Atomistic molecular simulations of protein folding

Folding Kinetics and Unfolded State Dynamics of the GB1 Hairpin from Molecular Simulation

The C-terminal β-hairpin of protein G is a 16-residue peptide that folds in a two-state fashion akin to many larger proteins. However, with an experimental folding time of ∼6 μs, it remains a challenging system for all-atom, explicitly solvated, molecular dynamics simulations. Here, we use a large simulation data set (0.7 ms total) of the hairpin at 300 and 350 K to interpret its folding via a master equation approach. We find a separation of over an order of magnitude between the longest and second longest relaxation times, with the slowest relaxation corresponding to folding. However, in spite of this apparent two-state dynamics, the folding rate determined based on a first-passage time analysis depends on the initial conditions chosen, with a nonexponential distribution of first passage times being obtained in some cases. Using the master equation model, we are now able to account quantitatively for the observed distribution of first passage times. The deviation from the expected exponential distribution for a two-state system arises from slow dynamics in the unfolded state, associated with formation and melting of helical structures. Our results help to reconcile recent findings of slow dynamics in unfolded proteins with observed two-state folding kinetics. At the same time, they indicate that care is required in estimating folding kinetics from many short folding simulations. Last, we are able to use the master equation model to obtain details of the folding mechanism and folding transition state, which appear consistent with the "zipper" mechanism inferred from the experiment.

Potential conformational heterogeneity of p53 bound to S100B(ββ)

The negative regulatory domain (NRD) of the p53 tumor suppressor is intrinsically disordered. It contains several posttranslational modification (PTM) sites that are important for regulation of p53 activity. Calcium-dependent binding of dimeric S100B(ββ) to p53-NRD blocks access to these PTM sites and disrupts the p53 tetramer to inhibit p53 activation. Previous nuclear magnetic resonance (NMR) structural studies have suggested that p53-NRD folds into a stable helix upon binding to S100B(ββ). Intriguingly, despite the well-converged and stably folded nature of the NMR structure ensemble, experimentally resolved intermolecular nuclear Overhauser enhancements (NOEs) are extremely weak; most have 5- to 6-Å upper bounds, and mainly involve the C-terminal segment of p53-NRD. Such a systematic lack of strong intermolecular NOEs could suggest that the p53/S100B(ββ) interface is more dynamic than currently believed. Indeed, extensive atomistic simulations in explicit solvent (with 1.0μs total effective sampling) revealed large heterogeneity in the S100B(ββ)-bound conformation of p53-NRD. Helix unwinding at the C-terminus allows key hydrophobic residues (Leu383 and Phe385) to make more extensive intermolecular contacts, whereas the highly helical N-terminus displays substantial flexibility in packing with S100B(ββ). Importantly, the predicted heterogeneous ensemble as a whole is highly consistent with experimental intermolecular NOEs, although many conformational sub-states coexist and individual sub-states satisfy only subsets of the NOE restraints. Furthermore, the simulated ensemble provides similar shielding of key PTM sites to support p53 inhibition. This study not only provides new insights into the structural basis of the p53/S100B(ββ) recognition but also highlights the importance of recognizing dynamic complexes in structural studies of intrinsically disordered protein interactions.

Critical Assessment of Current Force Fields. Short Peptide Test Case

The applicability of molecular dynamics simulations for studies of protein folding or intrinsically disordered proteins critically depends on quality of energetic functions-force fields. The four popular force fields for biomolecular simulations, CHARMM22/CMAP, AMBER FF03, AMBER FF99SB, and OPLS-AA/L, were compared in prediction of conformational propensities of all common proteinogenic amino acids. The minimalistic model of terminally block amino acids (dipeptides) was chosen for assessment of side chain effects on backbone propensities. The precise metadynamics simulations revealed striking inconsistency of trends in conformational preferences as manifested by investigated force fields for both backbone and side chains. To trace this disapproval between force fields, the two related AMBER force fields were studied more closely. In the cases of FF99SB and FF03, we uncovered that the distinct tends were driven by different charge models. Additionally, the effects of recent correction for side chain torsion (FF99SB-ILDN) were examined on affected amino acids and exposed significant coupling between free energy profiles and propensities of backbone and side chain conformers. These findings have important consequences for further force field development.

Discrete kinetic models from funneled energy landscape simulations

A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK). In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an “inside-out”, nucleation-propagation like character.

