Improving the Wang–Landau algorithm for polymers and proteins

Abstract

The 1/t Wang-Landau algorithm is tested on simple models of polymers and proteins. It is found that this method resolves the problem of the saturation of the error present in the original algorithm for lattice polymers. However, for lattice proteins, which have a rough energy landscape with an unknown energy minimum, it is found that the density of states does not converge in all runs. A new variant of the Wang-Landau algorithm that appears to solve this problem is described and tested. In the new variant, the optimum modification factor is calculated in the same straightforward way throughout the simulation. There is only one free parameter for which a value of unity appears to give near optimal convergence for all run lengths for lattice homopolymers when pull moves are used. For lattice proteins, a much smaller value of the parameter is needed to ensure rapid convergence of the density of states for energies discovered late in the simulation, which unfortunately results in poor convergence early on in the run.

Phase diagrams of knotted and unknotted ring polymers

“…Our simulation approach involves the detailed determination of the phase diagram for a single ring polymer, using a Monte Carlo method that determines the density of states for the entire accessible range of energies and confinement in one go. Similar examples of this approach have appeared before, notably in studies of peptide and polymer collapse, crystallization, adsorption and confinement [22][23][24][25][26][27][28][29][30][31][32][33][34][35], both on-and off-lattice.…”

“…We have recently investigated the optimization of convergence of the Wang-Landau method for lattice polymers [33]. The new version of the algorithm is based on the for-…”

Control of accuracy in the Wang-Landau algorithm

“…Obtaining the appropriate value of t 0 can be quite cumbersome because the rule of thumb for choosing t 0 given in [8] is violated even by the 128 × 128 Ising model [17]. The WL-1/t algorithm and its further improvements [18][19][20] seem to perform more reliably. Here, we use the WL-1/t algorithm, although the main obtained results are qualitatively independent of the modification choice.…”

Studying the Adsorption of Polymers and Biomolecules on Surfaces Using Enhanced Sampling Methods

“…The essential ideas behind the current work have been presented already in the context of the HP model and the simulation of confined ring polymers [21][22][23][24], so only a brief summary will be given here. G therefore has an internal energy -n G e .…”

“…The original prescription [25,26] for reducing f at each stage was f ® f but there are arguments for using a more conservative scheme, and this is what we employ here [22][23][24]. Finally, we note that we employ a Monte Carlo move set known as "pull moves" [3,17,[21][22][23][24] which allows the peptide to explore configuration space efficiently. The essential output from a single Wang-Landau simulation is the density of states itself, which may be used to compute thermodynamic properties, and other quantities, in the canonical ensemble at any desired temperature.…”