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The Journal of Physiological Sciences

, Volume 68, Issue 5, pp 541–554 | Cite as

A new myofilament contraction model with ATP consumption for ventricular cell model

  • Yuttamol Muangkram
  • Akinori Noma
  • Akira AmanoEmail author
Original Paper

Abstract

A new contraction model of cardiac muscle was developed by combining previously described biochemical and biophysical models. The biochemical component of the new contraction model represents events in the presence of Ca2+–crossbridge attachment and power stroke following inorganic phosphate release, detachment evoked by the replacement of ADP by ATP, ATP hydrolysis, and recovery stroke. The biophysical component focuses on Ca2+ activation and force (F b) development assuming an equivalent crossbridge. The new model faithfully incorporates the major characteristics of the biochemical and biophysical models, such as F b activation by transient Ca2+ ([Ca2+]–F b), [Ca2+]–ATP hydrolysis relations, sarcomere length–F b, and F b recovery after jumps in length under the isometric mode and upon sarcomere shortening after a rapid release of mechanical load under the isotonic mode together with the load–velocity relationship. ATP consumption was obtained for all responses. When incorporated in a ventricular cell model, the contraction model was found to share approximately 60% of the total ATP usage in the cell model.

Keywords

Myofilament model Mechano-energetics Actomyosin–ATPase Crossbridge kinetics Troponin system 

Notes

Author Contributions

YM and AN designed the study and developed the mathematical model. YM analyzed the experimental simulations and drafted the manuscript. AN and AA interpreted the data, discussed the results, and revised the manuscript. All authors have approved the final version of the submitted manuscript.

Compliance with ethical standards

Funding

The authors received no external funding for this research.

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Supplementary material

12576_2017_560_MOESM1_ESM.doc (364 kb)
Supplementary material 1 (DOC 364 kb)

