Complex folding pathways in a simple beta-hairpin

Mechanism of β-hairpin formation in AzoChignolin and Chignolin

AzoChignolin is a photoswitchable variant of the mini-protein Chignolin with an azobenzene (AMPP) replacing the central loop. AzoChignolin is unfolded with AMPP in the trans-isomer. Transition to the cis-isomer causes β-hairpin folding similar to Chignolin. The AzoChignolin system is excellently suited for comprehensive analysis of folding nucleation kinetics. Utilizing multiple long-time MD simulations of AzoChignolin and Chignolin in MeOH and water, we estimated Markov models to examine folding kinetics of both peptides. We show that while AzoChignolin mimics Chignolin's structure well, the folding kinetics are quite different. Not only folding times but also intermediate states differ, particularly Chignolin is able to fold in MeOH into an α-helical intermediate which is impossible to form in AzoChignolin. The Markov models demonstrate that AzoChignolin's kinetics are generally faster, specifically when comparing the two main microfolding processes of hydrophobic collapse and turn formation. Photoswitchable loops are used frequently to understand the kinetics of elementary protein folding nucleation. However, our results indicate that intermediates and folding kinetics may differ between natural loops and photoswitchable variants.

GB1 hairpin kinetics: capturing the folding pathway with molecular dynamics, replica exchange and optimal dimensionality reduction

We have performed molecular dynamics (MD) and replica-exchange (REMD) simulations of folding of the GB1 hairpin peptide in aqueous solution. REMD results were consistent with a cooperative zipper folding model. 120 μ s MD trajectories at 320 K yielded relaxation times of 1.8 μ s and 100 ns, with the slower assigned to global folding. The MD folding/unfolding transitions also followed the cooperative zipper model, specifying nucleation at the central turn followed by consecutive hydrogen bond formation. Formation of hydrogen bonds and hydrophobic contacts were highly correlated. Coarse-grained kinetic models constructed with the Optimal Dimensionality Reduction (ODR) approach found a folding time of 3.3 μ s and unfolding time of 4.0 μ s . Additionally, relaxation times in the 130-170 ns range could be assigned to formation of the transition state and off-path intermediates. The unfolded state was the most highly populated and, significantly, most heterogenous, assembling the largest number of microstates, primarily composed of extended and turn structures. The folded state was also heterogenous, but a to a lesser degree, involving the fully folded and partially folded in-register hairpins at early stages of the zipper pathway. The transition state corresponded to the nucleated hairpin, with central turn and first beta-sheet hydrogen bond, while the off-path intermediates were off-register partial hairpins. Our simulation results were in excellent agreement with experimental data on folded fraction, relaxation time and folding mechanism. The new findings from this work suggest a highly cooperative zipper folding mechanism, nascent hairpin transition state and ∼100 ns relaxation related to intermediate formation.Communicated by Ramaswamy H. Sarma.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

Structures of the intrinsically disordered Aβ, tau and α-synuclein proteins in aqueous solution from computer simulations

Intrinsically disordered proteins (IDPs) play many biological roles in the human proteome ranging from vesicular transport, signal transduction to neurodegenerative diseases. The Aβ and tau proteins, and the α-synuclein protein, key players in Alzheimer's and Parkinson's diseases, respectively are fully disordered at the monomer level. The structural heterogeneity of the monomeric and oligomeric states and the high self-assembly propensity of these three IDPs have precluded experimental structural determination. Simulations have been used to determine the atomic structures of these IDPs. In this article, we review recent computer models to capture the equilibrium ensemble of Aβ, tau and α-synuclein proteins at different association steps in aqueous solution and present new results of the PEP-FOLD framework on α-synuclein monomer.

Chirality Driven Twisting as a Driving Force of Primitive Folding in Binary Mixtures

The N-trifluoroacetylated α-aminoalcohols (TFAAAs) are able to form quasi-one-dimensional supramolecular fibers (strings) when chirally pure, and isometric precipitates in the racemate. The strings' formation leads to the reversible gelation of the solution. The fresh gels occupy all the available volume, however during the incubation, they contract and concentrate in the central region of the tube. The microscopic observations revealed the growth of the strings' diameter and their rotation in the course of the incubation at the hour time-scale. The rotation provides for the hairpins forming that serve as hooks on the rotating string, which provides for coiling of the strings, which was observed as gel contraction. The morphology of the twisted strings resembles the structures observed in modern proteins, which allows drawing an analogy between the folding of biopolymers and the formation of the clew of strings. In addition, the rotation found in the TFAAA gels is an example of a simple system converting the energy of intermolecular agglutination to the rotational movement, so they could be considered as molecular motors.

