The coupling between neighboring backbone ϕ and ψ dihedral angles (torsions) has been well appreciated in protein force field development, as in correction map (CMAP) potentials. However, although preferences of backbone torsions are significantly affected by side-chain conformation, there has been no easy way to optimize this coupling. Herein, we prove that the three-dimensional (3D) free energy hypersurface of joint (ϕ, ψ, χ₁) torsions can be decomposed into three separated 2D surfaces. Thus, each of the 2D torsional surfaces can be efficiently and automatically optimized using a CMAP potential. This strategy is then used to reparameterize an AMBER force field such that the resulting χ₁-dependent backbone conformational preference can agree excellently with the reference protein coil library statistics. In various validation simulations (including the folding of seven peptides/proteins, backbone dynamics of three folded proteins, and two intrinsically disordered peptides), the new RSFF2C (residue-specific force field with CMAP potentials) force field gives similar or better performance compared with RSFF2. This strategy can be used to implement our RSFF force fields into a variety of molecular dynamics packages easily.

中文翻译：

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基于CMAP势和自由能分解的残余比力场的通用实现

在蛋白质力场发展中，如在校正图（CMAP）电位中，已经很好地认识到相邻主干ϕ和ψ二面角（扭转）之间的耦合。然而，尽管主链扭转的偏好受侧链构象的影响很大，但是还没有简便的方法可以优化这种耦合。这里，我们证明了三维（3D）接合的自由能超曲面（φ，ψ，χ ₁）扭转可以被分解成三个分离的2D表面。因此，可以使用CMAP电势有效地并且自动地优化每个2D扭转表面。然后，该策略被用于重新参数化的AMBER力场使得所得χ ₁依赖的骨架构象偏好可以与参考蛋白线圈文库统计数据非常吻合。在各种验证模拟中（包括七个肽/蛋白质的折叠，三个折叠蛋白质的主链动力学以及两个固有无序的肽），新的RSFF2C（具有CMAP电位的残基比力场）的力场与RSFF2。此策略可用于将我们的RSFF力场轻松实现为各种分子动力学程序包。