References

  1. 1.
    Suga H (1990) Ventricular energetics. Physiol Rev 70:247–277CrossRefPubMedGoogle Scholar
  2. 2.
    Asakura K, Cha CY, Yamaoka H, Horikawa Y, Memida H, Powell T, Amano A, Noma A (2014) EAD and DAD mechanisms analyzed by developing a new human ventricular cell model. Prog Biophys Mol Biol 116:11–24CrossRefPubMedGoogle Scholar
  3. 3.
    Himeno Y, Asakura K, Cha CY, Memida H, Powell T, Amano A, Noma A (2015) A human ventricular myocyte model with a refined representation of excitation-contraction coupling. Biophys J 109:415–427CrossRefPubMedPubMedCentralGoogle Scholar
  4. 4.
    Lombardi V, Piazzesi G (1990) The contractile response during steady lengthening of stimulated frog muscle fibres. J Physiol 431:141–171CrossRefPubMedPubMedCentralGoogle Scholar
  5. 5.
    Månsson A (2010) Actomyosin-ADP states, interhead cooperativity, and the force–velocity relation of skeletal muscle. Biophys J 98:1237–1246CrossRefPubMedPubMedCentralGoogle Scholar
  6. 6.
    Månsson A, Rassier D, Tsiavaliaris G (2015) Poorly understood aspects of striated muscle contraction. Biomed Res Int. doi: 10.1155/2015/245154 PubMedPubMedCentralCrossRefGoogle Scholar
  7. 7.
    Piazzesi G, Lombardi V (1995) A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle. Biophys J 68:1966–1979CrossRefPubMedPubMedCentralGoogle Scholar
  8. 8.
    Landesberg A, Sideman S (1994) Mechanical regulation of cardiac muscle by coupling calcium kinetics with cross-bridge cycling: a dynamic model. Am J Physiol Heart Circ Physiol 267:H779–H795CrossRefGoogle Scholar
  9. 9.
    Razumova MV, Bukatina AE, Campbell KB (1999) Stiffness-distortion sarcomere model for muscle simulation. J Appl Physiol 87:1861–1876CrossRefPubMedGoogle Scholar
  10. 10.
    Razumova MV, Bukatina AE, Campbell KB (2000) Different myofilament nearest-neighbor interactions have distinctive effects on contractile behavior. Biophys J 78:3120–3137CrossRefPubMedPubMedCentralGoogle Scholar
  11. 11.
    Campbell KB, Razumova MV, Kirkpatrick RD, Slinker BK (2001) Nonlinear myofilament regulatory processes affect frequency-dependent muscle fiber stiffness. Biophys J 81:2278–2296CrossRefPubMedPubMedCentralGoogle Scholar
  12. 12.
    Rice JJ, Wang F, Bers DM, de Tombe PP (2008) Approximate model of cooperative activation and crossbridge cycling in cardiac muscle using ordinary differential equations. Biophys J 95:2368–2390CrossRefPubMedPubMedCentralGoogle Scholar
  13. 13.
    Negroni JA, Lascano EC (1996) A cardiac muscle model relating sarcomere dynamics to calcium kinetics. J Mol Cell Cardiol 28:915–929CrossRefPubMedGoogle Scholar
  14. 14.
    Negroni JA, Lascano EC (2008) Simulation of steady state and transient cardiac muscle response experiments with a Huxley-based contraction model. J Mol Cell Cardiol 45:300–312CrossRefPubMedGoogle Scholar
  15. 15.
    Rice JJ, Stolovitzky G, Tu Y, de Tombe PP (2003) Ising model of cardiac thin filament activation with nearest-neighbor cooperative interactions. Biophys J 84:897–909CrossRefPubMedPubMedCentralGoogle Scholar
  16. 16.
    Hussan J, de Tombe PP, Rice JJ (2006) A spatially detailed myofilament model as a basis for large-scale biological simulations. IBM J Res Dev 50:582–600CrossRefGoogle Scholar
  17. 17.
    Kentish JC (1986) The effects of inorganic phosphate and creatine phosphate on force production in skinned muscles from rat ventricle. J Physiol 370:585–604CrossRefPubMedPubMedCentralGoogle Scholar
  18. 18.
    de Tombe PP, ter Keurs HE (1991) Sarcomere dynamics in cat cardiac trabeculae. Circ Res 68:588–596CrossRefPubMedGoogle Scholar
  19. 19.
    Moriarty TF (1980) The law of Laplace. Its limitation as a relation for diastolic pressure, volume, or wall stress of the left ventricle. Circ Res 46:321–331CrossRefPubMedGoogle Scholar
  20. 20.
    Gibbs CL (1978) Cardiac energetics. Physiol Rev 58:174–254CrossRefPubMedGoogle Scholar
  21. 21.
    Lab MJ, Allen DG, Orchard CH (1984) The effects of shortening on myoplasmic calcium concentration and on the action potential in mammalian ventricular muscle. Circ Res 55:825–829CrossRefPubMedGoogle Scholar
