Atomistic Description of the Folding of a Dimeric Protein

Machine learning coarse-grained potentials of protein thermodynamics

A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics.

Binding-and-Folding Recognition of an Intrinsically Disordered Protein Using Online Learning Molecular Dynamics

Intrinsically disordered proteins participate in many biological processes by folding upon binding to other proteins. However, coupled folding and binding processes are not well understood from an atomistic point of view. One of the main questions is whether folding occurs prior to or after binding. Here we use a novel, unbiased, high-throughput adaptive sampling approach to reconstruct the binding and folding between the disordered transactivation domain of c-Myb and the KIX domain of the CREB-binding protein. The reconstructed long-term dynamical process highlights the binding of a short stretch of amino acids on c-Myb as a folded α-helix. Leucine residues, especially Leu298-Leu302, establish initial native contacts that prime the binding and folding of the rest of the peptide, with a mixture of conformational selection on the N-terminal region with an induced fit of the C-terminal.

Transient exposure of a buried phosphorylation site in an autoinhibited protein

Autoinhibition is a mechanism used to regulate protein function, often by making functional sites inaccessible through the interaction with a cis-acting inhibitory domain. Such autoinhibitory domains often display a substantial degree of structural disorder when unbound, and only become structured in the inhibited state. These conformational dynamics make it difficult to study the structural origin of regulation, including effects of regulatory post-translational modifications. Here, we study the autoinhibition of the Dbl Homology domain in the protein Vav1 by the so-called acidic inhibitory domain. We use molecular simulations to study the process by which a mostly unstructured inhibitory domain folds upon binding and how transient exposure of a key buried tyrosine residue makes it accessible for phosphorylation. We show that the inhibitory domain, which forms a helix in the bound and inhibited stated, samples helical structures already before binding and that binding occurs via a molten-globule-like intermediate state. Together, our results shed light on key interactions that enable the inhibitory domain to sample a finely tuned equilibrium between an inhibited and a kinase-accessible state.

Native or Non-Native Protein-Protein Docking Models? Molecular Dynamics to the Rescue

Molecular docking excels at creating a plethora of potential models of protein-protein complexes. To correctly distinguish the favorable, native-like models from the remaining ones remains, however, a challenge. We assessed here if a protocol based on molecular dynamics (MD) simulations would allow distinguishing native from non-native models to complement scoring functions used in docking. To this end, the first models for 25 protein-protein complexes were generated using HADDOCK. Next, MD simulations complemented with machine learning were used to discriminate between native and non-native complexes based on a combination of metrics reporting on the stability of the initial models. Native models showed higher stability in almost all measured properties, including the key ones used for scoring in the Critical Assessment of PRedicted Interaction (CAPRI) competition, namely the positional root mean square deviations and fraction of native contacts from the initial docked model. A random forest classifier was trained, reaching a 0.85 accuracy in correctly distinguishing native from non-native complexes. Reasonably modest simulation lengths of the order of 50-100 ns are sufficient to reach this accuracy, which makes this approach applicable in practice.

Biomolecular modeling thrives in the age of technology

The biomolecular modeling field has flourished since its early days in the 1970s due to the rapid adaptation and tailoring of state-of-the-art technology. The resulting dramatic increase in size and timespan of biomolecular simulations has outpaced Moore's law. Here, we discuss the role of knowledge-based versus physics-based methods and hardware versus software advances in propelling the field forward. This rapid adaptation and outreach suggests a bright future for modeling, where theory, experimentation and simulation define three pillars needed to address future scientific and biomedical challenges.

