Hill's equation of muscle performance and its hidden insight on molecular mechanisms

Journal of General Physiology

Volumn 142, Issue 6, 2013, Pages 561-573

  Seow, Chun Y ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

MYOSIN;

ACTIN FILAMENT; ANIMAL; HUMAN; METABOLISM; MUSCLE CONTRACTION; PHYSIOLOGY; REVIEW; SKELETAL MUSCLE;

ACTIN CYTOSKELETON; ANIMALS; HUMANS; MUSCLE CONTRACTION; MUSCLE, SKELETAL; MYOSINS;

EID: 84890241330     PISSN: 00221295     EISSN: 15407748     Source Type: Journal    
DOI: 10.1085/jgp.201311107     Document Type: Review

References (88)

1. Abbott, B.C., and D.R. Wilkie. 1953. The relation between velocity of shortening and the tension-length curve of skeletal muscle. J. Physiol. 120:214-223.
2. Albet-Torres, N., M.J. Bloemink, T. Barman, R. Candau, K. Frölander, M.A. Geeves, K. Golker, C. Herrmann, C. Lionne, C. Piperio, et al. 2009. Drug effect unveils inter-head cooperativity and strain-dependent ADP release in fast skeletal actomyosin. J. Biol. Chem. 284:22926-22937. http://dx.doi.org/10.1074/jbc .M109.019232
3. Baker, J.E., and D.D. Thomas. 2000. A thermodynamic muscle model and a chemical basis for A.V. Hill's muscle equation. J. Muscle Res. Cell Motil. 21:335-344. http://dx.doi.org/10.1023/A:1005615925390
4. Bárány, M. 1967. ATPase activity of myosin correlated with speed of muscle shortening. J. Gen. Physiol. 50:197-218. http://dx.doi.org/ 10.1085/jgp.50.6.197
5. Barclay, C.J., J.K. Constable, and C.L. Gibbs. 1993. Energetics of fast- and slow-twitch muscles of the mouse. J. Physiol. 472:61-80.
6. Barclay, C.J., R.C. Woledge, and N.A. Curtin. 2010. Inferring crossbridge properties from skeletal muscle energetics. Prog. Biophys. Mol. Biol. 102:53-71. http://dx.doi.org/10.1016/j.pbiomolbio .2009.10.003
7. Brooks, S.V., and J.A. Faulkner. 1988. Contractile properties of skeletal muscles from young, adult and aged mice. J. Physiol. 404: 71-82.
8. Caremani, M., L. Melli, M. Dolfi, V. Lombardi, and M. Linari. 2013. The working stroke of the myosin II motor in muscle is not tightly coupled to release of orthophosphate from its active site. J. Physiol. 591:5187-5205. http://dx.doi.org/10.1113/ jphysiol.2013.257410
9. Cecchi, G., F. Colomo, and V. Lombardi. 1978. Force-velocity relation in normal and nitrate-treated frog single muscle fibres during rise of tension in an isometric tetanus. J. Physiol. 285:257-273.
10. Chin, L., P. Yue, J.J. Feng, and C.Y. Seow. 2006. Mathematical simulation of muscle cross-bridge cycle and force-velocity relationship. Biophys. J. 91:3653-3663. http://dx.doi.org/10.1529/ biophysj.106.092510
11. Civan, M.M., and R.J. Podolsky. 1966. Contraction kinetics of striated muscle fibres following quick changes in load. J. Physiol. 184:511-534.
12. Claflin, D.R., and J.A. Faulkner. 1989. The force-velocity relationship at high shortening velocities in the soleus muscle of the rat. J. Physiol. 411:627-637.
13. Close, R. 1964. Dynamic properties of fast and slow skeletal muscles of the rat during development. J. Physiol. 173:74-95.
14. Cooke, R., and W. Bialek. 1979. Contraction of glycerinated muscle fibers as a function of the ATP concentration. Biophys. J. 28:241-258. http://dx.doi.org/10.1016/S0006-3495(79)85174-7
15. Cooke, R., and E. Pate. 1985. The effects of ADP and phosphate on the contraction of muscle fibers. Biophys. J. 48:789-798. http:// dx.doi.org/10.1016/S0006-3495(85)83837-6
16. Cooke, R., K. Franks, G.B. Luciani, and E. Pate. 1988. The inhibition of rabbit skeletal muscle contraction by hydrogen ions and phosphate. J. Physiol. 395:77-97.
17. Dantzig, J.A., Y.E. Goldman, N.C. Millar, J. Lacktis, and E. Homsher. 1992. Reversal of the cross-bridge force-generating transition by photogeneration of phosphate in rabbit psoas muscle fibres. J. Physiol. 451:247-278.
