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Models for Fully-Activated Muscle

  • David Aitchison Smith
Chapter

Abstract

Having surveyed the mechanics and biochemistry of striated muscle, the next step is to formulate theories and models of contractility at full calcium-activation, based on the unit cell of the lattice in one half-sarcomere. To construct a robust and comprehensive theory, Huxley’s model can be updated to include physically motivated strain-dependent kinetics, the working stroke and simplified forms of the biochemical contraction cycle. Starting with the application of Kramers-Smoluchowski theory to strain-dependent transitions in the biochemical cycle, we survey vernier and lattice models of contraction, computational methods, the effects of filament compliance, and models with multiple actin sites and buckling rods. Then these models are tested against experiment for their steady-state contractile behaviour, including the effects of changing [ADP], [Pi], [ATP] and temperature.

Keywords

Strain Working stroke Contraction cycle Tension ATPase Efficiency 

References

  1. Adamovic I, Mijailovich SM, Karplus M (2008) The elastic properties of the structurally characterized myosin II S2 subdomain: a molecular dynamics and normal mode analysis. Biophys J 94:3779–3789PubMedPubMedCentralCrossRefGoogle Scholar
  2. Arata T, Mukohata Y, Tonomura Y (1977) Structure and function of the two heads of the myosin molecule. VI. ATP hydrolysis, shortening and tension development of myofibrils. Biochemistry 82:801–812CrossRefGoogle Scholar
  3. Bagni MA, Cecchi G, Colomo F, Poggesi C (1990) Tension and stiffness of frog muscle fibers at full filament overlap. J Muscle Res Cell Motil 11:371–377PubMedCrossRefPubMedCentralGoogle Scholar
  4. Barclay CJ, Woledge RC, Curtin NA (2010) Inferring crossbridge properties from skeletal muscle energetics. Prog Biophys Mol Biol 102:53–71PubMedCrossRefPubMedCentralGoogle Scholar
  5. Bickham DC, West TG, Webb MR, Woledge RC, Curtin NA (2011) Millisecond biochemical response to change in strain. Biophys J 101:2445–2454PubMedPubMedCentralCrossRefGoogle Scholar
  6. Bowater R, Sleep J (1988) Demembranated muscle fibers catalyze a more rapid exchange between phosphate and adenosine triphosphate than actomyosin subfragment 1. Biochemistry 27:5314–5323PubMedCrossRefPubMedCentralGoogle Scholar
  7. Brenner B (1991) Rapid dissociation and reassociation of actomyosin cross-bridges during force generation: a newly observed facet of cross-bridge action in muscle. Proc Natl Acad Sci USA 88:10490–10494PubMedCrossRefPubMedCentralGoogle Scholar
  8. Brunello E, Reconditi M, Elangovan R, Linari M, Sun YB, Narayanan T, Panine P, Piazzesi G, Irving M, Lombardi V (2007) Skeletal muscle resists stretch by rapid binding of the second motor domain of myosin to actin. Proc Natl Acad Sci USA 104:20114–20119PubMedCrossRefGoogle Scholar
  9. Caremani M, Dantzig J, Goldman YE, Lombardi V, Linari M (2008) Effect of inorganic phosphate on the force and number of myosin cross-bridges during the isometric contraction of permeabilized muscle fibres from rabbit psoas. Biophys J 95:5798–5808PubMedPubMedCentralCrossRefGoogle Scholar
  10. Carlson FD, Wilkie DR (1974) Muscle physiology. Prentice-Hall, Englewood CliffsGoogle Scholar
  11. Chase PB, Macpherson JM, Daniel TD (2004) A spatially explicit nanomechanical model of the half-sarcomere: myofilament compliance affects Ca2+-activation. Ann Biomed Eng 32:1559–1568PubMedCrossRefPubMedCentralGoogle Scholar
  12. Chen B, Gao H (2011) Motor force homeostasis in skeletal muscle contraction. Biophys J 101:396–403PubMedPubMedCentralCrossRefGoogle Scholar
