Hierarchical model of the actomyosin molecular motor based on ultrametric diffusion with drift

We discuss the approach to investigate molecular machines using systems of integro–differential ultrametric (p-adic) reaction–diffusion equations with drift. This approach combines the features of continuous and discrete dynamic models. We apply this model to investigation of actomyosin molecular motor. The introduced system of equations is solved analytically using p-adic wavelet theory. We find explicit stationary solutions and behavior in the relaxation regime.

[1]  W. A. Zúñiga-Galindo,et al.  Taibleson operators, p-adic parabolic equations and ultrametric diffusion , 2007, 0712.1018.

[2]  Sibani,et al.  Diffusion in hierarchies. , 1988, Physical review. A, General physics.

[3]  S. Albeverio,et al.  p-Adic Multiresolution Analysis and Wavelet Frames , 2008, 0802.1079.

[4]  S. V. Kozyrev,et al.  Application of p-adic analysis to models of breaking of replica symmetry , 1999 .

[5]  S. V. Kozyrev,et al.  Replica Symmetry Breaking Related to a General Ultrametric Space I: Replica Matrices and Functionals , 2022 .

[6]  Anatoly N. Kochubei,et al.  Pseudo-differential equations and stochastics over non-archimedean fields , 2001 .

[7]  Lars Montelius,et al.  Actin filament guidance on a chip: toward high-throughput assays and lab-on-a-chip applications. , 2006, Langmuir : the ACS journal of surfaces and colloids.

[8]  Qiang Cui,et al.  Mechanochemical coupling in myosin: A theoretical analysis with molecular dynamics and combined QM/MM reaction path calculations , 2004 .

[9]  M. Karplus,et al.  The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics , 1997 .

[10]  Cees Dekker,et al.  Motor Proteins at Work for Nanotechnology , 2007, Science.

[11]  S. V. Kozyrev,et al.  Dynamics on rugged landscapes of energy and ultrametric diffusion , 2010 .

[12]  S. M. Mijailovich,et al.  Towards a Unified Theory of Muscle Contraction. I: Foundations , 2008, Annals of Biomedical Engineering.

[13]  G. Parisi,et al.  P-adic numbers and replica symmetry breaking , 1999, cond-mat/9906095.

[14]  R D Young,et al.  Protein states and proteinquakes. , 1985, Proceedings of the National Academy of Sciences of the United States of America.

[15]  T. Duke,et al.  Molecular model of muscle contraction. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Haibo Yu,et al.  Mechanochemical Coupling in the Myosin Motor Domain. I. Insights from Equilibrium Active-Site Simulations , 2006, PLoS Comput. Biol..

[17]  H Frauenfelder,et al.  Myoglobin: The hydrogen atom of biology and a paradigm of complexity , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[18]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[19]  F. Guerra Spin Glasses , 2005, cond-mat/0507581.

[20]  George Oster,et al.  Rotary protein motors. , 2003, Trends in cell biology.

[21]  V. A. Avetisov,et al.  Application of p-adic analysis to models of spontaneous breaking of the replica symmetry , 2008 .

[22]  Ogielski,et al.  Dynamics on ultrametric spaces. , 1985, Physical review letters.

[23]  Random walks on ultrametric spaces: low temperature patterns , 1986 .

[24]  V. Avetisov,et al.  PROTEIN ULTRAMETRICITY AND SPECTRAL DIFFUSION IN DEEPLY FROZEN PROTEINS , 2008 .

[25]  R. Candau,et al.  Drug Effect Unveils Inter-head Cooperativity and Strain-dependent ADP Release in Fast Skeletal Actomyosin* , 2009, The Journal of Biological Chemistry.

[26]  W. A. Zúñiga-Galindo Local zeta functions and fundamental solutions for pseudo-differential operators over p-adic fields , 2011 .

[27]  D. A. Meshkov,et al.  O ct 2 01 3 Fractal globule as an artificial molecular machine , 2013 .

[28]  Sergei Kozyrev,et al.  Wavelet analysis as a p-adic spectral analysis , 2008 .

[29]  Heiner Linke,et al.  Mechanochemical model for myosin V , 2009, Proceedings of the National Academy of Sciences.

[30]  V A Avetisov,et al.  p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes , 2002 .

[31]  Per Bak,et al.  How Nature Works , 1996 .

[32]  S. M. Mijailovich,et al.  Toward a Unified Theory of Muscle Contraction. II: Predictions with the Mean-Field Approximation , 2008, Annals of Biomedical Engineering.

[33]  First passage time distribution and the number of returns for ultrametric random walks , 2008, 0808.3066.

[34]  V. M. Shelkovich,et al.  p-Adic Haar Multiresolution Analysis and Pseudo-Differential Operators , 2007, 0705.2294.

[35]  P. Wolynes,et al.  The energy landscapes and motions of proteins. , 1991, Science.

[36]  S. M. Mijailovich,et al.  Toward a Unified Theory of Muscle Contraction. II: Predictions with the Mean-Field Approximation , 2008, Annals of Biomedical Engineering.

[37]  S. Nechaev,et al.  Some physical applications of random hierarchical matrices , 2009 .

[38]  S. V. Kozyrev,et al.  Replica Symmetry Breaking Related to a General Ultrametric Space Ii: Rsb Solutions and the N → 0 Limit , 2022 .

[39]  Anatoly N. Kochubei,et al.  Cauchy problem for fractional diffusion equations , 2003 .

[40]  M. Fisher,et al.  Molecular motors: a theorist's perspective. , 2007, Annual review of physical chemistry.

[41]  V. Avetisov,et al.  p-Adic description of characteristic relaxation in complex systems , 2002, cond-mat/0210447.

[42]  E. Shakhnovich,et al.  The role of topological constraints in the kinetics of collapse of macromolecules , 1988 .

[43]  K. Binder,et al.  Spin glasses: Experimental facts, theoretical concepts, and open questions , 1986 .

[44]  Lars Montelius,et al.  In vitro sliding of actin filaments labelled with single quantum dots. , 2004, Biochemical and biophysical research communications.

[45]  Sam Walcott,et al.  Mechanical coupling between myosin molecules causes differences between ensemble and single-molecule measurements. , 2012, Biophysical journal.

[46]  Lars Montelius,et al.  Guiding motor-propelled molecules with nanoscale precision through silanized bi-channel structures , 2005 .

[47]  Replica symmetry breaking related to a general ultrametric space III: The case of general measure , 2007 .

[48]  V. S. Vladimirov,et al.  P-adic analysis and mathematical physics , 1994 .

[49]  Sean X. Sun,et al.  Mechanochemical models of processive molecular motors , 2012 .

[50]  Alf Månsson,et al.  Actomyosin-ADP states, interhead cooperativity, and the force-velocity relation of skeletal muscle. , 2010, Biophysical journal.

[51]  D. Warshaw,et al.  Modeling smooth muscle myosin's two heads: long-lived enzymatic roles and phosphorylation-dependent equilibria. , 2010, Biophysical journal.

[52]  David M. Raup,et al.  How Nature Works: The Science of Self-Organized Criticality , 1997 .

[53]  J. B. Johnson,et al.  Ligand binding to heme proteins: connection between dynamics and function. , 1991, Biochemistry.