribution

It introduces a more physical hydrophobic effect model, clarifies parameter meanings, and provides a method for obtaining realistic bilayer density profiles.

Findings

Numerical results align with physical experimental data.

The model exhibits expected behaviour under varying background concentrations.

A novel numerical approach facilitates gradient flow minimization.

Abstract

We study a continuum model of the lipid bilayer based on minimizing the free energy of a mixture of water and lipid molecules. This paper extends previous work by Blom & Peletier (2004) in the following ways. (a) It formulates a more physical model of the hydrophobic effect to facilitate connections with microscale simulations. (b) It clarifies the meaning of the model parameters. (c) It outlines a method for determining parameter values so that physically-realistic bilayer density profiles can be obtained, for example for use in macroscale simulations. Points (a)-(c) suggest that the model has potential to robustly connect some micro- and macroscale levels of multiscale blood flow simulations. The mathematical modelling in point (a) is based upon a consideration of the underlying physics of inter-molecular forces. The governing equations thus obtained are minimized by gradient flows via a novel numerical approach; this enables point (b). The numerical results are shown to behave physically in terms of the effect of background concentration, in contrast to the earlier model which is shown here to not display the expected behaviour. A "short-tail" approximation of the lipid molecules also gives an analytical tool which yields critical values of some parameters under certain conditions. Point (c) involves the first quantitative comparison of the numerical data with physical experimental results.