  13. Cooke R, Bialek W (1979) Contraction of glycerinated muscle fibers as a function of the ATP concentration. Biophys Soc 28:241–258Google Scholar
  14. Cooke R, Franks K (1980) All myosin heads form bonds with actin in rigor rabbit skeletal muscle. Biochemistry 19:2264–2269CrossRefGoogle Scholar
  15. Cooke R, Pate E (1985) The effects of ADP and phosphate on the contraction of muscle fibers. Biophys J 48:789–798PubMedPubMedCentralCrossRefGoogle Scholar
  16. Cooke R, Franks K, Luciani GB, Pate E (1988) The inhibition of rabbit skeletal muscle contraction by hydrogen ions and phosphate. J Physiol (London) 395:77–97CrossRefGoogle Scholar
  17. Cooke R, White H, Pate E (1994) A model of the release of myosin heads from actin in rapidly contracting muscle fibers. Biophys J 66:778–788PubMedPubMedCentralCrossRefGoogle Scholar
  18. Coupland ME, Puchet E, Ranatunga KW (2001) Temperature dependence of active tension in mammalian (rabbit psoas) fibres: effect of inorganic phosphate. J Physiol (London) 536(6):879–891CrossRefGoogle Scholar
  19. Cremo CR, Geeves MA (1998) Interaction of actin and ADP with the head domain of smooth muscle myosin: implications for strain-dependent ADP release in smooth muscle. Biochemistry 37:1969–1978PubMedCrossRefPubMedCentralGoogle Scholar
  20. Curtin N, Gilbert C, Kretschmar KM, Wilkie DR (1974) The effect of the performance of work on total energy output and metabolism during muscular contraction. J Physiol (London) 238:455–472CrossRefGoogle Scholar
  21. Daniel TL, Trimble AC, Chase PB (1998) Compliant realignment of binding sites in muscle: transient behavior and mechanical tuning. Biophys J 74:1611–1621PubMedPubMedCentralCrossRefGoogle Scholar
  22. Dantzig JA, Goldman YE, Millar NC, Lacktis J, Homsher E (1992) Reversal of the cross-bridge force-generating transition by photogeneration of phosphate in rabbit psoas muscle fibers. J Physiol (London) 451:247–278CrossRefGoogle Scholar
  23. DeCostre V, Bianco P, Lombardi V, Piazzesi G (2005) Effect of temperature on the working stroke of muscle myosin. Proc Natl Acad Sci USA 102:13927–13932PubMedCrossRefPubMedCentralGoogle Scholar
  24. Dobbie I, Linari M, Piazzesi G, Reconditi M, Koubassova N, Ferenczi MA, Lombardi V, Irving M (1998) Elastic bending and tilting of myosin heads during muscle contraction. Nature 396:383–387PubMedCrossRefPubMedCentralGoogle Scholar
  25. Duke TAJ (1999) Molecular model of muscle contraction. Proc Natl Acad Sci USA 96:2770–2775PubMedCrossRefPubMedCentralGoogle Scholar
  26. Edman KAP (1988) Double-hyperbolic force-velocity relation in frog muscle fibres. J Physiol (London) 404:301–321CrossRefGoogle Scholar
  27. Edman KAP, Curtin NA (2001) Synchronous oscillations of length and stiffness during loaded shortening of frog muscle fibers. J Physiol (London) 534(2):553–563CrossRefGoogle Scholar
  28. Edman KAP, Reggiani C, Schiaffino S, Te Kronnie G (1988) Maximum velocity of shortening related to myosin isoform composition in frog skeletal muscle fibres. J Physiol (London) 395:679–694CrossRefGoogle Scholar
  29. Edman KAP, Mansson A, Caputo C (1997) The biphasic force-velocity relationship in frog muscle fibres and its evaluation in terms of cross-bridge function. J Physiol (London) 503(1):141–156CrossRefGoogle Scholar
  30. Elemans CPH, Mead AF, Rome LC, Goller F (2008) Superfast vocal muscles control song production in songbirds. PLoS One 3:e2581PubMedPubMedCentralCrossRefGoogle Scholar