Amyloid assembly is dominated by misregistered kinetic traps on an unbiased energy landscape

Atomistic description of protein fibril formation has been elusive due to the complexity and long time scales of the conformational search. Here, we develop a multiscale approach combining numerous atomistic simulations in explicit solvent to construct Markov State Models (MSMs) of fibril growth. The search for the in-register fully bound fibril state is modeled as a random walk on a rugged two-dimensional energy landscape defined by β-sheet alignment and hydrogen-bonding states, whereas transitions involving states without hydrogen bonds are derived from kinetic clustering. The reversible association/dissociation of an incoming peptide and overall growth kinetics are then computed from MSM simulations. This approach is applied to derive a parameter-free, comprehensive description of fibril elongation of Aβ_16-22 and how it is modulated by phenylalanine-to-cyclohexylalanine (CHA) mutations. The trajectories show an aggregation mechanism in which the peptide spends most of its time trapped in misregistered β-sheet states connected by weakly bound states twith short lifetimes. Our results recapitulate the experimental observation that mutants CHA19 and CHA1920 accelerate fibril elongation but have a relatively minor effect on the critical concentration for fibril growth. Importantly, the kinetic consequences of mutations arise from cumulative effects of perturbing the network of productive and nonproductive pathways of fibril growth. This is consistent with the expectation that nonfunctional states will not have evolved efficient folding pathways and, therefore, will require a random search of configuration space. This study highlights the importance of describing the complete energy landscape when studying the elongation mechanism and kinetics of protein fibrils.

Atomic-level characterization of protein-protein association

Most proteins associate with other proteins to function, forming complexes that are central to almost all physiological processes. Determining the structures of these complexes and understanding how they associate are problems of fundamental importance. Using long-timescale molecular dynamics simulations, some performed using a new enhanced sampling method, we observed spontaneous association and dissociation of five protein–protein systems to and from their experimentally determined native complexes. By analyzing the simulations of these five systems, which include members of diverse structural and functional classes, we are able to draw general mechanistic conclusions about protein association.

Despite the biological importance of protein–protein complexes, determining their structures and association mechanisms remains an outstanding challenge. Here, we report the results of atomic-level simulations in which we observed five protein–protein pairs repeatedly associate to, and dissociate from, their experimentally determined native complexes using a molecular dynamics (MD)–based sampling approach that does not make use of any prior structural information about the complexes. To study association mechanisms, we performed additional, conventional MD simulations, in which we observed numerous spontaneous association events. A shared feature of native association for these five structurally and functionally diverse protein systems was that if the proteins made contact far from the native interface, the native state was reached by dissociation and eventual reassociation near the native interface, rather than by extensive interfacial exploration while the proteins remained in contact. At the transition state (the conformational ensemble from which association to the native complex and dissociation are equally likely), the protein–protein interfaces were still highly hydrated, and no more than 20% of native contacts had formed.

Atomic-Level Description of Protein Folding inside the GroEL Cavity

Chaperonins (ubiquitous facilitators of protein folding) sequester misfolded proteins within an internal cavity, thus preventing protein aggregation during the process of refolding. GroEL, a tetradecameric bacterial chaperonin, is one of the most studied chaperonins, but the role of the internal cavity in the refolding process is still unclear. It has been suggested that rather than simply isolating proteins while they refold, the GroEL cavity actively promotes protein folding. A detailed characterization of the folding dynamics and thermodynamics of protein substrates encapsulated within the cavity, however, has been difficult to obtain by experimental means, due to the system's complexity and the many steps in the folding cycle. Here, we examine the influence of the GroEL cavity on protein folding based on the results of unbiased, atomistic molecular dynamics simulations. We first verified that the computational setup, which uses a recently developed state-of-the-art force field that more accurately reproduces the aggregation propensity of unfolded states, could recapitulate the essential structural dynamics of GroEL. In these simulations, the GroEL tetradecamer was highly dynamic, transitioning among states corresponding to most of the structures that have been observed experimentally. We then simulated a small, unfolded protein both in the GroEL cavity and in bulk solution and compared the protein's folding process within these two environments. Inside the GroEL cavity, the unfolded protein interacted strongly with the disordered residues in GroEL's C-terminal tails. These interactions stabilized the protein's unfolded states relative to its compact states and increased the roughness of its folding free-energy surface, resulting in slower folding compared to the rate in solution. For larger proteins, which are more typical GroEL substrates, we speculate that these interactions may allow substrates to more quickly escape kinetic traps associated with compact, misfolded states, thereby actively promoting folding.

