Atomistic molecular simulations of protein folding

Microscopic interpretation of folding ϕ-values using the transition path ensemble

All-atom molecular dynamics simulations now allow us to create movies of proteins folding and unfolding. However, it is difficult to assess the accuracy of the folding mechanisms observed because experiments cannot yet directly resolve events occurring along the transition paths between unfolded and folded states. Protein folding ϕ-values provide residue-resolved information about folding mechanisms by comparing the effects of mutations on folding rates and stability, but determining ϕ-values by separately simulating mutant proteins would be computationally demanding and prone to large statistical errors. Here we use transition path theory to develop a method for computing ϕ-values directly from the transition path ensemble, without the need for additional simulations. This path-based approach uses the full transition path information available from equilibrium folding and unfolding trajectories, or from transition path sampling, and does not require identification of folding transition states. Applying our approach to a set of simulations of 10 small proteins by Shaw and coworkers [Lindorff-Larsen K, Piana S, Dror RO, Shaw DE (2011) Science 334(6055):517-520; Piana S, Lindorff-Larsen K, Shaw DE (2011) Biophys J100(9):L47-L49; and Piana S, Lindorff-Larsen K, Shaw DE (2013) Proc Natl Acad Sci USA 110(15):5915-5920], we find good agreement with experiments in most cases where data are available. We can further resolve the contributions to fractional ϕ-values coming from partial contact formation versus transition path heterogeneity. Although in some cases, there is substantial heterogeneity of folding mechanism, in others, such as Ubiquitin, the mechanism is strongly conserved.

Conformational Changes and Free Energies in a Proline Isomerase

Proteins are dynamic molecules and their ability to adopt alternative conformations is central to their biological function. The structural and biophysical properties of transiently and sparsely populated states are, however, difficult to study and an atomic-level description of those states is challenging. We have used enhanced-sampling all-atom, explicit-solvent molecular simulations, guided by structural information from X-ray crystallography and NMR, to describe quantitatively the transition between the major and a minor state of Cyclophilin A, thus providing new insight into how dynamics can affect enzyme function. We calculate the conformational free energy between the two states, and comparison with experiments demonstrates a surprisingly high accuracy for both the wild type protein and a mutant that traps the protein in its alternative conformation. Our results demonstrate how the combination of state-of-the-art force fields and enhanced sampling methods can provide a detailed and quantitative description of the conformational changes in proteins such as those observed in Cyclophilin A.

Binding of Disordered Peptides to Kelch: Insights from Enhanced Sampling Simulations

Keap1 protein plays an essential role in regulating cellular oxidative stress response and is a crucial binding hub for multiple proteins, several of which are intrinsically disordered proteins (IDP). Among Kelch's IDP binding partners, NRF2 and PTMA are the two most interesting cases. They share a highly similar binding motif; however, NRF2 binds to Kelch with a binding affinity of approximately 100-fold higher than that of PTMA. In this study, we perform an exhaustive sampling composed of 6 μs well-tempered metadynamics and 2 μs unbiased molecular dynamics (MD) simulations aiming at characterizing the binding mechanisms and structural properties of these two peptides. Our results agree with previous experimental observations that PTMA is remarkably more disordered than NRF2 in both the free and bound states. This explains PTMA's lower binding affinity. Our extensive sampling also provides valuable insights into the vast conformational ensembles of both NRF2 and PTMA, supports the hypothesis of coupled folding-binding, and confirms the essential role of linear motifs in IDP binding.

Reduction of All-Atom Protein Folding Dynamics to One-Dimensional Diffusion

Theoretical models have often modeled protein folding dynamics as diffusion on a low-dimensional free energy surface, a remarkable simplification. However, the accuracy of such an approximation and the number of dimensions required were not clear. For all-atom folding simulations of ten small proteins in explicit solvent we show that the folding dynamics can indeed be accurately described as diffusion on just a single coordinate, the fraction of native contacts (Q). The diffusion models reproduce both folding rates, and finer details such as transition-path durations and diffusive propagators. The Q-averaged diffusion coefficients decrease with chain length, as anticipated from energy landscape theory. Although the Q-diffusion model does not capture transition-path durations for the protein NuG2, we show that this can be accomplished by designing an improved coordinate Qopt. Overall, one-dimensional diffusion on a suitable coordinate turns out to be a remarkably faithful model for the dynamics of the proteins considered.