  22. 22.
    Yue DT, Marban E, Wier WG (1986) Relationship between force and intracellular [Ca2+] in tetanized mammalian heart muscle. J Gen Physiol 87:223–242CrossRefPubMedPubMedCentralGoogle Scholar
  23. 23.
    Janssen PM, Stull LB, Marban E (2002) Myofilament properties comprise the rate-limiting step for cardiac relaxation at body temperature in the rat. Am J Physiol Heart Circ Physiol 282:H499–H507CrossRefPubMedGoogle Scholar
  24. 24.
    Stehle R, Iorga B (2010) Kinetics of cardiac sarcomere processes and rate-limiting steps in contraction and relaxation. J Mol Cell Cardiol 48:843–850CrossRefPubMedGoogle Scholar
  25. 25.
    Negroni JA, Morotti S, Lascano EC, Gomes AV, Grandi E, Puglisi JL, Bers DM (2015) β-adrenergic effects on cardiac myofilaments and contraction in an integrated rabbit ventricular myocyte model. J Mol Cell Cardiol 81:162–175CrossRefPubMedPubMedCentralGoogle Scholar
  26. 26.
    Hunter PJ, McCulloch AD, Ter Keurs HEDJ (1998) Modelling the mechanical properties of cardiac muscle. Prog Biophys Mol Biol 69:289–331CrossRefPubMedGoogle Scholar
  27. 27.
    Jafri MS, Rice JJ, Winslow RL (1998) Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys J 74:1149–1168CrossRefPubMedPubMedCentralGoogle Scholar
  28. 28.
    Matsuoka S, Sarai N, Kuratomi S, Ono K, Noma A (2003) Role of individual ionic current systems in ventricular cells hypothesized by a model study. Jpn J Physiol 53:105–123CrossRefPubMedGoogle Scholar
  29. 29.
    Matsuoka S, Sarai N, Jo H, Noma A (2004) Simulation of ATP metabolism in cardiac excitation–contraction coupling. Prog Biophys Mol Biol 85:279–299CrossRefPubMedGoogle Scholar
  30. 30.
    Coutu P, Metzger JM (2005) Genetic manipulation of calcium-handling proteins in cardiac myocytes. II. Mathematical modeling studies. Am J Physiol Heart Circ Physiol 288:H613–H631CrossRefPubMedGoogle Scholar
  31. 31.
    Okada JI, Sugiura S, Nishimura S, Hisada T (2005) Three-dimensional simulation of calcium waves and contraction in cardiomyocytes using the finite element method. Am J Physiol Cell Physiol 288:C510–C522CrossRefPubMedGoogle Scholar
  32. 32.
    Shim EB, Amano A, Takahata T, Shimayoshi T, Noma A (2007) The cross-bridge dynamics during ventricular contraction predicted by coupling the cardiac cell model with a circulation model. J Physiol Sci 57:275–285CrossRefPubMedGoogle Scholar
  33. 33.
    Shim EB, Jun HM, Leem CH, Matusuoka S, Noma A (2008) A new integrated method for analyzing heart mechanics using a cell-hemodynamics-autonomic nerve control coupled model of the cardiovascular system. Prog Biophys Mol Biol 96:44–59CrossRefPubMedGoogle Scholar
  34. 34.
    Soltis AR, Saucerman JJ (2010) Synergy between CaMKII substrates and β-adrenergic signaling in regulation of cardiac myocyte Ca2+ handling. Biophys J 99:2038–2047CrossRefPubMedPubMedCentralGoogle Scholar
  35. 35.
    Potter JD (1974) The content of troponin, tropomyosin, actin, and myosin in rabbit skeletal muscle myofibrils. Arch Biochem Biophys 162:436–441CrossRefPubMedGoogle Scholar
  36. 36.
    Murakami U, Uchida K (1985) Contents of myofibrillar proteins in cardiac, skeletal, and smooth muscles. J Biochem 98:187–197CrossRefPubMedGoogle Scholar
  37. 37.
    Kuhn HJ, Bletz C, Rüegg JC (1990) Stretch-induced increase in the Ca2+ sensitivity of myofibrillar ATPase activity in skinned fibres from pig ventricles. Pflug Arch 415:741–746CrossRefGoogle Scholar
  38. 38.
    Barsotti RJ, Ferenczi MA (1988) Kinetics of ATP hydrolysis and tension production in skinned cardiac muscle of the guinea pig. J Biol Chem 263:16750–16756PubMedGoogle Scholar
  39. 39.
    Hooijman P, Stewart MA, Cooke R (2011) A new state of cardiac myosin with very slow ATP turnover: a potential cardioprotective mechanism in the heart. Biophys J 100:1969–1976CrossRefPubMedPubMedCentralGoogle Scholar
  40. 40.
    Gwathmey JK, Hajjar RJ (1990) Relation between steady-state force and intracellular [Ca2+] in intact human myocardium. Index of myofibrillar responsiveness to Ca2+. Circulation 82:1266–1278CrossRefPubMedGoogle Scholar
