Protein folding kinetics and thermodynamics from atomistic simulations

Folding Kinetics and Volume Variation of the β-Hairpin Peptide Chignolin upon Ultrafast pH-Jumps

In-depth characterization of fundamental folding steps of small model peptides is crucial for a better understanding of the folding mechanisms of more complex biomacromolecules. We have previously reported on the folding/unfolding kinetics of a model α-helix. Here, we study folding transitions in chignolin (GYDPETGTWG), a short β-hairpin peptide previously used as a model to study conformational changes in β-sheet proteins. Although previously suggested, until now, the role of the Tyr2-Trp9 interaction in the folding mechanism of chignolin was not clear. In the present work, pH-dependent conformational changes of chignolin were characterized by circular dichroism (CD), nuclear magnetic resonance (NMR), ultrafast pH-jump coupled with time-resolved photoacoustic calorimetry (TR-PAC), and molecular dynamics (MD) simulations. Taken together, our results present a comprehensive view of chignolin's folding kinetics upon local pH changes and the role of the Tyr2-Trp9 interaction in the folding process. CD data show that chignolin's β-hairpin formation displays a pH-dependent skew bell-shaped curve, with a maximum close to pH 6, and a large decrease in β-sheet content at alkaline pH. The β-hairpin structure is mainly stabilized by aromatic interactions between Tyr2 and Trp9 and CH-π interactions between Tyr2 and Pro4. Unfolding of chignolin at high pH demonstrates that protonation of Tyr2 is essential for the stability of the β-hairpin. Refolding studies were triggered by laser-induced pH-jumps and detected by TR-PAC. The refolding of chignolin from high pH, mainly due to the protonation of Tyr2, is characterized by a volume expansion (10.4 mL mol-1), independent of peptide concentration, in the microsecond time range (lifetime of 1.15 μs). At high pH, the presence of the deprotonated hydroxyl (tyrosinate) hinders the formation of the aromatic interaction between Tyr2 and Trp9 resulting in a more disorganized and dynamic tridimensional structure of the peptide. This was also confirmed by comparing MD simulations of chignolin under conditions mimicking neutral and high pH.

Probing Methyl Group Dynamics in Proteins by NMR Cross-Correlated Dipolar Relaxation and Molecular Dynamics Simulations

Nuclear magnetic resonance (NMR) spin relaxation is the most informative approach to experimentally probe the internal dynamics of proteins on the picosecond to nanosecond time scale. At the same time, molecular dynamics (MD) simulations of biological macromolecules are steadily improving through better physical models, enhanced sampling methods, and increased computational power, and they provide exquisite information about flexibility and its role in protein stability and molecular interactions. Many examples have shown that MD is now adept in probing protein backbone motion, but improvements are still required toward a quantitative description of the dynamics of side chains, for example, probed by the dynamics of methyl groups. Thus far, the comparison of computation with experiment for side chain dynamics has primarily focused on the relaxation of ¹³C and ²H nuclei induced by autocorrelated variation of spin interactions. However, the cross-correlation of ¹³C-¹H dipolar interactions in methyl groups offers an attractive alternative. Here, we establish a computational framework to extract cross-correlation relaxation parameters of methyl groups in proteins from all-atom MD simulations. To demonstrate the utility of the approach, cross-correlation relaxation rates of ubiquitin are computed from MD simulations performed with the AMBER99SB*-ILDN and CHARMM36 force fields. Simulation results were found to agree well with those obtained by experiment. Moreover, the data obtained with the two force fields are highly consistent.

