To adequately simulate muscular diseases and their treatments a model is required that incorporates the internal processes and structures of muscle. Previous models have focused on either the chemical processes or the bulk muscle output. The aim of this project was to build a model that would bridge the gap between individual crossbridge chemistry and bulk muscle output providing a means to investigate those internal processes and structures and their influence on the force-displacement output of muscle.
muscle’s force-displacement output. To address this difficulty a model of a repeat unit within the sarcomere was constructed consisting of an actin filament, composite myosin filament and a composite titin protein. The selection of this unit enabled the examination of individual crossbridges, the interaction of multiple crossbridges and part of the passive mechanical structure of the sarcomere. The identification of this repeat unit provides future potential for scaling the input and output functions of the unit to the myofibril and motor unit level.
At the scale of the model, in vitro data were available for comparison in the form of chemical, chemo-mechanical data for a single crossbridge and actin filament force and displacement. The availability of in vitro data at different length scales proved useful in addressing the issue of the high number of model parameters. Some parameter values have been identified with high confidence in the literature; others are ambiguous or unknown. Whilst ongoing advancements in experimental techniques improve that understanding, the model described in this project provides a means to examine the parameter values and associated mechanisms across several length scales.
The model generated force and displacement results comparable to in vitro data for a single crossbridge and multiple crossbridges acting along a filament in isometric loading and low load contraction scenarios. The importance was observed of the mechanical structure of the sarcomere in defining the timing and state across the actin filament of the individual crossbridges resulting in variations in filament speed and efficiency. Some elements of refinement and further parameter study have been identified in the current model, e.g. post-lever reaction duration strain dependency. In this project, in vitro data have been used from a variety of experimental sources where muscle samples have been taken from a diverse selection of muscles and animals. To refine and further exploit the model it would be useful to have coherent in vitro data, that is, samples which relate chemical, crossbridges, filament and myofilament characteristics to chemical and force-displacement data from common sources and where possible with identified isoforms.
The work described in this thesis has demonstrated the principles for implementing a chemo-mechanical model of the most fundamental reactions and structures that determine the function of a muscle. It provides a foundation from which to develop models of myofibril, fibre, motor unit and finally, bulk muscle. As the length scale of the model increases to that of the myofibril and fibre, in vitro data become more readily available. With these increases in scale, additional properties become
significant and will require consideration: the chemical activation of the muscle, delays in the diffusion of that stimulation through a motor unit, the input and export of chemicals and heat. The structure of the model provides a means to cross-reference and test the in vitro data at different length scales as these refinements are made providing a means to improve the understanding of muscle function.
Bibliography
[1] R. L. Lieber, Skeletal Muscle Structure, Function and Plasticity: The
physiological basis of rehabilitation. Second Edition, Lippincott, Williams and Wilkins, Baltimore, (2002).
[2] E. N. Marieb, Human Anatomy & Physiology, Fifth Edition, Addison
Wesley Longman Inc., Baltimore, (2001).
[3] G. E. Loeb, C. A. Pratt, C. M. Chanaud, F. J. R. Richmond, Distribution and
innervation of short, interdigitated muscle fibres in parallel-fibred muscles of the cat hind limb. J. of Morphology, (1987), 191, 1-15.
[4] M. Ounjian, R. R. Roy, E. Eldred, A. Garfinkel, J. R. Payne, A. Armstrong,
A. W. Toga, V. R. Edgerton, Physiological and developmental implications of motor unit anatomy. J. of Neurobiology, (1991), 22, 547-559, 1991.
[5] S. F. Street, Lateral transmission of tension in frog myofibers: a myofibrillar
network and transverse cytoskeletal connections are possible transmitters. J. of Cellular Physiology, (1983), 114, 346-364.
[6] S. C. Bodine, R. R. Roy, E. Eldred, V. R. Edgerton, Maximal force as a
function of anatomical features of motor units in the cat tibialis anterior. J. of Neurophysiology, (1987), 6, 1730-1745.
[7] Y. V. Pereverzev, O. V. Prezhdo, M. Forero, E. V. Sokurenko, W. E.
