Journal of Muscle Research & Cell Motility

, Volume 12, Issue 6, pp 517–531 | Cite as

Four aspects of creep phenomena in striated muscle

  • R. P. Saldana
  • D. A. Smith


Four aspects of the slow creep of tension and sarcomere lengths observed during fixed-end tetani are studied with computer simulations, using the instantaneous steady-state (adiabatic) approximation. (1) Most aspects of fixed-end creep phenomena can be simulated in the presence of the passive forces which correctly produce initially shortened end sarcomeres. However, the very large maximum tensions observed with fibres of low resting force for sarcomere lengths > 3.0μm cannot be simulated within the adiabatic approximation. (2) Random variations in the passive tension-length curve between different sarcomeres can predict the reported incidence of contracting sarcomeres in the middle of the fibre, while avoiding significant tension creep when a central segment is length-clamped. They can also reverse the velocity of these sarcomeres during creep in fibres with high resting tension, as observed by Altringham and Bottinelli (1985). At sarcomere lengths of ⩾ 3.4μm we find that spatial variations in passive tension strength also contribute to tension creep. (3) Crossbridge fluctuations in active tension have been estimated from the sliding-filament model, and do not contribute significantly to tension creep. (4) The need for inter-sarcomere stiffness or other mechanisms to produce an additional slow rise in tension at long times, and to smooth the sarcomere length distribution, is assessed.


Striate Muscle Spatial Variation Length Distribution Sarcomere Length Active Tension 
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.

Mathematical symbols used for muscle variables and parameters, including standard parameter values


slope of active tension-velocity curve in contraction per unit isometric tension


slope (as above) in extension per unit isometric tension


equals α± for sarcomere number i, (i = 1, ...,n)


random sarcomere length shift for passive tension, sarc. no. i


r.m.s. value of the passive length shifts


random sarcomere length fluctuation from active tension


r.m.s. value of the active length fluctuations


decay exponent per sarcomere for extra end tension strength


sarcomere number [i = l(middle), ...,n(end)]


length of sarcomere i at time t


average sarcomere length of a fibre segment at one end


slack length per sarcomere


total length of fibre


coefficient of viscous passive tension n number of sarcomeres in half-fibre


exponent for length dependence of extra end tension




correlation time for active tension fluctuations


overall rate of the contraction cycle


isometric ATP-ase rate per half-sarcomere


total tension per filament at time t

T(l, υ)

steady-state tension function (per filament)


isometric active tension for sarc. length l


homogeneous passive tension function of sarc. length l


inhomogeneous passive tension for sarc. no. i, length li


strength of passive tension function TP(l) (at 3.6 μm)


extra end tension function for sarc. no. i


strength of extra end tension function for sarc. no. i (at 3.6 μm)


strength of extra end tension (T E n ) at end of fibre (i = n)