Hydrophobic Collapse in N-Methylacetamide-Water Mixtures

Aqueous N-methylacetamide solutions were investigated by polarization-resolved pump-probe and 2D infrared spectroscopy (2D IR), using the amide I mode as a reporter. The 2D IR results are compared with molecular dynamics simulations and spectral calculations to gain insight into the molecular structures in the mixture. N-Methylacetamide and water molecules tend to form clusters with "frozen" amide I dynamics. This is driven by a hydrophobic collapse as the methyl groups of the N-methylacetamide molecules cluster in the presence of water. Since the studied system can be considered as a simplified model for the backbone of proteins, the present study forms a convenient basis for understanding the structural and vibrational dynamics in proteins. It is particularly interesting to find out that a hydrophobic collapse as the one driving protein folding is observed in such a simple system.

Modeling the mechanism of CLN025 beta-hairpin formation

Beta-hairpins are substructures found in proteins that can lend insight into more complex systems. Furthermore, the folding of beta-hairpins is a valuable test case for benchmarking experimental and theoretical methods. Here, we simulate the folding of CLN025, a miniprotein with a beta-hairpin structure, at its experimental melting temperature using a range of state-of-the-art protein force fields. We construct Markov state models in order to examine the thermodynamics, kinetics, mechanism, and rate-determining step of folding. Mechanistically, we find the folding process is rate-limited by the formation of the turn region hydrogen bonds, which occurs following the downhill hydrophobic collapse of the extended denatured protein. These results are presented in the context of established and contradictory theories of the beta-hairpin folding process. Furthermore, our analysis suggests that the AMBER-FB15 force field, at this temperature, best describes the characteristics of the full experimental CLN025 conformational ensemble, while the AMBER ff99SB-ILDN and CHARMM22* force fields display a tendency to overstabilize the native state.

PELE: Protein Energy Landscape Exploration. A Novel Monte Carlo Based Technique

Combining protein structure prediction algorithms and Metropolis Monte Carlo techniques, we provide a novel method to explore all-atom energy landscapes. The core of the technique is based on a steered localized perturbation followed by side-chain sampling as well as minimization cycles. The algorithm and its application to ligand diffusion are presented here. Ligand exit pathways are successfully modeled for different systems containing ligands of various sizes:  carbon monoxide in myoglobin, camphor in cytochrome P450cam, and palmitic acid in the intestinal fatty-acid-binding protein. These initial applications reveal the potential of this new technique in mapping millisecond-time-scale processes. The computational cost associated with the exploration is significantly less than that of conventional MD simulations.

The OPEP protein model: from single molecules, amyloid formation, crowding and hydrodynamics to DNA/RNA systems

The OPEP coarse-grained protein model has been applied to a wide range of applications since its first release 15 years ago. The model, which combines energetic and structural accuracy and chemical specificity, allows the study of single protein properties, DNA-RNA complexes, amyloid fibril formation and protein suspensions in a crowded environment. Here we first review the current state of the model and the most exciting applications using advanced conformational sampling methods. We then present the current limitations and a perspective on the ongoing developments.

Detailed microscopic unfolding pathways of an α-helix and a β-hairpin: direct observation and molecular dynamics

We present a combined experimental and computational study of unfolding pathways of a model 21-residue α-helical heteropeptide (W1H5-21) and a 16-residue β-hairpin (GB41-56). Experimentally, we measured fluorescence energy transfer efficiency as a function of temperature, employing natural tryptophans as donors and dansylated lysines as acceptors. Secondary structural analysis was performed with circular dichroism and Fourier transform infrared spectroscopy. Our studies present markedly different unfolding pathways of the two elementary secondary structural elements. During thermal denaturation, the helical peptide exhibits an initial decrease in length, followed by an increase, while the hairpin undergoes a systematic increase in length. In the complementary computational part of the project, we performed microsecond length replica-exchange molecular dynamics simulations of the peptides in explicit solvent, yielding a detailed microscopic picture of the unfolding processes. For the α-helical peptide, we found a large heterogeneous population of intermediates that are primarily frayed single helices or helix-turn-helix motifs. Unfolding starts at the termini and proceeds through a stable helical region in the interior of the peptide but shifted off-center toward the C-terminus. The simulations explain the experimentally observed non-monotonic variation of helix length with temperature as due primarily to the presence of frayed-end single-helix intermediate structures. For the β-hairpin peptide, our simulations indicate that folding is initiated at the turn, followed by formation of the hairpin in zipper-like fashion, with Cα···Cα contacts propagating from the turn to termini and hairpin hydrogen bonds forming in parallel with these contacts. In the early stages of hairpin formation, the hydrophobic side-chain contacts are only partly populated. Intermediate structures with low numbers of β-hairpin hydrogen bonds have very low populations. This is in accord with the "broken zipper" model of Scheraga. The monotonic increase in length with temperature may be explained by the zipper-like breaking of the hairpin hydrogen bonds and backbone contacts.