Thomas, The two-pathway model for the catch-slip transition in biological adhesion. Biophysical Journal, (2005), vol:89, 1446-1454.
[8] A. F. Huxley, Muscle structure and theories of contraction, Prog. Biophys.
Biophys. Chem., (1957), 7: 255-318.
[9] T. J. Burkholder, R. L. Lieber, Sacromere length operating range of
vertebrate muscles during movement. The Journal of Experimental Biology, (2001), 204, 1529-1536.
[10] J. Howard, Mechanics of Motor Proteins and the Cytoskeleton. Sineauer
Associates, Sunderland, Massachusetts, (2001).
[11] J. A. Spudich, How molecular motors work. Nature, (1994), 372, 515-18.
[12] R. C. Woledge, N. A. Curtin, E. Homsher, Energetic aspects of muscle
contraction, Monogr. Physiol. Society, (1985) 41:1-357.
[13] J. B. Peter, R. J. Barnard, V. R. Edgerton, C. A. Gillespie, K. E. Stempel,
Metabolic profiles on three fibre types of skeletal muscle in guinea pigs and rabbits. Biochemistry, (1972), 11, 2627-2733.
[14] M. Barany, ATPase activity of myosin correlated with speed of muscle shortening. Journal of General Physiology, (1967), 50, 197-216.
[15] C. Reggiani, R. Bottinelli, G. J. M. Stienen, Sarcomere myosin isoforms: fine
tuning of a molecular motor. News. Physiol. Sci, (2000), 15: 26-33.
[16] D. I. Resnicow, J. C. Deacon, H. M. Warrick, J. A. Spudich, L. A. Leinwand,
Functional diversity among a family of human skeletal muscle myosin motors. Proc. National Academy of Science, Biochemistry, (2009), 107,3, 1053-1058.
[17] S. Schiaffino, C. Reggiani , Molecular diversity of myofibrillar proteins: gene
regulation and functional significance. Physiological Reviews, (1996), 76, 2, 371 – 423.
[18] T. P. Martin, S. Bodine-Fowler, R. R. Roy, E. Eldred, V. R. Edgerton,
Metabolic and fibre size properties of cat tibialis anterior motor units. American J. of Physiology, (1988), 255, C43-C50.
[19] R. E. Burke, Motor unit types of cat triceps surae muscle. J. of Physiology
(London), (1967), 193, 141-160.
[20] R. E. Burke, D. N. Levine, F. E. Zajac, P. Tsairis, W. K. Engel, Mammalian
motor units: physiological-histochemical correlation in three types in cat gastrocnemius. Science, (1971), 174, 709-712.
[21] K. Hilber, S. Galler, B. Gohlsch, D. Pette, Kinetic properties of myosin heavy
chain isoforms in single fibres from human skeletal muscle. FEBS Letters , (1999), 455, 267-270.
[22] G. J. M. Stienen, J. L. Kiers, R. Bottinelli, C. Reggiani, Myofibrillar ATPase
activity in skinned human skeletal muscle fibres: fibre type and temperature dependency. Journal of Physiology, (1996), 493:2 299-307.
[23] D. Pette, R. S. Staron, Myosin isoforms, muscle fibre types, and transitions.
Microscopy Research and Technique. (2000), 50:500-509.
[24] J. F. Finer, R. M. Simmons, J. A. Spudich, Single myosin molecule
mechanics: piconewton forces and nanometre steps. Nature, (1994), 368.
[25] M. P. Sheetz, J. A. Spudich, Movement of myosin-coated fluorescent beads
on actin cables in vitro. Nature, (1983), 303, 31-35.
[26] M. P. Sheetz, S. M. Block, J. A. Spudich, Myosin movement in vitro: a
quantitative assay using oriented actin cables from Nitella. Methods in Enzymology, (1986), 134, 531-544.
[28] S.J. Kron, J. A. Spudich, Fluorescent actin filaments move on myosin fixed to a glass surface. Proc. Natl. Acad. Sci, USA, (1986), 83, 6272-6276.
