Computational Estimation of Microsecond to Second Atomistic Folding Times

Abstract

Despite the development of massively parallel computing hardware including inexpensive graphics processing units (GPUs), it has remained infeasible to simulate the folding of atomistic proteins at room temperature using conventional molecular dynamics (MD) beyond the μs scale. Here we report the folding of atomistic, implicitly solvated protein systems with folding times τ f ranging from ~10 μs to ~100 ms using the weighted ensemble (WE) strategy in combination with GPU computing. Starting from an initial structure or set of structures, WE organizes an ensemble of GPU-accelerated MD trajectory segments via intermittent pruning and replication events to generate statistically unbiased estimates of rate constants for rare events such as folding; no biasing forces are used. Although the variance among atomistic WE folding runs is significant, multiple independent runs are used to reduce and quantify statistical uncertainty. Folding times are estimated directly from WE probability flux and from history-augmented Markov analysis of the WE data. Three systems were examined: NTL9 at low solvent viscosity (yielding τ f = 0.8 − μs), NTL9 at water-like viscosity (τ f = 0.2 − 2 ms), and Protein G at low viscosity (τ f = 3 − 200 ms). In all cases the folding time, uncertainty, and ensemble properties could be estimated from WE simulation; for Protein G, this characterization required significantly less overall computing than would be required to observe a single folding event with conventional MD simulations. Our results suggest that the use and calibration of force fields and solvent models for precise estimation of kinetic quantities is becoming feasible.

Accelerated Estimation of Long-timescale Kinetics by Combining Weighted Ensemble Simulation with Markov Model “Microstates” using Non-Markovian Theory

“…Here we extend upon the protein G WE simulations and haMSM analysis we reported in Ref. 19, finding that in our atomistic WE folding simulations we observe slow relaxation to steady-state indicative of the presence of long-lived intermediates on the folding pathway.…”

“…To that end, we apply the haMSM analysis to WE simulations of diffusion in a 2D random energy landscape, and atomistic protein folding, described in detail in Ref. 19. We are interested in the extent to which haMSMs with many (thousands of) microbins can accelerate the estimation of the SS flux compared to the SS relaxation time.…”

“…The spread in values reflects variation in the clustering process, and not the variation between the 5 runs in the training set. The validation CR (blue) is from a Bayesian bootstrap analysis of the SS flux from an independent set of 10 WE simulations out to t mol = 12ns examined in 19 . Direct flux confidence region (shaded red) from the set of 5 WE simulations in the training set, and friction-rescaled ( γ sim γ water ) experimental folding rate (gold).…”

A Suite of Tutorials for the WESTPA Rare-Events Sampling Software [Article v1.0]

“…If WE was performed with a "recycling" condition where trajectories reaching B are fed back to A, then the rate constant for the process can be estimated from the probability flux arriving to state B if the simulation achieves steady state and hence constant flux [20,21]. If a WE simulation does not achieve steady state, it is still possible in principle to estimate rate constants using a non-Markovian analysis, also called a history-augmented Markov State Model [11,22,23].…”

“…The WESTPA software also includes plugins for using a WE-based string method [6] and a WE strategy utilizing hierarchical Voronoi bins (WExplore) [7]. The WESTPA software package has enabled efficient atomistic simulations of host-guest associations [8], protein binding processes [9,10], and protein folding [11]. This efficiency (relative to standard "brute force" simulations) has been demonstrated to increase exponentially with the effective free energy barrier of the rare event [12].…”