Detailed Balance and four State Models of Smooth Muscle Activation

  • Carlos A. Lazalde
  • Lloyd Barr
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 304)


Regulation of smooth muscle contraction involves a number of chemical networks which in turn involve reactions at fixed sites. This occurs because of the organized nature of the contractile filament system. The formalisms introduced by T. L. Hill (1977) in his analyses of the hypotheses of A. F. Huxley (1957) have been useful in the study of several other motile systems and draw on the concepts of thermodynamics and statistical mechanics, and are expressed in the language of continuous time Markov chains. The definition of a state plays an important role in such analyses as does the notion of Detailed Balance. Models which do not comply with the Principle of Detailed Balance are at least inconsistent and may have no more significance than fitting a curve to a mathematical expression.


Smooth Muscle Smooth Muscle Contraction Detailed Balance Continuous Time Markov Chain Chemical Network 
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. Bak, T., 1963, “Contributions to the Theory of Chemical Kinetics”, Benjamin Press, New York.Google Scholar
  2. Bozler, E., 1976, Mechanical properties of contractile elements of smooth muscle, in: “Physiology of Smooth Muscle”, E. Bülbring and M. F. Shuba, eds., Raven Press, New York, p. 217.Google Scholar
  3. Butler, T. M., Siegman, M. J., Mooers, S. U., and Davies, R. E., 1976, Calcium-dependent resistance to stretch and stress relaxation in resting smooth muscles, Am. J. Physiol., 231: 1501.PubMedGoogle Scholar
  4. Denbigh, K., 1951, “Thermodynamics of the Steady State”, Methuen, London.Google Scholar
  5. Denbigh, K., 1981, “The Principles of Chemical Equilibrium”, Cambridge University Press, Cambridge.Google Scholar
  6. Dillon, P. F., Askoy, M. O., Driska, S. P., and Murphy, R. A., 1981, Myosin phosphorylation and the cross-bridge cycle in arterial smooth muscle, Science, 211: 495.PubMedCrossRefGoogle Scholar
  7. Driska, S., 1987, High myosin light chain phosphatase activity in arterial smooth muscle: Can it explain the latch phenomenon?, in: “Regulation and Contraction of Smooth Muscle”, M. J. Siegman, A. P. Somlyo, and N. L. Stephens, eds., Alan R. Liss, New York, p. 387.Google Scholar
  8. Fowler, R. H. and Milne, E. A., 1925, A note on the principle of detailed balancing, Proc. Nat’l Acad. Sci. U.S.A., 11: 400.CrossRefGoogle Scholar
  9. Hai, C.-M. and Murphy, R. A., 1988, Cross-bridge phosphorylation and regulation of latch-bridge state in smooth muscle, Am. J. Physiol., 254: C99.PubMedGoogle Scholar
  10. Hibberd, M. G. and Trentham, D. R., 1986, Relationships between chemical and mechanical events during muscular contraction, Ann. Rev. Biophys. Biophys. Chem., 15: 119.CrossRefGoogle Scholar
  11. Hill, T. L., 1977, “Free Energy Transduction in Biology”, Academic Press, New York.Google Scholar
  12. Huxley, A. F., 1957, Muscle structure and theories of contraction, Prog. Biophys. Mol. Biol., 7: 255.Google Scholar
  13. Lazalde, C. A. and Barr, L., 1990, Identification of four state models of regulation of contraction of smooth muscle, in: “Frontiers of Smooth Muscle Research”, N. Sperelakis and J. D. Wood, eds., Wiley-Liss, New York, p. 51.Google Scholar
  14. Lewis, G. N., 1925, A new principle of equilibrium, Proc. Nat’l. Acad. Sci. U.S.A., 11: 179.CrossRefGoogle Scholar
  15. Mahan, B. H., 1975, Microscopic reversibility and detailed balance, J. Chem. Ed., 52: 299.CrossRefGoogle Scholar
  16. Morowitz, H. J., 1966, Physical background of cycles in biological systems, J. Theor. Biol., 13: 60.CrossRefGoogle Scholar
  17. Morrissey, B. W., 1975, Microscopic reversibility and detailed balance, J. Chem. Ed., 52: 296.CrossRefGoogle Scholar
  18. Murphy, R. A., Rembold, C. M., and Hai, C.-M., 1990, Contraction in smooth muscle: What is Latch?, in: “Frontiers of Smooth Muscle Research”, N. Sperelakis and J. D. Wood, eds., Wiley-Liss, New York, p. 39.Google Scholar
  19. Onsager, L., 1931, Reciprocal relations in irreversible processes, J. Phys. Rev., 37: 405.CrossRefGoogle Scholar
  20. Rüegg, J. C., 1971, Smooth muscle tone, Physiol. Rev., 51: 201.PubMedGoogle Scholar
  21. Tolman, R. C., 1924., Duration of molecules in quantum states, J. Phys. Rev., 23: 693.Google Scholar
  22. Tolman, R. C., 1925, The principle of microscopic reversibility, Proc. Nat’l. Acad. Sci. U.S.A., 11: 436.CrossRefGoogle Scholar
  23. Tolman, R. C., 1938, “The principles of Statistical Mechanics”, Dover reprint, 1979, Oxford University Press, Oxford.Google Scholar
  24. Walsh, M. P., Bridenbaugh, R., Hartshorne, D. J., and Kerrick, W. G. L., 1982, Phosphorylation dependent activated tension in skinned gizzard muscle fibers in the absence of Ca++, J. Biol. Chem., 256: 5987.Google Scholar
  25. Wegscheider, R., 1901, über simultane gleichgewichte und die Beziehungen zwischen thermodynamik und reaktionskinetik homogener systeme, Z. Physik. Chem., 39: 257.Google Scholar
  26. Yourgrau, W., van der Merwe, A., Raw, G., 1982, “Treatise on Irreversible and Statistical Thermophysics”, Dover, New York.Google Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Carlos A. Lazalde
    • 1
  • Lloyd Barr
    • 1
  1. 1.Department of Physiology and BiophysicsUniversity of Illinois at UrbanaUrbanaUSA

Personalised recommendations