Annals of Biomedical Engineering

, Volume 32, Issue 11, pp 1559–1568 | Cite as

A Spatially Explicit Nanomechanical Model of the Half-Sarcomere: Myofilament Compliance Affects Ca2+-Activation

  • P. Bryant Chase
  • J. Michael Macpherson
  • Thomas L. Daniel


The force exerted by skeletal muscle is modulated by compliance of tissues to which it is connected. Force of the muscle sarcomere is modulated by compliance of the myofilaments. We tested the hypothesis that myofilament compliance influences Ca2+ regulation of muscle by constructing a computational model of the muscle half sarcomere that includes compliance of the filaments as a variable. The biomechanical model consists of three half-filaments of myosin and 13 thin filaments. Initial spacing of motor domains of myosin on thick filaments and myosin-binding sites on thin filaments was taken to be that measured experimentally in unstrained filaments. Monte-Carlo simulations were used to determine transitions around a three-state cycle for each cross-bridge and between two-states for each thin filament regulatory unit. This multifilament model exhibited less “tuning” of maximum force than an earlier two-filament model. Significantly, both the apparent Ca2+-sensitivity and cooperativity of activation of steady-state isometric force were modulated by myofilament compliance. Activation-dependence of the kinetics of tension development was also modulated by filament compliance. Tuning in the full myofilament lattice appears to be more significant at submaximal levels of thin filament activation.

Muscle Actin filament Myosin filament Cross- bridge Troponin Tropomyosin Calcium regulation Force Kinetics of tension development 