[29] M. Kaya, H. Higuchi, Nonlinear elasticity and an 8nm working stroke of
single myosin molecules in myofilaments. Science, (2010), vol. 329, 686- 689.
[30] M. Kawai, K. Kawaguchi, M. Saito and S. Ishiwata, Temperature change
does not affect force between single actin filaments and HMM from rabbit muscles. Biophysical Journal, (2000), 78, 3112-3119.
[31] M. Kawai, T. Kido, M. Vogel, R. H. A. Fink and S. Ishiwata, Temperature
change does not affect force between regulated actin filaments and heavy meromyosin in single-molecule experiment. J. Physiology, (2006), 574.3, 877-887.
[32] J. A. Spudich, Optical trapping: motor molecules in motion. Nature, (1990),
348, 284-285.
[33] S. J. Kron, Y. Y. Toyoshima, T. Q. P. Uyeda and J. A. Spudich, Assays for
actin sliding movement over myosin-coated surfaces. Methods in Enzymology. (1991), 196, 399-416.
[34] G. T. Yamaguchi, Dynamic modelling of musculoskeletal motion: a
vectorised approach for biomechanical analysis in three dimensions. Kluwer Academic Publishers, Dordrecht, (2003), pp5.
[35] A. V. Hill, The Effect of Load on the Heat of Shortening of Muscle.
Proceedings of the Royal Society of London, Biological Sciences, (1964), vol. 159, 975, 297-318.
[36] E. J. Perrault, C. J. Heckman, T. G. Sandercock, Hill muscle model errors
during movement are greatest within the physiologically relevant range of motor unit firing rates. Journal of Biomechanics, (2003), 36: 211-218.
[37] D. G. Thelen, F. C. Anderson, Using computed muscle control to generate
forward dynamic simulations of human walking from experimental data. J. Biomechanics, (2006), 39: 1107-1115.
[38] G. H. Shue, P. E. Crago, Muscle-tendon model with length history-dependent
activation-velocity coupling. Annals of Biomedical Engineering, (1998), 26: 369-380.
[39] L.A. Gilchrist, D.A. Winter, A multi-segment computer simulation of normal
human gait. IEEE Transactions on Rehabilitation Engineering, (1997) 5:4, 290-299.
[40] K. S. Campbell, Interactions between connected half-sarcomeres produce emergent mechanical behaviour in a mathematical model of muscle. PloS Computational Biology, (2009), 5 (11): e1000560.
[41] D.A. Martyn, P.B. Chase, M. Regnier, a. M. Gordon, A simple model with
myofilament compliance predicts activation-dependent crossbridge kinetics in skinned skeletal fibers. Biophysical Journal, (2002), vol. 83, 3425-3434.
[42] I. A. Telley, J. Denoth, E. Strussi, G. Pfitzer, R. Stehle, Half-sarcomere
dynamics in myofibrils during activation and relaxation studied by tracking fluorescent markers. Biophysical Journal, (2006), vol. 90, 514-530.
[43] D. A. Smith, The theory of sliding filament models for muscle contraction. II.
Biochemically-based models of the contraction cycle. (1990) 146, 157-175.
[44] D. A. Smith, S. Sicilia, The theory of sliding filament models for muscle
contraction. I. The two state model. J. Theoret. Biology, (1987) , 127, 1-30.
[45] D. A. Smith, The theory of sliding filament models for muscle contraction.
III. Dynamics of the five state model. (1990), J. Theoret. Biology (1990), 146, 433-466.
[46] T. Hill, E. Eisenberg, Y. Chen, R. J. Podolsky, Some self-consistent two state
sliding filament models of muscle contraction. Biophysical Journal, (1975) vol. 15, 335-372.
[47] T. A. J. Duke, Molecular model of muscle contraction. Proc. Natl. Academy
of Science , U.S.A., (1999), 96 (6): 2770-2775.
[48] M. P. Slawnych, C. Y. Seow, A. F. Huxley, L. E. Ford, A program for
developing a comprehensive mathematical description of the crossbridge cycle of muscle. Biophysical Journal, (1994), vol. 67, 1669-1677.
[49] C. R. Bagshaw, Muscle Contraction. Chapman & Hall, Cambridge, UK,
(1993).
