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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011, Issue 1(22), Pages 9–15 (Mi vsgtu906)  

This article is cited in 11 scientific papers (total in 11 papers)

Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Mathematical Physics

Mathematical Modeling of Molecular “nano-machines”

V. A. Avetisova, A. Kh. Bikulova, A. P. Zubarevb

a Lab. of Complex Systems Theory, N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow
b Lab. of Mathematical Physics, Samara State University, Samara

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.

Keywords: mathematical modeling, proteins, molecular nano-machines, reaction-diffusion processes, ultrametricity, $p$–adic equations

DOI: https://doi.org/10.14498/vsgtu906

Full text: PDF file (573 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
UDC: 519.2+577.3
MSC: 82D80
Original article submitted 21/XII/2010
revision submitted – 21/II/2011

Citation: V. A. Avetisov, A. Kh. Bikulov, A. P. Zubarev, “Mathematical Modeling of Molecular “nano-machines””, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 9–15

Citation in format AMSBIB
\Bibitem{AveBikZub11}
\by V.~A.~Avetisov, A.~Kh.~Bikulov, A.~P.~Zubarev
\paper Mathematical Modeling of Molecular ``nano-machines''
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 1(22)
\pages 9--15
\mathnet{http://mi.mathnet.ru/vsgtu906}
\crossref{https://doi.org/10.14498/vsgtu906}


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

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  zmath  elib
    2. A. Kh. Bikulov, A. P. Zubarev, “Application of $p$-adic analysis methods in describing Markov processes on ultrametric spaces isometrically embeddable into $\mathbb Q_p$”, p-Adic Numbers, Ultrametric Analysis, and Applications, 7:2 (2015), 121–132, arXiv: 1504.03629 [math-ph]  crossref  mathscinet  zmath  scopus
    3. A. Kh. Bikulov, A. P. Zubarev, On one real basis for $L_2(\mathbb Q_p)$, 2015, 15 pp., arXiv: 1504.03624 [math-ph]
    4. S. V. Kozyrev, “Ultrametricity in the theory of complex systems”, Theoret. and Math. Phys., 185:2 (2015), 1665–1677  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. Andrei Khrennikov, Sergei Kozyrev, Alf Månsson, “Hierarchical model of the actomyosin molecular motor based on ultrametric diffusion with drift”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top., 18 (2015), 1550013, 16 pp., arXiv: 1312.7528 [q-bio.BM]  crossref  mathscinet  zmath  isi  scopus
    6. E. V. Borisova, “Voprosy tekhnologicheskoi modernizatsii rossiiskoi ekonomiki”, Gumanitarnye, sotsialno-ekonomicheskie i obschestvennye nauki, 2016, no. 1-2, 150–152  elib
    7. A. Kh. Bikulov, A. P. Zubarev, “Polnye sistemy sobstvennykh funktsii operatora Vladimirova v $L^{2}(B_r)$ i $L^{2}(\mathbb{Q}_{p})$”, Fundament. i prikl. matem., 21:3 (2016), 39–56  mathnet
    8. 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 Analysis and Applications, 9:2 (2017), 87–121, arXiv: 1705.04758 [math-ph]  crossref  mathscinet  zmath  scopus
    9. A. I. Mikhailov, “O granitsakh reduktsii”, Vestnik Moskovskogo universiteta. Seriya 7: Filosofiya, 2017, no. 5, 61–76  elib
    10. E. V. Borscheva, V. A. Avetisov, “Rol konformatsionnoi dinamiki belka v regulyatsii fermentativnoi aktivnosti”, Nanostruktury. Matematicheskaya fizika i modelirovanie, 16:2(30) (2017), 5–24  elib
    11. A. K. Bikulov, A. P. Zubarev, “Model of $p$-Adic Random Walk in a Potential”, $p$-Adic Numbers, Ultrametric Analysis, and Applications, 10:2 (2018), 130–150  crossref  mathscinet  isi  scopus
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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