Circular dichroism spectroscopic assessment of structural changes upon protein thermal unfolding at contrasting pH: Comparison with molecular dynamics simulations

In most instances, the usual fastness of protein unfolding events hinders determining changes in secondary structures associated with this process because these determinations rely on the recording of high-resolution circular dichroism (CD) spectra. In this work, far-UV CD spectra, recorded at ten-minute intervals, were used to evaluate the time course followed by four classes of secondary structures in the slow temperature-induced unfolding of yeast triosephosphate isomerase (yTIM) under distinct pH conditions. CONTIN-LL and SELCON3 algorithms were used for the deconvolution of spectra. Both algorithms furnished helix and unordered structure contents that changed according to first-order kinetics, agreeing with the behavior shown by CD data at specific wavelengths. Analyses of unfolded yTIM spectra, using a dataset that includes spectra of unfolded proteins and either one of the two algorithms, clearly showed a more unordered protein structure at high pH; this finding was corroborated with analysis of the difference spectra. Molecular dynamics (MD) simulations performed with AMBER and OPLS force fields resulted in more extensive loss of helices and gain in coils at high pH, in agreement with spectroscopic results. However, structural differences between low- and high-pH unfolded yTIM were relatively small. Comparison of results from CD and MD thus point to the need of fine-tuning of MD procedures.

Granger Causality Analysis of Chignolin Folding

Constantly advancing computer simulations of biomolecules provide huge amounts of data that are difficult to interpret. In particular, obtaining insights into functional aspects of macromolecular dynamics, often related to cascades of transient events, calls for methodologies that depart from the well-grounded framework of equilibrium statistical physics. One of the approaches toward the analysis of complex temporal data which has found applications in the fields of neuroscience and econometrics is Granger causality analysis. It allows determining which components of multidimensional time series are most influential for the evolution of the entire system, thus providing insights into causal relations within the dynamic structure of interest. In this work, we apply Granger analysis to a long molecular dynamics trajectory depicting repetitive folding and unfolding of a mini β-hairpin protein, CLN025. We find objective, quantitative evidence indicating that rearrangements within the hairpin turn region are determinant for protein folding and unfolding. On the contrary, interactions between hairpin arms score low on the causality scale. Taken together, these findings clearly favor the concept of zipperlike folding, which is one of two postulated β-hairpin folding mechanisms. More importantly, the results demonstrate the possibility of a conclusive application of Granger causality analysis to a biomolecular system.

Coarse-Grained Simulations of Protein Folding: Bridging Theory and Experiments

Computational coarse-grained models play a fundamental role as a research tool in protein folding, and they are important in bridging theory and experiments. Folding mechanisms are generally discussed using the energy landscape framework, which is well mapped within a class of simplified structure-based models. In this chapter, simplified computer models are discussed with special focus on structure-based ones.

Transient Excursions to Membrane Core as Determinants of Influenza Virus Fusion Peptide Activity

Fusion of viral and host cell membranes is a critical step in the life cycle of enveloped viruses. In the case of influenza virus, it is mediated by subunit 2 of hemagglutinin (HA) glycoprotein whose N-terminal fragments insert into the target membrane and initiate lipid exchange. These isolated fragments, known as fusion peptides (HAfp), already possess own fusogenic activity towards liposomes. Although they have long been studied with the hope to uncover the details of HA-mediated fusion, their actual mechanism of action remains elusive. Here, we use extensive molecular dynamics simulations combined with experimental studies of three HAfp variants to fully characterize their free energy landscape and interaction with lipid bilayer. In addition to customary assumed peptides localization at lipid-water interface, we characterize membrane-spanning configurations, which turn out to be metastable for active HAfps and unstable for the fusion inactive W14A mutant. We show that, while the degree of membrane perturbation by surface peptide configurations is relatively low and does not show any mutation-related differences, the effect of deeply inserted configurations is significant and correlates with insertion depth of the N-terminal amino group which is the highest for the wild type HAfp. Finally, we demonstrate the feasibility of spontaneous peptide transition to intramembrane location and the critical role of strictly conserved tryptofan residue 14 in this process.

