Abstract
The results of constructing a nonlinear model of sarcomere contraction are summarized. A strange attractor has been obtained, which is related to the randomness of the dynamics of the order parameter during sarcomere deformation. A hypothesis is proposed that upon fixation of the actin filaments in the sarcomere the myosin system undergoes nonlinear oscillations with dissipation, which leads to elevation of solution temperature. The increase in temperature has been determined for pulsations of the inertial range. Normalized power spectra of the pulsations of the order parameter have been constructed for the model by Fourier transform. The thermodynamics of sarcomere contraction is considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. B. Rubin, Biophysics (Nauka, Moscow, 2000), Vol. 2 [in Russian].
A. Hill, Mechanics of Muscle Contraction (Mir, Moscow, 1972) [in Russian].
V. I. Deshcherevsky, Mathematical Models of Muscle Contraction (Nauka, Moscow, 1977) [in Russian].
J. Bendall, Muscles, Molecules, and Movement (Mir, Moscow, 1970) [in Russian].
F. Blyakhman, A. Tourovskaya, and G. H. Pollack, Biophys. J. 81, 1093 (2001).
E. Nagornyak, F. Blyakhman, and G. H. Pollack, J. Muscle Res. Cell Motility 25, 37 (2004).
G. P. Bystrai, A. S. Vorokh, and S. V. Andreev, Biofizika 50(5), 851 (2005).
L. D. Landau and E. M. Lifshits, Elasticity Theory (Nauka, Moscow, 1965) [in Russian].
G. P. Bystrai and A. V. Boginich, Vestn. Kibernet. (IPS SO RAN) no. 6, 77 (2007).
G. P. Bystrai, L. V. Makarov, and G. F. Shilin, Nonequilibrium Thermodynamics of Mining Insustry Processes (Nedra, Moscow, 1991) [in Russian].
R. Gilmore, Applied Catastrophe Theory (Mir, Moscow, 1984) [in Russian].
G. Schuster, Deterministic Chaos. Introduction (Mir, Moscow, 1988) [in Russian].
N. N. Krasovskii and A. N. Kotel’nikova, Izv. Ural’sk. Gos. Un-ta no. 32, 12 (2004).
A. V. Kim, Diff. Uravneniya 21(3), 385 (1985).
G. P. Bystrai, S. I. Studenok, and S. I. Ivanova, Teplofiz. Vysok. Temper. 40(5), 779 (2002).
G. P. Bystrai, Thermodynamics of Open Systems: A Text-book (Izd. Ural. Un-ta, Yekaterinburg, 2007) [in Russian].
M. V. Volkenshtein, Usp. Fiz. Nauk 100(4), 681 (1970).
A. M. Obukhov, Izv. AN SSSR, Ser. Geogr. Geofiz. 13, 58 (1949).
L. D. Landau and E. M. Lifshits, hydrodynamics (Nauka, Moscow, 1988) [in Russian].
V. I. Arnold, Catastrophe Theory (Nauka, Moscow, 1990) [in Russian].
I. K. Kikoin, Table of Physical Quantities (Atomizdat, Moscow, 1976) [in Russian].
A. P. Mirabel, in Studies on Turbulence (Nauka, Moscow, 1994) [in Russian].
I. O. Hintze, Turbulence (Fizmatgiz, Moscow, 1963) [in Russian].
D. Meksyn, New Methods in Laminar Boundary Layer Theory (Pergamon Press, London, 1961).
O. M. Belotserkovskii and V. A. Andryushchenko, Dynamics of Spatial Vortex Flows in an Inhomogeneous Atmosphere (Yanus-K, Moscow, 2000) [in Russian].
Author information
Authors and Affiliations
Additional information
Original Russian Text © G.P. Bystrai, S.A. Okhotnikov, 2010, published in Biofizika, 2010, Vol. 55, No. 3, pp. 467–480.
Rights and permissions
About this article
Cite this article
Bystrai, G.P., Okhotnikov, S.A. Mathematical and computation modeling of self-organizing sarcomere with chaotic dynamics of the order parameter. BIOPHYSICS 55, 412–424 (2010). https://doi.org/10.1134/S0006350910030103
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0006350910030103