Walcott, Sam; Herzog, Walter Modeling residual force enhancement with generic cross-bridge models. (English) Zbl 1153.92011 Math. Biosci. 216, No. 2, 172-186 (2008). Summary: The interaction of actin and myosin through cross-bridges explains much of muscle behavior. However, some properties of muscle, such as residual force enhancement, cannot be explained by current cross-bridge models. There is ongoing debate whether conceptual cross-bridge models, as pioneered by A. F. Huxley [Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7, 255 ff (1957)] could, if suitably modified, fit experimental data showing residual force enhancement. We prove that there are only two ways to explain residual force enhancement with these ‘traditional’ cross-bridge models: the first requires cross-bridges to become stuck on actin (the stuck cross-bridge model) while the second requires that cross-bridges that are pulled off beyond a critical strain enter a ‘new’ unbound state that leads to a new force-producing cycle (the multi-cycle model). Stuck cross-bridge models cannot fit the velocity and stretch amplitude dependence of residual force enhancement, while the multi-cycle models can. The results of this theoretical analysis demonstrate that current kinetic models of cross-bridge action cannot explain the experimentally observed residual force enhancement. Either cross-bridges in the force-enhanced state follow a different kinetic cycle than cross-bridges in a ‘normal’ force state, or the assumptions underlying traditional cross-bridge models must be violated during experiments that show residual force enhancement. MSC: 92C30 Physiology (general) 93A30 Mathematical modelling of systems (MSC2010) 37N25 Dynamical systems in biology Keywords:force enhancement; molecular history-dependence; stuck cross-bridge model; multi-cycle model; strain-dependent rate constants PDFBibTeX XMLCite \textit{S. Walcott} and \textit{W. Herzog}, Math. Biosci. 216, No. 2, 172--186 (2008; Zbl 1153.92011) Full Text: DOI References: [1] Abbott, B. C.; Aubert, X. M., The force exerted by active striated muscle during and after change of length, J. Physiol. (Lond.), 117, 77 (1952) [2] Baker, J. E.; Thomas, D. D., A thermodynamic muscle model and a chemical basis for A.V. Hill’s muscle equation, J. Muscle Res. Cell Motil., 21, 335 (2000) [3] Baker, J. E.; Brosseau, C.; Joel, P. B.; Warshaw, D. M., The biochemical kinetics underlying actin movement generated by one and many skeletal muscle myosin molecules, Biophys. J., 82, 2134 (2002) [4] Burton, K.; Simmons, R. M.; Sleep, J.; Simmons, R. M.; Burton, K.; Smith, D. A., Kinetics of force recovery following length changes in active skinned single fibres from rabbit psoas muscle, J. Physiol., 573, 305 (2006) [5] Cook, C. S.; McDonagh, M. J., Force responses to controlled stretches of electrically stimulated human muscle-tendon complex, Exp. Physiol., 80, 477 (1995) [6] De Ruiter, C. J.; Didden, W. J.M.; Jones, D. A.; De Haan, A., The force-velocity relation of human adductor pollicis muscle and the effects of fatigue, J. Physiol. (Lond.), 526, 671 (2000) [7] Debold, E. P.; Patlak, J. B.; Warshaw, D. M., Slip sliding away: load-dependence of velocity generated by skeletal muscle myosin molecules in the laser trap, Biophys. J., 89, L34 (2005) [8] Dillon, P. F.; Aksoy, M. O.; Driska, S. P.; Murphy, R. A., Myosin phosphorylation and the cross-bridge cycle in arterial smooth muscle, Science, 211, 495 (1981) [9] Duke, T. A.J., Molecular model of muscle contraction, Proc. Natl. Acad. Sci. USA, 96, 2770 (1999) [10] Edman, K. A.P.; Tsuchiya, T., Strain of passive elements during force enhancement by stretch in frog muscle