Determining Equilibrium Constants for Dimerization Reactions from Molecular Dynamics Simulations
Determining Equilibrium Constants for Dimerization Reactions from Molecular Dynamics Simulations
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DOI：
10.1002/jcc.21776
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发表时间：
2011-07-15
影响因子：
3
通讯作者：
Grubmueller, Helmut
中科院分区：
文献类型：
--
作者：
De Jong, Djurre H.;Schafer, Lars V.;Grubmueller, Helmut
随着今天可用的计算机能力，从平衡分子动力学模拟中“通过计数”计算自由能对越来越多的反应变得可行。一个例子是跨膜-螺旋的二聚化反应。如果对两个螺旋的扩展模拟涵盖了足够多的二聚化和解离事件，它们的结合自由能很容易从观察到两个螺旋以二聚体形式存在的时间分数中推导出来。然而，究竟如何计算自由能的正确值尚不清楚，而且确实使用了几种不同的和相互矛盾的方法。特别是，通过玻尔兹曼统计得到的结果不同于通过质量作用定律得到的结果。在这里，我们提出了一种理论来解决这种差异。我们表明，对于包含两个分子的模拟系统，二聚化自由能由形式为δ G α ln（P-1/P-0）的公式给出。我们的理论也适用于高浓度，通常必须在分子动力学模拟中使用，以保持模拟系统的小，其中教科书稀释近似失败。它还涵盖了模拟与任意数量的单体和二聚体，并提供严格的误差估计。与具有不同粒子数的简单Lennard Jones系统的试验模拟以及从径向分布函数得到的参考自由能值的比较表明，结合自由能和二聚化统计完全一致。(C) 2011 Wiley期刊公司[J] .计算机工程学报，2011,31 (2):393 - 398
With today's available computer power, free energy calculations from equilibrium molecular dynamics simulations "via counting" become feasible for an increasing number of reactions. An example is the dimerization reaction of transmembrane alpha-helices. If an extended simulation of the two helices covers sufficiently many dimerization and dissociation events, their binding free energy is readily derived from the fraction of time during which the two helices are observed in dimeric form. Exactly how the correct value for the free energy is to be calculated, however, is unclear, and indeed several different and contradictory approaches have been used. In particular, results obtained via Boltzmann statistics differ from those determined via the law of mass action. Here, we develop a theory that resolves this discrepancy. We show that for simulation systems containing two molecules, the dimerization free energy is given by a formula of the form Delta G alpha ln(P-1/P-0). Our theory is also applicable to high concentrations that typically have to be used in molecular dynamics simulations to keep the simulation system small, where the textbook dilute approximations fail. It also covers simulations with an arbitrary number of monomers and dimers and provides rigorous error estimates. Comparison with test simulations of a simple Lennard Jones system with various particle numbers as well as with reference free energy values obtained from radial distribution functions show full agreement for both binding free energies and dimerization statistics. (C) 2011 Wiley Periodicals, Inc. J Comput Chem 32: 1919-1928, 2011