  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).
