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. 1995 Aug;69(2):524–537. doi: 10.1016/S0006-3495(95)79926-X

Strain-dependent cross-bridge cycle for muscle.

D A Smith 1, M A Geeves 1
PMCID: PMC1236278  PMID: 8527667

Abstract

The cross-bridge cycle for actin, S1 myosin, and nucleotides in solution is applied to the sliding filament model for fully activated striated muscle. The cycle has attached and rotated isomers of each actomyosin state. It is assumed that these forms have different zero-strain conformations with respect to the filament and that strain-free rate constants are the nominal solution values. Only one S1 unit of heavy meromyosin is considered. Transition-state theory is used to predict the strain dependences of S1 binding to actin, the force-generating transition to rotated states, and the release/binding of nucleotide and phosphate. We propose that ADP release and ATP binding are blocked by positive strain and phosphate release by negative strain. At large strains, rapid dissociation of S1 nucleotide from actin is expected when the compliant element of the cross-bridge is strained in either direction beyond its elastic limits. The dynamical behavior of this model of muscle contraction is discussed in general terms. Its computed steady-state properties are presented in an accompanying paper.

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Selected References

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  1. Alberty R. A. Effect of pH and metal ion concentration on the equilibrium hydrolysis of adenosine triphosphate to adenosine diphosphate. J Biol Chem. 1968 Apr 10;243(7):1337–1343. [PubMed] [Google Scholar]
  2. Astumian RD, Bier M. Fluctuation driven ratchets: Molecular motors. Phys Rev Lett. 1994 Mar 14;72(11):1766–1769. doi: 10.1103/PhysRevLett.72.1766. [DOI] [PubMed] [Google Scholar]
  3. Barclay C. J., Constable J. K., Gibbs C. L. Energetics of fast- and slow-twitch muscles of the mouse. J Physiol. 1993 Dec;472:61–80. doi: 10.1113/jphysiol.1993.sp019937. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Bartels E. M., Cooke P. H., Elliott G. F., Hughes R. A. The myosin molecule--charge response to nucleotide binding. Biochim Biophys Acta. 1993 May 7;1157(1):63–73. doi: 10.1016/0304-4165(93)90079-n. [DOI] [PubMed] [Google Scholar]
  5. Brenner B., Eisenberg E. Rate of force generation in muscle: correlation with actomyosin ATPase activity in solution. Proc Natl Acad Sci U S A. 1986 May;83(10):3542–3546. doi: 10.1073/pnas.83.10.3542. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Brenner B., Schoenberg M., Chalovich J. M., Greene L. E., Eisenberg E. Evidence for cross-bridge attachment in relaxed muscle at low ionic strength. Proc Natl Acad Sci U S A. 1982 Dec;79(23):7288–7291. doi: 10.1073/pnas.79.23.7288. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Chalovich J. M., Chock P. B., Eisenberg E. Mechanism of action of troponin . tropomyosin. Inhibition of actomyosin ATPase activity without inhibition of myosin binding to actin. J Biol Chem. 1981 Jan 25;256(2):575–578. [PMC free article] [PubMed] [Google Scholar]
  8. Cooke R. The mechanism of muscle contraction. CRC Crit Rev Biochem. 1986;21(1):53–118. doi: 10.3109/10409238609113609. [DOI] [PubMed] [Google Scholar]