18. Dawson, M.J., D.G. Gadian, and D.R. Wilkie. 1978. Muscular fatigue investigated by phosphorus nuclear magnetic resonance. Nature. 274:861-866. http://dx.doi.org/10.1038/274861a0
19. Debold, E.P., H. Dave, and R.H. Fitts. 2004. Fiber type and temperature dependence of inorganic phosphate: implications for fatigue. Am. J. Physiol. Cell Physiol. 287:C673-C681. http://dx.doi .org/10.1152/ajpcell.00044.2004
20. Debold, E.P., J. Romatowski, and R.H. Fitts. 2006. The depressive effect of Pi on the force-pCa relationship in skinned single muscle fibers is temperature dependent. Am. J. Physiol. Cell Physiol. 290:C1041-C1050. http://dx.doi.org/10.1152/ajpcell .00342.2005
21. Debold, E.P., S.E. Beck, and D.M. Warshaw. 2008. Effect of low pH on single skeletal muscle myosin mechanics and kinetics. Am. J. Physiol. Cell Physiol. 295:C173-C179. http://dx.doi.org/10.1152/ ajpcell.00172.2008
22. Devrome, A.N., and B.R. MacIntosh. 2007. The biphasic forcevelocity relationship in whole rat skeletal muscle in situ. J. Appl. Physiol. 102:2294-2300. http://dx.doi.org/10.1152/japplphysiol .00276.2006
23. Edman, K.A. 1988. Double-hyperbolic force-velocity relation in frog muscle fibres. J. Physiol. 404:301-321.
24. Edman, K.A., and A.R. Mattiazzi. 1981. Effects of fatigue and altered pH on isometric force and velocity of shortening at zero load in frog muscle fibres. J. Muscle Res. Cell Motil. 2:321-334. http:// dx.doi.org/10.1007/BF00713270
25. Edman, K.A., L.A. Mulieri, and B. Scubon-Mulieri. 1976. Nonhyperbolic force-velocity relationship in single muscle fibres. Acta Physiol. Scand. 98:143-156. http://dx.doi.org/10.1111/j.1748-1716 .1976.tb00234.x
26. Edman, K.A., A. Månsson, and C. Caputo. 1997. The biphasic forcevelocity relationship in frog muscle fibres and its evaluation in terms of cross-bridge function. J. Physiol. 503:141-156. http:// dx.doi.org/10.1111/j.1469-7793.1997.141bi.x
27. Eisenberg, E., T.L. Hill, and Y. Chen. 1980. Cross-bridge model of muscle contraction. Quantitative analysis. Biophys. J. 29:195-227. http://dx.doi.org/10.1016/S0006-3495(80)85126-5
28. Elangovan, R., M. Capitanio, L. Melli, F.S. Pavone, V. Lombardi, and G. Piazzesi. 2012. An integrated in vitro and in situ study of kinetics of myosin II from frog skeletal muscle. J. Physiol. 590:1227-1242.
29. Ferenczi, M.A., Y.E. Goldman, and R.M. Simmons. 1984. The dependence of force and shortening velocity on substrate concentration in skinned muscle fibres from Rana temporaria. J. Physiol. 350:519-543.
30. Fitts, R.H. 2008. The cross-bridge cycle and skeletal muscle fatigue. J. Appl. Physiol. 104:551-558. http://dx.doi.org/10.1152/ japplphysiol.01200.2007
31. Gilliver, S.F., H. Degens, J. Rittweger, A.J. Sargeant, and D.A. Jones. 2009. Variation in the determinants of power of chemically skinned human muscle fibres. Exp. Physiol. 94:1070-1078. http:// dx.doi.org/10.1113/expphysiol.2009.048314
32. Gilliver, S.F., D.A. Jones, J. Rittweger, and H. Degens. 2011. Variation in the determinants of power of chemically skinned type I rat soleus muscle fibres. J. Comp. Physiol. A Neuroethol. Sens. Neural Behav. Physiol. 197:311-319. http://dx.doi.org/10.1007/ s00359-010-0613-6
33. Goldman, Y.E., and R.M. Simmons. 1984. Control of sarcomere length in skinned muscle fibres of Rana temporaria during mechanical transients. J. Physiol. 350:497-518.
34. Grange, R.W., C.R. Cory, R. Vandenboom, and M.E. Houston. 1995. Myosin phosphorylation augments force-displacement and force-velocity relationships of mouse fast muscle. Am. J. Physiol. 269:C713-C724.
