Journal of Muscle Research & Cell Motility

, Volume 10, Issue 3, pp 181–196 | Cite as

A model of crossbridge action: the effects of ATP, ADP and Pi

  • Edward Pate
  • Roger Cooke


We have explored a model of crossbridge kinetics that explains many of the effects on steady-state muscle contraction of ligands that bind to the nucleotide site on myosin. The mathematical model follows the basic framework for crossbridge function first established by A. F. Huxley. In the model, detached crossbridges initially bind in a weakly Attached, A.M.D.Pi state (A, actin; M, myosin; D, ADP; Pi, orthophosphate) at the beginning of the region of positive force production. Pi release then results in transition to a strongly-bound A.M.D state, as has been suggested by other investigators from both biochemical and mechanical data. Mg2+ ADP release and subsequent crossbridge detachment due to Mg2+ ATP binding to the A.M state occur at the end of the region of positive force production. Work in a number of laboratories has now defined the effects on steady-state contraction of variations in the concentrations of Mg2+ ATP, Mg2+ ADP and Pi. These data provide valuable constraints that can be used to further refine current models. The maximum velocity of shortening (Vmax) and ATPase activity of muscle fibres exhibit classical saturation behaviour with respect to Mg2+ ATP concentration, with Mg2+ ADP acting as a competitive inhibitor. The model can reproduce this behaviour. The model also explains the observations that increasing [Mg2+ ATP] decreases isometric tension and increasing [Mg2+ ADP] increases tension. As the concentration of Pi increases, model predictions suggest that tension should decrease approximately as log[Pi], that ATPase activity should decrease less than tension and thatVmax should be almost unchanged, as has been found experimentally. The model also demonstrates that the connection between the parameters of contraction and the free energy of hydrolysis of Mg2+ ATP can be complex.


