Simulation of stochastic processes in motile crossbridge systems
- 56 Downloads
The underlying stochastic nature of many models of the actomyosin interaction should result in fluctuations in both force and shortening velocity. In classical experimental approaches involving intact or glycerinated muscle preparations these fluctuations are too small to resolve owing to the large numbers of crossbridges involved. However, new experimental techniques allow mechanical measurements to be made in systems in which small numbers of myosin heads act on a single actin filament, or small numbers of kinesin molecules act on a single tubulin filament. In these systems, stochastic effects should be evident. To understand better the nature of the expected stochastic effects, we have used computer simulation to investigate the fluctuations predicted by the original model for muscle crossbridge mechanics proposed by A. F. Huxley. We consider three situations : (1) the translation of actin or tubulin filaments by myosin or kinesin motors immobilized on a fixed substrate, (2) the production of tension by ensembles of immobilized myosin which involve the displacement of an elastic load, and (3) the fluctuations in axial displacement of a single, bipolar myosin thick filament interacting with actin filaments as in a sarcomere. In all three cases, fluctuations are clearly evident in simulations involving small numbers of motors. For case (1), we show that translation velocities can vary with crossbridge density. Whether one motor translates a filament faster, slower or at the same speed as many motors depends on the relative magnitudes of the attachment and detachment rate functions. Analytical expressions are provided to quantitate this relationship. For case (2), we show that fluctuations predicted assuming perfectly isometric conditions differ from those observed when the ‘isometric state’ is achieved against an elastic load. ‘Elastic damping’ of the fluctuations in the system results from the presence of many attached motors. In case (3) we show that in spite of the presence of stochastic fluctuations which can destabilize the uniformity of filament overlap in a sarcomere, the magnitude of thick filament displacement is less than might be anticipated over time periods ofin vivo contraction. Taken together, these simulations allow one to better interpret experimental data in terms of current models of motor function.
KeywordsActin Filament Stochastic Effect Myosin Head Thick Filament Stochastic Fluctuation
Unable to display preview. Download preview PDF.
- Cox, R. G. (1970) The motion of long slender bodies in a viscous fluid. Part 1. General theory.J. Fluid Mech. 44, 791–810.Google Scholar
- Edwards, R. H. T., Hill, D. K. &Jones, D. A. (1975) Metabolic changes associated the slowing of relaxation in fatigued mouse muscle.J. Physiol. 276, 233–55.Google Scholar
- Goldman, Y. E. (1987) Kinetics of the actomyosin ATPase in muscle fibers.Ann. Rev. Physiol. 49, 637–54.Google Scholar
- Hill, A. V. (1938) The heat of shortening and the dynamic constraints of muscle.Proc. Roy. Soc. Lond. B126, 136–95.Google Scholar
- Hill, T. L. (1977)Free Energy Transduction in Biology, Ch. 4. New York: Academic Press.Google Scholar
- Huxley, H. E. (1963) Electron microscope studies on the structure of natural and synthetic protein filaments from striated muscle.J. Mol. Biol. 7, 281–308.Google Scholar
- Johnson, K. A. (1985) Pathway of the microtubule-dynein ATPase and the structure of dynein: a comparison with actomyosin.Ann. Rev. Biophys. Biophys. Chem. 14, 161–88.Google Scholar
- Lin, C. C. &Segel, L. A. (1974)Mathematics Applied to Deterministic Problems in the Natural Sciences, Ch. 6. New York: Macmillan.Google Scholar
- Pate, E. &Cooke, R. (1989) A model of crossbridge action: the effects of ATP, ADP, and Pi.J. Muscle Res. Cell Mot. 10, 181–96.Google Scholar
- Segel, L. A. (1977)Mathematics Applied to Continuum Mechanics, Ch. 3. New York: Macmillan.Google Scholar
- Spriet, L. L., Soderlund, K. &Hultman, E. (1988) Energy cost and metabolic regulation during intermittant and continuous tetanic contractions in human skeletal muscle.Can. J. Physiol. Pharm. 66, 134–9.Google Scholar