Assessment of the utility of contact-based restraints in accelerating the prediction of protein structure using molecular dynamics simulations

Molecular dynamics (MD) simulation is a well-established tool for the computational study of protein structure and dynamics, but its application to the important problem of protein structure prediction remains challenging, in part because extremely long timescales can be required to reach the native structure. Here, we examine the extent to which the use of low-resolution information in the form of residue-residue contacts, which can often be inferred from bioinformatics or experimental studies, can accelerate the determination of protein structure in simulation. We incorporated sets of 62, 31, or 15 contact-based restraints in MD simulations of ubiquitin, a benchmark system known to fold to the native state on the millisecond timescale in unrestrained simulations. One-third of the restrained simulations folded to the native state within a few tens of microseconds-a speedup of over an order of magnitude compared with unrestrained simulations and a demonstration of the potential for limited amounts of structural information to accelerate structure determination. Almost all of the remaining ubiquitin simulations reached near-native conformations within a few tens of microseconds, but remained trapped there, apparently due to the restraints. We discuss potential methodological improvements that would facilitate escape from these near-native traps and allow more simulations to quickly reach the native state. Finally, using a target from the Critical Assessment of protein Structure Prediction (CASP) experiment, we show that distance restraints can improve simulation accuracy: In our simulations, restraints stabilized the native state of the protein, enabling a reasonable structural model to be inferred.

Accelerated molecular dynamics simulations of protein folding

Folding of four fast-folding proteins, including chignolin, Trp-cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred-of-microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2-2.1 Å of the native NMR or X-ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second-order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein-folding studies.

Multiscale enhanced sampling of intrinsically disordered protein conformations

In a recently developed multiscale enhanced sampling (MSES) technique, topology-based coarse-grained (CG) models are coupled to atomistic force fields to enhance the sampling of atomistic protein conformations. Here, the MSES protocol is refined by designing more sophisticated Hamiltonian/temperature replica exchange schemes that involve additional parameters in the MSES coupling restraint potential, to more carefully control how conformations are coupled between the atomistic and CG models. A specific focus is to derive an optimal MSES protocol for simulating conformational ensembles of intrinsically disordered proteins (IDPs). The efficacy of the refined protocols, referred to as MSES-soft asymptote (SA), was evaluated using two model peptides with various levels of residual helicities. The results show that MSES-SA generates more reversible helix-coil transitions and leads to improved convergence on various ensemble conformational properties. This study further suggests that more detailed CG models are likely necessary for more effective sampling of local conformational transition of IDPs. © 2015 Wiley Periodicals, Inc.

Elucidation of Ligand-Dependent Modulation of Disorder-Order Transitions in the Oncoprotein MDM2

Numerous biomolecular interactions involve unstructured protein regions, but how to exploit such interactions to enhance the affinity of a lead molecule in the context of rational drug design remains uncertain. Here clarification was sought for cases where interactions of different ligands with the same disordered protein region yield qualitatively different results. Specifically, conformational ensembles for the disordered lid region of the N-terminal domain of the oncoprotein MDM2 in the presence of different ligands were computed by means of a novel combination of accelerated molecular dynamics, umbrella sampling, and variational free energy profile methodologies. The resulting conformational ensembles for MDM2, free and bound to p53 TAD (17-29) peptide identify lid states compatible with previous NMR measurements. Remarkably, the MDM2 lid region is shown to adopt distinct conformational states in the presence of different small-molecule ligands. Detailed analyses of small-molecule bound ensembles reveal that the ca. 25-fold affinity improvement of the piperidinone family of inhibitors for MDM2 constructs that include the full lid correlates with interactions between ligand hydrophobic groups and the C-terminal lid region that is already partially ordered in apo MDM2. By contrast, Nutlin or benzodiazepinedione inhibitors, that bind with similar affinity to full lid and lid-truncated MDM2 constructs, interact additionally through their solubilizing groups with N-terminal lid residues that are more disordered in apo MDM2.