Validation of DBFOLD: An efficient algorithm for computing folding pathways of complex proteins

Atomistic simulations can provide valuable, experimentally-verifiable insights into protein folding mechanisms, but existing ab initio simulation methods are restricted to only the smallest proteins due to severe computational speed limits. The folding of larger proteins has been studied using native-centric potential functions, but such models omit the potentially crucial role of non-native interactions. Here, we present an algorithm, entitled DBFOLD, which can predict folding pathways for a wide range of proteins while accounting for the effects of non-native contacts. In addition, DBFOLD can predict the relative rates of different transitions within a protein’s folding pathway. To accomplish this, rather than directly simulating folding, our method combines equilibrium Monte-Carlo simulations, which deploy enhanced sampling, with unfolding simulations at high temperatures. We show that under certain conditions, trajectories from these two types of simulations can be jointly analyzed to compute unknown folding rates from detailed balance. This requires inferring free energies from the equilibrium simulations, and extrapolating transition rates from the unfolding simulations to lower, physiologically-reasonable temperatures at which the native state is marginally stable. As a proof of principle, we show that our method can accurately predict folding pathways and Monte-Carlo rates for the well-characterized Streptococcal protein G. We then show that our method significantly reduces the amount of computation time required to compute the folding pathways of large, misfolding-prone proteins that lie beyond the reach of existing direct simulation. Our algorithm, which is available online, can generate detailed atomistic models of protein folding mechanisms while shedding light on the role of non-native intermediates which may crucially affect organismal fitness and are frequently implicated in disease.

Many proteins must adopt a specific structure in order to function. Computational simulations have been used to shed light on the mechanisms of protein folding, but unfortunately, realistic simulations can typically only be run for small proteins, due to severe limits in computational speed. Here, we present a method to solve this problem, whereby instead of directly simulating folding from an unfolded state, we run simulations that allow for computation of equilibrium folding free energies, alongside high temperature simulations to compute unfolding rates. From these quantities, folding rates can be computed using detailed balance. Importantly, our method can account for the effects of nonnative contacts which transiently form during folding and must be broken prior to adoption of the native state. Such contacts, which are often excluded from simple models of folding, may crucially affect real protein folding pathways and are often observed in folding intermediates implicated in disease.

Long-time methods for molecular dynamics simulations: Markov State Models and Milestoning

Molecular dynamics (MD) studies of biomolecules require the ability to simulate complex biochemical systems with an increasingly larger number of particles and for longer time scales, a problem that cannot be overcome by computational hardware advances alone. A main problem springs from the intrinsically high-dimensional and complex nature of the underlying free energy landscape of most systems, and from the necessity to sample accurately such landscapes for identifying kinetic and thermodynamic states in the configurations space, and for accurate calculations of both free energy differences and of the corresponding transition rates between states. Here, we review and present applications of two increasingly popular methods that allow long-time MD simulations of biomolecular systems that can open a broad spectrum of new studies. A first approach, Markov State Models (MSMs), relies on identifying a set of configuration states in which the system resides sufficiently long to relax and loose the memory of previous transitions, and on using simulations for mapping the underlying complex energy landscape and for extracting accurate thermodynamic and kinetic information. The Markovian independence of the underlying transition probabilities creates the opportunity to increase the sampling efficiency by using sets of appropriately initialized short simulations rather than typically long MD trajectories, which also enhances sampling. This allows MSM-based studies to unveil bio-molecular mechanisms and to estimate free energy barriers with high accuracy, in a manner that is both systematic and relatively automatic, which accounts for their increasing popularity. The second approach presented, Milestoning, targets accurate studies of the ensemble of pathways connecting specific end-states (e.g., reactants and products) in a similarly systematic, accurate and highly automatic manner. Applications presented range from studies of conformational dynamics and binding of amyloid-forming peptides, cell-penetrating peptides and the DFG-flip dynamics in Abl kinase. As highlighted by the increasing number of studies using both methods, we anticipate that they will open new avenues for the investigation of systematic sampling of reactions pathways and mechanisms occurring on longer time scales than currently accessible by purely computational hardware developments.

The role of cations in uranyl nanocluster association: a molecular dynamics study

Actinyl ions can self-assemble in aqueous solution to form closed cage clusters ranging from 1.5 to 4.0 nm in diameter. The self-assembly, stability, and behavior of the nanoclusters depend on the nature of the aqueous environment, such as the pH and cations present. In this work, a classical force field for [(UO2)20(O2)30]20- (U20) peroxide nanoclusters in aqueous solution was developed from quantum-mechanical calculations. Using molecular dynamics simulations, the preferred binding sites of six cations (Li+, Na+, K+, Rb+, Cs+, and Ca2+) to the nanocluster were determined. Replica exchange molecular dynamics was used to equilibrate the structure and determine the equilibrium distribution of cations and water with respect to the nanocluster cage. In addition, the free energy barriers associated with cations entering the cluster were computed. Finally, the association of two cages was investigated by computing the free energy as a function of intercage distance. The free energy profiles reveal that the nanoclusters prefer to be associated when neutralized with divalent cations, but do not associate when neutralized with monovalent cations. This could explain the formation of tertiary structures observed experimentally.

