Accurate Estimation of Protein Folding and Unfolding Times: Beyond Markov State Models

Suárez, Ernesto; Adelman, Joshua L.; Zuckerman, Daniel M.

doi:10.1021/acs.jctc.6b00339

Cited by 76 publications

(111 citation statements)

References 40 publications

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“…We note that tracking the most-recent-state history avoids a Markov assumption and is necessary for estimating an unbiased MFPT because first-passage processes refer explicitly to events occurring in a given direction: A to B, or B to A (20, 28, 65, 66). Mixing the two types of trajectories in a history-agnostic Markov analysis can lead to significant bias in the MFPT and its reciprocal, the rate constant (62), and this also holds for analyzing standard MD trajectories (61, 63). Equilibrium probabilities can also be calculated via the

k_{i j}^{μ ν}

transition rates, although the color information is not strictly necessary (10, 62).…”

Section: Theorymentioning

confidence: 99%

Weighted Ensemble Simulation: Review of Methodology, Applications, and Software

Zuckerman

Chong

2017

Annu. Rev. Biophys.

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262

330

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The weighted ensemble (WE) methodology orchestrates quasi-independent parallel simulations run with intermittent communication that can enhance sampling of rare events such as protein conformational changes, folding, and binding. The WE strategy can achieve superlinear scaling—the unbiased estimation of key observables such as rate constants and equilibrium state populations to greater precision than would be possible with ordinary parallel simulation. WE software can be used to control any dynamics engine, such as standard molecular dynamics and cell-modeling packages. This article reviews the theoretical basis of WE and goes on to describe successful applications to a number of complex biological processes—protein conformational transitions, (un)binding, and assembly processes, as well as cell-scale processes in systems biology. We furthermore discuss the challenges that need to be overcome in the next phase of WE methodological development. Overall, the combined advances in WE methodology and software have enabled the simulation of long-timescale processes that would otherwise not be practical on typical computing resources using standard simulation.

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k_{i j}^{μ ν}

transition rates, although the color information is not strictly necessary (10, 62).…”

Section: Theorymentioning

confidence: 99%

Weighted Ensemble Simulation: Review of Methodology, Applications, and Software

Zuckerman

Chong

2017

Annu. Rev. Biophys.

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262

330

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“…[66][67] We also employed haMSM analysis, which is unbiased for steady-state flux estimation at arbitrary lag times, and small lag times allow fuller use of the extensive WE data. 56,64,68 The approach is of particular interest for Protein G because, in principle, a haMSM can estimate steady-state behavior using trajectories generated in the transient period -i.e., in the approach to steady state. As noted, the flux profile for Protein G indicates those WE simulations clearly remained in the transient regime.…”

Section: Resultsmentioning

confidence: 99%

Computational estimation of ms-sec atomistic folding times

Adhikari

Mostofian

Copperman

et al. 2018

Preprint

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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 f ranging from ~100 µs to ~1s 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 f = 0.8 − 9.0 s), NTL9 at water-like viscosity ( f = 0.2 − 1.9 ms), and Protein G at low viscosity ( f = 3.3 − 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.

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“…In the latter context, the ability to account for directionality and history is critical – particularly tracing back any given trajectory to the most recently occupied state (A or B, “initial” or “target” state), which enables unbiased rate calculation [*11,12,13]; see also [14,15]. This insight from path theory has important practical implications for analyzing ordinary MD simulations and avoiding the Markov assumption [16]. …”

Section: Path Sampling Methods and Recent Advancesmentioning

confidence: 99%

Path-sampling strategies for simulating rare events in biomolecular systems

Chong

Saglam

Zuckerman

2017

Current Opinion in Structural Biology

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Despite more than three decades of effort with molecular dynamics simulations, long-timescale (ms and beyond) biologically relevant phenomena remain out of reach in most systems of interest. This is largely because important transitions, such as conformational changes and (un)binding events, tend to be rare for conventional simulations (< 10 µs). That is, conventional simulations will predominantly dwell in metastable states instead of making large transitions in complex biomolecular energy landscapes. In contrast, path sampling approaches focus computing effort specifically on transitions of interest. Such approaches have been in use for nearly 20 years in biomolecular systems and enabled the generation of pathways and calculation of rate constants for ms processes, including large protein conformational changes, protein folding, and protein (un)binding.

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Accurate Estimation of Protein Folding and Unfolding Times: Beyond Markov State Models

Cited by 76 publications

References 40 publications

Weighted Ensemble Simulation: Review of Methodology, Applications, and Software

Weighted Ensemble Simulation: Review of Methodology, Applications, and Software

Computational estimation of ms-sec atomistic folding times

Path-sampling strategies for simulating rare events in biomolecular systems

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