Annals of Biomedical Engineering

, Volume 29, Issue 5, pp 384–405 | Cite as

Myofilament Kinetics in Isometric Twitch Dynamics

  • Kenneth B. Campbell
  • Maria V. Razumova
  • Robert D. Kirkpatrick
  • Bryan K. Slinker


To better understand the relationship between kinetic processes of contraction and the dynamic features of an isometric twitch, studies were conducted using a mathematical model that included: (1) kinetics of cross bridge (XB) cycling; (2) kinetics of thin filament regulatory processes; (3) serial and feedback interactions between these two kinetic processes; and (4) time course of calcium activation. Isometric twitch wave forms were predicted, morphometric features of the predicted twitch wave form were evaluated, and sensitivities of wave form morphometric features to model kinetic parameters were assessed. Initially, the impulse response of the XB cycle alone was analyzed with the findings that dynamic constants of the twitch transient were much faster than turnover number of steady-state XB cycling, and, although speed and duration of the twitch wave form were sensitive to XB cycle kinetic constants, parameters of wave shape were not. When thin filament regulatory unit (RU) kinetics were added to XB cycle kinetics, the system impulse response was slowed with only little effect on wave shape. When cooperative neighbor interactions between RU and XB were added, twitch wave shape (as well as amplitude, speed and duration) proved to be sensitive to variation in cooperativity. Importantly, persistence and shape of the falling phase could be strongly modified. When kinetic coefficients of XB attachment were made to depend on sarcomere length, changes in wave shape occurred that did not occur when only sliding filament mechanisms were operative. Indeed, the force–length relationship proved to be highly sensitive to length-dependent XB attachment in combination with cooperative interactions. These model findings are the basis of hypotheses for the role of specific kinetic events of contraction in generating twitch wave form features. © 2001 Biomedical Engineering Society.