Life as we know it depends on interactions between proteins. There is substantial evidence that many interactions between proteins involve very flexible protein regions. These disordered regions may undergo disorder/order transitions upon forming an interaction with another protein. Many successful approaches to medicinal chemistry are based on mimicking the interactions of biological molecules with man-made small molecules. However how drug-like small-molecules may modulate protein disorder is currently poorly understood, largely because it is difficult to measure in details this type of interaction with experimental methods. Here we have used computer simulations to resolve with great details the process by which different small-molecules modulate the flexibility of a disordered region of the protein MDM2. This protein is overexpressed in many cancers and small-molecules that recognize MDM2 have been developed over the last decade as possible novel anti-cancer agents. We show that the flexible MDM2 “lid” region adopts different conformational states in the presence of different small-molecules. Our results suggest why some classes of small-molecules form favorable interactions with the lid region, whereas others do not. These findings may prove crucial to develop new and more effective MDM2 inhibitors, and more generally to help drug designers target disordered proteins regions with small-molecules.

Interaction Networks in Protein Folding via Atomic-Resolution Experiments and Long-Time-Scale Molecular Dynamics Simulations

The integration of atomic-resolution experimental and computational methods offers the potential for elucidating key aspects of protein folding that are not revealed by either approach alone. Here, we combine equilibrium NMR measurements of thermal unfolding and long molecular dynamics simulations to investigate the folding of gpW, a protein with two-state-like, fast folding dynamics and cooperative equilibrium unfolding behavior. Experiments and simulations expose a remarkably complex pattern of structural changes that occur at the atomic level and from which the detailed network of residue-residue couplings associated with cooperative folding emerges. Such thermodynamic residue-residue couplings appear to be linked to the order of mechanistically significant events that take place during the folding process. Our results on gpW indicate that the methods employed in this study are likely to prove broadly applicable to the fine analysis of folding mechanisms in fast folding proteins.

Exact dynamical coarse-graining without time-scale separation

A family of collective variables is proposed to perform exact dynamical coarse-graining even in systems without time scale separation. More precisely, it is shown that these variables are not slow in general, yet satisfy an overdamped Langevin equation that statistically preserves the sequence in which any regions in collective variable space are visited and permits to calculate exactly the mean first passage times from any such region to another. The role of the free energy and diffusion coefficient in this overdamped Langevin equation is discussed, along with the way they transform under any change of variable in collective variable space. These results apply both to systems with and without inertia, and they can be generalized to using several collective variables simultaneously. The view they offer on what makes collective variables and reaction coordinates optimal breaks from the standard notion that good collective variable must be slow variable, and it suggests new ways to interpret data from molecular dynamics simulations and experiments.

Conformational stability of PCID2 upon DSS1 binding with molecular dynamics simulation

DSS1 is a small acidic intrinsically disordered protein (IDP) that can fold upon binding with PCID2 TREX-2. The resulting complex plays a key role in mRNA export. However, the binding mechanism between DSS1 and PCID2 is unsolved. Here, three independent 500-ns molecular dynamics (MD) simulations were performed to study the DSS1-PCID2 binding mechanism by comparing apo-PCID2 and bound PCID2. The results show that the conformational variation of bound PCID2 is smaller than that of apo-PCID2, especially in the binding domain of two helices (helix IV and VIII). The probability of coil formation between helix III and helix IV of bound PCID2 increases, and a short anti-parallel β-sheet forms upon DSS1 binding. The decomposition of binding free energy into protein and residue pairs suggests that electrostatic and hydrophobic interactions play key roles in the recognition between DSS1 and PCID2. There is a hydrophobic core of seven residues in DSS1 favorable to the binding of PCID2. These analytical methods can be used to reveal the recognition mechanisms of other IDPs and their partners.

Frustration in biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their own structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of frustration in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and especially how biomolecular structure connects to function by means of localized frustration. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding mechanisms. We review here how the biological functions of proteins are related to subtle local physical frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. In this review, we also emphasize that frustration, far from being always a bad thing, is an essential feature of biomolecules that allows dynamics to be harnessed for function. In this way, we hope to illustrate how Frustration is a fundamental concept in molecular biology.

Reconstructing folding energy landscapes by single-molecule force spectroscopy

Folding may be described conceptually in terms of trajectories over a landscape of free energies corresponding to different molecular configurations. In practice, energy landscapes can be difficult to measure. Single-molecule force spectroscopy (SMFS), whereby structural changes are monitored in molecules subjected to controlled forces, has emerged as a powerful tool for probing energy landscapes. We summarize methods for reconstructing landscapes from force spectroscopy measurements under both equilibrium and nonequilibrium conditions. Other complementary, but technically less demanding, methods provide a model-dependent characterization of key features of the landscape. Once reconstructed, energy landscapes can be used to study critical folding parameters, such as the characteristic transition times required for structural changes and the effective diffusion coefficient setting the timescale for motions over the landscape. We also discuss issues that complicate measurement and interpretation, including the possibility of multiple states or pathways and the effects of projecting multiple dimensions onto a single coordinate.