35. Herron, T.J., F.S. Korte, and K.S. McDonald. 2001. Loaded shortening and power output in cardiac myocytes are dependent on myosin heavy chain isoform expression. Am. J. Physiol. Heart Circ. Physiol. 281:H1217-H1222.
36. Hill, A.V. 1938. The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. Lond. B Biol. Sci. 126:136-195. http:// dx.doi.org/10.1098/rspb.1938.0050
37. Hill, A.V. 1964. The effect of load on the heat of shortening of muscle. Proc. R. Soc. Lond. B Biol. Sci. 159:297-318. http://dx.doi .org/10.1098/rspb.1964.0004
38. Huxley, A.F. 1957. Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7:255-318.
39. Huxley, A.F., and R.M. Simmons. 1971. Proposed mechanism of force generation in striated muscle. Nature. 233:533-538. http:// dx.doi.org/10.1038/233533a0
40. Johnston, I.A., and J. Salamonski. 1984. Power output and forcevelocity relationship of red and white muscle fibres from the Pacific blue marlin (Makaira nigricans). J. Exp. Biol. 111:171-177.\
41. Johnston, I.A., and B.D. Sidell. 1984. Differences in temperature dependence of muscle contractile properties and myofibrillar ATPase activity in a cold-temperature fish. J. Exp. Biol. 111:179-189.
42. Jones, D.A. 2010. Changes in the force-velocity relationship of fatigued muscle: implications for power production and possible causes. J. Physiol. 588:2977-2986. http://dx.doi.org/10.1113/ jphysiol.2010.190934
43. Jones, D.A., C.J. de Ruiter, and A. de Haan. 2006. Change in contractile properties of human muscle in relationship to the loss of power and slowing of relaxation seen with fatigue. J. Physiol. 576:913-922. http://dx.doi.org/10.1113/jphysiol.2006.116343
44. Julian, F.J., L.C. Rome, D.G. Stephenson, and S. Striz. 1986. The maximum speed of shortening in living and skinned frog muscle fibres. J. Physiol. 370:181-199.
45. Karatzaferi, C., K. Franks-Skiba, and R. Cooke. 2008. Inhibition of shortening velocity of skinned skeletal muscle fibers in conditions that mimic fatigue. Am. J. Physiol. Regul. Integr. Comp. Physiol. 294:R948-R955. http://dx.doi.org/10.1152/ajpregu.00541.2007
46. Katz, B. 1939. The relation between force and speed in muscular contraction. J. Physiol. 96:45-64.
47. Knuth, S.T., H. Dave, J.R. Peters, and R.H. Fitts. 2006. Low cell pH depresses peak power in rat skeletal muscle fibres at both 30 degrees C and 15 degrees C: implications for muscle fatigue. J. Physiol. 575:887-899. http://dx.doi.org/10.1113/jphysiol.2006.106732
48. Landesberg, A., and S. Sideman. 2000. Force-velocity relationship and biochemical-to-mechanical energy conversion by the sarcomere. Am. J. Physiol. Heart Circ. Physiol. 278:H1274-H1284.
49. Langeron, O., C. Coirault, S. Fratea, G. Orliaguet, P. Coriat, and B. Riou. 1999. The effects of dantrolene on the contraction, relaxation, and energetics of the diaphragm muscle. Anesth. Analg. 89:466-471.
50. Lännergren, J. 1978. The force-velocity relation of isolated twitch and slow muscle fibres of Xenopus laevis. J. Physiol. 283:501-521.
51. Lännergren, J., P. Lindblom, and B. Johansson. 1982. Contractile properties of two varieties of twitch muscle fibres in Xenopus laevis. Acta Physiol. Scand. 114:523-535. http://dx.doi.org/10.1111/ j.1748-1716.1982.tb07020.x
52. Levine, R.J., R.W. Kensler, Z. Yang, J.T. Stull, and H.L. Sweeney. 1996. Myosin light chain phosphorylation affects the structure of rabbit skeletal muscle thick filaments. Biophys. J. 71:898-907. http://dx.doi.org/10.1016/S0006-3495(96)79293-7
53. Linari, M., M. Caremani, and V. Lombardi. 2010. A kinetic model that explains the effect of inorganic phosphate on the mechanics and energetics of isometric contraction of fast skeletal muscle. Proc. Biol. Sci. 277:19-27. http://dx.doi.org/10.1098/rspb.2009.1498