  31. Elliott GF, Worthington CR (2001) Muscle contraction: viscous-like forces and the impulsive model. Int J Biol Macromol 29:213–218PubMedCrossRefPubMedCentralGoogle Scholar
  32. Evans E (2001) Probing the relation between force-lifetime and chemistry in single molecular bonds. Ann Rev Biophys Biomol Struct 30:105–128CrossRefGoogle Scholar
  33. Ferenczi M, Goldman YE, Simmons RM (1984) The dependence of force and shortening velocity on substrate concentration in skinned muscle fibres from rana temporaria. J Physiol (London) 350:519–543CrossRefGoogle Scholar
  34. Ferenczi MA, Bershitsky SY, Koubassova N, Sithanandan V, Helsby WI, Panine P, Roessle M, Narayanan T, Tsaturyan A (2005) The “roll and lock” mechanism of force generation in muscle. Structure 13:131–141PubMedCrossRefPubMedCentralGoogle Scholar
  35. Fischer S, Windschugel B, Horak D, Holmes KC, Smith JC (2005) Structural mechanism of the recovery stroke in the myosin molecular motor. Proc Natl Acad Sci USA 102:6873–6878PubMedCrossRefPubMedCentralGoogle Scholar
  36. Ford L, Huxley AF, Simmons RM (1977) Tension responses to sudden length change in stimulated frog muscle fibres near slack length. J Physiol (London) 269:441–515PubMedCentralCrossRefPubMedGoogle Scholar
  37. Ford L, Huxley AF, Simmons RM (1981) The relation between stiffness and filament overlap in stimulated frog muscle fibres. J Physiol (London) 311:219–249PubMedCentralCrossRefPubMedGoogle Scholar
  38. Fusi L, Reconditi M, Linari M, Brunello E, Elangovan R, Lombardi V, Piazzesi G (2010) The mechanism of resistance to stretch of isometrically contracting single muscle fibres. J Physiol (London) 588:495–510CrossRefGoogle Scholar
  39. Geeves MA, Conibear PB (1995) The role of three-state docking of myosin S1 with actin in force generation. Biophys J 68:194s–201sPubMedPubMedCentralGoogle Scholar
  40. Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comp Phys 22:403–434CrossRefGoogle Scholar
  41. Glyn H, Sleep J (1985) Dependence of adenosine triphosphatase activity of rabbit psoas muscle fibres and myofibrils on substrate concentration. J Physiol (London) 365:259–276CrossRefGoogle Scholar
  42. Gollub J, Cremo CR, Cooke R (1996) ADP release produces a rotation of the neck region of smooth myosin but not skeletal myosin. Nat Struct Biol 3:796–802PubMedCrossRefPubMedCentralGoogle Scholar
  43. Gordon AM, Huxley AF, Julian F (1966) The variation in isometric tension with sarcomere length in vertebrate muscle fibres. J Physiol (London) 184:170–192CrossRefGoogle Scholar
  44. Gourlay AR (1970) A note on trapezoidal methods for the solution of initial value problems. Math Comput 24:629–633CrossRefGoogle Scholar
  45. Guo B, Guilford WH (2006) Mechanics of actomyosin bonds in different nucleotide states are tuned to muscle contraction. Proc Natl Acad Sci USA 103:9844–9849PubMedCrossRefPubMedCentralGoogle Scholar
  46. Hanggi P, Talkner P, Borovec M (1990) Reaction-rate theory: fifty years after Kramers. Rev Mod Phys 62:251–341CrossRefGoogle Scholar
  47. Happel J, Brenner H (1983) Low Reynolds number hydrodynamics. Martinus Nijhoff, The HagueGoogle Scholar
  48. He Z-H, Chillingworth RK, Brune M, Corrie JET, Webb MR, Ferenczi MA (1999) The efficiency of muscle contraction in rabbit skeletal muscle fibres, determined from the rate of release of inorganic phosphate. J Physiol (London) 517(3):8390–8854CrossRefGoogle Scholar
  49. Hill AV (1938) The heart of shortening and the dynamic constants of muscle. Proc R Soc B 126:136–195Google Scholar
  50. Hill TL (1974) Theoretical formalism for the sliding filament model of contraction of striated muscle. Part I. Prog Biophys Mol Biol 28:267–340PubMedCrossRefPubMedCentralGoogle Scholar
