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.

中文翻译：

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膜的渗透性：氧气的特征时间和长度以及不均匀溶解度-扩散模型的基于模拟的测试

氧气在磷脂膜中的正常和径向（横向）扩散的平衡对于生物学功能至关重要。基于非均质溶解度扩散模型的Smoluchowski方程，贝叶斯分析（BA）可以应用于氧气的分子动力学轨迹，以提取自由能以及正态和径向扩散曲线。本文提出了一种理论形式主义，将这些轮廓转换为与进入，逃逸或完全穿过膜相关的特征时间和长度。形式主义计算平均第一次通过时间，并适用于离散状态之间的速率方程式描述的任何过程。对八种具有不同脂质组成和温度的模型膜进行模拟的BA结果表明，当在15到32 ns的时间内穿过膜时，氧气在径向上的传播距离是法线方向的3到5倍，从而证实了被动氧气的各向异性膜运输。此外，将先前从BA估计的时间和距离与在轨迹中明确观察到的280个膜出口的总和进行了比较。膜内氧气径向扩散距离的BA预测值与相应的模拟值在统计上是无法区分的，但是BA膜内部的氧气逸出时间比模拟值短约20％（在七个系统中平均）。比较支持BA方法，因此，Smoluchowski方程对膜扩散的适用性。考虑到BA所需的轨迹较短，这些结果验证了BA在估算特征时间和径向距离时，可作为直接观察出口的一种具有计算吸引力的替代方案。还讨论了集体膜起伏对BA的影响。