54. Luff, A.R. 1981. Dynamic properties of the inferior rectus, extensor digitorum longus, diaphragm and soleus muscles of the mouse. J. Physiol. 313:161-171.
55. Månsson, A. 2010. Actomyosin-ADP states, interhead cooperativity, and the force-velocity relation of skeletal muscle. Biophys. J. 98:1237-1246. http://dx.doi.org/10.1016/j.bpj.2009.12.4285
56. Metzger, J.M., M.L. Greaser, and R.L. Moss. 1989. Variations in crossbridge attachment rate and tension with phosphorylation of myosin in mammalian skinned skeletal muscle fibers. Implications for twitch potentiation in intact muscle. J. Gen. Physiol. 93:855-883. http://dx.doi.org/10.1085/jgp.93.5.855
57. Moss, R.L., G.M. Diffee, and M.L. Greaser. 1995. Contractile properties of skeletal muscle fibers in relation to myofibrillar protein isoforms. Rev. Physiol. Biochem. Pharmacol. 126:1-63. http://dx.doi .org/10.1007/BFb0049775
58. Negroni, J.A., and E.C. Lascano. 2008. Simulation of steady state and transient cardiac muscle response experiments with a Huxley-based contraction model. J. Mol. Cell. Cardiol. 45:300-312. http://dx.doi .org/10.1016/j.yjmcc.2008.04.012
59. Nosek, T.M., K.Y. Fender, and R.E. Godt. 1987. It is diprotonated inorganic phosphate that depresses force in skinned skeletal muscle fibers. Science. 236:191-193. http://dx.doi.org/10.1126/ science.3563496
60. Pate, E., and R. Cooke. 1989. A model of crossbridge action: the effects of ATP, ADP and Pi. J. Muscle Res. Cell Motil. 10:181-196. http://dx.doi.org/10.1007/BF01739809
61. Pellegrino, M.A., M. Canepari, R. Rossi, G. D'Antona, C. Reggiani, and R. Bottinelli. 2003. Orthologous myosin isoforms and scaling of shortening velocity with body size in mouse, rat, rabbit and human muscles. J. Physiol. 546:677-689. http://dx.doi.org/10.1113/ jphysiol.2002.027375
62. Persechini, A., J.T. Stull, and R. Cooke. 1985. The effect of myosin phosphorylation on the contractile properties of skinned rabbit skeletal muscle fibers. J. Biol. Chem. 260:7951-7954.
63. Piazzesi, G., and V. Lombardi. 1995. A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle. Biophys. J. 68:1966-1979. http://dx.doi.org/10.1016/ S0006-3495(95)80374-7
64. Piazzesi, G., M. Reconditi, M. Linari, L. Lucii, P. Bianco, E. Brunello, V. Decostre, A. Stewart, D.B. Gore, T.C. Irving, et al. 2007. Skeletal muscle performance determined by modulation of number of myosin motors rather than motor force or stroke size. Cell. 131:784-795. http://dx.doi.org/10.1016/j.cell.2007.09.045
65. Potma, E.J., I.A. van Graas, and G.J. Stienen. 1995. Influence of inorganic phosphate and pH on ATP utilization in fast and slow skeletal muscle fibers. Biophys. J. 69:2580-2589. http://dx.doi.org/10.1016/ S0006-3495(95)80129-3
66. Ranatunga, K.W. 1982. Temperature-dependence of shortening velocity and rate of isometric tension development in rat skeletal muscle. J. Physiol. 329:465-483.
67. Ranatunga, K.W. 1984. The force-velocity relation of rat fast- and slow-twitch muscles examined at different temperatures. J. Physiol. 351:517-529.
68. Rayment, I., H.M. Holden, M. Whittaker, C.B. Yohn, M. Lorenz, K.C. Holmes, and R.A. Milligan. 1993. Structure of the actin-myosin complex and its implications for muscle contraction. Science. 261:58-65. http://dx.doi.org/10.1126/science.8316858
69. Schiaffino, S., and C. Reggiani. 1996. Molecular diversity of myofibrillar proteins: gene regulation and functional significance. Physiol. Rev. 76:371-423.
70. Seow, C.Y., and L.E. Ford. 1991. Shortening velocity and power output of skinned muscle fibers from mammals having a 25,000-fold range of body mass. J. Gen. Physiol. 97:541-560. http://dx.doi.org/10 .1085/jgp.97.3.541