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  1. 1.
    Adams, G. R., V. J. Caiozzo, and K. M. Baldwin. Skeletal muscle unweighting: Spaceflight and ground-based models. J. Appl. Physiol. 95:2185–2201, 2003.Google Scholar
  2. 2.
    Bagshaw, C. R. Muscle Contraction. London: Chapman & Hall, 1993.Google Scholar
  3. 3.
    Brandt, P. W., M. S. Diamond, and F. H. Schachat. The thin filament of vertebrate skeletal muscle co-operatively activates as a unit. J. Mol. Biol. 180:379–384, 1984.Google Scholar
  4. 4.
    Brenner, B. Effect of Ca2+ on cross-bridge turnover kinetics in skinned single rabbit psoas fibers: Implications for regulation of muscle contraction. Proc. Natl. Acad. Sci. U.S.A. 85:3265–3269, 1988.Google Scholar
  5. 5.
    Brenner, B., and E. Eisenberg. Rate of force generation in mus-cle: Correlation with actomyosin ATPase activity in solution. Proc. Natl. Acad. Sci. U.S.A. 83:3542–3546, 1986.Google Scholar
  6. 6.
    Bukatina, A. E., and F. Fuchs. Effect of phalloidin on the ATPase activity of striated muscle myofibrils. J. Muscle Res. Cell Motil. 15:29–36, 1994.Google Scholar
  7. 7.
    Bukatina, A. E., F. Fuchs, and P. W. Brandt. Thin filament ac-tivation by phalloidin in skinned cardiac muscle. J. Mol. Cell. Cardiol. 27:1311–1315, 1995.PubMedGoogle Scholar
  8. 8.
    Campbell, K. Rate constant of muscle force redevelopment reflects cooperative activation as well as cross-bridge kinetics. Biophys. J. 72:254–262, 1997.Google Scholar
  9. 9.
    Chase, P. B., M. Macpherson, and T. L. Daniel. A spatially explicit, 3-D model of the muscle sarcomere. Biophys. J. 82:5a, 2002.Google Scholar
  10. 10.
    Chase, P. B., D. A. Martyn, and J. D. Hannon. Isometric force redevelopment of skinned muscle fibers from rabbit with and without Ca2+. Biophys. J. 67:1994–2001, 1994.Google Scholar
  11. 11.
    Daniel, T. L., A. C. Trimble, and P. B. Chase. Compliant re-alignment of binding sites in muscle: Transient behavior and mechanical tuning. Biophys. J. 74:1611–1621, 1998.Google Scholar
  12. 12.
    Daniel, T. L., and M. S. Tu. Animal movement, mechanical tuning and coupled systems. J. Exp. Biol. 202 Pt 23:3415–3421, 1999.Google Scholar
  13. 13.
    Farley, C. T., J. Glasheen, and T. A. McMahon. Running springs: Speed and animal size. J. Exp. Biol. 185:71–86, 1993.Google Scholar
  14. 14.
    Fatkin, D., and R. M. Graham. Molecular mechanisms of inherited cardiomyopathies. Physiol. Rev. 82:945–980, 2002.Google Scholar
  15. 15.
    Gafurov, B.,S. Fredricksen, A. Cai, B. Brenner, P.B. Chase, and J. M. Chalovich. The 14 mutant of troponin T enhances ATPase activity and alters the cooperative binding of S1-ADP to regulated actin. Biochemistry, In press.Google Scholar
  16. 16.
    Gittes, F., B. Mickey, J. Nettleton, and J. Howard. Flexural rigid-ity of microtubules and actin filaments measured from thermal fluctuations in shape. J. Cell Biol. 120:923–934, 1993.Google Scholar
  17. 17.
    Gordon, A. M., E. Homsher, and M. Regnier. Regulation of contraction in striated muscle. Physiol. Rev. 80:853–924, 2000.PubMedGoogle Scholar
  18. 18.
    Hancock, W. O., L. L. Huntsman, and A. M. Gordon. Models of calcium activation account for differences between skeletal and cardiac force redevelopment kinetics. J. Muscle Res. Cell Motil. 18:671–681, 1997.Google Scholar
  19. 19.
    Higuchi, H., T. Yanagida, and Y. E. Goldman. Compliance of thin filaments in skinned fibers of rabbit skeletal muscle. Bio-phys. J. 69:1000–1010, 1995.Google Scholar
  20. 20.
    Howard, J. Mechanics of Motor Proteins and the Cytoskeleton. Sunderland, MA: Sinaur Associates, 2001.Google Scholar
  21. 21.
    Huxley, H. E., A. Stewart, H. Sosa, and T. Irving. X-ray diffrac-tion measurements of the extensibility of actin and myosin filaments in contracting muscle. Biophys. J. 67:2411–2421, 1994.Google Scholar
  22. 22.
    Isambert, H., P. Venier, A. C. Maggs, A. Fattoum, R. Kassab, D. Pantaloni, and M.-F. Carlier. Flexibility of actin filaments derived from thermal fluctuations. Effect of bound nucleotide, phalloidin, and muscle regulatory proteins. J. Biol. Chem. 270:11437–11444, 1995.PubMedGoogle Scholar
  23. 23.
    Köhler, J., Y. Chen, B. Brenner, A. M. Gordon, T. Kraft, D. A. Martyn, M. Regnier, A. J. Rivera, C.-K. Wang, and P. B. Chase. Familial hypertrophic cardiomyopathy mutations in troponin I (K183Δ, G203S, K206Q) enhance filament sliding. Physiol. Genomics 14:117–128, 2003.Google Scholar
  24. 24.
    Lambeth, M. J., and M. J. Kushmerick. A computational model for glycogenolysis in skeletal muscle. Ann. Biomed. Eng. 30:808–827, 2002.Google Scholar
  25. 25.
