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 were recognized as a basis for studying the properties of the fluctuation dynamic mobility of protein molecules. As early as 2001, the authors demonstrated that the model of ultrametric random walk with a reaction sink well reproduces the experimental curves of CO binding to myoglobin in the high-temperature region. Later, in 2014, the authors proposed a modified model and demonstrated that it can reproduce the experimental results over the whole temperature range covered in the experiment. In the present study, we formulate a rigorous mathematical theory of conformational dynamics of protein molecules on the basis of this model. We demonstrate that this theory provides not only a complete description of the experiment over the whole temperature range of $\left(60÷300\right)$ K and in the observation time window of $\left(10^{-7}÷10^2\right)$ s, but also a unified picture of the conformational mobility of a protein molecule; moreover, it demonstrates that the mobility changes in a self-similar way. This specific feature of protein molecules, which has remained hidden to date, significantly expands our view of dynamic symmetry that proteins apparently possess. In addition, we show that the model can predict the behavior of the kinetic curves of the experiment in the low-temperature range of $\left(60÷180\right)$ K at times not covered by the experiment (greater than $10^2$ s).

该论文致力于系统地说明蛋白质分子的构象动力学理论。作为该理论应用的一个例子，我们提供了关于 CO 与肌红蛋白结合的动力学实验的完整分析描述，该实验由 Frauenfelder 小组在 30 多年前进行，并被认为是研究这些特性的基础蛋白质分子的波动动态迁移率。早在 2001 年，作者就证明了带有反应槽的超测量随机游走模型很好地再现了 CO 在高温区域与肌红蛋白结合的实验曲线。后来，在 2014 年，作者提出了一个修改后的模型，并证明它可以在实验覆盖的整个温度范围内重现实验结果。在目前的研究中，在此模型的基础上，我们制定了严格的蛋白质分子构象动力学数学理论。我们证明该理论不仅提供了对整个温度范围内的实验的完整描述$\left(60÷300\right)$ K 和在观察时间窗口 $\left(10^{-7}÷10^2\right)$s，也是蛋白质分子构象迁移率的统一图；此外，它表明流动性以自相似的方式变化。蛋白质分子的这一特殊特征，至今仍是隐藏的，极大地扩展了我们对蛋白质显然具有的动态对称性的看法。此外，我们表明该模型可以预测实验在低温范围内的动力学曲线的行为。$\left(60÷180\right)$ K 有时未包含在实验中（大于 $10^2$ s)。