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arXiv 0802.3932cond-mat.soft
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中尺度脂双层:物理连续介质模式

The lipid bilayer at the mesoscale: a physical continuum model

Phillip L. Wilson, Huaxiong Huang, Shu Takagi

摘要:

我们研究了一个连续模型的基础上最大限度地减少水和脂质分子的混合物的自由能的脂质双层。本文从以下几个方面扩展了Blom & Peletier(2004)的工作。(a)它制定了一个更物理模型的疏水效应,以促进与微观模拟的连接。(b)阐明了模型参数的含义。(c)它概述了一种方法,用于确定参数值,使物理现实的双层密度分布可以得到,例如用于在宏观模拟。点(a)-(c)表明,该模型有可能鲁棒地连接一些微观和宏观层次的多尺度血流模拟。点(a)中的数学建模基于对分子间力的基本物理的考虑。这样得到的控制方程通过一种新的数值方法用梯度流最小化;这使(b)点成为可能。数值结果显示,在物理行为方面的背景浓度的影响,在这里所示的早期模型,不显示预期的行为。一个“短尾”近似的脂质分子也给出了一个分析工具,在某些条件下产生的一些参数的临界值。第(c)点涉及数值数据与物理实验结果的第一次定量比较。

英文摘要:

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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