[50] R. D. Keynes, D. J. Aidley, Nerve and Muscle. Third Edition, Cambridge
University Press, New York, (2001).
[51] I. Rayment, H. M. Holden, The three-dimensional structure of a molecular
motor. Trends in Biochemical Sciences, (1994), 19, 129.
[52] S. Lowey, G. S. Waller, K. M. Trybus, Function of skeletal muscle myosin
heavy and light chain isoforms by an in vitro motility assay. The Journal of Biological Chemistry, (1993), vol. 268:27, 20414-20418.
[53] K. Wakabayashi, Y. Sugimoto, H. Tanaka, Y. Ueno, Y. Takezawa, Y.
[54] Y. E. Goldman, A. F. Huxley, Actin compliance: are you pulling my chain? Journal of Biophysics, (1994), 67 (6): 2131-2133.
[55] H. Kojima, A. Ishuima, T. Yanagida, Direct measurement of stiffness of
single actin filaments with and without tropomyosin by in vitro
nanomanipulation. Proc. Natl. Acad. Sci. USA, (1994), vol. 91 12962-12966.
[56] Y. Tsuda, H. Yasutake, A. Ishijima, T. Yanagida, Torsional rigidity of single
actin filaments and actin-bond breaking force under torsion measured directly by in vitro micromanipulation. Proc. Natl. Acad. Sci. USA, (1996), vol. 93 12937-12942.
[57] P. VanBuren, G. S. Waller, D. E. Harris, K. M. Trybus, D. M. Warshaw and
S. Lowy, The essential light chain is required for full force production by skeletal muscle myosin. Proc., National Acad. Science, (1994), 91, 12403- 12407.
[58] J. J. Sherwood, G. S. Waller, D. M. Warshaw and S. Lowy, A point mutation
in the regulatory light chain reduces the step size of skeletal muscle myosin. PNAS, (2004), vol. 101, 30, 10973-10978.
[59] Y. Y. Toyoshima, S. J. Kron, E. M. McNally, K. R. Niebling, C. Toyoshima,
J. A. Spudich, Myosin subfragment-1 is sufficient to move actin filaments in vitro. Nature, (1987), vol. 328.
[60] H. E. Huxley, Sliding filaments and molecular motile systems. The Journal of
Biological Chemistry, (1990), vol.265-15, 8347-8350.
[61] I. Adamovic, S. M. Mijailovich, M. Karplus, The elastic properties of the
structurally characterized myosin II S2 subdomain: a molecular dynamics and normal mode analysis. Biophysical Journal, (2008), 94, 3779-3789.
[62] A. Lewalle, W. Steffen, O. Stevenson, Z. Ouyang, J. Sleep, Single-molecule
measurement of the stiffness of the rigor myosin head. Biophysical Journal, (2008), 94, 2160-2169.
[63] Y. Takagi, E. E. Homsher, Y. E. Goldman, H. Shuman, Force generation in
single conventional actomyosin complexes under high dynamic load. Biophysical Journal, (2006), vol. 90, 1295-1307.
[64] J. E. Molloy, J. E. Burns, J. C. Sparrow, R. T. Tregear, J. Kendrick-Jones and
D. C. S. White, Single-molecule mechanics of heavy meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers. Biophysical Journal, (1995), vol.68, 298s-305s.
[65] J. E. Molloy, J. E. Burns, J. Kendrick-Jones, R. T. Tregear, D. C. S. White,
Movement and force produced by a single myosin head. Nature, (1995), vol. 378, 9, November.
[66] H. Higuchi, T. Yanagida, Y. E. Goldman, Compliance of thin filaments in skinned fibres of rabbit skeletal muscle. Biophys J., (1995), 69(3), 1000- 1010.
[67] M. J. Tyska, D. E. Dupuis, W. H. Guilford, J. B. Patlak, G. S. Waller, K. M.
Trybus, D. M. Warshaw, S. Lowey, Two heads are better than one for generating force and motion. Proc. Natl. Acad. Sci. U.S.A., (1999), 13:96(8):4402-7.
