The development of methods that allow a structural interpretation of linear and nonlinear vibrational spectra is of great importance, both for spectroscopy and for optimizing force field quality. The experimentally measured signals are ensemble averages over all accessible configurations, which complicates spectral calculations. To account for this, we present a recipe for calculating vibrational amide-I spectra of proteins based on metadynamics molecular dynamics simulations. For each frame, a one-exciton Hamiltonian is set up for the backbone amide groups, in which the couplings are estimated with the transition-charge coupling model for nonnearest neighbors, and with a parametrized map of ab initio calculations that give the coupling as a function of the dihedral angles for nearest neighbors. The local-mode frequency variations due to environmental factors such as hydrogen bonds are modeled by exploiting the linear relationship between the amide C-O bond length and the amide-I frequency. The spectra are subsequently calculated while taking into account the equilibrium statistical weights of the frames that are determined using a previously published reweighting procedure. By implementing all these steps in an efficient Fortran code, the spectra can be averaged over very large amounts of structures, thereby extensively covering the phase space of proteins. Using this recipe, the spectral responses of 2.5 million frames of a metadynamics simulation of the miniprotein Trp-cage are averaged to reproduce the experimental temperature-dependent IR spectra very well. The spectral calculations provide new insight into the origin of the various spectral signatures (which are typically challenging to disentangle in the congested amide-I region), and allow for a direct structural interpretation of the experimental spectra and for validation of the molecular dynamics simulations of ensembles.

中文翻译：

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从非平衡宏动力学模拟中估计 Trp-cage 蛋白的振动光谱


开发允许对线性和非线性振动光谱进行结构解释的方法对于光谱学和优化力场质量都非常重要。实验测量的信号是所有可访问配置的集合平均值，这使得频谱计算复杂化。为了解决这个问题，我们提出了一种基于宏动力学分子动力学模拟计算蛋白质振动酰胺-I 光谱的配方。对于每个框架，为主链酰胺基团设置一个单激子哈密顿量，其中耦合是使用非最近邻的过渡-电荷耦合模型估计的，并使用从头计算的参数化映射，将耦合作为最近邻的二面角的函数。通过利用酰胺 C-O 键长和酰胺 I 频率之间的线性关系，对由氢键等环境因素引起的局模频率变化进行建模。随后计算光谱，同时考虑使用先前发布的重新加权程序确定的帧的平衡统计权重。通过在高效的 Fortran 代码中实现所有这些步骤，可以在非常大量的结构上对光谱进行平均，从而广泛覆盖蛋白质的相空间。使用这个配方，对微型蛋白 Trp 笼的宏动力学模拟的 250 万帧的光谱响应进行平均，以很好地再现实验温度依赖性的红外光谱。 光谱计算为各种光谱特征的来源提供了新的见解（在拥挤的酰胺 I 区域中通常难以解开），并允许对实验光谱进行直接结构解释和验证系综的分子动力学模拟。