Folding simulation of Trp-cage utilizing a new AMBER compatible force field with coupled main chain torsions

A newly developed AMBER compatible force field with coupled backbone torsion potential terms (AMBER032D) is utilized in a folding simulation of a mini-protein Trp-cage. Through replica exchange and direct molecular dynamics (MD) simulations, a multi-step folding mechanism with a synergetic folding of the hydrophobic core (HPC) and the α-helix in the final stage is suggested. The native structure has the lowest free energy and the melting temperature predicted from the specific heat capacity Cvis only 12 K higher than the experimental measurement. This study, together with our previous study, shows that AMBER032Dis an accurate force field that can be used for protein folding simulations.

Statistical mechanics of the denatured state of a protein using replica-averaged metadynamics

The characterization of denatured states of proteins is challenging because the lack of permanent structure in these states makes it difficult to apply to them standard methods of structural biology. In this work we use all-atom replica-averaged metadynamics (RAM) simulations with NMR chemical shift restraints to determine an ensemble of structures representing an acid-denatured state of the 86-residue protein ACBP. This approach has enabled us to reach convergence in the free energy landscape calculations, obtaining an ensemble of structures in relatively accurate agreement with independent experimental data used for validation. By observing at atomistic resolution the transient formation of native and non-native structures in this acid-denatured state of ACBP, we rationalize the effects of single-point mutations on the folding rate, stability, and transition-state structures of this protein, thus characterizing the role of the unfolded state in determining the folding process.

Quantifying the Sources of Kinetic Frustration in Folding Simulations of Small Proteins

Experiments and atomistic simulations of polypeptides have revealed structural intermediates that promote or inhibit conformational transitions to the native state during folding. We invoke a concept of “kinetic frustration” to quantify the prevalence and impact of these behaviors on folding rates within a large set of atomistic simulation data for 10 fast-folding proteins, where each protein’s conformational space is represented as a Markov state model of conformational transitions. Our graph theoretic approach addresses what conformational features correlate with folding inhibition and therefore permits comparison among features within a single protein network and also more generally between proteins. Nonnative contacts and nonnative secondary structure formation can thus be quantitatively implicated in inhibiting folding for several of the tested peptides.

A theoretical view of protein dynamics

Proteins are fascinating supramolecular structures, which are able to recognize ligands transforming binding information into chemical signals. They can transfer information across the cell, can catalyse complex chemical reactions, and are able to transform energy into work with much more efficiency than any human engine. The unique abilities of proteins are tightly coupled with their dynamic properties, which are coded in a complex way in the sequence and carefully refined by evolution. Despite its importance, our experimental knowledge of protein dynamics is still rather limited, and mostly derived from theoretical calculations. I will review here, in a systematic way, the current state-of-the-art theoretical approaches to the study of protein dynamics, emphasizing the most recent advances, examples of use and the expected lines of development in the near future.

Performance of the MM/GBSA scoring using a binding site hydrogen bond network-based frame selection: the protein kinase case

Conformational clustering using hydrogen bond network analysis improved the MM/GBSA scoring for some protein-kinase–ligand systems used as case studies.

Effects of desolvation barriers and sidechains on local–nonlocal coupling and chevron behaviors in coarse-grained models of protein folding

Coarse-grained protein chain models with desolvation barriers or sidechains lead to stronger local–nonlocal coupling and more linear chevron plots.

Formulation of probabilistic models of protein structure in atomic detail using the reference ratio method

We propose a method to formulate probabilistic models of protein structure in atomic detail, for a given amino acid sequence, based on Bayesian principles, while retaining a close link to physics. We start from two previously developed probabilistic models of protein structure on a local length scale, which concern the dihedral angles in main chain and side chains, respectively. Conceptually, this constitutes a probabilistic and continuous alternative to the use of discrete fragment and rotamer libraries. The local model is combined with a nonlocal model that involves a small number of energy terms according to a physical force field, and some information on the overall secondary structure content. In this initial study we focus on the formulation of the joint model and the evaluation of the use of an energy vector as a descriptor of a protein's nonlocal structure; hence, we derive the parameters of the nonlocal model from the native structure without loss of generality. The local and nonlocal models are combined using the reference ratio method, which is a well-justified probabilistic construction. For evaluation, we use the resulting joint models to predict the structure of four proteins. The results indicate that the proposed method and the probabilistic models show considerable promise for probabilistic protein structure prediction and related applications.