[68] M. R. Webb, D. R. Trentham, Chemical mechanism of myosin-catalyzed
ATP hydrolysis. Handbook of Physiology (1983), American Physiological Society (237-255).
[69] R. W. Lymn, E. W. Taylor, Mechanism of adenosine triphosphate hydrolysis
by actomyosin. Biochemistry, (1971), 10, 4617- 4624.
[70] J. A. Spudich, J. Finer, B. Simmons, K. Ruppel, B. Patterson, T. Uyeda,
Myosin structure and function. Cold Spring Harbour, Symposium Quant. Biol. (1995), 60, 783-91.
[71] A. Ishijima, H. Kolima, T. Funatsu, M. Tokunaga, H. Higuchi, H. Tanaka
and T. Yanagida, Simultaneous observations of individual ATPase and mechanical events by a single myosin molecule during interaction with actin. Cell, (1998), vol. 92, 2, 161-171.
[72] R. Ait-Haddou, W. Herzog, Force and motion generation of myosin motors:
muscle contraction. Journal of Electromyography and Kinesiology, (2002), 12, 435-445.
[73] B. Guo, W.H. Guilford, Mechanics of actomyosin bonds in different
nucleotide states are tuned to muscle contraction. PNAS, (2006), 103:26, 9844-9849.
[74] G. I. Bell, Model for the specific adhesion of cells to cells. Science, (1978)
vol. 200, 618-627.
[75] E. Evans, K. Ritchie, Dynamic strength of molecular adhesion bonds.
Biophysical Journal, (1997), vol:72, 1541-1555.
[76] R. Cooke, Actomyosin interaction in striated muscle. Physiological Review,
(1997), 77, 671-697.
[77] J. A. Dantzig, Y. E. Goldman, N. C. Millar, J. Lacktis, E. Homsher, Reversal
of the crossbridge force-generation transition by photogeneration of
phosphate in rabbit psoas muscle fibres. Journal of Physiology, (1992), 451, 247-278.
[78] M. G. Hibberd, J.A. Dantzig, D.R. Trentham, Y.E. Goldman, Phosphate release and force generation in skeletal muscle fibres. Science, (1985), 228, 1317-1319.
[79] E. Homsher, N.C. Millar, Caged compounds and striated muscle
contractions. Annual Review Physiol., (1990), 875-896.
[80] Y. Y. Toyashima, C. Toyoshima, J. A. Spudich, Bidirectional movement of
actin filaments along tracks of myosin heads. Nature, (1987), 341 154-156.
[81] L. E. Ford, A. F. Huxley, R. M. Simmons, Tension transients during steady
shortening of frog muscle fibres. Journal of Physiology. (1985), 361, 131- 150.
[82] E. Eisenberg, T. L. Hill, A crossbridge model of muscle contraction. Prog.
Biophysics & Mol. Biology. (1979) 33: 55-82.
[83] R. C. Woledge, N. A. Curtin and E. Homsher, Energetic aspects of muscle
contraction. Monogr. Physiology Society, (1985), 41:1-357.
[84] A. F. Huxley, R. M. Simmons, Proposed mechanism of force generation in
striated muscle. Nature, (1971), 233, 533-538.
[85] Y. M. Haddad, Viscoelasticity of Engineering Materials. Chapman & Hall,
London, (1995), P49.
[86] G.Wang, M. Kawai, Effect of temperature on elementary steps of the cross-
bridge cycle in rabbit soleus slow-twitch muscle fibres. Journal of Physiology, (2001), 531.1, 219-234.
[87] T. J. Lorenzen, V. L. Anderson, Design of Experiments: A No-Name
Approach. Marcel Dekker Inc. New York, (1993).
[88] G. E. P. Box, J. S. Hunter, W. G. Hunter, Statistics for Experimenters.
Second Edition, John Wiley & Sons, Hoboken, (2005).
[89] D. E. Harris and D. M. Warshaw, Smooth and skeletal muscle myosin both
exhibit low duty cycles at zero load in vitro. The Journal of Biological Chemistry, (1993), 268: 20, 14764-14768.
