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Mapping the classical cross-bridge theory and backward steps in a three bead laser trap setup. (English) Zbl 1208.92023
Summary: According to the cross-bridge theory [A. F. Huxley, Prog. Biophys. Biophys. Chem. 7, 255 ff (1957)], the interaction between myosin and actin is governed by a deterministic process where the myosin molecule pulls the actin filament in one specific direction only. However, studies on single myosin-actin interactions produced displacements of actin not only in the preferred but also in the opposite direction. This phenomenon is typically referred to as backward steps by the myosin head. J. E. Molloy et al. [Biophys. J. 68, 298 ff (1995)] speculated that these backward steps are not caused by the molecular interactions of actin with myosin but are an artifact of the Brownian motion associated with these molecular level experiments. The aim of this study was to investigate, whether a theoretical model can support Molloy’s speculation. We therefore developed a theoretical model of actin-myosin based muscle contraction that was strictly based on Huxley’s assumption of one stepping direction only, but incorporated Brownian motion, as observed in single cross-bridge-actin interactions. The mathematical model is based on Langevin equations describing the classical three-bead laser trap setup and uses a novel semi-analytical approach to study the percentage of backward steps. We analyzed the effects of different initial actin attachment site distribution and laser trap stiffness on the ratio of forward to backward steps. Our results demonstrate that backward steps and the classical cross-bridge theory are perfectly compatible in a three-bead laser trap setup.
92C40 Biochemistry, molecular biology
92C10 Biomechanics
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Full Text: DOI
[1] Huxley, A.F., Muscle structure and theories of contraction, Prog. biophys. biophys. chem., 7, 255, (1957)
[2] Molloy, J.E., Single molecule mechanics of heavy meromyosin and S1 interacting with rabbit or drosophila actins using optical tweezers, Biophys. J., 68, 298, (1995)
[3] Huxley, A.F.; Simons, R.M., Proposed mechanism of force generation in striated muscle, Nature, 352, 301, (1971)
[4] Hibberd, M.C.; Trentham, D.R., Relationships between chemical and mechanical events during muscle contraction, Ann. rev. biophys. chem., 15, 119, (1986)
[5] Pate, E.; Cooke, R., A model of crossbridge action: the effects of ATP, ADP and pi, J. muscle res. cell motil., 10, 181, (1989)
[6] Smith, D.A.; Geeves, M.A., Strain-dependent cross-bridge cycle for muscle, Biophys. J., 69, 524, (1995)
[7] Finer, J.T.; Simmons, R.M.; Spudich, J.A., Single myosin molecule mechanics: piconewton force and nanometre steps, Nature, 368, 113, (1994)
[8] Ishijima, A., Sub-piconewton force fluctuations of actomyosin in vitro, Nature, 352, 301, (1991)
[9] Ishijima, A., Multiple- and single-molecule analysis of the actomyosin motor by nanometer – piconewton manipulation with a microneedle: unitary stops and forces, Biophys. J., 70, 383, (1996)
[10] 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)
[11] Smith, D.A., Hidden – markov methods for the analysis of single-molecule actomyosin displacement data: the variance-hidden – markov method, Biophys. J., 81, 5, 2795, (2001)
[12] Molloy, J.E., Movement, and force produced by a single myosin heads, Nature, 378, 209, (1995)
[13] Rock, R.S., Myosin VI is a processive motor with a large step size, Proc. natl. acad. sci. USA, 98, 24, 13655, (2001)
[14] Smith, D.A., Direct tests of muscle cross-bridge theories: predictions of a Brownian dumbbell model for position-dependent cross-bridge lifetimes and step, Biophys. J., 75, 2996, (1998)
[15] Bentil, D.E., Distribution of attachment events relative to actin binding sites as evidence in a bidirectional actomyosin interaction model, Bull. math. biol., 60, 973, (1998) · Zbl 0914.92001
[16] Shimokawa, T., A chemically driven fluctuating ratchet model for actomyosin interaction, Biosystems, 71, 1-2, 179, (2003)
[17] Guilford, W.H., Smooth muscle and skeletal muscle myosins produce similar unitary forces and displacements in the laser trap, Biophys. J., 72, 1006, (1997)
[18] Simmons, R.M.; Smith, D.A.; Sleep, J., Target zones on the actin filament and the myosin working stroke from optical trapping, Biophys. J., 80, 1, 80A, (2001), Meeting Abstract 35
[19] Steffen, W., Mapping the actin filament with myosin, Proc. natl. acad. sci. USA, 98, 26, (2001)
[20] Einstein, A., Über die von der molekularkinetischen theorie der Wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen, Ann. phys. (Berlin), 17, 549, (1905) · JFM 36.0975.01
[21] Gaveau, B.; Moreau, M.; Schuman, B., Microscopic model of the actin – myosin interaction in muscular contractions, Physiol. rev., 69, 011108.1, (2004)
[22] Risken, H., The fokker – planck equation – methods of solution and applications, vol. 2, (1989), Springer · Zbl 0665.60084
[23] Pate, E.; Cooke, R., Simulation of stochastic processes in motile cross-bridge systems, J. muscle res. cell motil., 12, 376, (1991)
[24] Brokaw, C.J., Computer simulation of movement generating cross-bridges, Biophys. J., 16, 1013, (1976)
[25] Øksendal, B., Stochastic differential equations, (2007), Springer Heidelberg
[26] Sleep, J.; Lewalle, A.; Smith, D., Reconciling the working strokes of a single head of skeletal muscle myosin estimated from laser-trap experiments and crystal structures, Proc. natl. acad. sci. USA, 103, 5, 1278, (2006)
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