From Sarcomere to Cell: An Efficient Algorithm for Linking Mathematical Models of Muscle Contraction

Bulletin of Mathematical Biology

Volumn 65, Issue 6, 2003, Pages 1141-1162

  Smith, Nicolas P ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0345393845     PISSN: 00928240     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0092-8240(03)00063-6     Document Type: Article

References (24)

1. Berzins, M., P. M. Dew and R. M. Furzeland (1989). Developing software for time-dependent problems using the method of lines and differential- algebraic integrators. Appl. Numer. Math. 5, 375-397.
2. Eisenberg, E., T. L. Hill and Y. D. Chen (1980). Cross-bridges model of muscle contraction: quantitative analysis. Biophys. J. 29, 195-227.
3. Guccione, J. M., I. Motabarzadeh and G. I. Zahalak (1998). A distribution-moment model of deactivation in cardiac muscle. J. Biomech. 31, 1069-1073.
4. Hill, T. L. (1975). Theoretical formalism for the sliding filament model ofcontraction of striated muscle, part ii. Prog. Biophys. Mol. Biol 29, 105-159.
5. Hunter, P. J. and T. K. Borg (2003). Integration from proteins to organs: the physiome project. Natl. Rev. Mol. Cell. Biol. 4, 237-243.
6. Hunter, P. J., A. D. McCulloch and H. E. D. J. ter Keurs (1998). Modelling the mechanical properties of cardiac muscle. Prog. Biophys. Mol. Biol. 69, 289-331.
7. Huxley, A. F. (1957). Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7, 255-318.
8. 2+ dynamics: the role of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys. J. 74, 1149-1168.
9. Kawai, M. and P. W. Brandt (1980). Sinusoidal analysis: a high resolution method for correlating biochemical reactions with physiological processes in activated skeletal muscles of rabbit, frog and crayfish. J. Muscle Res. Cell Motil. 3, 279-303.
10. Kawai, M., Y. Saeki and Y. Zhao (1993a). Crossbridge scheme and the kinetic constants of elementary steps deduced from chemically skinned papillary and trabecular muscles of the ferret. Circ. Res. 73, 35-50.
11. Kawai, M., Y Zhao and H. Halvorson (1993b). Elementary steps of contraction probed by sinusoidal analysis technique in rabbit psoas fibers. Adv. Exp. Med. Biol. 332, 567-580.
12. Luo, C.-H. and Y. Rudy (1994a). A dynamic model of the cardiac ventricular action potential: I. Simulations of ionic currents and concentration changes. Circ. Res. 74, 1071-1096.
13. Luo, C.-H. and Y. Rudy (1994b). A dynamic model of the cardiac ventricular action potential: II. After depolarizations, triggered activity, and potentiation. Circ. Res. 74, 1097-1113.
14. Mulquiney, P. J., W. A. Bubb and P. W. Kuchel (1999). Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: in-vivo kinetic characterisation of 2,3-bisphosphoglycerate synthase/phosphatase using 13C and 31P NMR. Biochem. J. 342, 567-580.
15. Mulquiney, P. J. and P. W. Kuchel (1999). Model of 2,3- bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: computer simulation and metabolic control analysis. Biochem. J. 342, 597-604.
16. ks, length and tension-dependent processes. Can. J. Cardiol. 14, 123-134.
17. Piazzesi, G. and V. Lombardi (1995). A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle. Biophys. J. 68, 1966-1979.
18. Smith, D. A. (1990). The theory of sliding filament models for muscle contraction iii: Dynamics of the five-state model. J. Theor. Biol. 146, 433-466.
19. Smith, D. A. (1998). A strain-dependent ratchet model of [phosphate]-and [atp]-dependent muscle contraction. J. Muscle Res. Cell Motil. 19, 189-211.
20. Smith, N. P., P. J. Mulquiney, M. P. Nash, C. P. Bradley, D. P. Nickerson and P. J. Hunter (2002). Mathematical modeling of the heart: cell to organ. Chaos Solitons Fractals 13, 1613-1621.
21. Vendelin, M., P. H. Bovendeerd, T. Arts, J. Engelbrecht and D. H. van Campen (2000). Cardiac mechanoenergetics replicated by cross-bridge model. Ann. Biomed. Eng. 28, 629-640.
22. Zahalak, G. I. (1981). A distribution-moment approximation for kinetic theories of muscular contraction. Math. Biosci. 55, 89-114.
23. Zahalak, G. I. (2000). The two-state cross-bridge model of muscle is an asymptotic limit of multistate models. J. Theor. Biol. 7, 67-82.
24. Zahalak, G. I. and S.-P. Ma (1990). Muscle activation and contraction: constitutive relations based directly on cross-bridge kinetics. ASME J. Biomech. Eng. 112, 52-62.