ATPase Activity Free Energy Maximum Velocity Competitive Inhibitor Basic Framework 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abbott, R. H. &Mannherz, H. G. (1970) Activation by Mg2+ADP and the correlation between tensions and ATPase activity in insect fibrillar muscle.Pflügers Arch. ges. Physiol. 321, 223–32.Google Scholar
  2. Alberty, R. A. (1968) Effect of pH and metal ion concentration on the equilibrium hydrolysis of adenosine triphosphate to adenosine diphosphate.J. biol. Chem. 243, 1337–43.Google Scholar
  3. Altringham, J. D. &Johnston, I. A. (1985) Effects of phosphate on the contractile properties of fast and slow muscle fibres from an Antarctic fish.J. Physiol. Lond. 468, 491–500.Google Scholar
  4. Bowater, R. &Sleep, J. (1988) Demembrated muscle fibres catalyze a more rapid exchange between phosphate and adenosine triphosphate than actomyosin subfragment 1.Biochemistry 27, 5314–23.Google Scholar
  5. Brenner, B., Chalovich, J. M., Greene, L. E., Eisenberg, E. &Schoenberg, M. (1986) Stiffness of skinned rabbit psoas fibres in MgATP and MgPPi solution.Biophys. J. 50, 685–91.Google Scholar
  6. Brokaw, C. J. (1976) Computer simulation of flagellar movement.Biophys. J. 16, 1029–41.Google Scholar
  7. Chase, P. B. &Kushmerick, M. J. (1988) Effects of pH on contraction of rabbit fast and slow skeletal muscle fibres.Biophys. J. 53, 935–46.Google Scholar
  8. Cooke, R. (1986) The mechanism of muscle contraction.CRC Crit. Rev. Biochem. 21, 53–118.Google Scholar
  9. Cooke, R. &Bialek, W. (1979) Contraction of glycerinated muscle fibers as a function of MgATP concentration.Biophys. J. 28, 241–58.Google Scholar
  10. Cooke, R. &Pate, E. (1985) The effects of ADP and phosphate on the contraction of muscle fibres.Biophys. J. 48, 789–98.Google Scholar
  11. Cooke, R., Franks, K., Lucianni, G. &Pate, E. (1988) The inhibition of rabbit skeletal muscle contraction by hydrogen ions and phosphate.J. Physiol., Lond. 395, 77–97.Google Scholar
  12. Dantzig, J. A., Laktis, J. W., Homsher, E. &Goldman, Y. (1987) Mechanical transients initiated by photolysis of caged Pi during active skeletal muscle contraction.Biophys. J. 51, 3a.Google Scholar
  13. Dawson, M. J., Gadian, D. G. &Wilkie, D. R. (1978) Muscular fatigue investigated by phosphorus nuclear magnetic resonance.Nature 274, 861–6.Google Scholar
  14. Dawson, M. J., Gadian, D. G. &Wilkie, D. R. (1980) Mechanical relaxation rate and metabolism studied in fatiguing muscle by phosphorus nuclear magnetic resonance.J. Physiol., Lond. 299, 465–84.Google Scholar
  15. Eisenberg, E. &Greene, L. (1980) The relation between muscle physiology and muscle biochemistry.Ann. Rev. Physiol. 42, 293–309.Google Scholar
  16. Eisenberg, E., Hill, T. &Chen, Y. (1980) Cross-bridge model of muscle contraction.Biophys. J. 29, 195–227.Google Scholar
  17. Ferenczi, M. A., Simmons, R. M. &Sleep, J. A. (1982) General considerations of crossbridge models in relation to the dependence on MgATP concentration of mechanical parameters of skinned fibres from frog muscle. InBasic Biology of Muscles: A Comparative Approach (edited byTwarog, B. M., Levine, R. J. C. &Dewey, M. M.) pp. 91–107. New York: Raven Press.Google Scholar
  18. Ferenczi, M. A., Goldman, Y. E. &Simmons, R. M. (1984) The dependence of force and shortening velocity on substrate concentration in skinned muscle fibres fromRana temporaria.J. Physiol., Lond. 350, 519–43.Google Scholar
  19. Goldman, Y. E., Hibberd, M. G. &Trentham, D. R. (1984) Initiation of active contraction by photogeneration of adenosine-5′-triphosphate in rabbit psoas muscle fibres.J. Physiol., Lond. 354, 605–24.Google Scholar
  20. Greene, L. E. &Eisenberg, E. (1980) Dissociation of the acin-subfragment 1 complex by adenyl-5′-yl imido-diphosphate, MgADP and PPi.J. biol. Chem. 251, 543–8.Google Scholar
  21. Herzig, J. W., Peterson, J. W., Ruegg, J. C. &Solaro, R. J. (1981) Vanadate and phosphate ions reduce tension and increase cross-bridge kinetics in chemically skinned heart muscle.Biochem. Biophys. Acta 672, 191–6.Google Scholar
  22. Hibberd, M. G., Dantzig, J. A., Trentham, D. R. &Goldman, Y. E. (1985) Phosphate release and force generation in skeletal muscle fibres.Science 228, 1317–9.Google Scholar
  23. Hibberd, M. G. &Trentham, D. R. (1986) Relationships between chemical and mechanical events during muscular contraction.Ann. Rev. Biophys. Biophys. Chem. 15, 119–61.Google Scholar
  24. Highsmith, S. (1977) The effect of temperature and salts on myosin subfragment-1 and F-actin association.Arch. Biochem. Biophys. 180, 404–8.Google Scholar
  25. Hill, T. L. (1974) Theoretical formalism for the sliding filament model of contraction of striated muscle, part I.Prog. Biophys. Molec. Biol. 28, 267–340.Google Scholar
  26. Huxley, A. F. (1957) Muscle structure and theories of contraction.Prog. Biophys. 7, 255–318.Google Scholar
  27. Huxley, A. F. (1973) A note suggesting that the crossbridge attachment during muscle contraction may take place in two stages.Proc. R. Soc. B183, 83–6.Google Scholar
  28. Huxley, A. F. &Simmons, R. M. (1971) Proposed mechanism of force generation in striated muscle.Nature 233, 533–8.Google Scholar
  29. Julian, F. J. &Sollins, M. R. (1973) Regulation of force and speed of shortening in muscle contraction.Cold Spring Harbor Symp. Quant. Biol. 37, 637–45.Google Scholar
