Structuring and sampling complex conformation space: Weighted ensemble dynamics simulations

Effectively explore metastable states of proteins by adaptive nonequilibrium driving simulations

Nonequilibrium drivings applied in molecular dynamics (MD) simulations can efficiently extend the visiting range of protein conformations, but might compel systems to go far away from equilibrium and thus mainly explore irrelevant conformations. Here we propose a general method, called adaptive nonequilibrium simulation (ANES), to automatically adjust the external driving on the fly, based on the feedback of the short-time average response of system. Thus, the ANES approximately keeps the local equilibrium but efficiently accelerates the global motion. We illustrate the capability of the ANES in highly efficiently exploring metastable conformations in the deca-alanine peptide and find that the 0.2-μs ANES approximately captures the important states and folding and unfolding pathways in the HP35 solution by comparing with the result of the recent 398-μs equilibrium MD simulation on Anton [S. Piana et al., Proc. Natl. Acad. Sci. USA 109, 17845 (2012)PNASA60027-842410.1073/pnas.1201811109].

Jarzynski matrix equality: Calculating the free-energy difference by nonequilibrium simulations with an arbitrary initial distribution

The Jarzynski equality (JE) method, which relates the work of a nonequilibrium process to the free-energy difference between its initial and final states, provides an efficient way to calculate free energies of thermodynamic systems in simulations or experiments. However, more extensive applications of the JE are hindered by the requirement that the initial state must be in equilibrium. In this work we extend the JE method to be the Jarzynski matrix equality (JME) method, which relates the work of trajectories connecting metastable conformational regions to their local free energies, and thus we can estimate the free energy from the nonequilibrium trajectories starting from an almost arbitrary initial distribution. We then apply the JME to toy models, Lennard-Jones fluids, and polymer chain models, demonstrating its efficiency in free-energy calculations with satisfactory accuracy. The JME extends the applicability of the nonequilibrium methods to complex systems whose initial equilibrium states are difficult to reach.

Equilibrium sampling by reweighting nonequilibrium simulation trajectories

Based on equilibrium molecular simulations, it is usually difficult to efficiently visit the whole conformational space of complex systems, which are separated into some metastable regions by high free energy barriers. Nonequilibrium simulations could enhance transitions among these metastable regions and then be applied to sample equilibrium distributions in complex systems, since the associated nonequilibrium effects can be removed by employing the Jarzynski equality (JE). Here we present such a systematical method, named reweighted nonequilibrium ensemble dynamics (RNED), to efficiently sample equilibrium conformations. The RNED is a combination of the JE and our previous reweighted ensemble dynamics (RED) method. The original JE reproduces equilibrium from lots of nonequilibrium trajectories but requires that the initial distribution of these trajectories is equilibrium. The RED reweights many equilibrium trajectories from an arbitrary initial distribution to get the equilibrium distribution, whereas the RNED has both advantages of the two methods, reproducing equilibrium from lots of nonequilibrium simulation trajectories with an arbitrary initial conformational distribution. We illustrated the application of the RNED in a toy model and in a Lennard-Jones fluid to detect its liquid-solid phase coexistence. The results indicate that the RNED sufficiently extends the application of both the original JE and the RED in equilibrium sampling of complex systems.

Systematically constructing kinetic transition network in polypeptide from top to down: trajectory mapping

Molecular dynamics (MD) simulation is an important tool for understanding bio-molecules in microscopic temporal/spatial scales. Besides the demand in improving simulation techniques to approach experimental scales, it becomes more and more crucial to develop robust methodology for precisely and objectively interpreting massive MD simulation data. In our previous work [J Phys Chem B 114, 10266 (2010)], the trajectory mapping (TM) method was presented to analyze simulation trajectories then to construct a kinetic transition network of metastable states. In this work, we further present a top-down implementation of TM to systematically detect complicate features of conformational space. We first look at longer MD trajectory pieces to get a coarse picture of transition network at larger time scale, and then we gradually cut the trajectory pieces in shorter for more details. A robust clustering algorithm is designed to more effectively identify the metastable states and transition events. We applied this TM method to detect the hierarchical structure in the conformational space of alanine-dodeca-peptide from microsecond to nanosecond time scales. The results show a downhill folding process of the peptide through multiple pathways. Even in this simple system, we found that single common-used order parameter is not sufficient either in distinguishing the metastable states or predicting the transition kinetics among these states.