We extract the folding free energy landscape and the time-dependent friction function, the two ingredients of the generalized Langevin equation (GLE), from explicit-water molecular dynamics (MD) simulations of the α-helix forming polypeptide alanine9 for a one-dimensional reaction coordinate based on the sum of the native H-bond distances. Folding and unfolding times from numerical integration of the GLE agree accurately with MD results, which demonstrate the robustness of our GLE-based non-Markovian model. In contrast, Markovian models do not accurately describe the peptide kinetics and in particular, cannot reproduce the folding and unfolding kinetics simultaneously, even if a spatially dependent friction profile is used. Analysis of the GLE demonstrates that memory effects in the friction significantly speed up peptide folding and unfolding kinetics, as predicted by the Grote–Hynes theory, and are the cause of anomalous diffusion in configuration space. Our methods are applicable to any reaction coordinate and in principle, also to experimental trajectories from single-molecule experiments. Our results demonstrate that a consistent description of protein-folding dynamics must account for memory friction effects.

我们从 α-螺旋形成多肽的显式水分子动力学 (MD) 模拟中提取折叠自由能图和时间相关摩擦函数，这是广义朗之万方程 (GLE) 的两个组成部分 一个升一个n一世n电子9对于基于天然 H 键距离总和的一维反应坐标。GLE 数值积分的折叠和展开时间与 MD 结果准确一致，这证明了我们基于 GLE 的非马尔可夫模型的稳健性。相比之下，马尔可夫模型不能准确地描述肽动力学，尤其是不能同时再现折叠和展开动力学，即使使用了空间相关的摩擦剖面。GLE 的分析表明摩擦中的记忆效应显着加速了肽折叠和展开的动力学，正如 Grote-Hynes 理论所预测的那样，并且是构型空间中异常扩散的原因。我们的方法适用于任何反应坐标，原则上也适用于单分子实验的实验轨迹。