Relating circular dichroism to atomic structure by means of MD simulations and computed CD spectra with α-peptoids as an example

Accurate TD-DFT calculations of electronic circular dichroism have been performed to characterise the 3D structure of α-peptoids.

Mutation-induced change in chignolin stability from π-turn to α-turn

A mutation from threonine to proline at the eighth residue in chignolin changes π-turn to α-turn.

Analysis of molecular dynamics simulations of 10-residue peptide, chignolin, using statistical mechanics: Relaxation mode analysis and three-dimensional reference interaction site model theory

Molecular dynamics simulation is a fruitful tool for investigating the structural stability, dynamics, and functions of biopolymers at an atomic level. In recent years, simulations can be performed on time scales of the order of milliseconds using special purpose systems. Since the most stable structure, as well as meta-stable structures and intermediate structures, is included in trajectories in long simulations, it is necessary to develop analysis methods for extracting them from trajectories of simulations. For these structures, methods for evaluating the stabilities, including the solvent effect, are also needed. We have developed relaxation mode analysis to investigate dynamics and kinetics of simulations based on statistical mechanics. We have also applied the three-dimensional reference interaction site model theory to investigate stabilities with solvent effects. In this paper, we review the results for designing amino-acid substitution of the 10-residue peptide, chignolin, to stabilize the misfolded structure using these developed analysis methods.

Replica sub-permutation method for molecular dynamics and monte carlo simulations

We propose an improvement of the replica-exchange and replica-permutation methods, which we call the replica sub-permutation method (RSPM). Instead of considering all permutations, this method uses a new algorithm referred to as sub-permutation to perform parameter transition. The RSPM succeeds in reducing the number of combinations between replicas and parameters without the loss of sampling efficiency. For comparison, we applied the replica sub-permutation, replica-permutation, and replica-exchange methods to a β-hairpin mini protein, chignolin, in explicit water. We calculated the transition ratio and number of tunneling events in the parameter space, the number of folding-unfolding events, the autocorrelation function, and the autocorrelation time as measures of sampling efficiency. The results indicate that among the three methods, the proposed RSPM is the most efficient in both parameter and conformational spaces. © 2019 Wiley Periodicals, Inc.

Molecular simulations by generalized-ensemble algorithms in isothermal-isobaric ensemble

Generalized-ensemble algorithms are powerful techniques for investigating biomolecules such as protein, DNA, lipid membrane, and glycan. The generalized-ensemble algorithms were originally developed in the canonical ensemble. On the other hand, not only temperature but also pressure is controlled in experiments. Additionally, pressure is used as perturbation to study relationship between function and structure of biomolecules. For this reason, it is important to perform efficient conformation sampling based on the isothermal-isobaric ensemble. In this article, we review a series of the generalized-ensemble algorithms in the isothermal-isobaric ensemble: multibaric-multithermal, pressure- and temperature-simulated tempering, replica-exchange, and replica-permutation methods. These methods achieve more efficient simulation than the conventional isothermal-isobaric simulation. Furthermore, the isothermal-isobaric generalized-ensemble simulation samples conformations of biomolecules from wider range of temperature and pressure. Thus, we can estimate physical quantities more accurately at any temperature and pressure values. The applications to the biomolecular system are also presented.