  51. Hill TL, Eisenberg E, Chen Y-D, Podolsky RJ (1975) Some self-consistent two-state sliding filament models of muscle contraction. Biophys J 15:335–372PubMedPubMedCentralCrossRefGoogle Scholar
  52. 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 50:583–600CrossRefGoogle Scholar
  53. Huxley AF (1957) Muscle structure and theories of contraction. Prog Biophys Biophys Chem 7:257–318PubMedCrossRefPubMedCentralGoogle Scholar
  54. Huxley AF (1980) Reflections on muscle: the Sherrington Lecture XIV. Liverpool Univrsity Press, LiverpoolGoogle Scholar
  55. Huxley AF, Simmons RM (1971) Proposed mechanism of force generation in striated muscle. Nature 233:533–538PubMedCrossRefGoogle Scholar
  56. Huxley HE, Stewart A, Sosa H, Irving M (1994) X-ray diffraction measurements of the extensibility of actin and myosin filaments in contracting muscle. Biophys J 67:2411–2421PubMedPubMedCentralCrossRefGoogle Scholar
  57. Irving M, St Claire Allen T, Sabido-David C, Craik JS, Brandmeier B, Kendrick-Jones JK, Corrie JET, Trentham DR, Goldman YE (1995) Tilting of the light-chain region of myosin during step length changes and active force generation in skeletal muscle. Nature 375:688–691CrossRefGoogle Scholar
  58. Iwamoto H (1995) Evidence for increased low force cross-bridge population in shortening skinned skeletal muscle fibers: implications for actomyosin kinetics. Biophys J 69:1022–1035PubMedPubMedCentralCrossRefGoogle Scholar
  59. Iwazumi T (1984) No tension fluctuation in normal and healthy single myofibrils. Biophys J 45:158aGoogle Scholar
  60. Iwazumi T (1988) Myofibril tension fluctuations and molecular mechanism of contraction. Adv Exp Med Biol 226:595–608. Sugi H (ed) Plenum PressGoogle Scholar
  61. Jontes JD, Wilson-Kubalek EM, Milligan RA (1995) A 32o tail swing in brush border myosin I on ADP release. Nature 378:751–753PubMedCrossRefPubMedCentralGoogle Scholar
  62. Julian FJ, Sollins KR, Sollins MR (1974) A model for the transient and steady-state mechanical behaviour of contracting muscle. Biophys J 14:546–562PubMedPubMedCentralCrossRefGoogle Scholar
  63. Karatzaferi C, Chinn MK, Cooke R (2004) The force exerted by a muscle cross-bridge depends directly on the strength of the actomyosin bond. Biophys J 87:2532–2544PubMedPubMedCentralCrossRefGoogle Scholar
  64. Kawai M, Guth K, Winnikes K, Haist C, Ruegg JC (1987) The effect of inorganic phosphate on the ATP hydrolysis rate and the tension transients in chemically skinned rabbit psoas fibers. Pflugers Arch 408:1–9PubMedCrossRefPubMedCentralGoogle Scholar
  65. Kaya M, Higuchi H (2010) Nonlinear elasticity and an 8-nm working stroke of single myosin molecules in myofilaments. Science 329:686–689CrossRefGoogle Scholar
  66. Knupp C, Offer G, Ranatunga KW, Squire JM (2009) Probing muscle myosin motor action: X-ray (M3 and M6) interference measurements report motor domain not lever arm movement. J Mol Biol 390:168–181PubMedCrossRefPubMedCentralGoogle Scholar
  67. Kohler J, Winkler G, Schulte I, Scholz T, McKenna W, Brenner B, Kraft T (2002) Mutation of the myosin converter domain alters cross-bridge elasticity. Proc Natl Acad Sci USA 99:3557–3562CrossRefGoogle Scholar
  68. Kojima H, Ishijima A, Yanagida T (1994) Direct measurement of stiffness of single actin filaments with and without tropomyosin using in vitro nano-manipulation. Proc Natl Acad Sci USA 91:12962–12966PubMedCrossRefPubMedCentralGoogle Scholar
  69. Kramers H (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physics 7:284–304Google Scholar
