Generalized-Ensemble Algorithms for Studying Protein Folding. In: Kuwajima K, Goto Y, Hirata F, Kataoka M, Terazima M, editors. Water and Biomolecules. Berlin: Springer Berlin Heidelberg; 2009. pp. 61-95. [DOI: 10.1007/978-3-540-88787-4_4]

GradNav: Accelerated Exploration of Potential Energy Surfaces with Gradient-Based Navigation

Exploring the potential energy surface (PES) of molecular systems is important for comprehending their complex behaviors, particularly through the identification of various metastable states. However, the transition between these states is often hindered by substantial energy barriers, demanding prolonged molecular simulations that consume considerable computational resources. Our study introduces the gradient-based navigation (GradNav) algorithm, which accelerates the exploration of the energy surface and enables proper reconstruction of the PES. This algorithm employs a strategy of initiating short simulation runs from updated starting points derived from prior observations to effectively navigate across potential barriers and explore new regions. To evaluate GradNav's performance, we introduce two metrics: the deepest well escape frame (DWEF) and the search success initialization ratio (SSIR). Through applications on Langevin dynamics within Müller-type PESs and molecular dynamics simulations of the Fs-peptide protein, these metrics demonstrate GradNav's enhanced ability to escape deep energy wells and its reduced reliance on initial conditions, as denoted by the reduced DWEF values and increased SSIR values, respectively. Consequently, this improved exploration capability enables more precise energy estimations from simulation trajectories.

Enhanced sampling algorithms

In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. Enhanced conformational sampling techniques are thus in great demand. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present various extensions of these three generalized-ensemble algorithms. The effectiveness of the methods is tested with short peptide and protein systems.