[90] Y. Y. Toyoshima, S. J. Kron, E. M. McNally, K. R. Niebling, C. Toyoshima,
J. A. Spudich, Myosin subfragment-1 is sufficient to move actin filaments in vitro. Nature, (1987), 328, 536-539.
[91] T. Q. P. Uyeda, S. J. Kron, J. A. Spudich, Myosin step size, estimation from
slow sliding movcement of actin over low densities of heavy meromyosin. Journal of Molecular Biology, (1990), 214, 699-710.
[92] C. Veigel, M. L. Bartoo, D. C. S. White, J. C. Sparrow, J. E. Molloy, The
stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer. Biophysical Journal, (1998), 75, 1424-1438.
[93] K. Wang, R. McCarter, J. Wright, J. Beverly, R. Ramirez-Mitchell,
Viscoelasticity of the sacromere matrix of skeletal muscles; the titin-myosin composite filament is a dual-stage molecular spring. Biophysical Journal, (1993), 64, 1161-1177.
[94] A. M. Gordon, A. F. Huxley, F. J. Julian, The variation in isometric tension
with sarcomere length in vertebrate muscle fibres, Journal of Physiology,
(1966), 184, 170-192.
[95] B. R. Eisenberg, Quantitative ultrastructure of mammalian skeletal muscle.
Skeletal Muscle, MD: American Physiological Society, (1983), 10, 73-112.
[96] W. H. Guilford, D. E. Dupuis, G. Kennedy, J. Wu, J. B. Patlak, D. W.
Warshaw, Smooth muscle and skeletal muscle myosins produce similar unitary forces and displacements in the laser trap. Biophysical Journal, (1997), 72: 1006-1021.
[97] Y. S. Han, P. C. Geiger, M. J. Cody, R. L. Macken, G. C. Sieck, ATP
consumption rate per crossbridge depends on myosin heavy chain isoform. J. Appl. Physiology, (2003) 94: 2188-2196.
[98] M. J. Kushmerick, T. S. Moerland, R. W. Wiseman, Mammalian skeletal
muscle fibres distinguished by contents of phosphocreatine. ATP and Pi. Proc. Natl. Acad. Sci. USA, (1992), 89, 7521-7525.
[99] P. VanBuren, S. S. Work, D. M. Warshaw, Enhanced force generation by
smooth muscle myosin in vitro. Proceeds National Academy of Science, USA, (1994), 91, 202-205.
[100] A. Kishino and T. Yanagida, Force measurements by micromanipulation of a
single actin filament by glass needles. Nature, (1988), 334, 74-76.
[101] M. J. Kushmerick, R. E. Davis, The chemical energetics of muscle
contraction. Proceed. Royal Society, London, (1969), B 174, 315-353.
[102] Y. B. Sun, K, Hilber, M. Irving, Effect of active shortening on the rate of
ATP utilisation by rabbit psoas muscle fibres. Journal of Physiology (London), (2001) 431, 781-791.
[103] A. Ishijima, Y. Harada, H. Kojima, T. Funatsu, Single_molecule analysis of
the actomyosin motor using nano-manipulation. Biomedical and Biophysical Research Communications, (1994), vol. 199:2, 1057-1063.
[104] M. Nyitrai, R. Rossi, N. Adamek, M. A. Pellegrino, R. Bottinelli, M. A.
Geeves, What limits the velocity of fast-skeletal muscle contraction in mammals? J. Molecular Biology, (2006) 355, 432-442.
[105] R. Bottinelli, M. Canepari, C. Reggiani, G. J. M. Stienen, Myofibrillar ATPase activity during isometric contraction and isomyosin composition in rat single skinned muscle fibres. Journal of Physiology, (1994) 663-675.
[106] R. Bottinelli, R. Betto, S. Schiaffino, C. Reggiani, Unloaded shortening
velocity and myosin heavy chain and alkali light chain isoform composition in rat skeletal muscle fibres. Journal of Physiology, (1994) 341-349.
[107] C. Reggiani, E.J. Potma, R. Bottinelli, M. Canepari, M. A. Pellegrino, G. J.