  70. Lan G, Sun SX (2005) Dynamics of myosin-driven skeletal muscle contraction: I. steady-state force generation. Biophys J 88:4107–4112PubMedPubMedCentralCrossRefGoogle Scholar
  71. Levy RM, Umazume Y, Kushmerick MJ (1976) Ca2+ dependence of tension and ADP production in segments of chemically skinned muscle fibres. Biochim Biophys Acta 430:352–365PubMedCrossRefPubMedCentralGoogle Scholar
  72. Linari M, Dobbie I, Reconditi M, Koubassova N, Irving M, Piazzesi G, Lombardi V (1998) The stiffness of skeletal muscle in isometric contraction and rigor: the fraction of myosin heads bound to actin. Biophys J 74:2459–2473PubMedPubMedCentralCrossRefGoogle Scholar
  73. Linari M, Piazzesi G, Dobbie I, Koubassova N, Reconditi M, Narayanan T, Diat O, Irving M, Lombardi V (2000) Interference fine structure and sarcomere length dependence of the axial x-ray pattern from active single muscle fibers. Proc Natl Acad Sci USA 97:7226–7231PubMedPubMedCentralCrossRefGoogle Scholar
  74. Linari M, Caremani M, Piperio C, Brandt P, Lombardi V (2007) Stiffness and fraction of myosin motors responsible for active force in permeabilized muscle fibers from rabbit psoas. Biophys J 92:2476–2490PubMedPubMedCentralCrossRefGoogle Scholar
  75. Linari M, Caremani M, Lombardi V (2010) A kinetic model that explains the effect of inorganic phosphate on the mechanics and energetics of isometric contraction of fast skeletal muscle. Proc R Soc B 277:19–27PubMedCrossRefPubMedCentralGoogle Scholar
  76. Linari M, Piazzesi G, Irving M (2011) A reinvestigation of the source of compliance of muscle cross-bridges. Biophys J 100 (Supplement 1):585aGoogle Scholar
  77. Lombardi V, Piazzesi G (1990) The contractile response during steady lengthening of stimulated frog muscle fibers. J Physiol (London) 431:141–171CrossRefGoogle Scholar
  78. Lombardi V, Piazzesi G (1992) Force response in steady lengthening of active single muscle fibers. In: Simmons RM (ed) Muscular contraction. Cambridge University Press, Cambridge, pp 237–255CrossRefGoogle Scholar
  79. Luo Y, Cooke R, Pate E (1994) Effect of series elasticity on delay in development of tension relative to stiffness during muscle activation. Am J Phys 267:C1598–C1606CrossRefGoogle Scholar
  80. Mansson A (2010) Actomyosin-ADP states, interhead cooperativity, and the force-velocity relation of skeletal muscle. Biophys J 98:1237–1246PubMedPubMedCentralCrossRefGoogle Scholar
  81. Mijailovich SM, Kayser-Herold O, Stojanovic B, Nedic D, Irving TC, Geeves MA (2016) Three-dimensional stochastic model of actin-myosin binding in the sarcomere lattice. J Gen Physiol 148:459–488PubMedPubMedCentralCrossRefGoogle Scholar
  82. Millar N, Geeves MA (1988) Protein fluorescence changes associated with ATP and adenosine 5′-[γ-thio]triphosphate binding to skeletal muscle myosin subfragment 1 and actomyosin subfragment 1. Biochem J 249:735–743PubMedPubMedCentralCrossRefGoogle Scholar
  83. Millar N, Homsher E (1990) The effect of phosphate and calcium on force generation in glycerinated rabbit skeletal muscle fibers. J Biol Chem 264:20234–20240Google Scholar
  84. Millar N, Howarth V, Gutfreund H (1987) A transient kinetic study of enthalpy changes during the reaction of myosin subfragment 1 with ATP. Biochem J 248:683–690PubMedPubMedCentralCrossRefGoogle Scholar
  85. Millman B (1991) The filament lattice of striated muscle. Physiol Rev 78:359–384CrossRefGoogle Scholar
  86. Nishiyama K, Shimizu H, Kometani K, Chaen S (1977) The three-state model for the elementary process of energy conversion in muscle. Biochem Biophys Acta 460:523–536PubMedPubMedCentralGoogle Scholar