  41. 41.
    de Tombe PP, Stienen GJM (1995) Protein kinase A does not alter economy of force maintenance in skinned rat cardiac trabeculae. Circ Res 76:734–741CrossRefPubMedGoogle Scholar
  42. 42.
    Grandi E, Pasqualini FS, Bers DM (2010) A novel computational model of the human ventricular action potential and Ca transient. J Mol Cell Cardiol 48:112–121CrossRefPubMedGoogle Scholar
  43. 43.
    O’Hara T, Virág L, Varró A, Rudy Y (2011) Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation. PLoS Comput Biol 7:e1002061CrossRefPubMedPubMedCentralGoogle Scholar
  44. 44.
    Hinch R, Greenstein JL, Tanskanen AJ, Xu L, Winslow RL (2004) A simplified local control model of calcium-induced calcium release in cardiac ventricular myocytes. Biophys J 87:3723–3736CrossRefPubMedPubMedCentralGoogle Scholar
  45. 45.
    Schramm M, Klieber HG, Daut J (1994) The energy expenditure of actomyosin-ATPase, Ca2+-ATPase and Na+, K+-ATPase in guinea-pig cardiac ventricular muscle. J Physiol 481:647–662CrossRefPubMedPubMedCentralGoogle Scholar
  46. 46.
    Utaki H, Taniguchi K, Konishi H, Himeno Y, Amano A (2016) A method for determining scale parameters in a hemodynamic model incorporating cardiac cellular contraction model. Adv Biomed Eng 5:32–42CrossRefGoogle Scholar
  47. 47.
    Piazzesi G, Francini F, Linari M, Lombardi V (1992) Tension transients during steady lengthening of tetanized muscle fibres of the frog. J Physiol 445:659–711CrossRefPubMedPubMedCentralGoogle Scholar
  48. 48.
    Edman KAP, Månsson A, Caputo C (1997) The biphasic force–velocity relationship in frog muscle fibres and its evaluation in terms of cross-bridge function. J Physiol 503:141–156CrossRefPubMedPubMedCentralGoogle Scholar
  49. 49.
    Siemankowski RF, White HD (1984) Kinetics of the interaction between actin, ADP, and cardiac myosin-S1. J Biol Chem 259:5045–5053PubMedGoogle Scholar
  50. 50.
    Rayment I, Holden HM, Whittaker M, Yohn CB, Lorenz M, Holmes KC, Milligan RA (1993) Structure of the actin–myosin complex and its implications for muscle contraction. Science 261:58–65CrossRefPubMedGoogle Scholar
  51. 51.
    Spudich JA (1994) How molecular motors work. Nature 372:515–518CrossRefPubMedGoogle Scholar
  52. 52.
    Yount RG, Lawson D, Rayment I (1995) Is myosin a “back door” enzyme? Biophys J 68:44S–49SPubMedPubMedCentralGoogle Scholar
  53. 53.
    Lymn RW, Taylor EW (1971) Mechanism of adenosine triphosphate hydrolysis by actomyosin. Biochemistry 10:4617–4624CrossRefPubMedGoogle Scholar
  54. 54.
    Sugi H, Minoda H, Inayoshi Y, Yumoto F, Miyakawa T, Miyauchi Y, Tanokura M, Akimoto T, Kobayashi T, Chaen S, Sugiura S (2008) Direct demonstration of the cross-bridge recovery stroke in muscle thick filaments in aqueous solution by using the hydration chamber. Proc Natl Acad Sci USA 105:17396–17401CrossRefPubMedGoogle Scholar
  55. 55.
    Ford LE (1991) Mechanical manifestations of activation in cardiac muscle. Circ Res 68:621–637CrossRefPubMedGoogle Scholar
  56. 56.
    Shimizu H, Fujita T, Ishiwata SI (1992) Regulation of tension development by MgADP and Pi without Ca2+. Role in spontaneous tension oscillation of skeletal muscle. Biophys J 61:1087–1098CrossRefPubMedPubMedCentralGoogle Scholar
  57. 57.
    Trentham DR, Eccleston JF, Bagshaw CR (1976) Kinetic analysis of ATPase mechanisms. Q Rev Biophys 9:217–281CrossRefPubMedGoogle Scholar
  58. 58.
    Geeves MA, Goody RS, Gutfreund H (1984) Kinetics of acto-S1 interaction as a guide to a model for the crossbridge cycle. J Muscle Res Cell Motil 5:351–361CrossRefPubMedGoogle Scholar
  59. 59.
    Goldman YE, Brenner B (1987) Special topic: molecular mechanism of muscle contraction. Annu Rev Physiol 49:629–636CrossRefPubMedGoogle Scholar
  60. 60.
    Huxley AF, Simmons RM (1971) Proposed mechanism of force generation in striated muscle. Nature 233:533–538CrossRefPubMedGoogle Scholar
  61. 61.
    Huxley AF (1974) Muscular contraction. J Physiol 243:1–43CrossRefPubMedPubMedCentralGoogle Scholar
  62. 62.