Comparing a simple theoretical model for protein folding with all-atom molecular dynamics simulations

Advances in computing have enabled microsecond all-atom molecular dynamics trajectories of protein folding that can be used to compare with and test critical assumptions of theoretical models. We show that recent simulations by the Shaw group (10, 11, 14, 15) are consistent with a key assumption of an Ising-like theoretical model that native structure grows in only a few regions of the amino acid sequence as folding progresses. The distribution of mechanisms predicted by simulating the master equation of this native-centric model for the benchmark villin subdomain, with only two adjustable thermodynamic parameters and one temperature-dependent kinetic parameter, is remarkably similar to the distribution in the molecular dynamics trajectories.

High-Resolution Free-Energy Landscape Analysis of α-Helical Protein Folding: HP35 and Its Double Mutant

The free-energy landscape can provide a quantitative description of folding dynamics, if determined as a function of an optimally chosen reaction coordinate. Here, we construct the optimal coordinate and the associated free-energy profile for all-helical proteins HP35 and its norleucine (Nle/Nle) double mutant, based on realistic equilibrium folding simulations [Piana et al. Proc. Natl. Acad. Sci. U.S.A.2012, 109, 17845]. From the obtained profiles, we directly determine such basic properties of folding dynamics as the configurations of the minima and transition states (TS), the formation of secondary structure and hydrophobic core during the folding process, the value of the pre-exponential factor and its relation to the transition path times, the relation between the autocorrelation times in TS and minima. We also present an investigation of the accuracy of the pre-exponential factor estimation based on the transition-path times. Four different estimations of the pre-exponential factor for both proteins give k₀^–1 values of approximately a few tens of nanoseconds. Our analysis gives detailed information about folding of the proteins and can serve as a rigorous common language for extensive comparison between experiment and simulation.

Predicting the Thermodynamics and Kinetics of Helix Formation in a Cyclic Peptide Model

The peptide Ac-(cyclo-2,6)-R[KAAAD]-NH2 (cyc-RKAAAD) is a short cyclic peptide known to adopt a remarkably stable single turn α-helix in water. Due to its simplicity and the availability of thermodynamic and kinetic experimental data, cyc-RKAAAD poses as an ideal model for evaluating the aptness of current molecular dynamics (MD) simulation methodologies to accurately sample conformations that reproduce experimentally observed properties. In this work, we extensively sample the conformational space of cyc-RKAAAD using microsecond-timescale MD simulations. We characterize the peptide conformational preferences in terms of secondary structure propensities and, using Cartesian-coordinate principal component analysis (cPCA), construct its free energy landscape, thus obtaining a detailed weighted discrimination between the helical and nonhelical subensembles. The cPCA state discrimination, together with a Markov model built from it, allowed us to estimate the free energy of unfolding (-0.57 kJ/mol) and the relaxation time (∼0.435 μs) at 298.15 K, which are in excellent agreement with the experimentally reported values (-0.22 kJ/mol and 0.42 μs, Serrano, A. L.; Tucker, M. J.; Gai, F. J. Phys. Chem. B, 2011, 115, 7472-7478.). Additionally, we present simulations conducted using two enhanced sampling methods: replica-exchange molecular dynamics (REMD) and bias-exchange metadynamics (BE-MetaD). We compare the free energy landscape obtained by these two methods with the results from MD simulations and discuss the sampling and computational gains achieved. Overall, the results obtained attest to the suitability of modern simulation methods to explore the conformational behavior of peptide systems with a high level of realism.