extension velocity per sarcomer


exponent for length dependence of passive tension


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Altringham, J. D. &Bottinelli, R. (1985) The descending limb of the sarcomere length-force relation in single muscle fibres of the frog.J. Muscle Res. Cell Motil. 6, 585–600.PubMedGoogle Scholar
  2. Ambrogi-Lorenzini, C., Colomo, F. &Lombardi, V. (1983) Development of force-velocity relation, stiffness and isometric tension in frog single muscle fibres.J. Physiol. (Lond.)333, 421–49.Google Scholar
  3. Bagni, M. A., Cecchi, G., Colomo, F. &Tesi, C. (1988) Plateau and descending limb of the sarcomere length-tension relation in short length-clamped segments of frog muscle fibres.J. Physiol. (Lond.)401, 481–95.Google Scholar
  4. Burton, K. &Baskin, R. J. (1986) Light diffraction patterns and sarcomere length variation in striated muscle fibres ofLimulus.Pflügers Arch. 406, 409–18.Google Scholar
  5. Burton, K., Zagotta, W. N. &Baskin, R. J. (1989) Sarcomere length behaviour along single frog muscle fibres at different lengths during isometric tetani.J. Muscle Res. Cell Motil. 10, 67–84.PubMedGoogle Scholar
  6. Cecchi, G., Colomo, F. &Lombardi, V. (1978) Force-velocity relation in normal and nitrate-treated frog single muscle fibres during rise of tension in an isometric tetanus.J. Physiol. (Lond.)285, 257–73.Google Scholar
  7. Edman, K. A. P. (1979) The velocity of unloaded shortening and its relation to sarcomere length and isometric force in vertebrate muscle fibres.J. Physiol. (Lond.)291, 145–56.Google Scholar
  8. Edman, K. A. P. (1988) Double-hyperbolic force-velocity relation in frog muscle fibres.J. Physiol. (Lond.)404, 301–21.Google Scholar
  9. Edman, K. A. P. &Reggiani, G. (1984) Redistribution of sarcomere length during isometric contraction of frog muscle fibres and its relation to tension creep.J. Physiol. (Lond.)351, 169–98.Google Scholar
  10. Edman, K. A. P., Mulieri, L. A. &Scubon-Mulieri, B. (1976) Non-hyperbolic force-velocity relationship in single muscle fibres.Acta Physiol. Scand. 98, 143–56.PubMedGoogle Scholar
  11. Edman, K. A. P., Elzinga, G. &Noble, M. I. M. (1978) Enhancement of mechanical performance by stretch during tetanic contractions of vertebrate skeletal muscle fibres.J. Physiol. (Lond.)281, 139–55.Google Scholar
  12. Edman, K. A. P., Reggiani, C. &Kronnie, G. te (1985) Differences in maximum velocity of shortening along single muscle fibres of the frog.J. Physiol. (Lond.)365, 147–63.Google Scholar
  13. Edman, K. A. P., Reggiani, C., Schiaffino, S. &Kronnie, G. te (1988) Maximum velocity of shortening related to myosin isoform composition in frog skeletal muscle fibres.J. Physiol. (Lond.)395, 679–94.Google Scholar
  14. Ehrenfest, P. (1916) On adiabatic changes of a system in connection with the quantum theory.Proc. Amsterdam Acad. 19, 576–97, reprinted inPaul Ehrenfest: Collected Scientific Papers (edited by M.J.Klein). North-Holland: Elsevier.Google Scholar
  15. Feller, W. (1957)An Introduction to Probability Theory and its Applications Vol. 1, 2nd edn. New York and London: Wiley.Google Scholar
  16. Ferenczi, M. A., Homsher, E., Simmons, R. M. &Trentham, D. R. (1978) Reaction mechanisms of the magnesium-ion dependent adenosine triphosphatase of frog muscle myosin and subfragment 1.Biochem. J. 171, 165–75.PubMedGoogle Scholar
  17. Fischer, E. (1926) Die Zerlegung der Muskelzuckung in Teilfunktionen. III. Die isometrische Muskelaktion des curarisierten und nicht-curarisierten Sartorius, seine Dehnbarkeit und die Fortpflanzung der Dehnungswelle.Pflügers Arch. Gesamte Physiologie 213, 352–69.Google Scholar
  18. Flitney, F. W. &Hirst, D. G. (1978) Cross-bridge detachment and sarcomere ‘give’ during stretch of active frog muscle.J. Physiol. (Lond.)385, 449–70.Google Scholar
  19. Gordon, A. M., Huxley, A. F. &Julian, F. J. (1966a) Tension development in highly stretched vertebrate muscle fibres.J. Physiol. (Lond.)184, 143–69.Google Scholar
  20. Gordon, A. M., Huxley, A. F. &Julian, F. J. (1966b) The variation in isometric tension with sarcomere length in vertebrate muscle fibres.J. Physiol. (Lond.)184, 170–92.Google Scholar
  21. Granzier, H. L. M. &Pollack, G. H. (1990) The descending limb of the force-sarcomere length relation of the frog revisited.J. Physiol. (Lond.)421, 595–615.Google Scholar
