### Abstract

We consider a Brownian ratchet model where the particle on the ratchet is coupled to a cargo. We show that in a distinguished limit where the diffusion coefficient of the cargo is small, and the amplitude of thermal fluctuations is small, the system becomes completely coherent: the times at which the particle jumps across the teeth of the ratchet become deterministic. We also show that the dynamics of the ratchet-cargo system do not depend on the fine structure of the Brownian ratchet. These results axe relevant in the context of molecular motors transporting a load, which axe often modeled as a ratchet-cargo compound. They explain the regularity of the motor gait that has been observed in numerical experiments, as well as justify the coarsening into Markov jump processes which is commonly done in the literature.

Original language | English (US) |
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Pages (from-to) | 431-446 |

Number of pages | 16 |

Journal | Communications in Mathematical Sciences |

Volume | 5 |

Issue number | 2 |

State | Published - Aug 1 2007 |

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### Keywords

- Brownian ratchets
- Molecular motors
- Self-induced stochastic resonance
- Stochastic resonance

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications in Mathematical Sciences*,

*5*(2), 431-446.