Conformational analysis of replica exchange MD: Temperature-dependent Markov networks for FF amyloid peptides

Recent molecular modeling methods using Markovian descriptions of conformational states of biomolecular systems have led to powerful analysis frameworks that can accurately describe their complex dynamical behavior. In conjunction with enhanced sampling methods, such as replica exchange molecular dynamics (REMD), these frameworks allow the systematic and accurate extraction of transition probabilities between the corresponding states, in the case of Markov state models, and of statistically-optimized transition rates, in the case of the corresponding coarse master equations. However, applying automatically such methods to large molecular dynamics (MD) simulations, with explicit water molecules, remains limited both by the initial ability to identify good candidates for the underlying Markovian states and by the necessity to do so using good collective variables as reaction coordinates that allow the correct counting of inter-state transitions at various lag times. Here, we show that, in cases when representative molecular conformations can be identified for the corresponding Markovian states, and thus their corresponding collective evolution of atomic positions can be calculated along MD trajectories, one can use them to build a new type of simple collective variable, which can be particularly useful in both the correct state assignment and in the subsequent accurate counting of inter-state transition probabilities. In the case of the ubiquitously used root-mean-square deviation (RMSD) of atomic positions, we introduce the relative RMSD (RelRMSD) measure as a good reaction coordinate candidate. We apply this method to the analysis of REMD trajectories of amyloid-forming diphenylalanine (FF) peptides-a system with important nanotechnology and biomedical applications due to its self-assembling and piezoelectric properties-illustrating the use of RelRMSD in extracting its temperature-dependent intrinsic kinetics, without a priori assumptions on the functional form (e.g., Arrhenius or not) of the underlying conformational transition rates. The RelRMSD analysis enables as well a more objective assessment of the convergence of the REMD simulations. This type of collective variable may be generalized to other observables that could accurately capture conformational differences between the underlying Markov states (e.g., distance RMSD, the fraction of native contacts, etc.).

Peptide dimerization-dissociation rates from replica exchange molecular dynamics

We show how accurate rates of formation and dissociation of peptide dimers can be calculated using direct transition counting (DTC) from replica-exchange molecular dynamics (REMD) simulations. First, continuous trajectories corresponding to system replicas evolving at different temperatures are used to assign conformational states. Second, we analyze the entire REMD data to calculate the corresponding rates at each temperature directly from the number of transition counts. Finally, we compare the kinetics extracted directly, using the DTC method, with indirect estimations based on trajectory likelihood maximization using short-time propagators and on decay rates of state autocorrelation functions. For systems with relatively low-dimensional intrinsic conformational dynamics, the DTC method is simple to implement and leads to accurate temperature-dependent rates. We apply the DTC rate-extraction method to all-atom REMD simulations of dimerization of amyloid-forming NNQQ tetrapetides in explicit water. In an assessment of the REMD sampling efficiency with respect to standard MD, we find a gain of more than a factor of two at the lowest temperature.

Analysis of Structural Stability of Chignolin

We discuss the stability of an entire protein and the influence of main chains and side chains of individual amino acids to investigate the protein-folding mechanism. For this purpose, we calculated the solvation free-energy contribution of individual atoms using the three-dimensional reference interaction site model with the atomic decomposition method. We generated structures of chignolin miniprotein by a molecular dynamics simulation and classified them into six types: native 1, native 2, misfolded 1, misfolded 2, intermediate, and unfolded states. The total energies of the native (-171.1 kcal/mol) and misfolded (-171.2 kcal/mol) states were almost the same and lower than those of the intermediate (-158.5 kcal/mol) and unfolded (-148.1 kcal/mol) states; however, their components were different. In the native state, the side-chain interaction between Thr6 and Thr8 is important for the formation of π-turn. On the other hand, the hydrogen bonds between the atoms of the main chains in the misfolded state become stronger than those in the intermediate state.

Thermodynamic and kinetic stability of the Josephin Domain closed arrangement: evidences from replica exchange molecular dynamics

BACKGROUND

Molecular phenomena driving pathological aggregation in neurodegenerative diseases are not completely understood yet. Peculiar is the case of Spinocerebellar Ataxia 3 (SCA3) where the conformational properties of the AT-3 N-terminal region, also called Josephin Domain (JD), play a key role in the first step of aggregation, having the JD an amyloidogenic propensity itself. For this reason, unraveling the intimate relationship between JD structural features and aggregation tendency may lead to a step forward in understanding the pathology and rationally design a cure. In this connection, computational modeling has demonstrated to be helpful in exploring the protein molecular dynamics and mechanism of action.

