Developing a molecular dynamics force field for both folded and disordered protein states.

Molecular dynamics (MD) simulation is a valuable tool for characterizing the structural dynamics of folded proteins and should be similarly applicable to disordered proteins and proteins with both folded and disordered regions. It has been unclear, however, whether any physical model (force field) used in MD simulations accurately describes both folded and disordered proteins. Here, we select a benchmark set of 21 systems, including folded and disordered proteins, simulate these systems with six state-of-the-art force fields, and compare the results to over 9,000 available experimental data points. We find that none of the tested force fields simultaneously provided accurate descriptions of folded proteins, of the dimensions of disordered proteins, and of the secondary structure propensities of disordered proteins. Guided by simulation results on a subset of our benchmark, however, we modified parameters of one force field, achieving excellent agreement with experiment for disordered proteins, while maintaining state-of-the-art accuracy for folded proteins. The resulting force field, a99SB-disp, should thus greatly expand the range of biological systems amenable to MD simulation. A similar approach could be taken to improve other force fields.

RNA force field with accuracy comparable to state-of-the-art protein force fields.

Molecular dynamics (MD) simulation has become a powerful tool for characterizing at an atomic level of detail the conformational changes undergone by proteins. The application of such simulations to RNA structures, however, has proven more challenging, due in large part to the fact that the physical models ("force fields") available for MD simulations of RNA molecules are substantially less accurate in many respects than those currently available for proteins. Here, we introduce an extensive revision of a widely used RNA force field in which the parameters have been modified, based on quantum mechanical calculations and existing experimental information, to more accurately reflect the fundamental forces that stabilize RNA structures. We evaluate these revised parameters through long-timescale MD simulations of a set of RNA molecules that covers a wide range of structural complexity, including single-stranded RNAs, RNA duplexes, RNA hairpins, and riboswitches. The structural and thermodynamic properties measured in these simulations exhibited dramatically improved agreement with experimentally determined values. Based on the comparisons we performed, this RNA force field appears to achieve a level of accuracy comparable to that of state-of-the-art protein force fields, thus significantly advancing the utility of MD simulation as a tool for elucidating the structural dynamics and function of RNA molecules and RNA-containing biological assemblies.

Mechanism of Coupled Folding-upon-Binding of an Intrinsically Disordered Protein.

Intrinsically disordered proteins (IDPs), which in isolation do not adopt a well-defined tertiary structure but instead populate a structurally heterogeneous ensemble of interconverting states, play important roles in many biological pathways. IDPs often fold into ordered states upon binding to their physiological interaction partners (a so-called "folding-upon-binding" process), but it has proven difficult to obtain an atomic-level description of the structural mechanisms by which they do so. Here, we describe in atomic detail the folding-upon-binding mechanism of an IDP segment to its binding partner, as observed in unbiased molecular dynamics simulations. In our simulations, we observed over 70 binding and unbinding events between the α-helical molecular recognition element (α-MoRE) of the intrinsically disordered C-terminal domain of the measles virus nucleoprotein (NTAIL) and the X domain (XD) of the measles virus phosphoprotein complex. We found that folding-upon-binding primarily occurred through induced-folding pathways (in which intermolecular contacts form before or concurrently with the secondary structure of the disordered protein)-an observation supported by previous experiments-and that the transition state ensemble was characterized by formation of just a few key intermolecular contacts and was otherwise highly structurally heterogeneous. We found that when a large amount of helical content was present early in a transition path, NTAIL typically unfolded and then refolded after additional intermolecular contacts formed. We also found that, among conformations with similar numbers of intermolecular contacts, those with less helical content had a higher probability of ultimately forming the native complex than conformations with more helical content, which were more likely to unbind. These observations suggest that even after intermolecular contacts have formed, disordered regions can have a kinetic advantage over folded regions in the folding-upon-binding process.

Identifying localized changes in large systems: Change-point detection for biomolecular simulations.