  9. Cooke R., White H., Pate E. A model of the release of myosin heads from actin in rapidly contracting muscle fibers. Biophys J. 1994 Mar;66(3 Pt 1):778–788. doi: 10.1016/s0006-3495(94)80854-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Dantzig J. A., Goldman Y. E., Millar N. C., Lacktis J., Homsher E. Reversal of the cross-bridge force-generating transition by photogeneration of phosphate in rabbit psoas muscle fibres. J Physiol. 1992;451:247–278. doi: 10.1113/jphysiol.1992.sp019163. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Dantzig J. A., Hibberd M. G., Trentham D. R., Goldman Y. E. Cross-bridge kinetics in the presence of MgADP investigated by photolysis of caged ATP in rabbit psoas muscle fibres. J Physiol. 1991 Jan;432:639–680. doi: 10.1113/jphysiol.1991.sp018405. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Eisenberg E., Hill T. L., Chen Y. Cross-bridge model of muscle contraction. Quantitative analysis. Biophys J. 1980 Feb;29(2):195–227. doi: 10.1016/S0006-3495(80)85126-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Eisenberg E., Hill T. L. Muscle contraction and free energy transduction in biological systems. Science. 1985 Mar 1;227(4690):999–1006. doi: 10.1126/science.3156404. [DOI] [PubMed] [Google Scholar]
  14. Fajer P. G., Fajer E. A., Thomas D. D. Myosin heads have a broad orientational distribution during isometric muscle contraction: time-resolved EPR studies using caged ATP. Proc Natl Acad Sci U S A. 1990 Jul;87(14):5538–5542. doi: 10.1073/pnas.87.14.5538. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Geeves M. A., Goody R. S., Gutfreund H. Kinetics of acto-S1 interaction as a guide to a model for the crossbridge cycle. J Muscle Res Cell Motil. 1984 Aug;5(4):351–361. doi: 10.1007/BF00818255. [DOI] [PubMed] [Google Scholar]
  16. Geeves M. A. The dynamics of actin and myosin association and the crossbridge model of muscle contraction. Biochem J. 1991 Feb 15;274(Pt 1):1–14. doi: 10.1042/bj2740001. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Goldman Y. E., Hibberd M. G., McCray J. A., Trentham D. R. Relaxation of muscle fibres by photolysis of caged ATP. Nature. 1982 Dec 23;300(5894):701–705. doi: 10.1038/300701a0. [DOI] [PubMed] [Google Scholar]
  18. Goldman Y. E., Huxley A. F. Actin compliance: are you pulling my chain? Biophys J. 1994 Dec;67(6):2131–2133. doi: 10.1016/S0006-3495(94)80700-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. HUXLEY A. F. Muscle structure and theories of contraction. Prog Biophys Biophys Chem. 1957;7:255–318. [PubMed] [Google Scholar]
  20. Harry J. D., Ward A. W., Heglund N. C., Morgan D. L., McMahon T. A. Cross-bridge cycling theories cannot explain high-speed lengthening behavior in frog muscle. Biophys J. 1990 Feb;57(2):201–208. doi: 10.1016/S0006-3495(90)82523-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Hibberd M. G., Trentham D. R. Relationships between chemical and mechanical events during muscular contraction. Annu Rev Biophys Biophys Chem. 1986;15:119–161. doi: 10.1146/annurev.bb.15.060186.001003. [DOI] [PubMed] [Google Scholar]
  22. Higuchi H., Goldman Y. E. Sliding distance between actin and myosin filaments per ATP molecule hydrolysed in skinned muscle fibres. Nature. 1991 Jul 25;352(6333):352–354. doi: 10.1038/352352a0. [DOI] [PubMed] [Google Scholar]
  23. 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]
  24. Huxley A. F. Muscular contraction. J Physiol. 1974 Nov;243(1):1–43. [PMC free article] [PubMed] [Google Scholar]
  25. Huxley A. F., Simmons R. M. Proposed mechanism of force generation in striated muscle. Nature. 1971 Oct 22;233(5321):533–538. doi: 10.1038/233533a0. [DOI] [PubMed] [Google Scholar]
