Center for Molecular Modeling , Ghent University , Technologiepark 903 , 9052 Gent , Belgium.
Laboratory of Computational Biology , National Heart Lung Blood Institute, National Institutes of Health , Bethesda , Maryland 20892 , United States.
J Chem Theory Comput. 2018 Jul 10;14(7):3811-3824. doi: 10.1021/acs.jctc.8b00115. Epub 2018 Jun 28.
The balance of normal and radial (lateral) diffusion of oxygen in phospholipid membranes is critical for biological function. Based on the Smoluchowski equation for the inhomogeneous solubility-diffusion model, Bayesian analysis (BA) can be applied to molecular dynamics trajectories of oxygen to extract the free energy and the normal and radial diffusion profiles. This paper derives a theoretical formalism to convert these profiles into characteristic times and lengths associated with entering, escaping, or completely crossing the membrane. The formalism computes mean first passage times and holds for any process described by rate equations between discrete states. BA of simulations of eight model membranes with varying lipid composition and temperature indicate that oxygen travels 3 to 5 times further in the radial than in the normal direction when crossing the membrane in a time of 15 to 32 ns, thereby confirming the anisotropy of passive oxygen transport in membranes. Moreover, the preceding times and distances estimated from the BA are compared to the aggregate of 280 membrane exits explicitly observed in the trajectories. BA predictions for the distances of oxygen radial diffusion within the membrane are statistically indistinguishable from the corresponding simulation values, yet BA oxygen exit times from the membrane interior are approximately 20% shorter than the simulation values, averaged over seven systems. The comparison supports the BA approach and, therefore, the applicability of the Smoluchowski equation to membrane diffusion. Given the shorter trajectories required for the BA, these results validate the BA as a computationally attractive alternative to direct observation of exits when estimating characteristic times and radial distances. The effect of collective membrane undulations on the BA is also discussed.
磷脂膜中氧的正常扩散和径向（横向）扩散的平衡对于生物功能至关重要。基于非均匀溶解-扩散模型的 Smoluchowski 方程，可以将氧的分子动力学轨迹应用于贝叶斯分析 (BA)，以提取自由能以及正常扩散和径向扩散分布。本文推导出一种理论形式，可将这些分布转换为与进入、逃离或完全穿过膜相关的特征时间和长度。该形式计算平均首次通过时间，适用于任何由离散状态之间的速率方程描述的过程。对具有不同脂质组成和温度的八种模型膜的模拟的 BA 表明，当氧在 15 到 32 ns 的时间内穿过膜时，其在径向方向上的扩散距离是正常方向上的 3 到 5 倍，从而证实了膜中被动氧传输的各向异性。此外，从 BA 估计的先前时间和距离与轨迹中明确观察到的 280 个膜出口的总和进行了比较。BA 对氧在膜内径向扩散的距离的预测与相应的模拟值在统计学上没有区别，但是从膜内部出来的 BA 氧的离开时间比模拟值短约 20%，这是七个系统的平均值。该比较支持 BA 方法，因此，Smoluchowski 方程适用于膜扩散。鉴于 BA 需要较短的轨迹，这些结果验证了 BA 在估计特征时间和径向距离时，作为直接观察出口的计算上有吸引力的替代方法。还讨论了集体膜波动对 BA 的影响。