fibres, J. Physiol. (Lond.), 490, 191 (1996) [11] Edman, K. A.P.; Elzinga, G.; Noble, M. I.M., Enhancement of mechanical performance by stretch during tetanic contractions of vertebrate skeletal muscle fibres, J. Physiol. (Lond.), 281, 139 (1978) [12] Edman, K. A.P.; Elzinga, G.; Noble, M. I.M., Residual force enhancement after stretch in contracting frog single muscle fibers, J. Gen. Physiol., 80, 769 (1982) [13] Eisenberg, E.; Hill, T. L.; Chen, Y. D., Cross-bridge model of muscle contraction. Quantitative analysis, Biophys. J., 29, 195 (1980) [14] Getz, E. B.; Cooke, R.; Lehman, S. L., Phase transition in force during ramp stretches of skeletal muscle, Biophys. J., 75, 2971 (1998) [15] Guilford, W. H.; Dupuis, D. E.; Kennedy, G.; Wu, J.; Patlak, J. B.; Warshaw, D. M., Smooth muscle and skeletal muscle myosins produce similar unitary forces and displacements in the laser trap, Biophys. J., 72, 1006 (1997) [16] Herzog, W.; Leonard, T. R., The history dependence of force production in mammalian skeletal muscle following stretch-shortening and shortening-stretch cycles, J. Biomech., 33, 531 (2000) [17] Herzog, W.; Leonard, T. R., Force enhancement following stretching of skeletal muscle, a new mechanism, J. Exp. Biol., 205, 1275 (2002) [18] Herzog, W.; Leonard, T. R., Depression of cat soleus forces following isokinetic shortening, J. Biomech., 30, 865 (1997) [19] W. Herzog, H.D. Lee, J. Wakeling, R. Schachar, T.R. Leonard. History dependent force properties of skeletal muscle: in vitro, in situ and in vivo considerations, in: Proceedings of the Congress of the XVIII International Society of Biomechanics, vol. 221, 2001.; W. Herzog, H.D. Lee, J. Wakeling, R. Schachar, T.R. Leonard. History dependent force properties of skeletal muscle: in vitro, in situ and in vivo considerations, in: Proceedings of the Congress of the XVIII International Society of Biomechanics, vol. 221, 2001. [20] Hill, T. L., Theoretical formalism for the sliding filament model of contraction of striated muscle, part I, Prog. Biophys. Mol. Biol., 28, 267 (1974) [21] Hill, T. L., Free Energy Transduction in Biology: The Steady-State Kinetic and Thermodynamic Formalism (1977), Academic Press: Academic Press New York [22] Hill, T. L.; Eisenberg, E.; Chen, Y. D.; Podolsky, R. J., Some self-consistent two-state sliding filament models of muscle contraction, Biophys. J., 15, 335 (1975) [23] Huxley, A. F., Muscle structure and theories of contraction, Prog. Biophys. Biophys. Chem., 7, 255 (1957) [24] Kad, N. M.; Rovner, A. S.; Fagnant, P. M.; Joel, P. B.; Kennedy, G. G.; Patlack, J. B.; Warshaw, D. M.; Trybus, K. M., A mutant heterodimeric myosin with one inactive head generates maximal displacement, J. Cell Biol., 162, 481 (2003) [25] Kad, N. M.; Patlack, J. B.; Fagnant, P. M.; Trybus, K. M.; Warshaw, D. M., Mutation for a conserved glycine in the SH1-SH2 helix affects the load-dependent kinetics of myosin, Biophys. J., 92, 1623 (2007) [26] Karatzaferi, C.; Chinn, M. K.; Cooke, R., The force exerted by a muscle cross-bridge depends directly on the strength of the actomyosin bond, Biophys. J., 87, 2532 (2004) [27] Labeit, D.; Watanabe, K.; Witt, C.; Fujita, H.; Wu, Y.; Lahmers, S.; Funck, T.; Labeit, S.; Granzier, H., Calcium-dependent molecular spring elements in the giant protein titin, Proc. Natl. Acad. Sci. USA, 100, 13716 (2003) [28] Linari, M.; Lucii, L.; Reconditi, M.; Vannicelli Casoni, M. E.; Amenitsch, H.; Bernstorff, S.; Piazzesi, G.; Lombardi, V., A combined mechanical and X-ray diffraction study of stretch potentiation in single frog muscle fibres, J. Physiol. (Lond.), 526, 589 (2000) [29] Lymn, R. W.; Taylor, E. W., Mechanism of adenosine triphosphate