  87. Nyitrai M, Rossi R, Adamek N, Pellegrino MA, Bottinelli R, Geeves MA (2006) What limits the velocity of fast-skeletal muscle contraction in mammals? J Mol Biol 355:432–442PubMedCrossRefPubMedCentralGoogle Scholar
  88. Offer G, Ranatunga KW (2013) A cross-bridge cycle with two tension-generating steps simulates skeletal muscle mechanics. Biophys J 105:928–940PubMedPubMedCentralCrossRefGoogle Scholar
  89. Offer G, Ranatunga KW (2015) The endothermic ATP hydrolysis and crossbridge attachment steps drive the increase of force with temperature in isometric and shortening muscle. J Physiol (London) 593(8):1997–2016CrossRefGoogle Scholar
  90. Park-Holohan SJ, West TG, Woledge RC, Ferenczi MA, Barclay CJ, Curtin NA (2010) Effect of phosphate and temperature on force exerted by white muscle fibres from dogfish. J Muscle Res Cell Motil 31:35–44PubMedPubMedCentralCrossRefGoogle Scholar
  91. Pate E, Cooke R (1989) A model of crossbridge action: the effects of ATP, ADP and Pi. J Muscle Res Cell Motil 10:181–196PubMedCrossRefPubMedCentralGoogle Scholar
  92. Piazzesi G, Lombardi V (1995) A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle. Biophys J 68:1966–1979PubMedPubMedCentralCrossRefGoogle Scholar
  93. Piazzesi G, Reconditi M, Linari M, Lucii L, Sun YB, Narayanan T, Boesecke P, Lombardi V, Irving M (2002) Mechanism of force generation by myosin heads in skeletal muscle. Nature 415:659–662PubMedCrossRefPubMedCentralGoogle Scholar
  94. Piazzesi G, Reconditi M, Koubassova N, Decostre V, Linari M, Lucii L, Lombardi V (2003) Temperature dependence of the force-generating process in single fibres from frog skeletal muscle. J Physiol (London) 549(1):93–106CrossRefGoogle Scholar
  95. Piazzesi G, Reconditi M, Linari M, Lucii L, Bianco P, Brunello E, Decostre V, Stewart A, Gore DB, Irving TC, Irving M, Lombardi V (2007) Skeletal muscle performance determined by modulation of number of myosin motors rather than motor force or stroke size. Cell 131:784–795PubMedCrossRefPubMedCentralGoogle Scholar
  96. Piazzesi G, Dolfi M, Brunello E, Fusi L, Reconditi M, Bianco P, Linari M, Lombardi V (2014) The myofilament elasticity and its effect on kinetics of force generation by the myosin motor. Arch Biochem Biophys 552:108–116PubMedCrossRefPubMedCentralGoogle Scholar
  97. Potma EJ, Steinen GJM (1996) Increase in ATP consumption during shortening in skinned fibres from rabbit psoas muscle: effects of inorganic phosphate. J Physiol (London) 496(1):1–12CrossRefGoogle Scholar
  98. Potma EJ, van Grass A, Steinen GJM (1995) Influence of inorganic phosphate and pH on ATP utilization in fast and slow skeletal muscle fibers. Biophys J 69:2580–2589PubMedPubMedCentralCrossRefGoogle Scholar
  99. Press WH, Teukolsky SA, Vetterling WT, Flannery BR (1992) Numerical recipes in Fortran, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  100. Rall JA, Woledge RC (1990) Influence of temperature on mechanics and energetics of muscle contraction. Am J Phys 259:R197–R203Google Scholar
  101. Ranatunga KW (1984) The force-velocity relation of rat fast- and slow-twitch muscles examined at different temperatures. J Physiol (London) 351:517–529CrossRefGoogle Scholar
  102. Ranatunga KW (1988) Temperature dependence of mechanical power output in mammalian (rat) skeletal muscle. Exp Physiol 83:371–376CrossRefGoogle Scholar
  103. Rees BB, Stephenson DG (1987) Thermal dependence of maximum Ca2+-activated force in skinned muscle fibres of the toad Bufo marinus acclimated at different temperatures. J Exp Biol 129:309–327PubMedPubMedCentralGoogle Scholar
