## Abstract

The biochemical cycle of a molecular motor provides the essential link between its thermodynamics and kinetics. The thermodynamics of the cycle determine the motor's ability to perform mechanical work, whilst the kinetics of the cycle govern its stochastic behaviour. We concentrate here on tightly coupled, processive molecular motors, such as kinesin and myosin V, which hydrolyse one molecule of ATP per forward step. Thermodynamics require that, when such a motor pulls against a constant load f, the ratio of the forward and backward products of the rate constants for its cycle is exp[-(ΔG + u_{0}f)/kT], where - ΔG is the free energy available from ATP hydrolysis and u_{0} is the motor's step size. A hypothetical one-state motor can therefore act as a chemically driven ratchet executing a biased random walk. Treating this random walk as a diffusion problem, we calculate the forward velocity v and the diffusion coefficient D and we find that its randomness parameter r is determined solely by thermodynamics. However, real molecular motors pass through several states at each attachment site. They satisfy a modified diffusion equation that follows directly from the rate equations for the biochemical cycle and their effective diffusion coefficient is reduced to D - v^{2}τ, where τ is the time-constant for the motor to reach the steady state. Hence, the randomness of multistate motors is reduced compared with the one-state case and can be used for determining τ. Our analysis therefore demonstrates the intimate relationship between the biochemical cycle, the force - velocity relation and the random motion of molecular motors.

Original language | English |
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Pages (from-to) | 2113-2122 |

Number of pages | 10 |

Journal | Proceedings of the Royal Society B: Biological Sciences |

Volume | 268 |

Issue number | 1481 |

DOIs | |

Publication status | Published - Oct 22 2001 |

## All Science Journal Classification (ASJC) codes

- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Environmental Science(all)
- Agricultural and Biological Sciences(all)