  26. Huxley H. E., Kress M. Crossbridge behaviour during muscle contraction. J Muscle Res Cell Motil. 1985 Apr;6(2):153–161. doi: 10.1007/BF00713057. [DOI] [PubMed] [Google Scholar]
  27. Kabsch W., Mannherz H. G., Suck D., Pai E. F., Holmes K. C. Atomic structure of the actin:DNase I complex. Nature. 1990 Sep 6;347(6288):37–44. doi: 10.1038/347037a0. [DOI] [PubMed] [Google Scholar]
  28. Kushmerick M. J., Davies R. E. The chemical energetics of muscle contraction. II. The chemistry, efficiency and power of maximally working sartorius muscles. Appendix. Free energy and enthalpy of atp hydrolysis in the sarcoplasm. Proc R Soc Lond B Biol Sci. 1969 Dec 23;174(1036):315–353. doi: 10.1098/rspb.1969.0096. [DOI] [PubMed] [Google Scholar]
  29. Lombardi V., Piazzesi G., Linari M. Rapid regeneration of the actin-myosin power stroke in contracting muscle. Nature. 1992 Feb 13;355(6361):638–641. doi: 10.1038/355638a0. [DOI] [PubMed] [Google Scholar]
  30. Lombardi V., Piazzesi G. The contractile response during steady lengthening of stimulated frog muscle fibres. J Physiol. 1990 Dec;431:141–171. doi: 10.1113/jphysiol.1990.sp018324. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Ma Y. Z., Taylor E. W. Kinetic mechanism of myofibril ATPase. Biophys J. 1994 May;66(5):1542–1553. doi: 10.1016/S0006-3495(94)80945-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Magnasco MO. Forced thermal ratchets. Phys Rev Lett. 1993 Sep 6;71(10):1477–1481. doi: 10.1103/PhysRevLett.71.1477. [DOI] [PubMed] [Google Scholar]
  33. Marston S. B., Taylor E. W. Comparison of the myosin and actomyosin ATPase mechanisms of the four types of vertebrate muscles. J Mol Biol. 1980 Jun 5;139(4):573–600. doi: 10.1016/0022-2836(80)90050-9. [DOI] [PubMed] [Google Scholar]
  34. Martin-Fernandez M. L., Bordas J., Diakun G., Harries J., Lowy J., Mant G. R., Svensson A., Towns-Andrews E. Time-resolved X-ray diffraction studies of myosin head movements in live frog sartorius muscle during isometric and isotonic contractions. J Muscle Res Cell Motil. 1994 Jun;15(3):319–348. doi: 10.1007/BF00123484. [DOI] [PubMed] [Google Scholar]
  35. McKillop D. F., Geeves M. A. Regulation of the acto.myosin subfragment 1 interaction by troponin/tropomyosin. Evidence for control of a specific isomerization between two acto.myosin subfragment 1 states. Biochem J. 1991 Nov 1;279(Pt 3):711–718. doi: 10.1042/bj2790711. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Nishiyama K., Shimizu H., Kometani K., Chaen S. The three-state model for the elementary process of energy conversion in muscle. Biochim Biophys Acta. 1977 Jun 9;460(3):523–536. doi: 10.1016/0005-2728(77)90090-1. [DOI] [PubMed] [Google Scholar]
  37. Pate E., Cooke R. A model of crossbridge action: the effects of ATP, ADP and Pi. J Muscle Res Cell Motil. 1989 Jun;10(3):181–196. doi: 10.1007/BF01739809. [DOI] [PubMed] [Google Scholar]
  38. Rayment I., Holden H. M., Whittaker M., Yohn C. B., Lorenz M., Holmes K. C., Milligan R. A. Structure of the actin-myosin complex and its implications for muscle contraction. Science. 1993 Jul 2;261(5117):58–65. doi: 10.1126/science.8316858. [DOI] [PubMed] [Google Scholar]
  39. Rayment I., Rypniewski W. R., Schmidt-Bäse K., Smith R., Tomchick D. R., Benning M. M., Winkelmann D. A., Wesenberg G., Holden H. M. Three-dimensional structure of myosin subfragment-1: a molecular motor. Science. 1993 Jul 2;261(5117):50–58. doi: 10.1126/science.8316857. [DOI] [PubMed] [Google Scholar]
