A differential equation model for tropomyosin-induced myosin cooperativity describes myosin-myosin interactions at low calcium

Cellular and Molecular Bioengineering

Volumn 6, Issue 1, 2013, Pages 13-25

  Walcott, Sam ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Cooperative unit; Multi scale; Muscle; Regulation

Indexed keywords

ADENOSINE TRIPHOSPHATE; CALCIUM; MYOSIN; TROPOMYOSIN;

ACTIN FILAMENT; ARTICLE; BINDING KINETICS; CHEMICAL PARAMETERS; CONTROLLED STUDY; COOPERATIVE BINDING; DIFFERENTIAL EQUATION MODEL; INTERMETHOD COMPARISON; LINEAR THEORY; MATHEMATICAL MODEL; MOLECULAR DYNAMICS; MOLECULAR MODEL; MONTE CARLO METHOD; MUSCLE CONTRACTION; NUMBER OF NEIGHBORING MOLECULE AFFECTED BY MYOSIN BINDING; PRIORITY JOURNAL; PROTEIN BINDING; PROTEIN PROTEIN INTERACTION; REGULATION SLOWS MYOSIN BINDING RATE TO ACTIN; STEADY STATE; THEORY; THIN FILAMENT; WEAKLY CORRELATED THEORY;

EID: 84875232106     PISSN: 18655025     EISSN: 18655033     Source Type: Journal    
DOI: 10.1007/s12195-012-0259-2     Document Type: Article

References (38)

