运动柔性分析：氢键模式赋予蛋白质运动的空间层次
Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion
摘要：
弹性网络模型（ENM）和基于约束的拓扑刚性分析是研究大分子构象柔性的两种不同的粗粒度方法。自引入以来的二十年中，两者都为深入了解蛋白质分子机制和功能做出了重大贡献。然而，尽管这些方法的共同目的，刚性分析的拓扑性质，从而缺乏运动模式，阻碍了直接比较。在这里，我们提出了一种替代的，运动学的方法来进行刚度分析，它规避了这些缺点。我们介绍了一种新的蛋白质氢键网络光谱分解，它提供了一个正交规范的基础上调制的集体运动的非共价相互作用，类似于正常模式的本征谱，并分解成刚性集群的蛋白质相同的拓扑刚性。我们的运动灵活性分析桥梁拓扑刚性理论和ENM，并使从这两种方法获得的运动模式的详细分析。我们的分析表明，集体的蛋白质运动，报告的香农熵，是显着较低的刚性理论与正常模式的方法。引人注目的是，运动学灵活性分析表明，氢键网络编码蛋白质折叠特定的，空间层次的运动，这在ENM几乎未被发现。这种层次结构揭示了不同的运动制度，合理化从实验和分子动力学模拟观察到的蛋白质刚度变化。从谱分解中推导出的自由能变化的正式表达式表明，近40%的模式的运动服从焓-熵补偿。总之，我们的分析表明，氢键网络已经进化到调节蛋白质结构和动力学。
英文摘要：
Elastic network models (ENM) and constraint-based, topological rigidity analysis are two distinct, coarse-grained approaches to study conformational flexibility of macromolecules. In the two decades since their introduction, both have contributed significantly to insights into protein molecular mechanisms and function. However, despite a shared purpose of these approaches, the topological nature of rigidity analysis, and thereby the absence of motion modes, has impeded a direct comparison. Here, we present an alternative, kinematic approach to rigidity analysis, which circumvents these drawbacks. We introduce a novel protein hydrogen bond network spectral decomposition, which provides an orthonormal basis for collective motions modulated by non-covalent interactions, analogous to the eigenspectrum of normal modes, and decomposes proteins into rigid clusters identical to those from topological rigidity. Our kinematic flexibility analysis bridges topological rigidity theory and ENM, and enables a detailed analysis of motion modes obtained from both approaches. Our analysis reveals that collectivity of protein motions, reported by the Shannon entropy, is significantly lower for rigidity theory versus normal mode approaches. Strikingly, kinematic flexibility analysis suggests that the hydrogen bonding network encodes a protein-fold specific, spatial hierarchy of motions, which goes nearly undetected in ENM. This hierarchy reveals distinct motion regimes that rationalize protein stiffness changes observed from experiment and molecular dynamics simulations. A formal expression for changes in free energy derived from the spectral decomposition indicates that motions across nearly 40% of modes obey enthalpy-entropy compensation. Taken together, our analysis suggests that hydrogen bond networks have evolved to modulate protein structure and dynamics.
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