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.

Assessing Protein Loop Flexibility by Hierarchical Monte Carlo Sampling

“…The application of this method on small peptide systems has shown reasonable agreement with experiments 25 . In the present work, we are interested in its performance in more complicated protein systems with flexible loops.…”

“…The number of inner steps N I is set to 20 which was reported as the upper bound of inner steps for generating precise distribution. For all protein systems studied in this work, a mixture of 50% POSH and 50% standard MC sampling, followed by the MTSMC procedure, is used due to its better performance as studied in the previous work 25 .…”

“…Specifically, it builds on loop prediction methods that exploit “inverse kinematics” methods for creating move sets that do not ‘break’ the loop 18–24 . The new contribution here is implementing these moves in a Monte Carlo scheme that also samples side chain DoF 25 . We apply the method to a number of proteins with flexible loops, including the well-known case of TIM.…”

Replica exchange with nonequilibrium switches: Enhancing equilibrium sampling by increasing replica overlap

“…With the development of RENS and similar methods, [6][7][8][9][10][11][12]16 it is important to further characterize the efficiency gains nonequilibrium simulations can bring to equilibrium sampling. The enhancement RENS can offer is very dependent upon how efficiently the switching simulations can be implemented in the computer code.…”

“…Other methodologies [8][9][10][11][12][13] have also incorporated nonequilibrium moves to enhance equilibrium sampling. Here, we further develop RENS from our previous work by extending the method to more general set of dynamics, and test its performance on a small molecule.…”