The recently developed NMR techniques enable estimation of protein configurational entropy change from the change in the average methyl order parameters. This experimental observable, however, does not directly measure the contribution of intramolecular couplings, protein main-chain motions, or angular dynamics. Here, we carry out a self-consistent computational analysis of the impact of these missing contributions on an extensive set of molecular dynamics simulations of different proteins undergoing binding. Specifically, we compare the configurational entropy change in protein complex formation as obtained by the maximum information spanning tree approximation (MIST), which treats the above entropy contributions directly, and the change in the average NMR methyl and NH order parameters. Our parallel implementation of MIST allows us to treat hard angular degrees of freedom as well as couplings up to full pairwise order explicitly, while still involving a high degree of sampling and tackling molecules of biologically relevant sizes. First, we demonstrate a remarkably strong linear relationship between the total configurational entropy change and the average change in both methyl and backbone-NH order parameters. Second, in contrast to canonical assumptions, we show that the main-chain and angular terms contribute significantly to the overall configurational entropy change and also scale linearly with it. Consequently, linear models starting from the average methyl order parameters are able to capture the contribution of main-chain and angular terms well. After applying the quantum-mechanical harmonic oscillator entropy formalism, we establish a similarly strong linear relationship for X-ray crystallographic B-factors. Finally, we demonstrate that the observed linear relationships remain robust against drastic undersampling and argue that they reflect an intrinsic property of compact proteins. Despite their remarkable strength, however, the above linear relationships yield estimates of configurational entropy change whose accuracy appears to be sufficient for qualitative applications only.

中文翻译：

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将蛋白质动力学的实验代理与配置熵连接起来的自洽框架

最近开发的 NMR 技术能够根据平均甲基级参数的变化来估计蛋白质构型熵的变化。然而，这个实验可观察到的并不能直接测量分子内耦合、蛋白质主链运动或角动力学的贡献。在这里，我们对这些缺失的贡献对经历结合的不同蛋白质的广泛分子动力学模拟的影响进行了自洽计算分析。具体来说，我们比较了通过直接处理上述熵贡献的最大信息生成树近似 (MIST) 获得的蛋白质复合物形成中的构型熵变化，以及平均 NMR 甲基和 NH 序参数的变化。我们对 MIST 的并行实现允许我们处理硬角自由度以及明确地耦合到完整的成对顺序，同时仍然涉及高度采样和处理生物学相关大小的分子。首先，我们证明了总构型熵变化与甲基和主链-NH 顺序参数的平均变化之间存在非常强的线性关系。其次，与典型假设相反，我们表明主链和角度项对整体构型熵变化有显着贡献，并且与它呈线性关系。因此，从平均甲基顺序参数开始的线性模型能够很好地捕捉主链和角项的贡献。在应用量子力学谐振子熵形式后，我们为 X 射线晶体学 B 因子建立了类似的强线性关系。最后，我们证明观察到的线性关系对剧烈的欠采样保持稳健，并认为它们反映了紧凑蛋白质的内在特性。然而，尽管它们具有显着的优势，但上述线性关系产生了对构型熵变化的估计，其准确性似乎仅适用于定性应用。