功能状态下蛋白质分子构象动力学的超定量理论及CO与肌红蛋白结合动力学实验的描述
Ultrametric theory of conformational dynamics of protein molecules in a functional state and the description of experiments on the kinetics of CO binding to myoglobin
摘要：
本文系统地阐述了蛋白质分子构象动力学理论。作为这一理论的应用的一个例子，我们提供了一个完整的分析描述的CO结合到肌红蛋白，这是由Frauenfelder的小组进行了30多年前，并获得了基础实验的地位，用于研究蛋白质分子的波动动态迁移率的性质的动力学实验。早在2001年，作者就可以证明，在具有反应汇的超度量随机游走模型中，CO与肌红蛋白结合的实验曲线可以在高温区域再现。后来，在2010年，作者提出了一个修改后的模型，并根据其数值分析，证明该模型可以在实验所涵盖的整个温度范围内再现实验结果。在本研究中，基于先前提出的模型，我们制定了一个严格的数学理论的蛋白质分子的构象动力学。我们证明，所提出的理论不仅提供了一个完整的描述的实验在整个温度范围内的$\left(60\div300\right)$ K和在观察时间窗口的$\left(10^{-7}\div10^{2}\right)$ s，但也是一个统一的图片的构象迁移率的蛋白质分子，以及允许一个实现的事实，即迁移率的变化在一个自相似的方式。蛋白质分子的这一至今仍被隐藏的特性，大大扩展了蛋白质显然具有的动态对称性的概念。此外，我们表明，该模型提供了一个预测的行为的动力学曲线的实验在低温范围内的$\left(60\div180\right)$ K的时间不包括由实验（超过$10^{2}$ s）。
英文摘要：
The paper is devoted to a systematic account of the theory of conformational dynamics of protein molecules. As an example of application of this theory, we provide a complete analytical description of experiments on the kinetics of CO binding to myoglobin, which were carried out by the group of Frauenfelder more than 30 years ago and acquired the status of base experiments for studying the properties of the fluctuation dynamic mobility of protein molecules. As early as 2001, the authors could demonstrate that, within the model of ultrametric random walk with a reaction sink, the experimental curves of CO binding to myoglobin can be reproduced in the high-temperature region. Later, in 2010, the authors proposed a modified model and, based on its numerical analysis, demonstrated that this model can reproduces the experimental results over the whole temperature range covered in the experiment. In the present study, based on the previously proposed model, we formulate a rigorous mathematical theory of conformational dynamics of protein molecules. We demonstrate that the proposed theory provides not only a complete description of the experiment over the whole temperature range of $\left(60\div300\right)$ K and in the observation time window of $\left(10^{-7}\div10^{2}\right)$ s but also a unified picture of the conformational mobility of a protein molecule, as well as allows one to realize the fact that the mobility changes in a self-similar way. This specific feature of protein molecules, which has remained hidden to date, significantly expands the ideas of dynamic symmetry that proteins apparently possess. In addition, we show that the model provides a prediction for the behavior of the kinetic curves of the experiment in the low-temperature range of $\left(60\div180\right)$ K at times not covered by the experiment (more than $10^{2}$ s).
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