RESULTS

Conformational dynamics of the JD is here finely investigated by replica exchange molecular dynamics simulations able to sample the microsecond time scale and to provide both a thermodynamic and kinetic description of the protein conformational changes. Accessible structural conformations of the JD have been identified in: open, intermediate and closed like arrangement. Data indicated the closed JD arrangement as the most likely protein arrangement. The protein transition from closed toward intermediate/open states was characterized by a rate constant higher than 700 ns. This result also explains the inability of classical molecular dynamics to explore transitions from closed to open JD configuration on a time scale of hundreds of nanoseconds.

CONCLUSION

This work provides the first kinetic estimation of the JD transition pathway from open-like to closed-like arrangement and vice-versa, indicating the closed-like arrangement as the most likely configuration for a JD in water environment. More widely, the importance of our results is also underscored considering that the ability to provide a kinetic description of the protein conformational changes is a scientific challenge for both experimental and theoretical approaches to date.

REVIEWERS

This article was reviewed by Oliviero Carugo, Bojan Zagrovic.

The folding mechanism and key metastable state identification of the PrP127–147 monomer studied by molecular dynamics simulations and Markov state model analysis

MD simulation combined with MSM analysis was employed to investigate the structural dynamics and the folding mechanism of the key fragment 127–147 monomer of prion protein.

Refined Parameterization of Nonbonded Interactions Improves Conformational Sampling and Kinetics of Protein Folding Simulations

Recent advances in computational technology have enabled brute-force molecular dynamics (MD) simulations of protein folding using physics-based molecular force fields. The extensive sampling of protein conformations afforded by such simulations revealed, however, considerable compaction of the protein conformations in the unfolded state, which is inconsistent with experiment. Here, we show that a set of surgical corrections to nonbonded interactions between amine nitrogen-carboxylate oxygen and aliphatic carbon-carbon atom pairs can considerably improve the realism of protein folding simulations. Specifically, we show that employing our corrections in ∼500 μs all-atom replica-exchange MD simulations of the WW domain and villin head piece proteins increases the size of the denatured proteins' conformations and does not destabilize the native conformations of the proteins. In addition to making the folded conformations a global minimum of the respective free energy landscapes at room temperature, our corrections also make the free energy landscape smoother, considerably accelerating the folding kinetics and, hence, reducing the computational expense of a protein folding simulation.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Enhanced sampling simulation analysis of the structure of lignin in the THF–water miscibility gap

Using temperature replica-exchange molecular dynamics, we characterize a globule-to-coil transition for a softwood-like lignin biopolymer in a tetrahydrofuran (THF)–water cosolvent system at temperatures at which the cosolvent undergoes a de-mixing transition.

Coarse kMC-based replica exchange algorithms for the accelerated simulation of protein folding in explicit solvent

In this paper, we present a coarse replica exchange molecular dynamics (REMD) approach, based on kinetic Monte Carlo (kMC).

Going clean: structure and dynamics of peptides in the gas phase and paths to solvation

The gas phase is an artificial environment for biomolecules that has gained much attention both experimentally and theoretically due to its unique characteristic of providing a clean room environment for the comparison between theory and experiment. In this review we give an overview mainly on first-principles simulations of isolated peptides and the initial steps of their interactions with ions and solvent molecules: a bottom up approach to the complexity of biological environments. We focus on the accuracy of different methods to explore the conformational space, the connections between theory and experiment regarding collision cross section evaluations and (anharmonic) vibrational spectra, and the challenges faced in this field.

Transition path sampling with quantum/classical mechanics for reaction rates

Predicting rates of biochemical reactions through molecular simulations poses a particular challenge for two reasons. First, the process involves bond formation and/or cleavage and thus requires a quantum mechanical (QM) treatment of the reaction center, which can be combined with a more efficient molecular mechanical (MM) description for the remainder of the system, resulting in a QM/MM approach. Second, reaction time scales are typically many orders of magnitude larger than the (sub-)nanosecond scale accessible by QM/MM simulations. Transition path sampling (TPS) allows to efficiently sample the space of dynamic trajectories from the reactant to the product state without an additional biasing potential. We outline here the application of TPS and QM/MM to calculate rates for biochemical reactions, by means of a simple toy system. In a step-by-step protocol, we specifically refer to our implementation within the MD suite Gromacs, which we have made available to the research community, and include practical advice on the choice of parameters.

