V. A. Avetisov, A. Kh. Bikulov, A. P. Zubarev, “Ultrametric random walk and dynamics of protein molecules”, Selected topics of mathematical physics and analysis, Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth, Trudy Mat. Inst. Steklova, 285, MAIK Nauka/Interperiodica, Moscow, 2014, 9–32; Proc. Steklov Inst. Math., 285 (2014), 3

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 285, Pages 9–32
DOI: https://doi.org/10.1134/S0371968514020022 (Mi tm3553)

This article is cited in 15 scientific papers (total in 15 papers)

Ultrametric random walk and dynamics of protein molecules

V. A. Avetisov^a, A. Kh. Bikulov^a, A. P. Zubarev^bc

^a N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia
^b S. P. Korolyov Samara State Aerospace University, Samara, Russia
^c Samara State Transport University, Samara, Russia

Full-text PDF (324 kB) Citations (15)

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DOI: https://doi.org/10.1134/S0371968514020022

Abstract: This paper is a brief survey of applications of the

p

$p$ -adic equation of ultrametric random walk to the description of conformational dynamics of protein molecules. Two main experiments are considered that determine the properties of the fluctuation dynamic mobility of protein molecules from

300

$300$ to

4

$4$ K: the studies of the kinetics of CO binding to myoglobin and spectral diffusion in proteins. It is shown that an ultrametric description allows one to build a unified picture of the conformational mobility of a protein molecule in the whole range of the indicated temperatures and realize the fact that it varies in a self-similar way. This feature of protein molecules, which has remained hidden to date, significantly expands the idea of the structure of nanoscale systems related to the family of molecular machines.

Received in September 2013

English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 285, Pages 3–25
DOI: https://doi.org/10.1134/S0081543814040026

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. A. Avetisov, A. Kh. Bikulov, A. P. Zubarev, “Ultrametric random walk and dynamics of protein molecules”, Selected topics of mathematical physics and analysis, Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth, Trudy Mat. Inst. Steklova, 285, MAIK Nauka/Interperiodica, Moscow, 2014, 9–32; Proc. Steklov Inst. Math., 285 (2014), 3–25

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https://doi.org/10.1134/S0371968514020022

https://www.mathnet.ru/eng/tm/v285/p9

This publication is cited in the following 15 articles:

David Weisbart, “p-adic Brownian motion is a scaling limit”, J. Phys. A: Math. Theor., 57:20 (2024), 205203
A. Kh. Bikulov, A. P. Zubarev, “Power Laws and Logarithmic Oscillations in Diffusion Processes on Discrete Ultrametric Spaces”, P-Adic Num Ultrametr Anal Appl, 16:4 (2024), 327
W.A. Zúñiga-Galindo, “Ultrametric diffusion, rugged energy landscapes and transition networks”, Physica A: Statistical Mechanics and its Applications, 597 (2022), 127221
Dragovich B., Khrennikov A.Yu., Kozyrev S.V., Misic N.Z., “P-Adic Mathematics and Theoretical Biology”, Biosystems, 199 (2021), 104288
Bikulov A.Kh., Zubarev A.P., “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”, Physica A, 583 (2021), 126280
Velasquez-Rodriguez J.P., “Hormander Classes of Pseudo-Differential Operators Over the Compact Group of P-Adic Integers”, P-Adic Numbers Ultrametric Anal. Appl., 12:2 (2020), 134–162
A. Kh. Bikulov, A. P. Zubarev, “New Bases in the Space of Square Integrable Functions on the Field of $p$ -Adic Numbers and Their Applications”, Proc. Steklov Inst. Math., 306 (2019), 20–32
D. A. Dawson, L. G. Gorostiza, “Transience and recurrence of random walks on percolation clusters in an ultrametric space”, J. Theor. Probab., 31:1 (2018), 494–526
A. Kh. Bikulov, A. P. Zubarev, “Model of $p$ -adic random walk in a potential”, P-Adic Numbers Ultrametric Anal. Appl., 10:2 (2018), 130–150
D. A. Dawson, L. G. Gorostiza, “Random systems in ultrametric spaces”, Adv. Appl. Probab., 50:A (2018), 83–97
B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, E. I. Zelenov, “ $p$ -Adic mathematical physics: the first 30 years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121
V. Avetisov, P. L. Krapivsky, S. Nechaev, “Native ultrametricity of sparse random ensembles”, J. Phys. A-Math. Theor., 49:3 (2016), 035101
A. Kh. Bikulov, A. P. Zubarev, “Complete systems of eigenfunctions of the Vladimirov operator in $L^{2}(B_r)$ and $L^{2}(\mathbb{Q}_{p})$ ”, J. Math. Sci., 237:3 (2019), 362–374
O. M. Sizova, “Ultrametricheskaya diffuziya v silnom tsentralno-simmetrichnom pole”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 87–104
S. V. Kozyrev, “Ultrametricity in the theory of complex systems”, Theoret. and Math. Phys., 185:2 (2015), 1665–1677

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

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