Stochastic formulation of sampling dynamics in generalized ensemble methods

Generalized simulated tempering for exploring strong phase transitions

An extension of the simulation tempering algorithm is proposed. It is shown to be particularly suited to the exploration of first-order phase transition systems characterized by the backbending or S-loop in the statistical temperature or a microcanonical caloric curve. A guided Markov process in an auxiliary parameter space systematically combines a set of parametrized Tsallis-weight ensemble simulations, which are targeted to transform unstable or metastable energy states of canonical ensembles into stable ones and smoothly join ordered and disordered phases across phase transition regions via a succession of unimodal energy distributions. The inverse mapping between the sampling weight and the effective temperature enables an optimal selection of relevant Tsallis-weight parameters. A semianalytic expression for the biasing weight in parameter space is adaptively updated "on the fly" during the simulation to achieve rapid convergence. Accelerated tunneling transitions with a comprehensive sampling for phase-coexistent states are explicitly demonstrated in systems subject to strong hysteresis including Potts and Ising spin models and a 147 atom Lennard-Jones cluster.

Statistical temperature molecular dynamics: Application to coarse-grained β-barrel-forming protein models

Recently the authors proposed a novel sampling algorithm, "statistical temperature molecular dynamics" (STMD) [J. Kim et al., Phys. Rev. Lett. 97, 050601 (2006)], which combines ingredients of multicanonical molecular dynamics and Wang-Landau sampling. Exploiting the relation between the statistical temperature and the density of states, STMD generates a flat energy distribution and efficient sampling with a dynamic update of the statistical temperature, transforming an initial constant estimate to the true statistical temperature T(U), with U being the potential energy. Here, the performance of STMD is examined in the Lennard-Jones fluid with diverse simulation conditions, and in the coarse-grained, off-lattice BLN 46-mer and 69-mer protein models, exhibiting rugged potential energy landscapes with a high degree of frustration. STMD simulations combined with inherent structure (IS) analysis allow an accurate determination of protein thermodynamics down to very low temperatures, overcoming quasiergodicity, and illuminate the transitions occurring in folding in terms of the energy landscape. It is found that a thermodynamic signature of folding is significantly suppressed by accurate sampling, due to an incoherent contribution from low-lying non-native IS in multifunneled landscapes. It is also shown that preferred accessibility to such IS during the collapse transition is intimately related to misfolding or poor foldability.

Inherent Structure Analysis of Protein Folding

An analysis in terms of the inherent structures (IS, local minima) of the multidimensional potential energy landscape is applied to proteins. Detailed calculations are performed for the 46 bead BLN model, which folds into a four-stranded beta-barrel. Enhanced sampling has allowed determination of 239 199 IS states, believed to encompass nearly all the compact, low-energy states, and of well-averaged thermodynamic quantities at low temperature. The density of states shows distinct lobes for compact and extended states, and entropic barriers for the collapse and local ordering transitions. A two-dimensional scatterplot or density of states clearly shows the multifunnel structure of the energy landscape. The anharmonic vibrational free energy is found to play a crucial role in protein folding. The problem of determining the folding transition in a multifunnel system is discussed, and novel indicators of folding are introduced. A particularly clear picture is obtained through the occupation probabilities, pi, of individual low-lying IS, which become finite below the collapse temperature; it is suggested that poor foldability corresponds to a large "misfolding interval" where the excited state pi>0 exceeds that of the native state p0.

Multicanonical molecular dynamics algorithm employing an adaptive force-biased iteration scheme

We present one effective multicanonical molecular dynamics (MCMD) algorithm accelerating the convergence of rough energy landscapes simulations via an adaptive force-biased iteration scheme. Our method utilizes several short MCMD simulations with dynamically updated weights and combines them to estimate the density of states via multiple histogram technique. The key step of our algorithm is the adaptive refinement for the derivative of multicanonical weight, which allows the system to enlarge the sampling energy range maintaining the statistical accuracy. The performance of our method has been validated for atomic Lennard-Jones clusters.

Generalized simulated tempering realized on expanded ensembles of non-Boltzmann weights

A generalized version of the simulated tempering operated in the expanded ensembles of non-Boltzmann weights has been proposed to mitigate a quasiergodicity problem occurring in simulations of rough energy landscapes. In contrast to conventional simulated tempering employing the Boltzmann weight, our method utilizes a parametrized, generalized distribution as a workhorse for stochastic exchanges of configurations and subensembles transitions, which allows a considerable enhancement for the rate of convergence of Monte Carlo and molecular dynamics simulations using delocalized weights. A feature of our method is that the exploration of the parameter space encouraging subensembles transitions is greatly accelerated using the dynamic update scheme for the weight via the average guide specific to the energy distribution. The performance and characteristic feature of our method have been validated in the liquid-solid transition of Lennard-Jones clusters and the conformational sampling of alanine dipeptide by taking two types of Tsallis [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] expanded ensembles associated with different parametrization schemes.

Dynamical origin of enhanced conformational searches of Tsallis statistics sampling

The characteristic sampling dynamics of importance samplings driven by the Tsallis weight [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] has been analyzed in terms of recently developed Langevin stochastic model by considering the effects of the density of states and the potential smoothing of the Tsallis transformation. Our study reveals that the fixed points, which are determined by the crossing points of the statistical temperature and the Tsallis effective temperature, play a critical role in overall dynamics of the Tsallis statistics sampling. The dynamical origin of enhanced conformational searches of the Tsallis weight has been investigated by unveiling the intimate relationship between the sampling dynamics and the stability change of corresponding fixed points. Based on this stochastic analysis, we propose one effective method to realize a broad energy distribution in the Tsallis statistics sampling by determining optimal Tsallis parameters systematically based on preliminary canonical samplings. The effectiveness of our method has been validated in the folding simulation of Met-Enkephalin and liquid-solid transition simulation of Lennard-Jones cluster systems.