  30. Kammermeier, H., Schmidt, P. &Jungling, E. (1982) Free energy change of ATP-hydrolysis: a causal factor of early hypoxic failure of the myocardium?J. molec. cell. Card. 14, 267–77.Google Scholar
  31. Kawai, M. (1982) Correlation between experimental processes and cross-bridge kinetics. InBasic Biology of Muscles: A Comparative Approach (edited byTwarog, B. M., Levine, R. J. C. &Dewey, M. M.) pp. 109–130. New York: Raven Press.Google Scholar
  32. Kawai, M. (1986) The role of orthophosphate in cross-bridge kinetics in chemically skinned rabbit psoas fibres as detected with sinusoidal and step length alterations.J. Musc. Res. Cell Motil. 7, 421–34.Google Scholar
  33. Kawai, M., Guth, K., Winnikes, K., Haist, C. &Ruegg, J. C. (1987) The effect of inorganic phosphate on the ATP hydrolysis rate and the tension transients in chemically skinned rabbit psoas fibers.Pflügers Arch. ges. Physiol. 408, 1–9.Google Scholar
  34. Kentish, J. C. (1986) The effects of inorganic phosphate and creatine phosphate in skinned muscles from rat ventricle.J. Physiol., Lond. 370, 585–604.Google Scholar
  35. Kress, M., Huxley, H. E., Farugi, A. R. &Hendrix, J. (1986) Structural changes during activation of frog studied by time-resolved X-ray diffraction.J. molec. Biol. 188, 325–42.Google Scholar
  36. Kushmerick, M. J. &Davies, R. E. (1969) The chemical energetics of muscle contraction. II. The chemistry, efficiency, and power of maximally working sartorious muscles.Proc. R. Soc. Lond. B174, 293–313.Google Scholar
  37. Kushmerick, M. J. (1986) Lessons for muscle energetics from31P NMR spectroscopy.Adv. exp. Med. Biol. 194, 647–63.Google Scholar
  38. Lacktis, J. W. &Homsher, E. (1987) The force response to photogenerated ADP in isometrically contracting glycerinated rabbit psoas muscle fibres.Biophys. J. 51, 475a.Google Scholar
  39. Luney, D. J. E. &Godt, R. (1987) The effect of pH, ADP, inorganic phosphate (Pi) and affinity on the maximum velocity of shortening and force production of skinned rabbit muscle fibers.Biophys. J. 51, 468a.Google Scholar
  40. Moss, R. L. (1982) The effect of calcium on the maximum velocity of shortening in skinned skeletal muscle fibres of the rabbit.J. Musc. Res. Cell Motil. 3, 295–311.Google Scholar
  41. Nosek, T. M., Fender, K. Y. &Godt, R. E. (1987) It is diprotonated inorganic phosphate that depresses force in skinned skeletal muscle fibers.Science 236, 191–3.Google Scholar
  42. Pate, E. &Cooke, R. (1985) The inhibition of muscle contraction by adenosine 5′(γ,-imido) triphosphate and by pyrophosphate.Biophys. J. 47, 773–80.Google Scholar
  43. Pate, E. &Cooke, R. (1986) A model for the interaction of muscle cross-bridges with ligands which compete with ATP.J. Theor. Biol. 118, 215–30.Google Scholar
  44. Podolsky, R. J., Noland, A. C. &Zaveler, S. A. (1969) Crossbridge properties derived from muscle isotonic velocity transients.Proc. natn. Acad. Sci. U.S.A. 64, 504–11.Google Scholar
  45. Ruegg, J. C., Schadler, M., Steiger, G. J. &Miller, G. (1971) Effects of inorganic phosphate on the contractile mechanism.Pflügers Arch. ges. Physiol. 325, 359–64.Google Scholar
  46. Schoenberg, M. &Wells, J. B. (1984) Stiffness, force and sarcomere shortening during a twitch in frog semitendinosus muscle bundles.Biophys. J. 45, 389–97.Google Scholar
  47. Siemankowski, R. F., Wiseman, M. O. &White, H. W. (1985) ADP dissociation from actomyosin subfragment 1 is sufficiently slow to limit the unloaded shortening velocity in vertebrate muscle.Proc. natn. Acad. Sci. U.S.A. 82, 658–62.Google Scholar
  48. Sleep, J. &Hutton, R. L. (1980) Exchange between inorganic phosphate and adenosine 5′-triphosphate in the medium by actomyosin subfragment 1.Biochemistry 19, 1276–83.Google Scholar
  49. Sleep, J. &Glyn, H. (1986) Inhibition of myofibrillar and actomyosin subfragment 1 adenosinetriphosphatase by adenosine 5′-diphosphate and adenyl-5′-yl imidodiphosphate.Biochemistry 25, 1149–54.Google Scholar
  50. Stein, L. A., Schwarz, R. P., Chock, P. B. &Eisenberg, E. (1979) Mechanism of actomyosin triphosphatase. Evidence that adenosine 5′-triphosphate hydrolysis can occur without dissociation of the actomyosin complex.Biochemistry 18, 3895–909.Google Scholar
  51. Taylor, E. W. (1979) Mechanism of actomyosin ATPase and the problem of muscle contraction.CRC Crit. Rev. Biochem. 7, 103–64.Google Scholar
  52. Thorson, J. &White, D. C. S. (1969) Distributed representation for actin-myosin interaction in the oscillatory contraction of muscle.Biophys. J. 9, 360–90.Google Scholar
  53. Webb, M. R., Hibberd, M. G., Goldman, Y. E. &Trentham, D. R. (1986) Oxygen exchange between Pi in the medium and water during ATP hydrolysis mediated by skinned fibers from rabbit skeletal muscle. Evidence for Pi binding to a force-generating state.J. biol. Chem. 261, 15557–64.Google Scholar
  54. White, D. C. S. &Thorson, J. (1972) Phosphate starvation and the nonlinear dynamics of insect fibrillar flight muscle.J. gen. Physiol. 60, 307–36.Google Scholar
  55. White, H. D. &Taylor, E. W. (1976) Energetics and mechanism of actomyosin adenosine triphosphatase.Biochemistry 15, 5818–26.Google Scholar

Copyright information

© Chapman and Hall Ltd. 1989

Authors and Affiliations

  • Edward Pate
    • 1
  • Roger Cooke
    • 2
  1. 1.Department of MathematicsWashington State UniversityPullmanUSA
  2. 2.Department of Biochemistry & Biophysics and the CVRIUniversity of California, San FranciscoSan FranciscoUSA

Personalised recommendations