Free Energy Differences from Molecular Simulations: Exact Confidence Intervals from Transition Counts

Supporting data for <strong>Free Energy Differences from Molecular Simulations: Exact Confidence Intervals from Transition Counts</strong> Molecular simulations make it possible to predict equilibrium constants and corresponding free energy differences. For a system that exists in two states A and B, the equilibrium constant K can be predicted as K = t_B / t_A, where<br> t_B and t_A are times spent in states B and A, respectively. The free energy can be calculated as Delta G = -kT log(K). Here we propose a new method for calculation of confidence intervals for K and Delta G. The ratio of the true<br> value of K and estimated K follows the F-distribution with degrees of freedom df1 = number of B to A transitions and df2 = number of A to B transitions. This makes it possible to calculated the confidence interval of K solely from<br> the number of transitions. The code in the directory errors was used to calculate Table 1 of the article. The code in the directory type1error was used to generate 10000 first time passage times for a transition from A to B and B to A as random numbers with<br> exponential distribution. This was done for different combinations of number of transition and values of K. Number of confidence intervals not spanning the predefined value of K (type 1 errors) was expected to be 5 % for 95-% confidence intervals. This was in agreement with the result. The code in the directory type1errorodd was used to run similar experiment as type1error, but with number of A to B transitions higher than B to A by one. The code in the directory threestates was used to run similar experiment as<br> type1error and type1errorodd but for a system with three states A, B and C. The directory glycerol contains a trajectory, evolution of values of torsion angles and the code for analysis of the simulation of glycerol in water. The directory ffmp contains evolution of values of RMSD from the native structure, manual assignments of folded and unfolded states and the code for analysis of simulations of fast folding miniproteins (original data from Lindorf-Larsen et al. Science 2011, 334(6055) 517-520). The directory se contains the code for calculation of standard errors numerically and by the method presented in the article. The directory parallel presents the code for calculations supporting our method to calculate rate and equilibrium constants in parallel simulations. Codes written in R were executed using R version 3.4.4 by running:<br> <em>$ R –no-save &lt; code.R &gt; code.log</em> File md5sums contains md5sum codes for all files.《分子模拟中的自由能差：基于跃迁计数的精确置信区间》支撑数据集。分子模拟可用于预测平衡常数及其对应的自由能差。对于存在双态A与B的体系，平衡常数K可表示为K = t_B / t_A，其中t_B与t_A分别为体系在态B与态A中停留的时长。自由能可通过ΔG = -kT log(K)计算得到。本研究提出一种全新方法，用于计算K与ΔG的置信区间。真实K值与估计K值的比值服从自由度df1 = B→A跃迁次数、df2 = A→B跃迁次数的F分布。这使得仅通过跃迁次数即可计算K的置信区间成为可能。 errors目录下的代码用于复现本文的表1。type1error目录下的代码用于生成10000组A→B与B→A跃迁的首通时间，这些首通时间为服从指数分布的随机数。该实验针对不同的跃迁次数与K值组合展开。对于95%置信区间，未覆盖预设K值的置信区间数量（即一类错误）理论占比应为5%，实验结果与该预期相符。 type1errorodd目录下的代码用于开展与type1error类似的实验，但本次实验中A→B的跃迁次数比B→A多一次。threestates目录下的代码用于开展与type1error、type1errorodd类似的实验，但针对的是包含三态A、B、C的体系。 glycerol目录包含甘油水溶液模拟的轨迹文件、二面角演化数据，以及对应的分析代码。ffmp目录包含天然态结构的均方根偏差（Root Mean Square Deviation, RMSD）演化数据、手动标注的折叠与解折叠状态信息，以及快速折叠微型蛋白模拟的分析代码（原始数据来自Lindorf-Larsen等人发表于《Science》2011年，334(6055)卷：517-520页的研究）。 se目录包含标准误差的数值计算代码，以及本文提出的标准误差计算方法的实现代码。parallel目录包含用于支撑本研究方法的并行模拟下速率与平衡常数计算代码。所有R语言代码均通过R 3.4.4版本执行，执行命令为：<em>$ R –no-save < code.R > code.log</em> md5sums文件包含所有文件的md5校验值。