Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland.
J Chem Theory Comput. 2020 Mar 10;16(3):1630-1645. doi: 10.1021/acs.jctc.9b00853. Epub 2020 Feb 27.
Alchemical free energy calculations using conventional molecular dynamics and thermodynamic integration rely on simulations performed at fixed values of the coupling parameter λ. When multiple conformers in equilibrium are separated by high barriers in the space orthogonal to λ, proper convergence may require extremely long simulations. Four main strategies can be employed to address this orthogonal-sampling problem: (a) λ-variations, where λ can change along the simulations to circumvent barriers; (b) λ-extrapolations, where statistical information is transferred between λ-points; (c) specific biasing, where orthogonal barriers are reduced using a biasing potential designed specifically for the system; and (d) generic biasing, where orthogonal barriers are reduced using a generic approach. Here, we investigate the relative merits of the first three strategies considering two benchmark systems. The KXK system involves a mutation of the central residue in a tripeptide to a glycine and the XTP system involves a hydrogen-to-bromine mutation in the base of a nucleotide. Three sampling methods are compared, the latter two involving λ-variations: molecular dynamics simulations with fixed λ-points, Hamiltonian replica exchange, and the recently introduced conveyor belt method. Two free energy estimators are applied, the second one involving λ-extrapolations: thermodynamic integration with Simpson quadrature and the multistate Bennett acceptance ratio. Finally, three different seeding schemes are considered for the generation of the initial configurations. For both benchmark systems, λ-extrapolations are found to provide little gain, whereas λ-variations can significantly enhance the convergence. They are sufficient on their own if the orthogonal barriers are low in at least one state (e.g., the glycine state in KXK). However, if the orthogonal barriers are high over the entire λ-range (e.g., the XTP system), λ-variations are only effective when applied together with a specific biasing for introducing such a low-barrier state.
使用传统分子动力学和热力学积分进行的炼金术自由能计算依赖于在耦合参数 λ 的固定值下进行的模拟。当处于平衡状态的多个构象在垂直于 λ 的空间中被高势垒隔开时，适当的收敛可能需要极其长的模拟。可以采用四种主要策略来解决这个正交采样问题：（a）λ 变化，其中 λ 可以沿模拟变化以避开势垒；（b）λ 外推，其中统计信息在 λ 点之间转移；（c）特定偏置，其中使用专门为系统设计的偏置势降低正交势垒；（d）通用偏置，其中使用通用方法降低正交势垒。在这里，我们考虑了两个基准系统来研究前三种策略的相对优点。KXK 系统涉及在三肽的中心残基处发生突变，将其突变为甘氨酸，而 XTP 系统涉及核苷酸碱基处的氢到溴的突变。比较了三种采样方法，后两种方法涉及 λ 变化：固定 λ 点的分子动力学模拟、哈密顿复制交换和最近引入的输送带方法。应用了两种自由能估计器，后者涉及 λ 外推：辛普森求积的热力学积分和多态贝内特接受率。最后，考虑了三种不同的播种方案来生成初始构型。对于这两个基准系统，λ 外推被发现几乎没有增益，而 λ 变化可以显著增强收敛性。如果在至少一个状态（例如 KXK 中的甘氨酸状态）中正交势垒较低，则 λ 变化本身就足够了。然而，如果正交势垒在整个 λ 范围内都很高（例如 XTP 系统），则只有在应用特定偏置来引入这种低势垒状态时，λ 变化才有效。
