@Article{CiCP-6-655,
author = {Phillip L. Wilson, Huaxiong Huang and Shu Takagi},
title = {Hydrophobic Effect in a Continuum Model of the Lipid Bilayer},
journal = {Communications in Computational Physics},
year = {2009},
volume = {6},
number = {3},
pages = {655--672},
abstract = {<p style="text-align: justify;">We study a continuum paradigm of the lipid bilayer based on minimizing
the free energy of a mixture of water and lipid molecules. This paper extends previous
work of Blom and Peletier [European J. Appl. Math., 15 (2004), pp. 487-508] in the
following ways. (a) It formulates a more general model of the hydrophobic effect to
facilitate connections with microscale simulations and first-principles analysis. (b) It
clarifies the meaning and role 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7699.html}
}