    Ford LE, Huxley AF, Simmons RM (1977) Tension responses to sudden length change in stimulated frog muscle fibres near slack length. J Physiol 269:441–515CrossRefPubMedPubMedCentralGoogle Scholar
  63. 63.
    Izakov VY, Katsnelson LB, Blyakhman FA, Markhasin VS, Shklyar TF (1991) Cooperative effects due to calcium binding by troponin and their consequences for contraction and relaxation of cardiac muscle under various conditions of mechanical loading. Circ Res 69:1171–1184CrossRefPubMedGoogle Scholar
  64. 64.
    Peterson JN, Hunter WC, Berman MR (1991) Estimated time course of Ca2+ bound to troponin C during relaxation in isolated cardiac muscle. Am J Physiol Heart Circ Physiol 260:H1013–H1024CrossRefGoogle Scholar
  65. 65.
    Brenner B, Schoenberg M, Chalovich JM, Greene LE, Eisenberg E (1982) Evidence for cross-bridge attachment in relaxed muscle at low ionic strength. Proc Natl Acad Sci USA 79:7288–7291CrossRefPubMedGoogle Scholar
  66. 66.
    Geeves MA, Holmes KC (1999) Structural mechanism of muscle contraction. Annu Rev Biochem 68:687–728CrossRefPubMedGoogle Scholar
  67. 67.
    Baumann BA, Liang H, Sale K, Hambly BD, Fajer PG (2004) Myosin regulatory domain orientation in skeletal muscle fibers: application of novel electron paramagnetic resonance spectral decomposition and molecular modeling methods. Biophys J 86:3030–3041CrossRefPubMedPubMedCentralGoogle Scholar
  68. 68.
    Ferenczi MA, Bershitsky SY, Koubassova N, Siththanandan V, Helsby WI, Panine P, Roessle M, Narayanan T, Tsaturyan AK (2005) The “roll and lock” mechanism of force generation in muscle. Structure 13:131–141CrossRefPubMedGoogle Scholar
  69. 69.
    Wu S, Liu J, Reedy MC, Tregear RT, Winkler H, Franzini-Armstrong C, Sasaki H, Lucaveche C, Goldman YE, Reedy MK, Taylor KA (2010) Electron tomography of cryofixed, isometrically contracting insect flight muscle reveals novel actin–myosin interactions. PLoS One 5:e12643CrossRefPubMedPubMedCentralGoogle Scholar
  70. 70.
    Smith DA, Geeves MA, Sleep J, Mijailovich SM (2008) Towards a unified theory of muscle contraction. I: foundations. Ann Biomed Eng 36:1624–1640CrossRefPubMedGoogle Scholar
  71. 71.
    Kentish JC, Stienen GJ (1994) Differential effects of length on maximum force production and myofibrillar ATPase activity in rat skinned cardiac muscle. J Physiol 475:175–184CrossRefPubMedPubMedCentralGoogle Scholar
  72. 72.
    Ebus JP, Stienen GJ, Elzinga G (1994) Influence of phosphate and pH on myofibrillar ATPase activity and force in skinned cardiac trabeculae from rat. J Physiol 476:501–516CrossRefPubMedPubMedCentralGoogle Scholar
  73. 73.
    Ebus JP, Stienen GJM (1996) ATPase activity and force production in skinned rat cardiac muscle under isometric and dynamic conditions. J Mol Cell Cardiol 28:1747–1757CrossRefPubMedGoogle Scholar
  74. 74.
    de Tombe PP, Stienen GJM (2007) Impact of temperature on cross-bridge cycling kinetics in rat myocardium. J Physiol 584:591–600CrossRefPubMedPubMedCentralGoogle Scholar
  75. 75.
    Wannenburg T, Janssen PM, Fan D, de Tombe PP (1997) The Frank-Starling mechanism is not mediated by changes in rate of cross-bridge detachment. Am J Physiol Heart Circ Physiol 273:H2428–H2435CrossRefGoogle Scholar
  76. 76.
    Siemankowski RF, Wiseman MO, White HD (1985) ADP dissociation from actomyosin subfragment 1 is sufficiently slow to limit the unloaded shortening velocity in vertebrate muscle. Proc Natl Acad Sci USA 82:658–662CrossRefPubMedGoogle Scholar
  77. 77.
    Burchfield DM, Rall JA (1986) Temperature dependence of the crossbridge cycle during unloaded shortening and maximum isometric tetanus in frog skeletal muscle. J Muscle Res Cell Motil 7:320–326CrossRefPubMedGoogle Scholar
  78. 78.
    Stienen GJ, Kiers JL, Bottinelli R, Reggiani C (1996) Myofibrillar ATPase activity in skinned human skeletal muscle fibres: fibre type and temperature dependence. J Physiol 493:299–307CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© The Physiological Society of Japan and Springer Japan KK 2017

Authors and Affiliations

  1. 1.Graduate School of Life SciencesRitsumeikan UniversityKusatsuJapan

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