Gaalswyk Kari, Awoonor-Williams Ernest, Rowley Christopher N
Department of Chemistry, Memorial University of Newfoundland , St. John's, NL A1B 3X9, Canada.
J Chem Theory Comput. 2016 Nov 8;12(11):5609-5619. doi: 10.1021/acs.jctc.6b00747. Epub 2016 Oct 12.
The membrane permeability coefficient of a solute can be estimated using the solubility-diffusion model. This model requires the diffusivity profile (D(z)) of the solute as it moves along the transmembrane axis, z. The generalized Langevin equation provides one strategy for calculating position-dependent diffusivity from straightforward molecular dynamics simulations where the solute is restrained to a series of positions on the z-coordinate by a harmonic potential. The diffusivity of the solute is calculated from its correlation functions, which are related to the friction experienced by the solute. Roux and Hummer have derived expressions for the diffusion coefficient from the velocity autocorrelation function (VACF) and position autocorrelation function (PACF), respectively. In this work, these methods are validated by calculating the diffusivity of HO and O in homogeneous liquids. These methods are then used to calculate transmembrane diffusivity profiles. The VACF method is less sensitive to thermostat forces and has incrementally lower errors but is more sensitive to the spring constant of the harmonic restraint. For the permeation of a solute through a lipid bilayer, the diffusion coefficients calculated using these methods provided significantly different results. Long-lived correlations of the restrained solute due to inhomogeneities in the bilayer can result in spuriously low diffusivity when using the PACF method. The method based on the VACF does not have this issue and predicts higher rates of diffusion inside the bilayer.
溶质的膜渗透系数可以使用溶解度-扩散模型来估算。该模型需要溶质沿跨膜轴z移动时的扩散系数分布（D(z)）。广义朗之万方程提供了一种从简单分子动力学模拟计算位置相关扩散系数的策略，在该模拟中，溶质通过谐振势被限制在z坐标上的一系列位置。溶质的扩散系数由其相关函数计算得出，这些相关函数与溶质所经历的摩擦力有关。鲁克斯和胡默尔分别从速度自相关函数（VACF）和位置自相关函数（PACF）推导出了扩散系数的表达式。在这项工作中，通过计算HO和O在均匀液体中的扩散系数来验证这些方法。然后使用这些方法计算跨膜扩散系数分布。VACF方法对恒温器力不太敏感，误差逐渐降低，但对谐振约束的弹簧常数更敏感。对于溶质通过脂质双层的渗透，使用这些方法计算出的扩散系数提供了显著不同的结果。当使用PACF方法时，由于双层中的不均匀性导致受约束溶质的长寿命相关性可能会导致扩散系数虚假地降低。基于VACF的方法不存在这个问题，并预测双层内部的扩散速率更高。
