Simple and effective application of the Wang–Landau method for multicanonical molecular dynamics simulation

Atomistic detailed free-energy landscape of intrinsically disordered protein studied by multi-scale divide-and-conquer molecular dynamics simulation

Calcineurin (CaN) is a eukaryotic serine/threonine protein phosphatase activated by both Ca²⁺ and calmodulin (CaM), including intrinsically disordered region (IDR). The region undergoes folding into an α-helix form in the presence Ca²⁺ -loaded CaM. To sample the ordered structure of the IDR by conventional all atom model (AAM) molecular dynamics (MD) simulation, the IDR and Ca²⁺ -loaded CaM must be simultaneously treated. However, it is time-consuming task because the coupled folding and binding should include repeated binding and dissociation. Then, in this study, we propose novel multi-scale divide-and-conquer MD (MSDC-MD), which combines AAM-MD and coarse-grained model MD (CGM-MD). To speed up the conformation sampling, MSDC-MD simulation first treats the IDR by CGM to sample conformations from wide conformation space; then, multiple AAM-MD in a limited area is initiated using the resultant CGM conformation, which is reconstructed by homology modeling method. To investigate performance, we sampled the ordered conformation of the IDR using MSDC-MD; the root-mean-square distance (RMSD) with respect to the experimental structure was 2.23 Å.

Enhanced sampling simulations to construct free-energy landscape of protein-partner substrate interaction

Molecular dynamics (MD) simulations using all-atom and explicit solvent models provide valuable information on the detailed behavior of protein-partner substrate binding at the atomic level. As the power of computational resources increase, MD simulations are being used more widely and easily. However, it is still difficult to investigate the thermodynamic properties of protein-partner substrate binding and protein folding with conventional MD simulations. Enhanced sampling methods have been developed to sample conformations that reflect equilibrium conditions in a more efficient manner than conventional MD simulations, thereby allowing the construction of accurate free-energy landscapes. In this review, we discuss these enhanced sampling methods using a series of case-by-case examples. In particular, we review enhanced sampling methods conforming to trivial trajectory parallelization, virtual-system coupled multicanonical MD, and adaptive lambda square dynamics. These methods have been recently developed based on the existing method of multicanonical MD simulation. Their applications are reviewed with an emphasis on describing their practical implementation. In our concluding remarks we explore extensions of the enhanced sampling methods that may allow for even more efficient sampling.

Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics

We show a direct formal relationship between the Wang-Landau iteration [PRL 86, 2050 (2001)], metadynamics [PNAS 99, 12562 (2002)], and statistical temperature molecular dynamics (STMD) [PRL 97, 050601 (2006)] that are the major work-horses for sampling from generalized ensembles. We demonstrate that STMD, itself derived from the Wang-Landau method, can be made indistinguishable from metadynamics. We also show that Gaussian kernels significantly improve the performance of STMD, highlighting the practical benefits of this improved formal understanding.

New methods for calculating the free energy of charged defects in solid electrolytes

A methodology for calculating the contribution of charged defects to the configurational free energy of an ionic crystal is introduced. The temperature-independent Wang-Landau Monte Carlo technique is applied to a simple model of a solid electrolyte, consisting of charged positive and negative defects on a lattice. The electrostatic energy is computed on lattices with periodic boundary conditions, and used to calculate the density of states and statistical-thermodynamic potentials of this system. The free energy as a function of defect concentration and temperature is accurately described by a regular solution model up to concentrations of 10% of defects, well beyond the range described by the ideal solution theory. The approach, supplemented by short-ranged terms in the energy, is proposed as an alternative to free energy methods that require a number of simulations to be carried out over a range of temperatures.