Abstract
We show that a p-adic equation of ultrametric diffusion describes the fluctuation dynamic mobility of a protein molecule according to the experimental data obtained at low temperatures by the spectral diffusion method. In the earlier paper published in the Proceedings of the Steklov Institute of Mathematics (2004, vol. 245), the same p-adic equation was employed to describe the kinetics of the enzymatic reaction of CO rebinding to myoglobin. Thus, the p-adic equation of ultrametric diffusion provides an adequate and surprisingly simple description of the fluctuation dynamic mobility of protein molecules that is observed in the range from helium to room temperature on a very wide range of time scales.
Similar content being viewed by others
References
H. Frauenfelder, “The Connection between Low-Temperature Kinetics and Life,” in Protein Structure: Molecular and Electronic Reactivity, Ed. by R. Austin et al. (Springer, New York, 1987), pp. 245–261.
R. Rammal, G. Toulouse, and M. A. Virasoro, “Ultrametricity for Physicists,” Rev. Mod. Phys. 58(3), 765–788 (1986).
H. Frauenfelder, “Complexity in Proteins,” Nat. Struct. Biol. 2, 821–823 (1995).
H. Frauenfelder and D. Th. Leeson, “The Energy Landscape in Non-biological and Biological Molecules,” Nat. Struct. Biol. 5, 757–759 (1998).
D. Th. Leeson and D. A. Wiersma, “Looking into the Energy Landscape of Myoglobin,” Nat. Struct. Biol. 2, 848–851 (1995).
A. T. Ogielski and D. L. Stein, “Dynamics on Ultrametric Spaces,” Phys. Rev. Lett. 55, 1634–1637 (1985).
V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev, and V. A. Osipov, “p-Adic Models of Ultrametric Diffusion Constrained by Hierarchical Energy Landscapes,” J. Phys. A: Math. Gen. 35(2), 177–189 (2002).
V. A. Avetisov, A. Kh. Bikulov, and V. A. Osipov, “p-Adic Models for Ultrametric Diffusion in Conformational Dynamics of Macromolecules,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 245, 55–64 (2004) [Proc. Steklov Inst. Math. 245, 48–57 (2004)].
V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, p-Adic Analysis and Mathematical Physics (Nauka, Moscow, 1994; World Sci., Singapore, 1994).
V. V. Ponkratov, J. Friedrich, J. M. Vanderkooi, A. L. Burin, and Yu. A. Berlin, “Physics of Proteins at Low Temperature,” J. Low Temp. Phys. 137, 289–317 (2004).
V. A. Avetisov, A. Kh. Bikulov, and A. P. Zubarev, “First Passage Time Distribution and Number of Returns for Ultrametric Random Walks,” J. Phys. A: Math. Theor. 42(8), 085003 (2009); arXiv: 0808.3066.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.A. Avetisov, A.Kh. Bikulov, 2009, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 265, pp. 82–89.
Rights and permissions
About this article
Cite this article
Avetisov, V.A., Bikulov, A.K. Ultrametricity of fluctuation dynamic mobility of protein molecules. Proc. Steklov Inst. Math. 265, 75–81 (2009). https://doi.org/10.1134/S0081543809020060
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543809020060