# The lipid bilayer at the mesoscale: a physical continuum model

Phillip L. Wilson, Huaxiong Huang, Shu Takagi

Arxiv ID: 0802.3932•Last updated: 6/5/2020

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.

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