  22. Hill, A. F. (1953) The mechanics of active muscle.Proc. R. Soc. B141, 104–17.Google Scholar
  23. Horowitz, R. &Podolsky, R. J. (1987) The positional stability of thick filaments in activated skeletal muscle depends on sarcomere length: evidence for the role of titin filaments.J. Cell Biol. 105, 2217–23.PubMedGoogle Scholar
  24. Huxley, A. F. (1957) Muscle structure and theories of contraction.Prog. Biophys. Biophys. Chem. 7, 255–318.PubMedGoogle Scholar
  25. Huxley, A. F. &Peachey, L. D. (1961) The maximum length for contraction in vertebrate striated muscle.J. Physiol. (Lond.)156, 150–65.Google Scholar
  26. Iwazumi, T. (1984) No tension fluctuations in normal and healthy single myofibrils,Biophys. J. 45, 158a.Google Scholar
  27. Iwazumi, T. (1986) No tension fluctuations during large slow stretch and release in rat psoas myofibrils.Biophys. J. 49, 10a.Google Scholar
  28. Iwazumi, T. &Pollack, G. H. (1981) The effects of sarcomere non-uniformity on the sarcomere-length relationship of skinned fibres.J. Cell. Physiol. 106, 321–37.PubMedGoogle Scholar
  29. Joyce, G. C. Rack, P. M. H. &Westbury, D. R. (1969) The mechanical performance of cat soleus muscle during controlled lengthening and shortening movements.J. Physiol. (Lond.)204, 461–74.Google Scholar
  30. Julian, F. J. Sollins, M. R. &Moss, R. I. (1978) Sarcomere length non-uniformity in relation to tetanic responses of stretched muscle fibres.Proc. R. Soc. B200, 109–16.Google Scholar
  31. Katz, B. (1939) The relation between force and speed in muscular contraction.J. Physiol. (Lond.)96, 45–64.Google Scholar
  32. Kushmerick, M. J. &Davies, R. E. (1969) The chemical energy of muscle contract. II. The chemistry, efficiency and power of maximally working sartorius muscles.Proc. R. Soc. B174, 315–53.Google Scholar
  33. Lieber, R. L., Yin Yeh &Baskin, R. J. (1984) Sarcomere length determination using laser diffraction.Biophys. J. 45, 1007–16.PubMedGoogle Scholar
  34. Magid, A., Ting-Beall, H. P., Carvell, M., Kontis, T. &Lucaveche, C. (1984) Connecting filaments, core filaments and side-struts: a proposal to add three new load-bearing structures to the sliding filament model. InContractile Mechanisms in Muscle (edited by Pollack, G. H. & Sugi, H. pp. 307–23. New York: Plenum Press.Google Scholar
  35. Marechal, G. &Mommaerts, W. F. H. M. (1963) The metabolism of phosphocreatine during an isometric tetanus in the frog muscle.Biochim. Biophys. Ada. 70, 53–67.Google Scholar
  36. Meinhardt, H. (1982)Models of Biological Pattern Formation, New York and London: Academic Press.Google Scholar
  37. Morgan, D. L. (1990) New insights into the behaviour of muscle during active lengthening.Biophys. J. 57, 209–22.PubMedGoogle Scholar
  38. Morgan, D. L., Mochon, S. &Julian F. J. (1982) A quantitative model of intersarcomere dynamics during fixed-end contractions of single frog muscle fibres.Biophys. J. 39, 189–196.PubMedGoogle Scholar
  39. Payne, J. P., Templeton, G. H. &Iwazumi, T. (1986) Analysis of tension noise in kinetic models of muscle contraction.Biophys. J. 49, 11a.Google Scholar
  40. Preston, B. N., Laurent, T. C., Comper, W. D. &Checkley, G. J. (1980) Rapid polymer transport in concentrated solutions through the formation of ordered structures.Nature 287, 499–503.Google Scholar
  41. Smith, D. A. (1990) The theory of sliding filament models for muscle contraction. III. Dynamics of the five-state model.J. Theor. Biol. (in press).Google Scholar
  42. Smith, D. A. &Sicilia, S. (1987) The theory of sliding filament models for muscle contraction. I. The two-state model.J. Theor. Biol. 127, 1–30.PubMedGoogle Scholar
  43. Ter Keurs, H. E. D. J., Iwazumi, T. &Pollack, G. H. (1978) The sarcomere length relation in skeletal muscle fibres.J. Gen. Physiol. 72, 565–92.PubMedGoogle Scholar
  44. Velarde, M. G. &Schecter, R. S. (1972) Thermal diffusion and convective stability. II. An analysis of the convected fluxes.15, 1707–14.Google Scholar
  45. Velarde, M. G. &Normand, C. (1980) Convection.Sci. Am. 243, 78–93.Google Scholar
  46. Zahalak, G. I. (1981) A distribution moment approximation for kinetic theories of muscular contraction.Math. Biosciences 55, 89–114.Google Scholar

Copyright information

© Chapman & Hall 1991

Authors and Affiliations

  • R. P. Saldana
    • 1
  • D. A. Smith
    • 1
  1. 1.Department of PhysicsMonash UniversityClaytonAustralia

Personalised recommendations