  40. Sellers J. R., Kachar B. Polarity and velocity of sliding filaments: control of direction by actin and of speed by myosin. Science. 1990 Jul 27;249(4967):406–408. doi: 10.1126/science.2377894. [DOI] [PubMed] [Google Scholar]
  41. Seo J. S., Krause P. C., McMahon T. A. Negative developed tension in rapidly shortening whole frog muscles. J Muscle Res Cell Motil. 1994 Feb;15(1):59–68. doi: 10.1007/BF00123833. [DOI] [PubMed] [Google Scholar]
  42. Siemankowski R. F., Wiseman M. O., White H. D. ADP dissociation from actomyosin subfragment 1 is sufficiently slow to limit the unloaded shortening velocity in vertebrate muscle. Proc Natl Acad Sci U S A. 1985 Feb;82(3):658–662. doi: 10.1073/pnas.82.3.658. [DOI] [PMC free article] [PubMed] [Google Scholar]
  43. Sleep J. A., Hutton R. L. Exchange between inorganic phosphate and adenosine 5'-triphosphate in the medium by actomyosin subfragment 1. Biochemistry. 1980 Apr 1;19(7):1276–1283. doi: 10.1021/bi00548a002. [DOI] [PubMed] [Google Scholar]
  44. Smith D. A. The theory of sliding filament models for muscle contraction. II. Biochemically-based models of the contraction cycle. J Theor Biol. 1990 Sep 21;146(2):157–175. doi: 10.1016/s0022-5193(05)80133-x. [DOI] [PubMed] [Google Scholar]
  45. Smith D. A. The theory of sliding filament models for muscle contraction. III. Dynamics of the five-state model. J Theor Biol. 1990 Oct 21;146(4):433–466. doi: 10.1016/s0022-5193(05)80372-8. [DOI] [PubMed] [Google Scholar]
  46. Squire J. M. The actomyosin interaction--shedding light on structural events: 'Plus ça change, plus c'est la même chose'. J Muscle Res Cell Motil. 1994 Jun;15(3):227–231. doi: 10.1007/BF00123475. [DOI] [PubMed] [Google Scholar]
  47. Stein L. A., Schwarz R. P., Jr, Chock P. B., Eisenberg E. Mechanism of actomyosin adenosine triphosphatase. Evidence that adenosine 5'-triphosphate hydrolysis can occur without dissociation of the actomyosin complex. Biochemistry. 1979 Sep 4;18(18):3895–3909. doi: 10.1021/bi00585a009. [DOI] [PubMed] [Google Scholar]
  48. Taylor E. W. Kinetic studies on the association and dissociation of myosin subfragment 1 and actin. J Biol Chem. 1991 Jan 5;266(1):294–302. [PubMed] [Google Scholar]
  49. Thomas D. D. Blitz and blizzard: crossbridges and chaos. Biophys J. 1993 Jul;65(1):21–22. doi: 10.1016/S0006-3495(93)81030-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  50. Trentham D. R., Eccleston J. F., Bagshaw C. R. Kinetic analysis of ATPase mechanisms. Q Rev Biophys. 1976 May;9(2):217–281. doi: 10.1017/s0033583500002419. [DOI] [PubMed] [Google Scholar]
  51. Vale R. D., Oosawa F. Protein motors and Maxwell's demons: does mechanochemical transduction involve a thermal ratchet? Adv Biophys. 1990;26:97–134. doi: 10.1016/0065-227x(90)90009-i. [DOI] [PubMed] [Google Scholar]
  52. Walker M., White H., Belknap B., Trinick J. Electron cryomicroscopy of acto-myosin-S1 during steady-state ATP hydrolysis. Biophys J. 1994 May;66(5):1563–1572. doi: 10.1016/S0006-3495(94)80948-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  53. Webb M. R., Hibberd M. G., Goldman Y. E., Trentham D. R. 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. 1986 Nov 25;261(33):15557–15564. [PubMed] [Google Scholar]
  54. Yanagida T. Loose coupling between chemical and mechanical reactions in actomyosin energy transduction. Adv Biophys. 1990;26:75–95. doi: 10.1016/0065-227x(90)90008-h. [DOI] [PubMed] [Google Scholar]

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