Efficient combination of Wang–Landau and transition matrix Monte Carlo methods for protein simulations

Abstract

An efficient combination of the Wang-Landau and transition matrix Monte Carlo methods for protein and peptide simulations is described. At the initial stage of simulation the algorithm behaves like the Wang-Landau algorithm, allowing to sample the entire interval of energies, and at the later stages, it behaves like transition matrix Monte Carlo method and has significantly lower statistical errors. This combination allows to achieve fast convergence to the correct values of density of states. We propose that the violation of TTT identities may serve as a qualitative criterion to check the convergence of density of states. The simulation process can be parallelized by cutting the entire interval of simulation into subintervals. The violation of ergodicity in this case is discussed. We test the algorithm on a set of peptides of different lengths and observe good statistical convergent properties for the density of states. We believe that the method is of general nature and can be used for simulations of other systems with either discrete or continuous energy spectrum.

Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble

“…There has already been a considerable effort devoted to numerical simulation of the densities of states for complex systems, especially in the context of biomolecules, 29,30 supercooled liquids and glassy systems, [26][27][28][31][32][33][34] as well as in spin systems. 35,36 The recent progress in developing "flat histogram" methods 29,32,33,35,36 has been responsible for much of this success.…”

“…35,36 The recent progress in developing "flat histogram" methods 29,32,33,35,36 has been responsible for much of this success. However, the computational simplicity of this energy-landscape route to the configurational entropy seems to offer some advantages when compared to the effort required by a number of other methods.…”

Random matrix ensembles: Wang-Landau algorithm for spectral densities

“…Since the method gives direct access to the density of states of the system, which is independent of the temperature, one can calculate various thermodynamic averages by canonical reweighting at arbitrary nonzero temperature [8]. There has been several improvements and refinements to the WLA by various authors [12][13][14][15][16][17], consequently it has been successfully applied to systems possessing continuous energy spectra also, e.g., liquid crystals, polymers, biomolecules etc. See for example [15], where the authors propose a hybrid algorithm based on the Wang-Landau and transition matrix Monte Carlo methods.…”

“…There has been several improvements and refinements to the WLA by various authors [12][13][14][15][16][17], consequently it has been successfully applied to systems possessing continuous energy spectra also, e.g., liquid crystals, polymers, biomolecules etc. See for example [15], where the authors propose a hybrid algorithm based on the Wang-Landau and transition matrix Monte Carlo methods. In our calculations we implement the t −1 variant [16,17] of WLA which facilitates, in general, a faster convergence rate than the conventional scheme.…”

Computer simulation of two continuous spin models using Wang–Landau-Transition-Matrix Monte Carlo algorithm

“…The method was tested by Shell et al [12] in two-dimensional Ising model and a Lenard-Jones fluid which suggests that the method is capable of handling both discrete and continuous systems. More recently Ghulghazaryan et al have applied the WLTM method [13] to simulate protein and peptide.…”