To milliseconds and beyond: challenges in the simulation of protein folding

Quantitatively accurate all-atom molecular dynamics (MD) simulations of protein folding have long been considered a holy grail of computational biology. Due to the large system sizes and long timescales involved, such a pursuit was for many years computationally intractable. Further, sufficiently accurate forcefields needed to be developed in order to realistically model folding. This decade, however, saw the first reports of folding simulations describing kinetics on the order of milliseconds, placing many proteins firmly within reach of these methods. Progress in sampling and forcefield accuracy, however, presents a new challenge: how to turn huge MD datasets into scientific understanding. Here, we review recent progress in MD simulation techniques and show how the vast datasets generated by such techniques present new challenges for analysis. We critically discuss the state of the art, including reaction coordinate and Markov state model (MSM) methods, and provide a perspective for the future.

Introduction

Understanding protein folding via molecular simulation has been an aspiration of computational chemists ever since Anfinsen uncovered the surprising fact that proteins folded to a unique structure [1, 2, 3]. Applying simulation to folding appeals for many reasons. Folding is rapid and complex, requiring atomic-level resolution at nanosecond timescales for a complete detailed picture — outside the hard limits of temporal and spatial resolution of most experimental techniques [4]. Furthermore, the complexity of protein native states and the inherent physical heterogeneity in the folding process have frustrated the search for microscopic physical theories of folding, though some advanced phenomenological approaches have been proposed [5, 6, 7, 8, 9]. Thus atomic-level simulations of folding, possessing intrinsically high resolution, have been aggressively pursued with the hope of surmounting these difficulties.

Three main problems must be overcome to achieve useful simulations of protein folding: accurate models (forcefields), sufficient sampling, and robust data analysis. Forcefield development has received much attention from the field, and has been extensively discussed [10, 11, 12, 13, 14, 15]. Although more remains to be done to build and validate even more accurate models, forcefields capable of folding proteins in good agreement with experiment already exist (Figure 1). Instead, the major challenge in producing reliable simulations of folding has been harnessing enough computer power to produce sufficient sampling to study folding. Because classical simulations must integrate Newton's equations of motion with femtosecond timesteps (10⁻¹⁵ s), folding simulations require ∼10¹² timesteps to reach millisecond timescales. This expense is compounded by large system sizes (∼10⁵ atoms for explicit solvent simulations) and the need to witness many events for statistical confidence, making the computational effort required to study folding via simulation enormous.

Very recently, advances in hardware, software, and sampling techniques have made millisecond simulations possible. In 2010, using an aggregate of 1.5 ms of data, Voelz et al. reported the first simulation describing the folding of a millisecond folder in implicit solvent, from data generated by the distributed computing network Folding@home [16•, 17]. Later that year, Bowman et al. reported a millisecond timescale in the folding dynamics of lambda repressor in explicit solvent [18]. More recently, using 30 ms of aggregate data, Voelz et al. studied the folding of ACBP on the 10 ms timescale, revealing that an experimentally observed folding intermediate was in fact a complex, heterogeneous ensemble of structures [19^••]. Finally, with the advent of ANTON, a computer specialized for protein simulation, the first single trajectory of millisecond length was reported near the end of 2010 [20^•], making it possible to predict folding times of up to 100 μs from a single trajectory.

While challenging, generating enough sampling in an accurate forcefield does not constitute the end of the road for a folding simulation. Another major challenge is gaining scientific insight from the simulation — turning data into knowledge. Insights gained from simulations have already begun to shape the protein folding field, through connection to experiment and analysis of the simulations themselves [18, 19••, 21, 22, 23, 24, 25]. These preliminary studies have revealed that the analysis of simulation data is difficult, with cases where certain techniques have led researchers to believe results inconsistent with their raw simulation data [20•, 26•, 27]. The simulation community needs to develop general, robust, and easy to use data analysis tools to continue toward the goal of understanding folding.

In this review, we briefly explain how the sampling problem has been overcome, and why we can expect the future to yield even longer simulations more efficiently. As sampling becomes less of an issue, a new challenge in folding simulations raises its head — given the massive amount of data extensive sampling provides, how does one make sense of it all? MD simulations are a high-dimensional time series, and therefore present a ‘Big Data’ challenge [28, 29]. We expect the techniques of data analysis will be the new limiting factor in the quest to understand folding through molecular simulation.