Mathematical modeling of molecular "nano-machines"


Cite item

Full Text

Abstract

A 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.

About the authors

Vladik A Avetisov

N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences

Email: avetisov@chph
д.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 Sciences

Albert Kh Bikulov

N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences

Email: bikulov1903@rambler.ru
к.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 Sciences

Alexander P Zubarev

Samara State University

Email: , apzubarev@mail.ru
к.ф.-м.н., ведущий научный сотрудник, лаб. математической физики; Самарский государственный университет; Samara State University

References

  1. Jencks W. P. Catalysis in Chemistry and Enzymology. New York: McGraw-Hill, 1969.
  2. Шайтан К. В., Рубин А. Б. Конформационная динамика белков и простейшие молекулярные «машины» // Биофизика, 1982. Т. 27, No 3. С. 386-390.
  3. Блюменфельд Л. А. Проблемы биологической физики / Физика жизненных процессов. М.: Наука, 1974. 336 с.
  4. 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.
  5. Frauenfelder H., Wolynes P. Biomolecules: Where the physics of complexity and simplicitymeet // Physics Today, 1994. Vol. 47, no. 2. Pp. 58-64.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Владимиров В. С, Волович И. В., Зеленов Е. И. p-Адический анализ и математическая физика. М.: Физматлит, 1994. 352 с.
  11. 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.
  12. 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.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2011 Samara State Technical University

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies