Ultrametricity of fluctuation dynamic mobility of protein molecules. (English. Russian original) Zbl 1179.92007
Proc. Steklov Inst. Math. 265, 75-81 (2009); translation from Tr. Mat. Inst. Steklova 265, 82-89 (2009).
Summary: 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 an earlier paper of the present authors and V.A. Osipov [Proc. Steklov Inst. Math. 245, 48–57 (2004; Zbl 1098.80007)] 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.
MSC:
| 92C05 | Biophysics |
| 92C40 | Biochemistry, molecular biology |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
| 54E35 | Metric spaces, metrizability |
Citations:
Zbl 1098.80007References:
| [1] | 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. |
| [2] | R. Rammal, G. Toulouse, and M. A. Virasoro, ”Ultrametricity for Physicists,” Rev. Mod. Phys. 58(3), 765–788 (1986). · doi:10.1103/RevModPhys.58.765 |
| [3] | H. Frauenfelder, ”Complexity in Proteins,” Nat. Struct. Biol. 2, 821–823 (1995). · doi:10.1038/nsb1095-821 |
| [4] | H. Frauenfelder and D. Th. Leeson, ”The Energy Landscape in Non-biological and Biological Molecules,” Nat. Struct. Biol. 5, 757–759 (1998). · doi:10.1038/1784 |
| [5] | D. Th. Leeson and D. A. Wiersma, ”Looking into the Energy Landscape of Myoglobin,” Nat. Struct. Biol. 2, 848–851 (1995). · doi:10.1038/nsb1095-848 |
| [6] | A. T. Ogielski and D. L. Stein, ”Dynamics on Ultrametric Spaces,” Phys. Rev. Lett. 55, 1634–1637 (1985). · doi:10.1103/PhysRevLett.55.1634 |
| [7] | 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). · Zbl 1038.82077 · doi:10.1088/0305-4470/35/2/301 |
| [8] | 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)]. · Zbl 1098.80007 |
| [9] | V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, p-Adic Analysis and Mathematical Physics (Nauka, Moscow, 1994; World Sci., Singapore, 1994). · Zbl 0812.46076 |
| [10] | 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). · doi:10.1023/B:JOLT.0000049058.81275.72 |
| [11] | 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. · Zbl 1162.82010 |
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