Research on change-point detection, the classical problem of detecting abrupt changes in sequential data, has focused predominantly on datasets with a single observable. A growing number of time series datasets, however, involve many observables, often with the property that a given change typically affects only a few of the observables. We introduce a general statistical method that, given many noisy observables, detects points in time at which various subsets of the observables exhibit simultaneous changes in data distribution and explicitly identifies those subsets. Our work is motivated by the problem of identifying the nature and timing of biologically interesting conformational changes that occur during atomic-level simulations of biomolecules such as proteins. This problem has proved challenging both because each such conformational change might involve only a small region of the molecule and because these changes are often subtle relative to the ever-present background of faster structural fluctuations. We show that our method is effective in detecting biologically interesting conformational changes in molecular dynamics simulations of both folded and unfolded proteins, even in cases where these changes are difficult to detect using alternative techniques. This method may also facilitate the detection of change points in other types of sequential data involving large numbers of observables--a problem likely to become increasingly important as such data continue to proliferate in a variety of application domains.

Atomic-level description of ubiquitin folding.

Equilibrium molecular dynamics simulations, in which proteins spontaneously and repeatedly fold and unfold, have recently been used to help elucidate the mechanistic principles that underlie the folding of fast-folding proteins. The extent to which the conclusions drawn from the analysis of such proteins, which fold on the microsecond timescale, apply to the millisecond or slower folding of naturally occurring proteins is, however, unclear. As a first attempt to address this outstanding issue, we examine here the folding of ubiquitin, a 76-residue-long protein found in all eukaryotes that is known experimentally to fold on a millisecond timescale. Ubiquitin folding has been the subject of many experimental studies, but its slow folding rate has made it difficult to observe and characterize the folding process through all-atom molecular dynamics simulations. Here we determine the mechanism, thermodynamics, and kinetics of ubiquitin folding through equilibrium atomistic simulations. The picture emerging from the simulations is in agreement with a view of ubiquitin folding suggested from previous experiments. Our findings related to the folding of ubiquitin are also consistent, for the most part, with the folding principles derived from the simulation of fast-folding proteins, suggesting that these principles may be applicable to a wider range of proteins.

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.

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.

Refinement of protein structure homology models via long, all-atom molecular dynamics simulations.

Accurate computational prediction of protein structure represents a longstanding challenge in molecular biology and structure-based drug design. Although homology modeling techniques are widely used to produce low-resolution models, refining these models to high resolution has proven difficult. With long enough simulations and sufficiently accurate force fields, molecular dynamics (MD) simulations should in principle allow such refinement, but efforts to refine homology models using MD have for the most part yielded disappointing results. It has thus far been unclear whether MD-based refinement is limited primarily by accessible simulation timescales, force field accuracy, or both. Here, we examine MD as a technique for homology model refinement using all-atom simulations, each at least 100 µs long-more than 100 times longer than previous refinement simulations-and a physics-based force field that was recently shown to successfully fold a structurally diverse set of fast-folding proteins. In MD simulations of 24 proteins chosen from the refinement category of recent Critical Assessment of Structure Prediction (CASP) experiments, we find that in most cases, simulations initiated from homology models drift away from the native structure. Comparison with simulations initiated from the native structure suggests that force field accuracy is the primary factor limiting MD-based refinement. This problem can be mitigated to some extent by restricting sampling to the neighborhood of the initial model, leading to structural improvement that, while limited, is roughly comparable to the leading alternative methods.

Structure and dynamics of an unfolded protein examined by molecular dynamics simulation.

The accurate characterization of the structure and dynamics of proteins in disordered states is a difficult problem at the frontier of structural biology whose solution promises to further our understanding of protein folding and intrinsically disordered proteins. Molecular dynamics (MD) simulations have added considerably to our understanding of folded proteins, but the accuracy with which the force fields used in such simulations can describe disordered proteins is unclear. In this work, using a modern force field, we performed a 200 µs unrestrained MD simulation of the acid-unfolded state of an experimentally well-characterized protein, ACBP, to explore the extent to which state-of-the-art simulation can describe the structural and dynamical features of a disordered protein. By comparing the simulation results with the results of NMR experiments, we demonstrate that the simulation successfully captures important aspects of both the local and global structure. Our simulation was ~2 orders of magnitude longer than those in previous studies of unfolded proteins, a length sufficient to observe repeated formation and breaking of helical structure, which we found to occur on a multimicrosecond time scale. We observed one structural feature that formed but did not break during the simulation, highlighting the difficulty in sampling disordered states. Overall, however, our simulation results are in reasonable agreement with the experimental data, demonstrating that MD simulations can already be useful in describing disordered proteins. Finally, our direct calculation of certain NMR observables from the simulation provides new insight into the general relationship between structural features of disordered proteins and experimental NMR relaxation properties.