Motional timescale predictions by molecular dynamics simulations: case study using proline and hydroxyproline sidechain dynamics

We propose a new approach for force field optimizations which aims at reproducing dynamics characteristics using biomolecular MD simulations, in addition to improved prediction of motionally averaged structural properties available from experiment. As the source of experimental data for dynamics fittings, we use ¹³C NMR spin-lattice relaxation times T₁ of backbone and sidechain carbons, which allow to determine correlation times of both overall molecular and intramolecular motions. For structural fittings, we use motionally averaged experimental values of NMR J couplings. The proline residue and its derivative 4-hydroxyproline with relatively simple cyclic structure and sidechain dynamics were chosen for the assessment of the new approach in this work. Initially, grid search and simplexed MD simulations identified large number of parameter sets which fit equally well experimental J couplings. Using the Arrhenius-type relationship between the force constant and the correlation time, the available MD data for a series of parameter sets were analyzed to predict the value of the force constant that best reproduces experimental timescale of the sidechain dynamics. Verification of the new force-field (termed as AMBER99SB-ILDNP) against NMR J couplings and correlation times showed consistent and significant improvements compared to the original force field in reproducing both structural and dynamics properties. The results suggest that matching experimental timescales of motions together with motionally averaged characteristics is the valid approach for force field parameter optimization. Such a comprehensive approach is not restricted to cyclic residues and can be extended to other amino acid residues, as well as to the backbone. Proteins 2014; 82:195–215. © 2013 Wiley Periodicals, Inc.

Molecular dynamics simulations with replica-averaged structural restraints generate structural ensembles according to the maximum entropy principle

In order to characterise the dynamics of proteins, a well-established method is to incorporate experimental parameters as replica-averaged structural restraints into molecular dynamics simulations. Here, we justify this approach in the case of interproton distance information provided by nuclear Overhauser effects by showing that it generates ensembles of conformations according to the maximum entropy principle. These results indicate that the use of replica-averaged structural restraints in molecular dynamics simulations, given a force field and a set of experimental data, can provide an accurate approximation of the unknown Boltzmann distribution of a system.

Insights into the Binding of Intrinsically Disordered Proteins from Molecular Dynamics Simulation

Intrinsically disordered proteins (IDPs) are a class of protein that, in the native state, possess no well-defined secondary or tertiary structure, existing instead as dynamic ensembles of conformations. They are biologically important, with approximately 20% of all eukaryotic proteins disordered, and found at the heart of many biochemical networks. To fulfil their biological roles, many IDPs need to bind to proteins and/or nucleic acids. And while unstructured in solution, IDPs typically fold into a well-defined three-dimensional structure upon interaction with a binding partner. The flexibility and structural diversity inherent to IDPs makes this coupled folding and binding difficult to study at atomic resolution by experiment alone, and computer simulation currently offers perhaps the best opportunity to understand this process. But simulation of coupled folding and binding is itself extremely challenging; these molecules are large and highly flexible, and their binding partners, such as DNA or cyclins, are also often large. Therefore, their study requires either or both simplified representations and advanced enhanced sampling schemes. It is not always clear that existing simulation techniques, optimized for studying folded proteins, are well-suited to IDPs. In this article, we examine the progress that has been made in the study of coupled folding and binding using molecular dynamics simulation. We summarise what has been learnt, and examine the state of the art in terms of both methodologies and models. We also consider the lessons to be learnt from advances in other areas of simulation and highlight the issues that remain of be addressed.

A systematic framework for molecular dynamics simulations of protein post-translational modifications

By directly affecting structure, dynamics and interaction networks of their targets, post-translational modifications (PTMs) of proteins play a key role in different cellular processes ranging from enzymatic activation to regulation of signal transduction to cell-cycle control. Despite the great importance of understanding how PTMs affect proteins at the atomistic level, a systematic framework for treating post-translationally modified amino acids by molecular dynamics (MD) simulations, a premier high-resolution computational biology tool, has never been developed. Here, we report and validate force field parameters (GROMOS 45a3 and 54a7) required to run and analyze MD simulations of more than 250 different types of enzymatic and non-enzymatic PTMs. The newly developed GROMOS 54a7 parameters in particular exhibit near chemical accuracy in matching experimentally measured hydration free energies (RMSE = 4.2 kJ/mol over the validation set). Using this tool, we quantitatively show that the majority of PTMs greatly alter the hydrophobicity and other physico-chemical properties of target amino acids, with the extent of change in many cases being comparable to the complete range spanned by native amino acids.