    Linari, M., I. Dobbie, M. Reconditi, N. Koubassova, M. Irving, G. Piazzesi, and V. Lombardi. The stiffness of skele-tal muscle in isometric contraction and rigor: The fraction of myosin heads bound to actin. Biophys. J. 74:2459–2473, 1998.Google Scholar
  26. 26.
    Luo, Y., R. Cooke, and E. Pate. A model of stress relaxation in cross-bridge systems: Effect of a series elastic element. Am. J. Physiol. 265:C279–C288, 1993.Google Scholar
  27. 27.
    Luo, Y., R. Cooke, and E. Pate. Effect of series elasticity on delay in development of tension relative to stiffness during muscle activation. Am.J.Physiol.267:C1598–C1606, 1994.Google Scholar
  28. 28.
    Martyn, D. A., and P. B. Chase. Faster force transient kinetics at submaximal Ca2+ activation of skinned psoas fibers from rabbit. Biophys. J. 68:235–242, 1995.Google Scholar
  29. 29.
    Martyn, D. A., P. B. Chase, M. Regnier, and A. M. Gordon. A simple model with myofilament compliance predicts activation dependent cross-bridge kinetics in skinned skeletal fibers. Biophys. J. 83:3425–3434, 2002.Google Scholar
  30. 30.
    McMahon, T. A., and P. R. Greene. The influence of track compliance on running. J. Biomech. 12:893–904, 1979.Google Scholar
  31. 31.
    Mijailovich, S. M., J. J. Fredberg, and J. P. Butler. On the theory of muscle contraction: Filament extensibility and the development of isometric force and stiffness. Biophys. J. 71:1475–1484, 1996.Google Scholar
  32. 32.
    Millman, B. M. The filament lattice of striated muscle. Physiol. Rev. 78:359–391, 1998.Google Scholar
  33. 33.
    Molloy, J. E., J. E. Burns, J. Kendrick-Jones, R. T. Tregear, and D. C. S. White. Movement and force produced by a single myosin head. Nature 378:209–212, 1995.Google Scholar
  34. 34.
    Molloy, J.E.,J.E. Burns, J.C. Sparrow, R.T. Tregear, J. Kendrick-Jones, and D. C. S. White. Single-molecule mechan-ics of heavy meromyosin and S1 interacting with rabbit or Drosophila actins using optical tweezers. Biophys. J. 68:298S–303S, S-5S, 1995.Google Scholar
  35. 35.
    Regnier, M., D. A. Martyn, and P. B. Chase. Calmidazolium alters Ca2+ regulation of tension redevelopment rate in skinned skeletal muscle. Biophys. J. 71:2786–2794, 1996.Google Scholar
  36. 36.
    Regnier, M., D. A. Martyn, and P. B. Chase. Calcium regulation of tension redevelopment kinetics with 2-deoxy-ATP or low [ATP] in rabbit skeletal muscle. Biophys. J. 74:2005–2015, 1998.Google Scholar
  37. 37.
    Regnier, M., A. J. Rivera, M. A. Bates, C.-K. Wang, P. B. Chase, and A. M. Gordon. Thin filament near-neighbor regulatory unit interactions affect rabbit skeletal muscle steady state force-Ca2+ relations. J. Physiol. 540:485–497, 2002.Google Scholar
  38. 38.
    Regnier, M., A. J. Rivera, P. B. Chase, L. B. Smillie, and M. M. Sorenson. Regulation of skeletal muscle tension redevelopment by troponin C constructs with different Ca2+ affinities. Biophys. J. 76:2664–2672, 1999.Google Scholar
  39. 39.
    Riley, D. A., J. L. Bain, J. L. Thompson, R. H. Fitts, J. J. Widrick, S. W. Trappe, T. A. Trappe, and D. L. Costill. Decreased thin filament density and length in human atrophic soleus muscle fibers after spaceflight. J. Appl. Physiol. 88:567–572, 2000.Google Scholar
  40. 40.
    Salem, J.E.,G.M. Saidel, W.C. Stanley,and M.E. Cabrera. Mechanistic model of myocardial energy metabolism under nor-mal and ischemic conditions. Ann. Biomed. Eng. 30:202–216, 2002.Google Scholar
  41. 41.
    Sweeney, H. L., and J. T. Stull. Alteration of cross-bridge ki-netics by myosin light chain phosphorylation in rabbit skeletal muscle: Implications for regulation of actin-myosin interaction. Proc. Natl. Acad. Sci. U.S.A. 87:414–418, 1990.Google Scholar
  42. 42.
    Veigel, C., M. L. Bartoo, D. C. S. White, J. C. Sparrow, and J. E. Molloy. The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer. Biophys. J. 75:1424–1438, 1998.Google Scholar
  43. 43.
    Wakabayashi, K., Y. Sugimoto, H. Tanaka, Y. Ueno, Y. Takezawa, and Y. Amemiya. X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction. Biophys. J. 67:2422–2435, 1994.Google Scholar
  44. 44.
    White, R. J., and M. Averner. Humans in space. Nature 409:1115–1118, 2001.Google Scholar

Copyright information

© Biomedical Engineering Society 2004

Authors and Affiliations

  • P. Bryant Chase
    • 1
  • J. Michael Macpherson
    • 2
  • Thomas L. Daniel
    • 3
  1. 1.Department of Biological Science and Program in Molecular BiophysicsFlorida State UniversityTallahassee
  2. 2.Department of Biological SciencesStanford UniversityStanford
  3. 3.Department of BiologyUniversity of WashingtonSeattle

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