Identification of two distinct inactive conformations of the beta2-adrenergic receptor reconciles structural and biochemical observations.

Fully understanding the mechanisms of signaling proteins such as G protein-coupled receptors (GPCRs) will require the characterization of their conformational states and the pathways connecting those states. The recent crystal structures of the beta(2)- and beta(1)-adrenergic receptors in a nominally inactive state constituted a major advance toward this goal, but also raised new questions. Although earlier biochemical observations had suggested that these receptors possessed a set of contacts between helices 3 and 6, known as the ionic lock, which was believed to form a molecular switch for receptor activation, the crystal structures lacked these contacts. The unexpectedly broken ionic lock has raised questions about the true conformation(s) of the inactive state and the role of the ionic lock in receptor activation and signaling. To address these questions, we performed microsecond-timescale molecular dynamics simulations of the beta(2)-adrenergic receptor (beta(2)AR) in multiple wild-type and mutant forms. In wild-type simulations, the ionic lock formed reproducibly, bringing the intracellular ends of helices 3 and 6 together to adopt a conformation similar to that found in inactive rhodopsin. Our results suggest that inactive beta(2)AR exists in equilibrium between conformations with the lock formed and the lock broken, whether or not the cocrystallized ligand is present. These findings, along with the formation of several secondary structural elements in the beta(2)AR loops during our simulations, may provide a more comprehensive picture of the inactive state of the beta-adrenergic receptors, reconciling the crystal structures with biochemical studies.

Development of Force Field Parameters for the Simulation of Single- and Double-Stranded DNA Molecules and DNA-Protein Complexes.

Although molecular dynamics (MD) simulations have been used extensively to study the structural dynamics of proteins, the role of MD simulation in studies of nucleic acid based systems has been more limited. One contributing factor to this disparity is the historically lower level of accuracy of the physical models used in such simulations to describe interactions involving nucleic acids. By modifying nonbonded and torsion parameters of a force field from the Amber family of models, we recently developed force field parameters for RNA that achieve a level of accuracy comparable to that of state-of-the-art protein force fields. Here we report force field parameters for DNA, which we developed by transferring nonbonded parameters from our recently reported RNA force field and making subsequent adjustments to torsion parameters. We have also modified the backbone charges in both the RNA and DNA parameter sets to make the treatment of electrostatics compatible with our recently developed variant of the Amber protein and ion force field. We name the force field resulting from the union of these three parameter sets (the new DNA parameters, the revised RNA parameters, and the existing protein and ion parameters) DES-Amber. Extensive testing of DES-Amber indicates that it can describe the thermal stability and conformational flexibility of single- and double-stranded DNA systems with a level of accuracy comparable to or, especially for disordered systems, exceeding that of state-of-the-art nucleic acid force fields. Finally, we show that, in certain favorable cases, DES-Amber can be used for long-timescale simulations of protein-nucleic acid complexes.

Climate change effects on bread wheat phenology and grain quality: A case study in the north of Italy.

Increasing temperatures, heat waves, and reduction of annual precipitation are all the expressions of climate change (CC), strongly affecting bread wheat (Triticum aestivum L.) grain yield in Southern Europe. Being temperature the major driving force of plants' phenological development, these variations also have effects on wheat phenology, with possible consequences on grain quality, and gluten protein accumulation. Here, through a case study in the Bolognese Plain (North of Italy), we assessed the effects of CC in the area, the impacts on bread wheat phenological development, and the consequences on grain gluten quality. The increasing trend in mean annual air temperature in the area since 1952 was significant, with a breakpoint identified in 1989, rising from 12.7 to 14.1°C, accompanied by the signals of increasing aridity, i.e., increase in water table depth. Bread wheat phenological development was compared in two 15-year periods before and after the breakpoint, i.e., 1952-1966 (past period), and 2006-2020 (present period), the latest characterized by aridity and increased temperatures. A significant shortening of the chronological time necessary to reach the main phenological phases was observed for the present period compared to the past period, finally shortening the whole life cycle. This reduction, as well as the higher temperature regime, affected gluten accumulation during the grain-filling process, as emerged analyzing gluten composition in grain samples of the same variety harvested in the area both before and after the breakpoint in temperature. In particular, the proportion of gluten polymers (i.e., gliadins, high and low molecular weight glutenins, and their ratio) showed a strong and significant correlation with cumulative growing degree days (CGDDs) accumulated during the grain filling. Higher CGDD values during the period, typical of CC in Southern Europe, accounting for higher temperature and faster grain filling, correlated with gliadins, high molecular weight glutenins, and their proportion with low molecular weight glutenins. In summary, herein reported, data might contribute to assessing the effects of CC on wheat phenology and quality, representing a tool for both predictive purposes and decision supporting systems for farmers, as well as can guide future breeding choices for varietal innovation.

How robust are protein folding simulations with respect to force field parameterization?

Molecular dynamics simulations hold the promise of providing an atomic-level description of protein folding that cannot easily be obtained from experiments. Here, we examine the extent to which the molecular mechanics force field used in such simulations might influence the observed folding pathways. To that end, we performed equilibrium simulations of a fast-folding variant of the villin headpiece using four different force fields. In each simulation, we observed a large number of transitions between the unfolded and folded states, and in all four cases, both the rate of folding and the structure of the native state were in good agreement with experiments. We found, however, that the folding mechanism and the properties of the unfolded state depend substantially on the choice of force field. We thus conclude that although it is important to match a single, experimentally determined structure and folding rate, this does not ensure that a given simulation will provide a unique and correct description of the full free-energy surface and the mechanism of folding.

Simulating micrometre-scale crystal growth from solution.

Understanding crystal growth is essential for controlling the crystallization used in industrial separation and purification processes. Because solids interact through their surfaces, crystal shape can influence both chemical and physical properties. The thermodynamic morphology can readily be predicted, but most particle shapes are actually controlled by the kinetics of the atomic growth processes through which assembly occurs. Here we study the urea-solvent interface at the nanometre scale and report kinetic Monte Carlo simulations of the micrometre-scale three-dimensional growth of urea crystals. These simulations accurately reproduce experimentally observed crystal growth. Unlike previous models of crystal growth, no assumption is made that the morphology can be constructed from the results for independently growing surfaces or from an a priori specification of surface defect concentration. This approach offers insights into the role of the solvent, the degree of supersaturation, and the contribution that extended defects (such as screw dislocations) make to crystal growth. It also connects observations made at the nanometre scale, through in situ atomic force microscopy, with those made at the macroscopic level. If extended to include additives, the technique could lead to the computer-aided design of crystals.

Improved side-chain torsion potentials for the Amber ff99SB protein force field.

Recent advances in hardware and software have enabled increasingly long molecular dynamics (MD) simulations of biomolecules, exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, we further advance simulation accuracy by improving the amino acid side-chain torsion potentials of the Amber ff99SB force field. First, we used simulations of model alpha-helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, we optimized the side-chain torsion potentials of these residues to match new, high-level quantum-mechanical calculations. Finally, we used microsecond-timescale MD simulations in explicit solvent to validate the resulting force field against a large set of experimental NMR measurements that directly probe side-chain conformations. The new force field, which we have termed Amber ff99SB-ILDN, exhibits considerably better agreement with the NMR data.

A kinetic model of trp-cage folding from multiple biased molecular dynamics simulations.

Trp-cage is a designed 20-residue polypeptide that, in spite of its size, shares several features with larger globular proteins.Although the system has been intensively investigated experimentally and theoretically, its folding mechanism is not yet fully understood. Indeed, some experiments suggest a two-state behavior, while others point to the presence of intermediates. In this work we show that the results of a bias-exchange metadynamics simulation can be used for constructing a detailed thermodynamic and kinetic model of the system. The model, although constructed from a biased simulation, has a quality similar to those extracted from the analysis of long unbiased molecular dynamics trajectories. This is demonstrated by a careful benchmark of the approach on a smaller system, the solvated Ace-Ala3-Nme peptide. For theTrp-cage folding, the model predicts that the relaxation time of 3100 ns observed experimentally is due to the presence of a compact molten globule-like conformation. This state has an occupancy of only 3% at 300 K, but acts as a kinetic trap.Instead, non-compact structures relax to the folded state on the sub-microsecond timescale. The model also predicts the presence of a state at Calpha-RMSD of 4.4 A from the NMR structure in which the Trp strongly interacts with Pro12. This state can explain the abnormal temperature dependence of the Pro12-delta3 and Gly11-alpha3 chemical shifts. The structures of the two most stable misfolded intermediates are in agreement with NMR experiments on the unfolded protein. Our work shows that, using biased molecular dynamics trajectories, it is possible to construct a model describing in detail the Trp-cage folding kinetics and thermodynamics in agreement with experimental data.

Development of a Force Field for the Simulation of Single-Chain Proteins and Protein-Protein Complexes.

The accuracy of atomistic physics-based force fields for the simulation of biological macromolecules has typically been benchmarked experimentally using biophysical data from simple, often single-chain systems. In the case of proteins, the careful refinement of force field parameters associated with torsion-angle potentials and the use of improved water models have enabled a great deal of progress toward the highly accurate simulation of such monomeric systems in both folded and, more recently, disordered states. In living organisms, however, proteins constantly interact with other macromolecules, such as proteins and nucleic acids, and these interactions are often essential for proper biological function. Here, we show that state-of-the-art force fields tuned to provide an accurate description of both ordered and disordered proteins can be limited in their ability to accurately describe protein-protein complexes. This observation prompted us to perform an extensive reparameterization of one variant of the Amber protein force field. Our objective involved refitting not only the parameters associated with torsion-angle potentials but also the parameters used to model nonbonded interactions, the specification of which is expected to be central to the accurate description of multicomponent systems. The resulting force field, which we call DES-Amber, allows for more accurate simulations of protein-protein complexes, while still providing a state-of-the-art description of both ordered and disordered single-chain proteins. Despite the improvements, calculated protein-protein association free energies still appear to deviate substantially from experiment, a result suggesting that more fundamental changes to the force field, such as the explicit treatment of polarization effects, may simultaneously further improve the modeling of single-chain proteins and protein-protein complexes.

Exploring the folding free energy landscape of insulin using bias exchange metadynamics.

The bias exchange metadynamics (BE-META) technique was applied to investigate the folding mechanism of insulin, one of the most studied and biologically important proteins. The BE-META simulations were performed starting from an extended conformation of chain B of insulin, using only eight replicas and seven reaction coordinates. The folded state, together with the intermediate states along the folding pathway were identified and their free energy was determined. Three main basins were found separated from one another by a large free energy barrier. The characteristic native fold of chain B was observed in one basin, while the other two most populated basins contained "molten-globule" conformations stabilized by electrostatic and hydrophobic interactions, respectively. Transitions between the three basins occur on the microsecond time scale. The implications and relevance of this finding to the folding mechanisms of insulin were investigated.

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.

A bias-exchange approach to protein folding.

By suitably extending a recent approach [Bussi, G.; et al. J. Am. Chem. Soc. 2006, 128, 13435] we introduce a powerful methodology that allows the parallel reconstruction of the free energy of a system in a virtually unlimited number of variables. Multiple metadynamics simulations of the same system at the same temperature are performed, biasing each replica with a time-dependent potential constructed in a different set of collective variables. Exchanges between the bias potentials in the different variables are periodically allowed according to a replica exchange scheme. Due to the efficaciously multidimensional nature of the bias the method allows exploring complex free energy landscapes with high efficiency. The usefulness of the method is demonstrated by performing an atomistic simulation in explicit solvent of the folding of a Triptophane cage miniprotein. It is shown that the folding free energy landscape can be fully characterized starting from an extended conformation with use of only 40 ns of simulation on 8 replicas.