Separability between overall and internal motion: a protein folding problem

The separability between overall and internal motions is evaluated over multiple folding trajectories of the villin headpiece subdomain. The analysis, which relies on the Prompers-Brüschweiler separability index, offers a potentially useful perspective on protein folding. The protein is considered folded in this study, not when it reaches some static target, but rather when it tumbles as a dynamically constrained object. The analysis also demonstrates how the separability index, when applied to protein folding simulations, can facilitate the analysis of NMR relaxation data.

Transition path times for nucleic Acid folding determined from energy-landscape analysis of single-molecule trajectories

The duration of structural transitions in biopolymers is only a fraction of the time spent searching diffusively over the configurational energy landscape. We found the transition time, τ(TP), and the diffusion constant, D, for DNA and RNA folding using energy landscapes obtained from single-molecule trajectories under tension in optical traps. DNA hairpins, RNA pseudoknots, and a riboswitch all had τ(TP)~10 μs and D~10(-13-14) m(2)/s, despite widely differing unfolding rates. These results show how energy-landscape analysis can be harnessed to characterize brief but critical events during folding reactions.

Protein folding kinetics and thermodynamics from atomistic simulation

Advances in simulation techniques and computing hardware have created a substantial overlap between the timescales accessible to atomic-level simulations and those on which the fastest-folding proteins fold. Here we demonstrate, using simulations of four variants of the human villin headpiece, how simulations of spontaneous folding and unfolding can provide direct access to thermodynamic and kinetic quantities such as folding rates, free energies, folding enthalpies, heat capacities, Φ-values, and temperature-jump relaxation profiles. The quantitative comparison of simulation results with various forms of experimental data probing different aspects of the folding process can facilitate robust assessment of the accuracy of the calculations while providing a detailed structural interpretation for the experimental observations. In the example studied here, the analysis of folding rates, Φ-values, and folding pathways provides support for the notion that a norleucine double mutant of villin folds five times faster than the wild-type sequence, but following a slightly different pathway. This work showcases how computer simulation has now developed into a mature tool for the quantitative computational study of protein folding and dynamics that can provide a valuable complement to experimental techniques.

A preformed binding interface in the unbound ensemble of an intrinsically disordered protein: evidence from molecular simulations

Intrinsically disordered proteins play an important role in cellular signalling, mediated by their interactions with other biomolecules. A key question concerns the nature of their binding mechanism, and whether the bound structure is induced only by proximity to the binding partner. This is difficult to answer through experiment alone because of the very heterogeneous nature of the unbound ensemble, and the probable rapid interconversion of the various unbound structures. Here we report the most extensive set of simulations on NCBD to date: we use large-scale replica exchange molecular dynamics to explore the unbound state. An important feature of the study is the use of an atomistic force field that has been parametrised against experimental data for weakly structured peptides, together with an accurate explicit water model. Neither the force field nor the starting conformations are biased towards a particular structure. The regions of NCBD that have high helical propensity in the simulations correspond closely to helices in the 'core' unbound conformation determined by NMR, although no single member of the simulated unbound ensemble closely resembles the core conformation, or either of the two known bound conformations. We have validated the results against NMR spectroscopy and SAXS measurements, obtaining reasonable agreement. The two helices which most stabilise the binding of NCBD with ACTR are formed readily; the third helix, which is less important for binding but is involved in most of the intraprotein contacts of NCBD in the bound conformation, is formed more rarely, and tends not to coexist with the other helices. These results support a mechanism by which NCBD gains the advantages of disorder, while forming binding-competent structures in the unbound state. We obtain support for this mechanism from coarse-grained simulations of NCBD with, and without, its binding partner.

Hybrid approaches to molecular simulation

Molecular dynamics (MD) simulation is an established method for studying the conformational changes that are important for protein function. Recent advances in hardware and software have allowed MD simulations over the same timescales as experiment, improving the agreement between theory and experiment to a large extent. However, running such simulations are costly, in terms of resources, storage, and trajectory analysis. There is still a place for techniques that involve short MD simulations. In order to overcome the sampling paucity of short time-scales, hybrid methods that include some form of MD simulation can exploit certain features of the system of interest, often combining experimental information in surprising ways. Here, we review some recent hybrid approaches to the simulation of proteins.