Heterodimer Binding Scaffolds Recognition via the Analysis of Kinetically Hot Residues

Physical interactions between proteins are often difficult to decipher. The aim of this paper is to present an algorithm that is designed to recognize binding patches and supporting structural scaffolds of interacting heterodimer proteins using the Gaussian Network Model (GNM). The recognition is based on the (self) adjustable identification of kinetically hot residues and their connection to possible binding scaffolds. The kinetically hot residues are residues with the lowest entropy, i.e., the highest contribution to the weighted sum of the fastest modes per chain extracted via GNM. The algorithm adjusts the number of fast modes in the GNM's weighted sum calculation using the ratio of predicted and expected numbers of target residues (contact and the neighboring first-layer residues). This approach produces very good results when applied to dimers with high protein sequence length ratios. The protocol's ability to recognize near native decoys was compared to the ability of the residue-level statistical potential of Lu and Skolnick using the Sternberg and Vakser decoy dimers sets. The statistical potential produced better overall results, but in a number of cases its predicting ability was comparable, or even inferior, to the prediction ability of the adjustable GNM approach. The results presented in this paper suggest that in heterodimers at least one protein has interacting scaffold determined by the immovable, kinetically hot residues. In many cases, interacting proteins (especially if being of noticeably different sizes) either behave as a rigid lock and key or, presumably, exhibit the opposite dynamic behavior. While the binding surface of one protein is rigid and stable, its partner's interacting scaffold is more flexible and adaptable.

Simple MD-based model for oxidative folding of peptides and proteins

Significant strides have been recently made to fold peptides and small proteins in silico using MD simulations. However, facilities are currently lacking to include disulfide bonding in the MD models of protein folding. To address this problem, we have developed a simple empirical protocol to model formation of disulfides, which is perturbation-free, retains the same speed as conventional MD simulations and allows one to control the reaction rate. The new protocol has been tested on 15-aminoacid peptide guanylin containing four cysteine residues; the net simulation time using Amber ff14SB force field was 61 μs. The resulting isomer distribution is in qualitative agreement with experiment, suggesting that oxidative folding of guanylin in vitro occurs under kinetic control. The highly stable conformation of the so-called isomer 2(B) has been obtained for full-length guanylin, which is significantly different from the poorly ordered structure of the truncated peptide PDB ID 1GNB. In addition, we have simulated oxidative folding of guanylin within the 94-aminoacid prohormone proguanylin. The obtained structure is in good agreement with the NMR coordinates 1O8R. The proposed modeling strategy can help to explore certain fundamental aspects of protein folding and is potentially relevant for manufacturing of synthetic peptides and recombinant proteins.

Complete protein-protein association kinetics in atomic detail revealed by molecular dynamics simulations and Markov modelling

Protein-protein association is fundamental to many life processes. However, a microscopic model describing the structures and kinetics during association and dissociation is lacking on account of the long lifetimes of associated states, which have prevented efficient sampling by direct molecular dynamics (MD) simulations. Here we demonstrate protein-protein association and dissociation in atomistic resolution for the ribonuclease barnase and its inhibitor barstar by combining adaptive high-throughput MD simulations and hidden Markov modelling. The model reveals experimentally consistent intermediate structures, energetics and kinetics on timescales from microseconds to hours. A variety of flexibly attached intermediates and misbound states funnel down to a transition state and a native basin consisting of the loosely bound near-native state and the tightly bound crystallographic state. These results offer a deeper level of insight into macromolecular recognition and our approach opens the door for understanding and manipulating a wide range of macromolecular association processes.

Computational Redesign of Thioredoxin Is Hypersensitive toward Minor Conformational Changes in the Backbone Template

Despite the development of powerful computational tools, the full-sequence design of proteins still remains a challenging task. To investigate the limits and capabilities of computational tools, we conducted a study of the ability of the program Rosetta to predict sequences that recreate the authentic fold of thioredoxin. Focusing on the influence of conformational details in the template structures, we based our study on 8 experimentally determined template structures and generated 120 designs from each. For experimental evaluation, we chose six sequences from each of the eight templates by objective criteria. The 48 selected sequences were evaluated based on their progressive ability to (1) produce soluble protein in Escherichia coli and (2) yield stable monomeric protein, and (3) on the ability of the stable, soluble proteins to adopt the target fold. Of the 48 designs, we were able to synthesize 32, 20 of which resulted in soluble protein. Of these, only two were sufficiently stable to be purified. An X-ray crystal structure was solved for one of the designs, revealing a close resemblance to the target structure. We found a significant difference among the eight template structures to realize the above three criteria despite their high structural similarity. Thus, in order to improve the success rate of computational full-sequence design methods, we recommend that multiple template structures are used. Furthermore, this study shows that special care should be taken when optimizing the geometry of a structure prior to computational design when using a method that is based on rigid conformations.

More than a look into a crystal ball: protein structure elucidation guided by molecular dynamics simulations

The 'form follows function' principle implies that a structural determination of protein structures is indispensable to understand proteins in their biological roles. However, experimental methods still show shortcomings in the description of the dynamic properties of proteins. Therefore, molecular dynamics (MD) simulations represent an essential tool for structural biology to investigate proteins as flexible and dynamic entities. Here, we will give an overview on the impact of MD simulations on structural investigations, including studies that aim at a prediction of protein-folding pathways, protein-assembly processes and the sampling of conformational space by computational means.

A many-body term improves the accuracy of effective potentials based on protein coevolutionary data

The study of correlated mutations in alignments of homologous proteins proved to be successful not only in the prediction of their native conformation but also in the development of a two-body effective potential between pairs of amino acids. In the present work, we extend the effective potential, introducing a many-body term based on the same theoretical framework, making use of a principle of maximum entropy. The extended potential performs better than the two-body one in predicting the energetic effect of 308 mutations in 14 proteins (including membrane proteins). The average value of the parameters of the many-body term correlates with the degree of hydrophobicity of the corresponding residues, suggesting that this term partly reflects the effect of the solvent.

Efficient molecular dynamics using geodesic integration and solvent-solute splitting

We present an approach to Langevin dynamics in the presence of holonomic constraints based on decomposition of the system into components representing geodesic flow, constrained impulse and constrained diffusion. We show that a particular ordering of the components results in an integrator that is an order of magnitude more accurate for configurational averages than existing alternatives. Moreover, by combining the geodesic integration method with a solvent-solute force splitting, we demonstrate that stepsizes of at least 8 fs can be used for solvated biomolecules with high sampling accuracy and without substantially altering diffusion rates, approximately increasing by a factor of two the efficiency of molecular dynamics sampling for such systems. The methods described in this article are easily implemented using the standard apparatus of modern simulation codes.

Encapsulated membrane proteins: A simplified system for molecular simulation

Over the past 50years there has been considerable progress in our understanding of biomolecular interactions at an atomic level. This in turn has allowed molecular simulation methods employing full atomistic modelling at ever larger scales to develop. However, some challenging areas still remain where there is either a lack of atomic resolution structures or where the simulation system is inherently complex. An area where both challenges are present is that of membranes containing membrane proteins. In this review we analyse a new practical approach to membrane protein study that offers a potential new route to high resolution structures and the possibility to simplify simulations. These new approaches collectively recognise that preservation of the interaction between the membrane protein and the lipid bilayer is often essential to maintain structure and function. The new methods preserve these interactions by producing nano-scale disc shaped particles that include bilayer and the chosen protein. Currently two approaches lead in this area: the MSP system that relies on peptides to stabilise the discs, and SMALPs where an amphipathic styrene maleic acid copolymer is used. Both methods greatly enable protein production and hence have the potential to accelerate atomic resolution structure determination as well as providing a simplified format for simulations of membrane protein dynamics. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Structural origin of slow diffusion in protein folding

Experimental, theoretical, and computational studies of small proteins suggest that interresidue contacts not present in the folded structure play little or no role in the self-assembly mechanism. Non-native contacts can, however, influence folding kinetics by introducing additional local minima that slow diffusion over the global free-energy barrier between folded and unfolded states. Here, we combine single-molecule fluorescence with all-atom molecular dynamics simulations to discover the structural origin for the slow diffusion that markedly decreases the folding rate for a designed α-helical protein. Our experimental determination of transition path times and our analysis of the simulations point to non-native salt bridges between helices as the source, which provides a quantitative glimpse of how specific intramolecular interactions influence protein folding rates by altering dynamics and not activation free energies.

Temperature Accelerated Molecular Dynamics with Soft-Ratcheting Criterion Orients Enhanced Sampling by Low-Resolution Information

Many proteins exhibit an equilibrium between multiple conformations, some of them being characterized only by low-resolution information. Visiting all conformations is a demanding task for computational techniques performing enhanced but unfocused exploration of collective variable (CV) space. Otherwise, pulling a structure toward a target condition biases the exploration in a way difficult to assess. To address this problem, we introduce here the soft-ratcheting temperature-accelerated molecular dynamics (sr-TAMD), where the exploration of CV space by TAMD is coupled to a soft-ratcheting algorithm that filters the evolving CV values according to a predefined criterion. Any low resolution or even qualitative information can be used to orient the exploration. We validate this technique by exploring the conformational space of the inactive state of the catalytic domain of the adenyl cyclase AC from Bordetella pertussis. The domain AC gets activated by association with calmodulin (CaM), and the available crystal structure shows that in the complex the protein has an elongated shape. High-resolution data are not available for the inactive, CaM-free protein state, but hydrodynamic measurements have shown that the inactive AC displays a more globular conformation. Here, using as CVs several geometric centers, we use sr-TAMD to enhance CV space sampling while filtering for CV values that correspond to centers moving close to each other, and we thus rapidly visit regions of conformational space that correspond to globular structures. The set of conformations sampled using sr-TAMD provides the most extensive description of the inactive state of AC up to now, consistent with available experimental information.

Assessing the potential of atomistic molecular dynamics simulations to probe reversible protein-protein recognition and binding

Protein-protein recognition and binding are governed by diffusion, noncovalent forces and conformational flexibility, entangled in a way that only molecular dynamics simulations can dissect at high resolution. Here we exploited ubiquitin's noncovalent dimerization equilibrium to assess the potential of atomistic simulations to reproduce reversible protein-protein binding, by running submicrosecond simulations of systems with multiple copies of the protein at millimolar concentrations. The simulations essentially fail because they lead to aggregates, yet they reproduce some specificity in the binding interfaces as observed in known covalent and noncovalent ubiquitin dimers. Following similar observations in literature we hint at electrostatics and water descriptions as the main liable force field elements, and propose that their optimization should consider observables relevant to multi-protein systems and unfolded proteins. Within limitations, analysis of binding events suggests salient features of protein-protein recognition and binding, to be retested with improved force fields. Among them, that specific configurations of relative direction and orientation seem to trigger fast binding of two molecules, even over 50 Å distances; that conformational selection can take place within surface-to-surface distances of 10 to 40 Å i.e. well before actual intermolecular contact; and that establishment of contacts between molecules further locks their conformations and relative orientations.

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.

Dynamical phase transitions reveal amyloid-like states on protein folding landscapes

Developing an understanding of protein misfolding processes presents a crucial challenge for unlocking the mysteries of human disease. In this article, we present our observations of β-sheet-rich misfolded states on a number of protein dynamical landscapes investigated through molecular dynamics simulation and Markov state models. We employ a nonequilibrium statistical mechanical theory to identify the glassy states in a protein's dynamics, and we discuss the nonnative, β-sheet-rich states that play a distinct role in the slowest dynamics within seven protein folding systems. We highlight the fundamental similarity between these states and the amyloid structures responsible for many neurodegenerative diseases, and we discuss potential consequences for mechanisms of protein aggregation and intermolecular amyloid formation.

Physics-based potentials for the coupling between backbone- and side-chain-local conformational states in the UNited RESidue (UNRES) force field for protein simulations

The UNited RESidue (UNRES) model of polypeptide chains is a coarse-grained model in which each amino-acid residue is reduced to two interaction sites, namely, a united peptide group (p) located halfway between the two neighboring α-carbon atoms (Cαs), which serve only as geometrical points, and a united side chain (SC) attached to the respective Cα. Owing to this simplification, millisecond molecular dynamics simulations of large systems can be performed. While UNRES predicts overall folds well, it reproduces the details of local chain conformation with lower accuracy. Recently, we implemented new knowledge-based torsional potentials (Krupa et al. J. Chem. Theory Comput. 2013, 9, 4620–4632) that depend on the virtual-bond dihedral angles involving side chains: Cα···Cα···Cα···SC (τ(1)), SC···Cα···Cα···Cα (τ(2)), and SC···Cα···Cα···SC (τ(3)) in the UNRES force field. These potentials resulted in significant improvement of the simulated structures, especially in the loop regions. In this work, we introduce the physics-based counterparts of these potentials, which we derived from the all-atom energy surfaces of terminally blocked amino-acid residues by Boltzmann integration over the angles λ(1) and λ(2) for rotation about the Cα···Cα virtual-bond angles and over the side-chain angles χ. The energy surfaces were, in turn, calculated by using the semiempirical AM1 method of molecular quantum mechanics. Entropy contribution was evaluated with use of the harmonic approximation from Hessian matrices. One-dimensional Fourier series in the respective virtual-bond-dihedral angles were fitted to the calculated potentials, and these expressions have been implemented in the UNRES force field. Basic calibration of the UNRES force field with the new potentials was carried out with eight training proteins, by selecting the optimal weight of the new energy terms and reducing the weight of the regular torsional terms. The force field was subsequently benchmarked with a set of 22 proteins not used in the calibration. The new potentials result in a decrease of the root-mean-square deviation of the average conformation from the respective experimental structure by 0.86 Å on average; however, improvement of up to 5 Å was observed for some proteins.

Mechanistic studies of the biogenesis and folding of outer membrane proteins in vitro and in vivo: what have we learned to date?

Research into the mechanisms by which proteins fold into their native structures has been on-going since the work of Anfinsen in the 1960s. Since that time, the folding mechanisms of small, water-soluble proteins have been well characterised. By contrast, progress in understanding the biogenesis and folding mechanisms of integral membrane proteins has lagged significantly because of the need to create a membrane mimetic environment for folding studies in vitro and the difficulties in finding suitable conditions in which reversible folding can be achieved. Improved knowledge of the factors that promote membrane protein folding and disfavour aggregation now allows studies of folding into lipid bilayers in vitro to be performed. Consequently, mechanistic details and structural information about membrane protein folding are now emerging at an ever increasing pace. Using the panoply of methods developed for studies of the folding of water-soluble proteins. This review summarises current knowledge of the mechanisms of outer membrane protein biogenesis and folding into lipid bilayers in vivo and in vitro and discusses the experimental techniques utilised to gain this information. The emerging knowledge is beginning to allow comparisons to be made between the folding of membrane proteins with current understanding of the mechanisms of folding of water-soluble proteins.

Iterative derivation of effective potentials to sample the conformational space of proteins at atomistic scale

The current capacity of computers makes it possible to perform simulations of small systems with portable, explicit-solvent potentials achieving high degree of accuracy. However, simplified models must be employed to exploit the behavior of large systems or to perform systematic scans of smaller systems. While powerful algorithms are available to facilitate the sampling of the conformational space, successful applications of such models are hindered by the availability of simple enough potentials able to satisfactorily reproduce known properties of the system. We develop an interatomic potential to account for a number of properties of proteins in a computationally economic way. The potential is defined within an all-atom, implicit solvent model by contact functions between the different atom types. The associated numerical values can be optimized by an iterative Monte Carlo scheme on any available experimental data, provided that they are expressible as thermal averages of some conformational properties. We test this model on three different proteins, for which we also perform a scan of all possible point mutations with explicit conformational sampling. The resulting models, optimized solely on a subset of native distances, not only reproduce the native conformations within a few Angstroms from the experimental ones, but show the cooperative transition between native and denatured state and correctly predict the measured free-energy changes associated with point mutations. Moreover, differently from other structure-based models, our method leaves a residual degree of frustration, which is known to be present in protein molecules.