  104. Rome (2006) Design and function of superfast muscles: new insights into the physiology of skeletal muscle. Annu Rev Physiol 68:193–221PubMedCrossRefPubMedCentralGoogle Scholar
  105. Seo JS, Krause PC, McMahon TA (1994) Negative developed tension in rapidly shortening whole frog muscles. J Muscle Res Cell Motil 15:59–68PubMedCrossRefPubMedCentralGoogle Scholar
  106. 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 82:658–662PubMedCrossRefPubMedCentralGoogle Scholar
  107. Siththanandan VB, Donnelly JI, Ferenczi MA (2006) Effect of strain on actomyosin kinetics in isometric muscle fibres. Biophys J 90:3653–3665PubMedPubMedCentralCrossRefGoogle Scholar
  108. Sleep J, Glyn H (1986) Inhibition of myofibrillar and actomyosin subfragment 1 adenosinetriphosphatase by adenosine 5′-diphosphate and adenyl-5′-yl imidodiphosphate. Biochemistry 25:1149–1154PubMedCrossRefPubMedCentralGoogle Scholar
  109. Smith DA (1990) The theory of sliding filament models for muscle contraction. III Dynamics of the five-state model. J Theor Biol 146:433–466PubMedCrossRefPubMedCentralGoogle Scholar
  110. Smith DA (2014) A new mechanokinetic model for muscle contraction, where force and movement are triggered by phosphate release. J Muscle Res Cell Motil 35:295–306PubMedCrossRefPubMedCentralGoogle Scholar
  111. Smith DA, Geeves MA (1995) Strain-dependent cross-bridge cycle for muscle. Biophys J 69:524–537PubMedPubMedCentralCrossRefGoogle Scholar
  112. Smith DA, Mijailovich SM (2008) Towards a unified theory of muscle contraction II: predictions with the mean-field approximation. Ann Biomed Eng 36:1353–1371PubMedCrossRefPubMedCentralGoogle Scholar
  113. Smith DA, Sleep J (2004) Mechanokinetics of rapid tension recovery in muscle: the myosin working stroke is followed by a slower release of phosphate. Biophys J 87:442–456PubMedPubMedCentralCrossRefGoogle Scholar
  114. Smith DA, Geeves MA, Sleep J, Mijailovich SM (2008) Towards a unified theory of muscle contraction. I: foundations. Ann Biomed Eng 36:1624–1640PubMedCrossRefPubMedCentralGoogle Scholar
  115. Smoluchowski MV (1916) Uber Brownsche Molekularbewegung unter Einwirkung aubere Krafte und deren Zusammenhang mit der verallgemeinerten Diffusionsgelichung. Ann Physik 352:1102–1112Google Scholar
  116. Steffen W, Smith D, Sleep J (2003) The working stroke upon myosin-nucleotide complexes binding to actin. Proc Natl Acad Sci USA 100:6434–6439PubMedCrossRefPubMedCentralGoogle Scholar
  117. Sun Y-B, Hilber K, Irving M (2001) Effect of active shortening on the rate of ATP utilization by rabbit psoas fibres. J Physiol (London) 531(3):781–791CrossRefGoogle Scholar
  118. Takagi Y, Shuman H, Goldman YE (2004) Coupling between phosphate release and force generation in muscle contraction. Proc R Soc B 359:1912–1920Google Scholar
  119. Takano M, Terada TP, Sasai M (2010) Unidirectional Brownian motion observed in an in silico single molecule experiment of an actomyosin motor. Proc Natl Acad Sci USA 107:7769–7774PubMedCrossRefPubMedCentralGoogle Scholar
  120. Takashi R, Putnam S (1979) A fluorimetric method for continuously assaying ATPase: applications to small specimens of glycerol-extracted muscle fibres. Anal Biochem 92:375–382PubMedCrossRefPubMedCentralGoogle Scholar
  121. Tanner BCW, Daniel TL, Regnier M (2007) Sarcomere lattice geometry influences cooperative myosin binding in muscle. PLOS Comp Biol 3:1195–1211CrossRefGoogle Scholar
  122. Tesi C, Colomo F, Nencini S, Piroddi N, Poggesi C (2000) The effect of inorganic phosphate on force generation in single myofibrils from rabbit skeletal muscle. Biophys J 78:3081–3092PubMedPubMedCentralCrossRefGoogle Scholar
