Hydrophobic Effect in a Continuum Model of the Lipid Bilayer (Communications in Computational Physics, 2009)
We study a continuum paradigm of the lipid bilayer based on minimizingthe free energy of a mixture of water and lipid molecules. This paper extends previouswork of Blom and Peletier [European J. Appl. Math., 15 (2004), pp. 487-508] in thefollowing ways. (a) It formulates a more general model of the hydrophobic effect tofacilitate connections with microscale simulations and first-principles analysis. (b) Itclarifies the meaning and role of the model parameters. (c) It outlines a method fordetermining parameter values so that physically-realistic bilayer density profiles canbe obtained, for example for use in macroscale simulations. Points (a)-(c) suggest thatthe model has potential to robustly connect some micro- and macroscale levels of multiscaleblood flow simulations. The mathematical modelling in point (a) is based upona consideration of the underlying physics of inter-molecular forces. The governingequations thus obtained are minimized by gradient flows via a novel numerical approach;this enables point (b). The numerical results are shown to behave physically interms of the effect of background concentration, in contrast to the earlier model whichis shown here to not display the expected behaviour. A “short-tail” approximation ofthe lipid molecules also gives an analytical tool which yields critical values of some parametersunder certain conditions. Point (c) involves the first quantitative comparisonof the numerical data with physical experimental results.