Skip to main content
Biophysical Journal logoLink to Biophysical Journal
. 1984 Oct;46(4):541–543. doi: 10.1016/S0006-3495(84)84051-5

The hill coefficient for the Ca2+-activation of striated muscle contraction.

J S Shiner, R J Solaro
PMCID: PMC1435008  PMID: 6498270

Abstract

The following arguments are presented for the observation that curves relating free Ca2+ and force development of thin filament regulated myofilaments of skinned muscle fibers have Hill coefficient (n) greater than 4, which is the number of Ca2+ binding sites on troponin: Activation of the myofilaments is a process relaxing to a nonequilibrium steady state or stationary state. Systems operating at nonequilibrium stationary states are known to display Hill coefficients greater than the number of interacting sites and similar results have been obtained for Ca2+ activation of myofilament isometric force. The size of the basic subunit of thin filament regulated muscle may be the entire thin filament rather than seven actins, one tropomyosin, and one troponin. In this case the number of interacting sites may be on the order of hundreds. Hysteresis in the Ca2+ activation of isometric force might result from multiple stationary states and also might give rise to Hill coefficients greater than 4.

Full text

PDF
541

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Adelstein R. S., Eisenberg E. Regulation and kinetics of the actin-myosin-ATP interaction. Annu Rev Biochem. 1980;49:921–956. doi: 10.1146/annurev.bi.49.070180.004421. [DOI] [PubMed] [Google Scholar]
  2. Bardsley W. G., Leff P., Kavanagh J., Waight R. D. Deviations from Michaelis-Menten kinetics. The possibility of complicated curves for simple kinetic schemes and the computer fitting of experimental data for acetylcholinesterase, acid phosphatase, adenosine deaminase, arylsulphatase, benzylamine oxidase, chymotrypsin, fumarase, galactose dehydrogenase, beta-galactosidase, lactate dehydrogenase, peroxidase and xanthine oxidase. Biochem J. 1980 Jun 1;187(3):739–765. doi: 10.1042/bj1870739. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Brandt P. W., Cox R. N., Kawai M. Can the binding of Ca2+ to two regulatory sites on troponin C determine the steep pCa/tension relationship of skeletal muscle? Proc Natl Acad Sci U S A. 1980 Aug;77(8):4717–4720. doi: 10.1073/pnas.77.8.4717. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Brandt P. W., Cox R. N., Kawai M., Robinson T. Effect of cross-bridge kinetics on apparent Ca2+ sensitivity. J Gen Physiol. 1982 Jun;79(6):997–1016. doi: 10.1085/jgp.79.6.997. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Fabiato A., Fabiato F. Effects of pH on the myofilaments and the sarcoplasmic reticulum of skinned cells from cardiace and skeletal muscles. J Physiol. 1978 Mar;276:233–255. doi: 10.1113/jphysiol.1978.sp012231. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Godt R. E., Lindley B. D. Influence of temperature upon contractile activation and isometric force production in mechanically skinned muscle fibers of the frog. J Gen Physiol. 1982 Aug;80(2):279–297. doi: 10.1085/jgp.80.2.279. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Hill T. L. Theoretical formalism for the sliding filament model of contraction of striated muscle. Part I. Prog Biophys Mol Biol. 1974;28:267–340. doi: 10.1016/0079-6107(74)90020-0. [DOI] [PubMed] [Google Scholar]
  8. Koshland D. E., Jr, Némethy G., Filmer D. Comparison of experimental binding data and theoretical models in proteins containing subunits. Biochemistry. 1966 Jan;5(1):365–385. doi: 10.1021/bi00865a047. [DOI] [PubMed] [Google Scholar]
  9. MONOD J., WYMAN J., CHANGEUX J. P. ON THE NATURE OF ALLOSTERIC TRANSITIONS: A PLAUSIBLE MODEL. J Mol Biol. 1965 May;12:88–118. doi: 10.1016/s0022-2836(65)80285-6. [DOI] [PubMed] [Google Scholar]
  10. Potter J. D., Gergely J. The calcium and magnesium binding sites on troponin and their role in the regulation of myofibrillar adenosine triphosphatase. J Biol Chem. 1975 Jun 25;250(12):4628–4633. [PubMed] [Google Scholar]
  11. Ridgway E. B., Gordon A. M., Martyn D. A. Hysteresis in the force-calcium relation in muscle. Science. 1983 Mar 4;219(4588):1075–1077. doi: 10.1126/science.6823567. [DOI] [PubMed] [Google Scholar]
  12. Robertson S. P., Johnson J. D., Holroyde M. J., Kranias E. G., Potter J. D., Solaro R. J. The effect of troponin I phosphorylation on the Ca2+-binding properties of the Ca2+-regulatory site of bovine cardiac troponin. J Biol Chem. 1982 Jan 10;257(1):260–263. [PubMed] [Google Scholar]
  13. Shiner J. S. A fully nonequilibrium concerted model for enzymes. Biopolymers. 1982 Nov;21(11):2241–2252. doi: 10.1002/bip.360211111. [DOI] [PubMed] [Google Scholar]
  14. Shiner J. S., Solaro R. J. Activation of thin-filament-regulated muscle by calcium ion: considerations based on nearest-neighbor lattice statistics. Proc Natl Acad Sci U S A. 1982 Aug;79(15):4637–4641. doi: 10.1073/pnas.79.15.4637. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Solaro R. J., Shiner J. S. Modulation of Ca2+ control of dog and rabbit cardiac myofibrils by Mg2+. Comparison with rabbit skeletal myofibrils. Circ Res. 1976 Jul;39(1):8–14. doi: 10.1161/01.res.39.1.8. [DOI] [PubMed] [Google Scholar]
  16. Tawada Y., Oara H., Ooi T., Tawada K. Non-polymerizable tropomyosin and control of the superprecipitation of actomyosin. J Biochem. 1975 Jul;78(1):65–72. [PubMed] [Google Scholar]
  17. Thompson C. J. Models for hemoglobin and allosteric enzymes. Biopolymers. 1968;6(8):1101–1118. doi: 10.1002/bip.1968.360060806. [DOI] [PubMed] [Google Scholar]
  18. Weber A., Murray J. M. Molecular control mechanisms in muscle contraction. Physiol Rev. 1973 Jul;53(3):612–673. doi: 10.1152/physrev.1973.53.3.612. [DOI] [PubMed] [Google Scholar]
  19. Wegner A. Equilibrium of the actin-tropomyosin interaction. J Mol Biol. 1979 Jul 15;131(4):839–853. doi: 10.1016/0022-2836(79)90204-3. [DOI] [PubMed] [Google Scholar]
  20. Whitehead E. P. The structure of steady-state enzyme kinetic equations: a graph-theoretical algorithm for obtaining conditions for reduction in degree by common-factor cancellation. J Theor Biol. 1979 Oct 7;80(3):355–381. doi: 10.1016/0022-5193(79)90099-7. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES