### 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 |
---|---|

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 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Proceedings of the Royal Society B: Biological Sciences*,

*268*(1481), 2113-2122. https://doi.org/10.1098/rspb.2001.1764

**Molecular motors : Thermodynamics and the random walk.** / Thomas, N.; Imafuku, Yasuhiro; Tawada, K.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society B: Biological Sciences*, vol. 268, no. 1481, pp. 2113-2122. https://doi.org/10.1098/rspb.2001.1764

}

TY - JOUR

T1 - Molecular motors

T2 - Thermodynamics and the random walk

AU - Thomas, N.

AU - Imafuku, Yasuhiro

AU - Tawada, K.

PY - 2001/10/22

Y1 - 2001/10/22

N2 - 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 + u0f)/kT], where - ΔG is the free energy available from ATP hydrolysis and u0 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 - v2τ, 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.

AB - 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 + u0f)/kT], where - ΔG is the free energy available from ATP hydrolysis and u0 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 - v2τ, 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.

UR - http://www.scopus.com/inward/record.url?scp=0035934881&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035934881&partnerID=8YFLogxK

U2 - 10.1098/rspb.2001.1764

DO - 10.1098/rspb.2001.1764

M3 - Article

C2 - 11600075

AN - SCOPUS:0035934881

VL - 268

SP - 2113

EP - 2122

JO - Proceedings of the Royal Society B: Biological Sciences

JF - Proceedings of the Royal Society B: Biological Sciences

SN - 0962-8452

IS - 1481

ER -