Rapid equilibrium sampling initiated from nonequilibrium data

Abstract

Simulating the conformational dynamics of biomolecules is extremely difficult due to the rugged nature of their free energy landscapes and multiple long-lived, or metastable, states. Generalized ensemble (GE) algorithms, which have become popular in recent years, attempt to facilitate crossing between states at low temperatures by inducing a random walk in temperature space. Enthalpic barriers may be crossed more easily at high temperatures; however, entropic barriers will become more significant. This poses a problem because the dominant barriers to conformational change are entropic for many biological systems, such as the short RNA hairpin studied here. We present a new efficient algorithm for conformational sampling, called the adaptive seeding method (ASM), which uses nonequilibrium GE simulations to identify the metastable states, and seeds short simulations at constant temperature from each of them to quantitatively determine their equilibrium populations. Thus, the ASM takes advantage of the broad sampling possible with GE algorithms but generally crosses entropic barriers more efficiently during the seeding simulations at low temperature. We show that only local equilibrium is necessary for ASM, so very short seeding simulations may be used. Moreover, the ASM may be used to recover equilibrium properties from existing datasets that failed to converge, and is well suited to running on modern computer clusters.generalized ensemble methods ͉ Markov state models ͉ molecular dynamics simulations ͉ RNA hairpin folding T he functions of biological macromolecules are in large part determined by their structure and dynamics. As such, many experimental techniques have been developed and applied to probe these properties, each of which has its strengths and weaknesses. Computational methods such as molecular dynamics (MD) and Monte Carlo (MC) simulations have the potential to complement such experiments by modeling the evolution of entire systems with atomic resolution. However, it is extremely difficult to obtain equilibrium sampling of even moderately sized systems in atomic simulations because of the rugged nature of the free energy landscapes that must be explored. Without adequate sampling, it is impossible to validate the parameters, or force fields, that determine the interactions between atoms or to address phenomena that occur on biologically relevant timescales.Many methods have been developed in an attempt to address the sampling problem. Generalized ensemble (GE) algorithms, such as the replica exchange method (REM), or parallel tempering (1, 2) and simulated tempering (ST) (3, 4), are popular approaches for studying biomolecular folding (5-15). They attempt to overcome the sampling problem by inducing a random walk in temperature space while maintaining canonical sampling at each temperature. At high temperatures, energetic barriers may be crossed easily; at low temperatures, the system is generally constrained to local minima. However, recent studies have shown that GE simulations do not yield conver...

Protein folded states are kinetic hubs

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