Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University21071Mathematical modeling of molecular "nano-machines"AvetisovVladik Aд.ф.-м.н., зав. лабораторией, лаб. теории сложных систем; Институт химической физики им. Н. Н. Семенова РАН; N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciencesavetisov@chphBikulovAlbert Khк.ф.-м.н., старший научный сотрудник, лаб. теории сложных систем; Институт химической физики им. Н. Н. Семенова РАН; N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciencesbikulov1903@rambler.ruZubarevAlexander Pк.ф.-м.н., ведущий научный сотрудник, лаб. математической физики; Самарский государственный университет; Samara State University, apzubarev@mail.ruN. N. Semenov Institute of Chemical Physics, Russian Academy of SciencesSamara State University1503201115191518022020Copyright © 2011, Samara State Technical University2011A new approach to mathematical modeling of "molecular machines", e.g. macromolecular structures which functional prototypes are the proteins, is presented. In the center of the approach lies the description of multi-scale fluctuation induced mobility of proteins by the ultrametric random processes. In order todemonstrate how p-adic equations of the reaction-diffusion type are described the molecular machine operation, a heuristic model is constructed in this article. It is shown that such multi-scale modeling allows to have an insight into unexpected resources that can be used in order to control the functional cycle.mathematical modelingproteinsmolecular nano-machinesreaction- diffusion processesultrametricityp-adic equationsматематическое моделированиебелкимолекулярные машиныпроцессы реакция-диффузияультраметрикаp-адические уравнения[Jencks W. P. Catalysis in Chemistry and Enzymology. New York: McGraw-Hill, 1969.][Шайтан К. В., Рубин А. Б. Конформационная динамика белков и простейшие молекулярные «машины» // Биофизика, 1982. Т. 27, No 3. С. 386-390.][Блюменфельд Л. А. Проблемы биологической физики / Физика жизненных процессов. М.: Наука, 1974. 336 с.][Fenimore P. W., Frauenfelder H., McMahom B. H., Young R. D. Proteins are paradigms of stochastic complexity // Physica A, 2005. Vol. 351, no. 1. Pp. 1-13.][Frauenfelder H., Wolynes P. Biomolecules: Where the physics of complexity and simplicitymeet // Physics Today, 1994. Vol. 47, no. 2. Pp. 58-64.][Avetisov V. A., Bikulov A. Kh., Kozyrev S. V. Application of p-adic analysis to models of breaking of replica symmetry // J. Phys. A, Math. Gen., 1999. Vol. 32, no. 50. Pp. 8785-8791.][Avetisov V. A., Bikulov A. Kh., Kozyrev S. V., Osipov V. A. p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes // J. Phys. A, Math. Gen., 2002. Vol. 35, no. 2. Pp. 177-189.][Avetisov V. A., Bikulov A. Kh. Osipov V. A. p-Adic description of characteristic relaxation in complex systems // J. Phys. A, Math. Gen., 2003. Vol. 36, no. 15. Pp. 4239-4246.][Avetisov V. A., Bikulov A. Kh. Protein ultrametricity and spectral diffusion in deeply frozen proteins // Biophys. Rev. and Lett., 2008. Vol. 3, no. 3. Pp. 387-396.][Владимиров В. С, Волович И. В., Зеленов Е. И. p-Адический анализ и математическая физика. М.: Физматлит, 1994. 352 с.][Zelenov E. I. p-Adic analysis and mathematical physics. Vol. 1 / Series on Soviet and East European Mathematics. Singapore: World Scientific Publishing Co., Inc., 1994. 319 pp.][Avetisov V. A., Bikulov A. Kh., Zubarev A. P. First passage time distribution and the number of returns for ultrametric random walks // J. Phys. A, Math. Theor., 2009. Vol. 42, no. 8. Pp. 085003-08521.]