Monte Carlo Sampling with Hierarchical Move Sets: POSH Monte Carlo.

Abstract

We present a new Monte Carlo method for sampling rugged energy landscapes that allows for efficient transitions across sparsely distributed local basins. The trial move consists of two steps. The first step is a large initial trial move, and the second step is a Monte Carlo trajectory generated using smaller trial moves. To maintain detailed balance, a reverse transition probability is estimated along a path that differs from the forward path. Since the forward and reverse transitions are different, we name the algorithm POSH (port out, starboard home) Monte Carlo. The process obeys detailed balance to the extent that the transition probabilities are correctly estimated. There is an optimal range of performance for a given energy landscape, which depends on how sparsely the low energy states of the system are distributed. For simple model systems, adequate precision is obtained over a large range of inner steps settings. Side chain sampling of residues in the binding region of progesterone antibody 1dba are studied, and show that significant improvement over a comparable standard protocol can be obtained using POSH sampling. To compare with experimental data, the phosphopeptide Ace-Gly-Ser-pSer-Ser-Nma is also studied, and the resulting NMR observables compare well with experiment. For the biomolecular systems studied, we show that POSH sampling generates precise distributions using the number of inner steps set up to 20.