1. Als-Nielson, J.; and R. J. Birgeneau. Mean field theory, the Ginzburg criterion and marginal dimensionality of phase transitions. Am. J. Phys. 45:554-560, 1977.
2. Campbell, K. S. Interactions between connected half-sarcomeres produce emergent mechanical behavior in a mathematical model of muscle. PLoS Comp. Biol. 7:e1000560, 2009.
3. Craig, R.; and W. Lehman. Crossbridge and tropomyosin positions observed in native, interacting thick and thin filaments. J. Mol. Biol. 311:1027-1036, 2001. (Pubitemid 32803718)
4. Debold, E. P.; W. Saber, Y. Cheema, C. S. Bookwalter, K. M. Trybus, D. M. Warshaw, and P. J. VanBuren. Human actin mutations associated with hypertrophic and dilated cardiomyopathies demonstrate distinct thin filament regulatory properties in vitro. Mol. Cell. Cardiol. 48:286-292, 2010.
5. Duke, T. A. J. Molecular model of muscle contraction. Proc. Natl. Acad. Sci. 96:2770-2775, 1999. (Pubitemid 29148793)
6. Eisenberg, E.; T. L. Hill, and Y.-D. Chen. Cross-bridge model of muscle contraction. Quantitative analysis. Biophys J. 29:195-227, 1980. (Pubitemid 10161281)
7. Finer, J. T.; R. M. Simmons, and J. A. Spudich. Single myosin molecule mechanics: piconewton forces and nanometre steps. Nature 368:113-119, 1994. (Pubitemid 24101520)
8. Geeves, M. A.; and S. S. Lehrer. Dynamics of the muscle thin filament regulatory switch: the size of the cooperative unit. Biophys. J. 67:273-282, 1994. (Pubitemid 24197892)
9. 2+]-dependent regulation of the rate of myosin binding to actin: solution data and the tropomyosin chain model. Biophys. J. 100:2679-2687, 2011.
10. Greene, L.; and E. Eisenberg. Cooperative binding of myosin subfragment-1 to the actin-troponin-tropomyosin complex. Proc. Natl. Acad. Sci. 77:2616-2620, 1980.
11. Guilford, W. H.; D. E. Depuis, G. Kennedy, J. Wu, J. B. Patlak, and D. M. Warshaw. Smooth muscle and skeletal muscle myosin produce similar unitary forces and displacements in the laser trap. Biophys. J. 72:1006-1021, 1997. (Pubitemid 27113629)
12. Harris, D. E.; and D. M. Warshaw. Smooth and skeletal muscle myosin both exhibit low duty cycles at zero load in vitro. J. Biol. Chem. 268:14764-14768, 1993. (Pubitemid 23206617)
13. Hill, T. L. Theoretical formalism for the sliding filament model of contraction of striated muscle. Part I. Prog. Biophys. Mol. Biol. 28:267-340, 1974.
14. Hill, T. L.; E. Eisenberg, and L. Greene. Theoretical model for the cooperative equilibrium binding of myosin subfragment 1 to the actin-troponin-tropomyosin complex. Proc. Natl. Acad. Sci. 77:3186-3190, 1980.
15. Hill, T. L.; E. Eisenberg, and J. M. Chalovich. Theoretical models for cooperative steady-state ATPase activity of myosin subfragment-1 on regulated actin. Biophys. J. 35:99-112, 1981. (Pubitemid 11079100)
16. Huxley, A. F. Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7:255-318, 1957.
17. Ishijima, A.; Y. Harada, H. Kojima, T. Funatsu, H. Higuchi, and T. Yanagida. Single-molecule analysis of the actomyosin motor using nano-manipulation. Biochem. Biophys. Res. Commun. 199:1057-1063, 1994. (Pubitemid 24181769)
18. Kad, N. M.; J. B. Patlak, P. M. Fagnant, K. M. Trybus, and D. M. Warshaw. Mutation of a conserved glycine in the SH1-SH2 helix affects the load-dependent kinetics of myosin. Biophys. J. 92:1623-1631, 2007. (Pubitemid 46393473)
19. Kad, N. M.; A. S. Rovner, P. M. Fagnant, P. B. Joel, G. G. Kennedy, J. B. Patlak, D. M. Warshaw, and K. M. Trybus. A mutant heterodimeric myosin with one inactive head generates maximal displacement. J. Cell. Biol. 162:481-488, 2003. (Pubitemid 36988556)
20. Kad, N. M.; S. Kim, D. M. Warshaw, P. VanBuren, and J. E. Baker. Single myosin crosbridge interactions with actin filaments regulated by troponin-tropomyosin. Proc. Natl. Acad. Sci. 102:16990-16995, 2005. (Pubitemid 41692671)
21. Lacker, H. M. Cross-bridge dynamics in skeletal muscle: mathematical methods for determining the reaction rate and force-extension curves of cross-bridges from the macroscopic behavior of muscle. PhD Thesis, NYU, 1977.
22. Lacker, H. M.; and C. S. Peskin. A mathematical method for the unique determination of cross-bridge properties from steady-state mechanical and energetic experiments on macroscopic muscle. Lect. Math. Life Sci. 16:121-153, 1986.
23. Liu, Y.; M. Scolari, W. Im, and H. J. Woo. Protein-protein interactions in actin-myosin binding and structural effects of R405Q mutation: a molecular dynamics study. Prot. Struct. Funct. Bioinf. 64:156-166, 2006. (Pubitemid 43830994)
24. Lymn, R. W.; and E. W. Taylor. Mechanism of adenosine triphosphate hydrolysis by actomyosin. Biochemistry 10:4617-4624, 1971.
25. McKillop, D. F. A.; and M. A. Geeves. Regulation of the interaction between actin and myosin subfragment I: evidence for three states of the thin filament. Biophys. J. 65:693-701, 1993. (Pubitemid 23263882)
26. Mijailovich, S. M.; X. Li, R. H. Griffiths, and M. A. Geeves. The Hill model for binding myosin S1 to regulated actin is not equivalent to the McKillop-Geeves model. J. Mol. Biol. 417:112-128, 2012.
27. Molloy, J. E.; J. E. Burns, J. Kendrick-Jones, R. T. Tregear, and D. C. S. White. Movement and force produced by a single myosin head. Nature 378:209-212, 1995.
28. Orlova, A.; and E. H. Egelman. Cooperative rigor binding of myosin to actin is a function of F-actin structure. J. Mol. Biol. 265:469-474, 1997. (Pubitemid 27113033)
29. Sich, N. M.; T. J. O'Donnell, S. A. Coulter, O. A. John, M. S. Carter, C. R. Cremo, and J. E. Baker. Effects of actin-myosin kinetics on the calcium sensitivity of regulated thin filaments. J. Biol. Chem. 285:39150-39159, 2010.
30. Smith, D. A. Path-integral theory of an axially confined worm-like chain. J. Phys. A: Math. Gen. 34:4507-4523, 2001.
31. Smith, D. A.; R. Maytum, and M. A. Geeves. Cooperative regulation of myosin-actin interactions by a continuous flexible chain I: actin-tropomyosin systems. Biophys. J. 84:3155-3167, 2003. (Pubitemid 36531763)
32. Steffen, W.; and J. Sleep. Repriming the acomyosin crossbridge cycle Proc. Natl. Acad. Sci. 101:12904-12909, 2004. (Pubitemid 39167556)
33. Stoecker, U.; I. A. Telley, E. Stüssi, and J. J. Denoth. A multisegmental cross-bridge kinetics model of the myofibril. J. Theor. Biol. 259:714-726, 2009.
34. Tanner, B. C. W.; T. L. Daniel, and M. Regnier. Sarcomere lattice geometry influences the cooperative myosin binding in muscle. PLoS Comp. Biol. 3:e115, 2007.
35. Uyeda, T. Q. P.; S. J. Kron, and J. A. Spudich. Myosin step size: estimation from slow sliding movement of actin over low densities of heavy meromyosin. J. Mol. Biol. 214:699-710, 1990. (Pubitemid 20267846)
36. Veigel, C.; J. E. Molloy, S. Schmitz, and J. Kendrick-Jones. Load-dependent kinetics of force production by smooth muscle myosin measured with optical tweezers. Nat. Cell Biol. 5:980-986, 2003. (Pubitemid 37406911)
37. Walcott, S.; and S. X. Sun. Hysteresis in cross-bridge models of muscle. Phys. Chem. Chem. Phys. 11:4871-4881, 2009.
38. Walcott, S.; D. M. Warshaw, and E. P. Debold. Mechanical coupling between myosin molecules causes differences between ensemble and single molecule measurements. Biophys. J. 103:501-510, 2012.