hydrolysis by actomyosin, Biochemistry, 10, 4617 (1971) [30] Maréchal, G.; Plaghki, L., The deficit of the isometric tetanic tension redeveloped after a release of frog muscle at a constant velocity, J. Gen. Physiol., 73, 453 (1979) [31] Mehta, A. D.; Finer, J. T.; Spudich, J. A., Detection of single-molecule interactions using correlated thermal diffusion, Proc. Natl. Acad. Sci. USA, 94, 7927 (1997) [32] Morgan, D. L.; Whitehead, N. P.; Wise, A. K.; Gregory, J. E.; Proske, U., Tension changes in the cat soleus muscle following slow stretch or shortening of the contracting muscle, J. Physiol. (Lond.), 522, 503 (2000) [33] Nakajima, H.; Kunioka, Y.; Nakano, K.; Shimizu, K.; Seto, M.; Ando, T., Scanning force microscopy of the interaction events between a single molecule of heavy meromyosin and actin, Biochem. Biophys. Res. Commun., 234, 178 (1997) [34] Nishizaka, T.; Miyata, H.; Yoshikawa, H.; Ishiwata, S.; Kinosita, K., Unbinding force of a single motor molecule of muscle measured using optical tweezers, Nature, 377, 251 (1995) [35] Nishizaka, T.; Seo, R.; Tadakuma, H.; Kinosita, K.; Ishiwata, S., Characterization of single actomyosin rigor bonds: load dependence of lifetime and mechanical properties, Biophys. J., 79, 962 (2000) [36] Nyitrai, M.; Geeves, M. A., Adenosine diphosphate and strain sensitivity in myosin motors, Philos. Trans. Roy. Soc. B, 359, 1867 (2004) [37] Pate, E.; Cooke, R., A model of crossbridge action: the effects of ATP, ADP and \(P_i\), J. Muscle Res. Cell Motil., 10, 181 (1989) [38] Peterson, D. R.; Rassier, D. E.; Herzog, W., Force enhancement in single skeletal muscle fibres on the ascending limb of the force-length relationship, J. Exp. Biol., 207, 2787 (2004) [39] Piazzesi, G.; Lombardi, V., A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle, Biophys. J., 68, 1966 (1995) [40] Pirani, A.; Xu, C.; Hatch, V.; Craig, R.; Tobacman, L. S.; Lehman, W., Single particle analysis of relaxed and activated muscle thin filaments, J. Mol. Biol., 346, 761 (2005) [41] Rassier, D. E.; Herzog, W., Considerations of the history dependence of muscle contraction, J. Appl. Physiol., 96, 419 (2004) [42] Rassier, D. E.; Herzog, W., Active force inhibition and stretch-induced force enhancement in frog muscle treated with BDM, J. Appl. Physiol., 97, 1395 (2004) [43] Rayment, I.; Holden, H. M.; Whittaker, M.; Yohn, C. B.; Lorenz, M.; Holmes, K. C.; Milligan, R. A., Structure of the actin-myosin complex and its implications for muscle contraction, Science, 261, 58 (1993) [44] Smith, D. A.; Geeves, M. A., Strain-dependent cross-bridge cycle for muscle, Biophys. J., 69, 524 (1995) [45] Sugi, H., Tension changes during and after stretch in frog muscle fibres, J. Physiol. (Lond.), 225, 237 (1972) [46] Sugi, H.; Tsuchiya, T., Stiffness changes during enhancement and deficit of isometric force by slow length changes in frog skeletal muscle fibres, J. Physiol. (Lond.), 407, 215 (1988) [47] Takegi, Y.; Homsher, E. E.; Goldman, Y. E.; Shuman, H., Force generation in single conventional actomyosin complexes under high dynamic load, Biophys. J., 90, 1295 (2006) [48] Veigel, C.; Bartoo, M. L.; White, D. C.S.; Sparrow, J. C.; Molloy, J. E., The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer, Biophys. J., 75, 1424 (1998) [49] Veigel, C.; Molloy, J. E.; Schmitz, S.; Kendrick-Jones, J., Load-dependent kinetics of force production by smooth muscle myosin measured with optical tweezers, Nat. Cell Biol., 5, 980 (2003) [50] Zahalak, G. I., A distribution-moment approximation for kinetic theories of muscular contraction, Math. Biosci., 55, 89 (1981) · Zbl 0475.92010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.