Web-based computational chemistry education with CHARMMing I: Lessons and tutorial

This article describes the development, implementation, and use of web-based “lessons” to introduce students and other newcomers to computer simulations of biological macromolecules. These lessons, i.e., interactive step-by-step instructions for performing common molecular simulation tasks, are integrated into the collaboratively developed CHARMM INterface and Graphics (CHARMMing) web user interface (http://www.charmming.org). Several lessons have already been developed with new ones easily added via a provided Python script. In addition to CHARMMing's new lessons functionality, web-based graphical capabilities have been overhauled and are fully compatible with modern mobile web browsers (e.g., phones and tablets), allowing easy integration of these advanced simulation techniques into coursework. Finally, one of the primary objections to web-based systems like CHARMMing has been that “point and click” simulation set-up does little to teach the user about the underlying physics, biology, and computational methods being applied. In response to this criticism, we have developed a freely available tutorial to bridge the gap between graphical simulation setup and the technical knowledge necessary to perform simulations without user interface assistance.

Folding of fourteen small proteins with a residue-specific force field and replica-exchange molecular dynamics

Ab initio protein folding via physical-based all-atom simulation is still quite challenging. Using a recently developed residue-specific force field (RSFF1) in explicit solvent, we are able to fold a diverse set of 14 model proteins. The obtained structural features of unfolded state are in good agreement with previous observations. The replica-exchange molecular dynamics simulation is found to be efficient, resulting in multiple folding events for each protein. Transition path time is found to be significantly reduced under elevated temperature.

Theoretical volume profiles as a tool for probing transition states: folding kinetics

The mechanism by which conformational changes, particularly folding and unfolding, occur in proteins and other biopolymers has been widely discussed in the literature. Molecular dynamics (MD) simulations of protein folding present a formidable challenge since these conformational changes occur on a time scale much longer than what can be afforded at the current level of computational technology. Transition state (TS) theory offers a more economic description of kinetic properties of a reaction system by relating them to the properties of the TS, or for flexible systems, the TS ensemble (TSE). The application of TS theory to protein folding is limited by ambiguity in the definition of the TSE for this process. We propose to identify the TSE for conformational changes in flexible systems by comparison of its experimentally determined volumetric property, known as the volume of activation, to the structure-specific volume profile of the process calculated using MD. We illustrate this approach by its successful application to unfolding of a model chain system.

Fast protein folding kinetics

Fast-folding proteins have been a major focus of computational and experimental study because they are accessible to both techniques: they are small and fast enough to be reasonably simulated with current computational power, but have dynamics slow enough to be observed with specially developed experimental techniques. This coupled study of fast-folding proteins has provided insight into the mechanisms, which allow some proteins to find their native conformation well <1 ms and has uncovered examples of theoretically predicted phenomena such as downhill folding. The study of fast folders also informs our understanding of even 'slow' folding processes: fast folders are small; relatively simple protein domains and the principles that govern their folding also govern the folding of more complex systems. This review summarizes the major theoretical and experimental techniques used to study fast-folding proteins and provides an overview of the major findings of fast-folding research. Finally, we examine the themes that have emerged from studying fast folders and briefly summarize their application to protein folding in general, as well as some work that is left to do.

Free-energy landscape of protein oligomerization from atomistic simulations

In the realm of protein-protein interactions, the assembly process of homooligomers plays a fundamental role because the majority of proteins fall into this category. A comprehensive understanding of this multistep process requires the characterization of the driving molecular interactions and the transient intermediate species. The latter are often short-lived and thus remain elusive to most experimental investigations. Molecular simulations provide a unique tool to shed light onto these complex processes complementing experimental data. Here we combine advanced sampling techniques, such as metadynamics and parallel tempering, to characterize the oligomerization landscape of fibritin foldon domain. This system is an evolutionarily optimized trimerization motif that represents an ideal model for experimental and computational mechanistic studies. Our results are fully consistent with previous experimental nuclear magnetic resonance and kinetic data, but they provide a unique insight into fibritin foldon assembly. In particular, our simulations unveil the role of nonspecific interactions and suggest that an interplay between thermodynamic bias toward native structure and residual conformational disorder may provide a kinetic advantage.