Comparison of volume and surface area nonpolar solvation free energy terms for implicit solvent simulations

Implicit solvent models for molecular dynamics simulations are often composed of polar and nonpolar terms. Typically, the nonpolar solvation free energy is approximated by the solvent-accessible-surface area times a constant factor. More sophisticated approaches incorporate an estimate of the attractive dispersion forces of the solvent and∕or a solvent-accessible volume cavitation term. In this work, we confirm that a single volume-based nonpolar term most closely fits the dispersion and cavitation forces obtained from benchmark explicit solvent simulations of fixed protein conformations. Next, we incorporated the volume term into molecular dynamics simulations and find the term is not universally suitable for folding up small proteins. We surmise that while mean-field cavitation terms such as volume and SASA often tilt the energy landscape towards native-like folds, they also may sporadically introduce bottlenecks into the folding pathway that hinder the progression towards the native state.

Dynamics of an intrinsically disordered protein reveal metastable conformations that potentially seed aggregation

Amyloid fibril deposits of the intrinsically disordered hIAPP peptide are found in 95% of type II diabetes patients, and the aggregation of this peptide is suggested to induce apoptotic cell-death in insulin-producing β-cells. Understanding the structure and dynamics of the hIAPP monomer in solution is thus important for understanding the nucleation of aggregation and the formation of oligomers. In this study, we identify the metastable conformational states of the hIAPP monomer and the dynamics of transitioning between them using Markov state models constructed from extensive molecular dynamics simulations. We show that the overall structure of the hIAPP peptide is random coil-like and lacks a dominant folded structure. Despite this fact, our model reveals a large number of reasonably well-populated metastable conformational states (or local free energy minima) having populations of a few percent or less. The time scales for transitioning between these states range from several microseconds to milliseconds. In contrast to folded proteins, there is no kinetic hub. More strikingly, a few states contain significant amounts of β-hairpin secondary structure and extended hydrophobic surfaces that are exposed to the solvent. We propose that these states may facilitate the nucleation of hIAPP aggregation through a significant component of the conformational selection mechanism, because they may increase their populations upon aggregation by promoting hydrophobic interactions and at the same time provide a flat geometry to seed the ordered β-strand packing of the fibrils.

Simulation of electron paramagnetic resonance spectra of spin-labeled molecules from replica-exchange molecular dynamics

We report a general approach for the simulation of the electron paramagnetic resonance (EPR) spectra of spin labels attached to peptides and proteins directly from replica-exchange molecular dynamics (REMD) trajectories. Conventional MD trajectories are generally inadequate for the prediction of EPR line shapes since the label can become trapped in one or more of a set of rotameric states, thus preventing both conformational sampling and accurate estimates of the exchange rates between different rotamers. The advantage of using REMD is its ability to provide both efficient conformational sampling and kinetic information for spin-label dynamics. Our approach is illustrated with spin-labeled peptide. This approach to REMD-EPR simulation paves the way for the wider application of MD modeling to the simulation and interpretation of EPR spectra of spin-labeled molecules.

Molecular dynamics simulations of a new branched antimicrobial peptide: a comparison of force fields

Branched antimicrobial peptides are promising as a new class of antibiotics displaying high activity and low toxicity and appear to work through a unique mechanism of action. We explore the structural dynamics of a covalently branched 18 amino acid peptide (referred to as B2088) in aqueous and membrane mimicking environments through molecular dynamics (MD) simulations. Towards this, we carry out conventional MD simulations and supplement these with replica exchange simulations. The simulations are carried out using four different force fields that are commonly employed for simulating biomolecular systems. These force fields are GROMOS53a6, CHARMM27 with cMAP, CHARMM27 without cMAP and AMBER99sb. The force fields are benchmarked against experimental data available from circular dichroism and nuclear magnetic resonance spectroscopies, and show that CHARMM27 without cMAP correction is the most successful in reproducing the structural dynamics of B2088 both in water and in the presence of micelles. Although the four force fields predict different structures of B2088, they all show that B2088 stabilizes against the head group of the lipid through hydrogen bonding of its Lys and Arg side chains. This leads us to hypothesize that B2088 is unlikely to penetrate into the hydrophobic region of the membrane owing to the high free energy costs of transfer from water, and possibly acts by carpeting and thus disrupting the membrane.

GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit

MOTIVATION

Molecular simulation has historically been a low-throughput technique, but faster computers and increasing amounts of genomic and structural data are changing this by enabling large-scale automated simulation of, for instance, many conformers or mutants of biomolecules with or without a range of ligands. At the same time, advances in performance and scaling now make it possible to model complex biomolecular interaction and function in a manner directly testable by experiment. These applications share a need for fast and efficient software that can be deployed on massive scale in clusters, web servers, distributed computing or cloud resources.

RESULTS

Here, we present a range of new simulation algorithms and features developed during the past 4 years, leading up to the GROMACS 4.5 software package. The software now automatically handles wide classes of biomolecules, such as proteins, nucleic acids and lipids, and comes with all commonly used force fields for these molecules built-in. GROMACS supports several implicit solvent models, as well as new free-energy algorithms, and the software now uses multithreading for efficient parallelization even on low-end systems, including windows-based workstations. Together with hand-tuned assembly kernels and state-of-the-art parallelization, this provides extremely high performance and cost efficiency for high-throughput as well as massively parallel simulations.

AVAILABILITY

GROMACS is an open source and free software available from http://www.gromacs.org.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Inclusion of many-body effects in the additive CHARMM protein CMAP potential results in enhanced cooperativity of α-helix and β-hairpin formation

Folding simulations on peptides and proteins using empirical force fields have demonstrated the sensitivity of the results to details of the backbone potential. A recently revised version of the additive CHARMM protein force field, which includes optimization of the backbone CMAP potential to achieve good balance between different types of secondary structure, correcting the α-helical bias present in the former CHARMM22/CMAP energy function, is shown to result in improved cooperativity for the helix-coil transition. This is due to retention of the empirical corrections introduced in the original CMAP to reproduce folded protein structures-corrections that capture many-body effects missing from an energy surface fitted to gas phase calculations on dipeptides. The experimental temperature dependence of helix formation in (AAQAA)(3) and parameters for helix nucleation and elongation are in much better agreement with experiment than those obtained with other recent force fields. In contrast, CMAP parameters derived by fitting to a vacuum quantum mechanical surface for the alanine dipeptide do not reproduce the enhanced cooperativity, showing that the empirical backbone corrections, and not some other feature of the force field, are responsible. We also find that the cooperativity of β-hairpin formation is much improved relative to other force fields we have studied. Comparison with (ϕ,ψ) distributions from the Protein Data Bank further justifies the inclusion of many-body effects in the CMAP. These results suggest that the revised energy function will be suitable for both simulations of unfolded or intrinsically disordered proteins and for investigating protein-folding mechanisms.

β-hairpin forms by rolling up from C-terminal: topological guidance of early folding dynamics

That protein folding is a non-random, guided process has been known even prior to Levinthal's paradox; yet, guided searches, attendant mechanisms and their relation to primary sequence remain obscure. Using extensive molecular dynamics simulations of a β-hairpin with key sequence features similar to those of >13,000 β-hairpins in full proteins, we provide significant insights on the entire pre-folding dynamics at single-residue levels and describe a single, highly coordinated roll-up folding mechanism, with clearly identifiable stages, directing structural progression toward native state. Additional simulations of single-site mutants illustrate the role of three key residues in facilitating this roll-up mechanism. Given the many β-hairpins in full proteins with similar residue arrangements and since β-hairpins are believed to act as nucleation sites in early-stage folding dynamics of full proteins, the topologically guided mechanism seen here may represent one of Nature's strategies for reducing early-stage folding complexity.