  123. Thorson J, White DCS (1969) Distributed representations for actin-myosin interaction in the oscillatory contraction of muscle. Biophys J 9:360–390PubMedPubMedCentralCrossRefGoogle Scholar
  124. Tregear RT, Reedy MC, Goldman YE, Taylor KA, Winkler H, Franzini-Armstrong C, Sasaki H, Lucaveche C, Reedy MK (2004) Cross-bridge number, position and angle in target zones of cryofixed isometrically active insect flight muscle. Biophys J 86:3009–3019PubMedPubMedCentralCrossRefGoogle Scholar
  125. Tsaturyan AK, Bershiksty SY, Butrns R, Ferenczi MA (1999) Strutural changes in the actin-myosin crossbridges associated with force generation induced by temperature jump in permeabilised frog muscle fibres. Biophys J 77:354–372PubMedPubMedCentralCrossRefGoogle Scholar
  126. Tsaturyan AK, Koubassova N, Ferenczi MA, Narayanan T, Roessle M, Bershiksty SY (2005) Strong binding of myosin heads stretches and twists the actin helix. Biophys J 88:1902–1910PubMedCrossRefPubMedCentralGoogle Scholar
  127. Veigel C, Coluccio LM, Jontes JD, Sparrow JC, Milligan RA, Molloy JE (1999) The motor protein myosin-I produces its working stroke in two steps. Nature 398:530–533PubMedCrossRefPubMedCentralGoogle Scholar
  128. Vilfan A, Duke T (2003) Instabilities in the transient response of muscle. Biophys J 85:818–827PubMedPubMedCentralCrossRefGoogle Scholar
  129. Von der Ecken J, Heissler SM, Pathan-Chhatbar S, Manstein DJ, Raunser S (2016) Cryo-EM structure of a human cytoplasmic actomyosin complex at near-atomic resolution. Nature 534:724–728PubMedCrossRefPubMedCentralGoogle Scholar
  130. Wakabayashi K, Sugimoto Y, Tanaka H, Ueno Y, Takezawa Y, Amemiya Y (1994) X-ray evidence for the extensibility of actin and myosin filaments during muscle contraction. Biophys J 67:2422–2435PubMedPubMedCentralCrossRefGoogle Scholar
  131. Weiss GH (1986) Overview of theoretical models of reaction rates. J Stat Phys 42:1–36CrossRefGoogle Scholar
  132. West TG, Hild G, Siththanandan VB, Webb MR, Corrie JET, Ferenczi MA (2009) Time course and strain dependence of ADP release during contraction of permeabilized skeletal muscle fibers. Biophys J 96:3281–3294PubMedPubMedCentralCrossRefGoogle Scholar
  133. Westerblad H, Allen DG, Lannergren J (2002) Muscle fatigue: lactic acid or inorganic phosphate the major cause? News Physiol Soc 17:17–21Google Scholar
  134. White HD, Taylor EW (1976) Energetics and mechanism of actomyosin adenosine triphosphatase. Biochemistry 15:5818–5826PubMedCrossRefGoogle Scholar
  135. White HD, Belknap B, Webb MR (1997) Kinetics of nucleoside triphosphate cleavage and phosphate release steps by associated rabbit skeletal actomyosin, measured using a novel fluorescent probe for phosphate. Biochemistry 36:11828–11836PubMedCrossRefGoogle Scholar
  136. Whittaker M, Wilson-Kubalek EM, Smith JE, Faust L, Milligan RA, Sweeney HL (1995) A 35-Ao movement of smooth muscle myosin on ADP release. Nature 378:748–751PubMedCrossRefGoogle Scholar
  137. Woledge RC (1968) The energetics of tortoise muscle. J Physiol (London) 197:685–707CrossRefGoogle Scholar
  138. Woledge RC, Curtin NA, Homsher E (1985) Energetic aspects of muscle contraction, Monographs physiological society no. 41. Academic Press, LondonGoogle Scholar
  139. Wood JE, Mann RW (1981) A sliding-filament cross-bridge ensemble model of muscle contraction for mechanical transients. Math Biosci 57:211–263CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • David Aitchison Smith
    • 1
  1. 1.Department of Physiology, Anatomy and MicrobiologyLa Trobe UniversityMelbourneAustralia

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