PAC01: 8715La, 8719Rr, 8719Ff, 8710+e, 8717Aa, 8717-d, 8716Ka, 8715By

Muscle contraction Mathematical model System dynamics Parameter sensitivity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barany, M. ATPase activity of myosin correlated with speed of muscle shortening. J.Gen.Physiol. 50:197–208, 1967.Google Scholar
  2. 2.
    Brandt, P. W., M. S. Diamond, J. S. Rutchik, and F. H. Sachat. Co-operative interactions between troponin-tropomyosin units extend the length of the thin filament in skeletal muscle. J.Mol.Biol. 195:885–896, 1987.Google Scholar
  3. 3.
    Brandt, P. W., M. S. Diamond, and F. H. Sachat. The thin filament of vertebrate skeletal muscle cooperatively activates as a unit. J.Mol.Biol. 180:379–384, 1984.Google Scholar
  4. 4.
    Bremel, R. D., and A. Weber. Cooperation within actin filament in vertebrate skeletal muscle. Nature (London), New Biol. 238:97–101, 1972.Google Scholar
  5. 5.
    Brenner, B. Correlation between the crossbridge cycle in muscle and actomyosin ATPase cycle in solution. J.Musc. Res. Cell Mot. 6:559–664, 1985.Google Scholar
  6. 6.
    Brenner, B. The cross-bridge cycle in muscle. Mechanical, biochemical, and structural studies on single kinetics muscle for correlation with the actomyosin-ATPase in solution. Basic Res.Cardiol. 81:1–15, 1986.Google Scholar
  7. 7.
    Campbell, K. Rate constant of muscle force redevelopment reflects cooperative activation as well as cross-bridge kinetics. Biophys.J. 72:254–262, 1997.Google Scholar
  8. 8.
    Campbell, K. B, M. Razumova, R. D. Kirkpatrick, and B. K. Slinker. Variably activated myofilament model for muscle contraction studies and applications. Thesis, Washington State University, Aug. 23, 2000, http:// Scholar
  9. 9.
    Cecchi, G., and M. A. Bagni. Myofilament lattice spacing affects tension in striated muscle. News Physiol.Sci. 9:3–7, 1994.Google Scholar
  10. 10.
    Daniels, T. L., A. C. Trimble, and P. B. Chase. Compliant realignment of binding sites in muscle: Transient behavior and mechanical tuning. Biophys.J. 74:1611–1621, 1998.Google Scholar
  11. 11.
    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.Google Scholar
  12. 12.
    Godt, R. E., and D. W. Maughan. Influence of osmotic compression on calcium activation and tension in skinned muscle fibers of the rabbit. Pfluegers Arch. 391:334–337, 1981.Google Scholar
  13. 13.
    Goldman, Y. Kinetics of the actomyosin ATPase in muscle fibers. Annu.Rev.Physiol. 49:637–654, 1987.Google Scholar
  14. 14.
    Guth, K., K. J. V. Poole, D. Maughan, and H. J. Kuhn. The apparent rates of crossbridge attachment and detachment estimated from ATPase activity in insect flight muscle. Biophys.J. 52:1039–1045, 1987.Google Scholar
  15. 15.
    Hill, T. L. Cooperativity Theory in Biochemistry. New York: Springer, 1985.Google Scholar
  16. 16.
    Huxley, A. F. Muscle structure and theories of contraction. Prog.Biophys.Biophys.Chem. 7:255–318, 1957.PubMedGoogle Scholar
  17. 17.
    Jansen, P. M. L., and W. C. Hunter. Force, not length, correlates with prologation of isosarcomeric contraction. Am.J.Physiol. 269:H676–H685, 1995.Google Scholar
  18. 18.
    Razumova, M. V., A. E. Bukatina, and K. B. Campbell. Stiffness-distortion sarcomere model for muscle simulation. J.Appl.Physiol. 87:1861–1876, 1999.Google Scholar
  19. 19.
    Razumova, M. V., A. E. Bukatina, and K. B. Campbell. Different myofilament nearest-neighbor interactions have distinctive effects on contractile behavior. Biophys.J. 78:1320–1876, 2000.Google Scholar
  20. 20.
    Rome, L. C., and S. L. Lindstedt. The quest for speed: Muscles built for high-frequency contractions. News Physiol.Sci. 13:261–268, 1998.Google Scholar
  21. 21.
    Rome, L. C., D. A. Syme, S. Hollingworth, S. L. Lindstedt, and S. M. Baylor. The whistle and the rattle: the design of sound producing muscles. Proc.Natl.Acad.Sci.U.S.A. 93:8095–8100, 1996.Google Scholar
  22. 22.
    S. M. Selby, editor, CRC Standard Math Tables, 16th ed. Cleveland, OH: The Chemical Rubber Company, 1968.Google Scholar
  23. 23.
    Solaro, R. J., and H. M. Rarick. Troponin and tropomyosin: Proteins that switch on and tune in the activity of cardiac myofilaments. Circ.Res. 83:471–480, 1998.Google Scholar
  24. 24.
    Tobacman, L. S. Thin filament mediated regulation of cardiac contraction. Annu.Rev.Physiol. 58:447–481, 1996.Google Scholar
  25. 25.
    Tobias, A. H., B. K. Slinker, R. D. Kirkpatrick, and K. B. Campbell. Mechanical determinants of left ventricular relaxation. Am.J.Physiol. 268:H170–H177, 1995.Google Scholar
  26. 26.
    Wray, J. S. Filament geometry and the activation of insect flight muscle. Nature (London) 280:325–326, 1979.Google Scholar

Copyright information

© Biomedical Engineering Society 2001

Authors and Affiliations

  • Kenneth B. Campbell
    • 1
    • 2
  • Maria V. Razumova
    • 3
  • Robert D. Kirkpatrick
    • 4
  • Bryan K. Slinker
    • 4
  1. 1.Department of VCAPPWashington State UniversityPullman
  2. 2.Department of Biological Systems EngineeringWashington State UniversityPullman
  3. 3.Department of PhysiologyUniversity of Wisconsin-MadisonMadison
  4. 4.Department of VCAPPWashington State UniversityPullman

Personalised recommendations