Post-translational modifications, i.e. chemical changes of protein amino acids, play a key role in different cellular processes, ranging from enzymatic activation to transcription and translation regulation to disease development and aging. However, our understanding of their effects on protein structure, dynamics and interaction networks at the atomistic level is still largely incomplete. In particular, molecular dynamics simulations, despite their power to provide a high-resolution insight into biomolecular function and underlying mechanisms, have been limited to unmodified, native proteins due to a surprising deficiency of suitable tools and systematically developed parameters for treating modified proteins. To fill this gap, we develop and validate force field parameters, an essential part of the molecular dynamics method, for more than 250 different types of enzymatic and non-enzymatic post-translational modifications. Additionally, using this tool, we quantitatively show that microscopic properties of target amino acids, such as hydrophobicity, are greatly affected by the majority of modifications. The parameters presented in this study greatly expand the range of applicability of computational methods, and in particular molecular dynamics simulations, to a large set of new systems with utmost biological and biomedical importance.

Matching of additive and polarizable force fields for multiscale condensed phase simulations

Inclusion of electronic polarization effects is one of the key aspects in which the accuracy of current biomolecular force fields may be improved. The principal drawback of such approaches is the computational cost, which typically ranges from 3 - 10 times that of the equivalent additive model, and may be greater for more sophisticated treatments of polarization or other many-body effects. Here, we present a multiscale approach which may be used to enhance the sampling in simulations with polarizable models, by using the additive model as a tool to explore configuration space. We use a method based on information theory to determine the charges for an additive model that has optimal overlap with the polarizable one, and we demonstrate the feasibility of enhancing sampling via a hybrid replica exchange scheme for several model systems. An additional advantage is that, in the process, we obtain a systematic method for deriving charges for an additive model that will be the natural complement to its polarizable parent. The additive charges are found by an effective coarse-graining of the polarizable force field, rather than by ad hoc procedures.

On the foldability of tryptophan-containing tetra- and pentapeptides: an exhaustive molecular dynamics study

Short peptides serve as minimal model systems to decipher the determinants of foldability due to their simplicity arising from their smaller size, their ability to echo protein-like structural characteristics, and their direct implication in force field validation. Here, we describe an effort to identify small peptides that can still form stable structures in aqueous solutions. We followed the in silico folding of a selected set of 8640 tryptophan-containing tetra- and pentapeptides through 15 210 molecular dynamics simulations amounting to a total of 272.46 μs using explicit representation of the solute and full treatment of the electrostatics. The evaluation and sorting of peptides is achieved through scoring functions, which include terms based on interatomic vector distances, atomic fluctuations, and rmsd matrices between successive frames of a trajectory. Highly scored peptides are studied further via successive simulation rounds of increasing simulation length and using different empirical force fields. Our method suggested only a handful of peptides with strong foldability prognosis. The discrepancies between the predictions of the various force fields for such short sequences are also extensively discussed. We conclude that the vast majority of such short peptides do not adopt significantly stable structures in water solutions, at least based on our computational predictions. The present work can be utilized in the rational design and engineering of bioactive peptides with desired molecular properties.

Characterization of the free-energy landscapes of proteins by NMR-guided metadynamics

The use of free-energy landscapes rationalizes a wide range of aspects of protein behavior by providing a clear illustration of the different states accessible to these molecules, as well as of their populations and pathways of interconversion. The determination of the free-energy landscapes of proteins by computational methods is, however, very challenging as it requires an extensive sampling of their conformational spaces. We describe here a technique to achieve this goal with relatively limited computational resources by incorporating nuclear magnetic resonance (NMR) chemical shifts as collective variables in metadynamics simulations. As in this approach the chemical shifts are not used as structural restraints, the resulting free-energy landscapes correspond to the force fields used in the simulations. We illustrate this approach in the case of the third Ig-binding domain of protein G from streptococcal bacteria (GB3). Our calculations reveal the existence of a folding intermediate of GB3 with nonnative structural elements. Furthermore, the availability of the free-energy landscape enables the folding mechanism of GB3 to be elucidated by analyzing the conformational ensembles corresponding to the native, intermediate, and unfolded states, as well as the transition states between them. Taken together, these results show that, by incorporating experimental data as collective variables in metadynamics simulations, it is possible to enhance the sampling efficiency by two or more orders of magnitude with respect to standard molecular dynamics simulations, and thus to estimate free-energy differences among the different states of a protein with a k(B)T accuracy by generating trajectories of just a few microseconds.