71. Seow, C.Y., and L.E. Ford. 1992. Contribution of damped passive recoil to the measured shortening velocity of skinned rabbit and sheep muscle fibres. J. Muscle Res. Cell Motil. 13:295-307. http:// dx.doi.org/10.1007/BF01766457
72. Seow, C.Y., and L.E. Ford. 1993. High ionic strength and low pH detain activated skinned rabbit skeletal muscle crossbridges in a low force state. J. Gen. Physiol. 101:487-511. http://dx.doi.org/10.1085/ jgp.101.4.487
73. Seow, C.Y., and L.E. Ford. 1997. Exchange of ATP for ADP on high-force cross-bridges of skinned rabbit muscle fibers. Biophys. J. 72:2719-2735. http://dx.doi.org/10.1016/S0006-3495(97)78915-X
74. Siemankowski, R.F., M.O. Wiseman, and H.D. White. 1985. ADP dissociation from actomyosin subfragment 1 is sufficiently slow to limit the unloaded shortening velocity in vertebrate muscle. Proc. Natl. Acad. Sci. USA. 82:658-662. http://dx.doi.org/10.1073/pnas.82.3.658
75. Slawnych, M.P., C.Y. Seow, A.F. Huxley, and L.E. Ford. 1994. A program for developing a comprehensive mathematical description of the crossbridge cycle of muscle. Biophys. J. 67:1669-1677. http://dx.doi.org/10.1016/S0006-3495(94)80639-3
76. Smith, D.A., M.A. Geeves, J. Sleep, and S.M. Mijailovich. 2008. Towards a unified theory of muscle contraction. I: Foundations. Ann. Biomed. Eng. 36:1624-1640. http://dx.doi.org/10.1007/s10439- 008-9536-6
77. Stienen, G.J.M., W.J. van der Laarse, and G. Elzinga. 1988. Dependency of the force-velocity relationships on Mg ATP in different types of muscle fibers from Xenopus laevis. Biophys. J. 53:849-855. http://dx.doi.org/10.1016/S0006-3495(88)83165-5
78. Sweeney, H.L., and J.T. Stull. 1986. Phosphorylation of myosin in permeabilized mammalian cardiac and skeletal muscle cells. Am. J. Physiol. 250:C657-C660.
79. Sweeney, H.L., and J.T. Stull. 1990. Alteration of cross-bridge kinetics by myosin light chain phosphorylation in rabbit skeletal muscle: implications for regulation of actin-myosin interaction. Proc. Natl. Acad. Sci. USA. 87:414-418. http://dx.doi.org/10.1073/pnas.87.1.414
80. Wahr, P.A., and J.M. Metzger. 1998. Peak power output is maintained in rabbit psoas and rat soleus single muscle fibers when CTP replaces ATP. J. Appl. Physiol. 85:76-83.
81. Wakayama, J., and T. Yamada. 2000. Contractility of single myofibrils of rabbit skeletal muscle studied at various MgATP concentrations. Jpn. J. Physiol. 50:533-542. http://dx.doi.org/10.2170/ jjphysiol.50.533
82. Wang, J., H. Jiang, and N.L. Stephens. 1994. A modified force-velocity equation for smooth muscle contraction. J. Appl. Physiol. 76:253-258.
83. Widrick, J.J., J.G. Romatowski, M. Karhanek, and R.H. Fitts. 1997. Contractile properties of rat, rhesus monkey, and human type I muscle fibers. Am. J. Physiol. Regul. Integr. Comp. Physiol. 272: R34-R42.
84. Wilson, J.R., K.K. McCully, D.M. Mancini, B. Boden, and B. Chance. 1988. Relationship of muscular fatigue to pH and diprotonated Pi in humans: a 31P-NMR study. J. Appl. Physiol. 64:2333-2339.
85. Woledge, R.C. 1968. The energetics of tortoise muscle. J. Physiol. 197:685-707.
86. Woledge, R.C., N.A. Curtin, and E. Homsher. 1985. Mechanics of contraction. In Energetic Aspects of Muscle Contraction. Academic Press, London. 47-71.
87. Yang, Z., J.T. Stull, R.J. Levine, and H.L. Sweeney. 1998. Changes in interfilament spacing mimic the effects of myosin regulatory light chain phosphorylation in rabbit psoas fibers. J. Struct. Biol. 122:139-148. http://dx.doi.org/10.1006/jsbi.1998.3979
88. Zhao, Y., and M. Kawai. 1994. Kinetic and thermodynamic studies of the cross-bridge cycle in rabbit psoas muscle fibers. Biophys. J. 67:1655-1668. http://dx.doi.org/10.1016/S0006-3495(94) 80638-1