## Abstract

We discuss multi-dimensional generalizations of multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function E_{0} by adding any physical quantity V of interest as a new energy term with a coupling constant λ. We then perform a multi-dimensional multicanonical simulation where a random walk in E _{0} and V space is realized. We can alternately perform a multi-dimensional simulated-tempering simulation where a random walk in temperature T and parameter λ is realized. The results of the multi-dimensional replica-exchange simulations can be used to determine the weight factors for these multi-dimensional multicanonical and simulated tempering simulations. Two examples of the above methods are presented for biomoleculr systems where the parameter λ corresponds to the solvation parameter and the pressure. In the former, a random walk in the conformational energy and solvation free energy is performed, and in the latter, a random walk in the potential energy and volume is realized.

Original language | English |
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Pages (from-to) | 89-105 |

Number of pages | 17 |

Journal | Physics Procedia |

Volume | 4 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

## Keywords

- Generalized-ensemble algorithms
- Molecular dynamics
- Mont Carlo
- Multicanonical algorithm
- Parallel tempering
- Replica-exchange method
- Simulated tempering

## ASJC Scopus subject areas

- Physics and Astronomy(all)