Exploring the free energy landscape of a model β-hairpin peptide and its isoform

Secondary structural transitions from α-helix to β-sheet conformations are observed in several misfolding diseases including Alzheimer's and Parkinson's. Determining factors contributing favorably to the formation of each of these secondary structures is therefore essential to better understand these disease states. β-hairpin peptides form basic components of anti-parallel β-sheets and are suitable model systems for characterizing the fundamental forces stabilizing β-sheets in fibrillar structures. In this study, we explore the free energy landscape of the model β-hairpin peptide GB1 and its E2 isoform that preferentially adopts α-helical conformations at ambient conditions. Umbrella sampling simulations using all-atom models and explicit solvent are performed over a large range of end-to-end distances. Our results show the strong preference of GB1 and the E2 isoform for β-hairpin and α-helical conformations, respectively, consistent with previous studies. We show that the unfolded states of GB1 are largely populated by misfolded β-hairpin structures which differ from each other in the position of the β-turn. We discuss the energetic factors contributing favorably to the formation of α-helix and β-hairpin conformations in these peptides and highlight the energetic role of hydrogen bonds and non-bonded interactions.

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

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

The Martini coarse-grained force field

The Martini force field is a coarse-grained force field suited for molecular dynamics simulations of biomolecular systems. The force field has been parameterized in a systematic way, based on the reproduction of partitioning free energies between polar and apolar phases of a large number of chemical compounds. In this chapter the methodology underlying the force field is presented together with details of its parameterization and limitations. Then currently available topologies are described with a short overview of the key elements of their parameterization. These include the new polarizable Martini water model. A set of three selected ongoing studies using the Martini force field is presented. Finally the latest lines of development are discussed.

Kinetics of amyloid aggregation: a study of the GNNQQNY prion sequence

The small amyloid-forming GNNQQNY fragment of the prion sequence has been the subject of extensive experimental and numerical studies over the last few years. Using unbiased molecular dynamics with the OPEP coarse-grained potential, we focus here on the onset of aggregation in a 20-mer system. With a total of 16.9 of simulations at 280 K and 300 K, we show that the GNNQQNY aggregation follows the classical nucleation theory (CNT) in that the number of monomers in the aggregate is a very reliable descriptor of aggregation. We find that the critical nucleus size in this finite-size system is between 4 and 5 monomers at 280 K and 5 and 6 at 300 K, in overall agreement with experiment. The kinetics of growth cannot be fully accounted for by the CNT, however. For example, we observe considerable rearrangements after the nucleus is formed, as the system attempts to optimize its organization. We also clearly identify two large families of structures that are selected at the onset of aggregation demonstrating the presence of well-defined polymorphism, a signature of amyloid growth, already in the 20-mer aggregate.

Protein aggregation plays an important pathological role in numerous neurodegenerative diseases such as Alzheimer's, Parkinson's, Creutzfeldt-Jakob, the Prion disease and diabetes mellitus. In most cases, misfolded proteins are involved and aggregate irreversibly to form highly ordered insoluble macrostructures, called amyloid fibrils, which deposit in the brain. Studies have revealed that all proteins are capable of forming amyloid fibrils that all share common structural features and therefore aggregation mechanisms. The toxicity of amyloid aggregates is however not attributed to the fibrils themselves but rather to smaller more disordered aggregates, oligomers, forming parallel to or prior to fibrils. Understanding the assembly process of these amyloid oligomers is key to understanding their toxicity mechanism in order to devise a possible treatment strategy targeting these toxic aggregates. Our approach here is to computationally study the aggregation dynamics of a 20-mer of an amyloid peptide GNNQQNY from a prion protein. Our findings suggest that the assembly is a spontaneous process that can be described as a complex nucleation and growth mechanism and which can lead to two classes of morphologies for the aggregates, one of which resembles a protofibril-like structure. Such numerical studies are crucial to understanding the details of fast biological processes and complement well experimental studies.

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.

Free-energy calculations along a high-dimensional fragmented path with constrained dynamics

Free-energy calculations for high-dimensional systems, such as peptides or proteins, always suffer from a serious sampling problem in a huge conformational space. For such systems, path-based free-energy methods, such as thermodynamic integration or free-energy perturbation, are good choices. However, both of them need sufficient sampling along a predefined transition path, which can only be controlled using restrained or constrained dynamics. Constrained simulations produce more reasonable free-energy profiles than restrained simulations. But calculations of standard constrained dynamics require an explicit expression of reaction coordinates as a function of Cartesian coordinates of all related atoms, which may be difficult to find for the complex transition of biomolecules. In this paper, we propose a practical solution: (1) We use restrained dynamics to define an optimized transition path, divide it into small fragments, and define a virtual reaction coordinate to denote a position along the path. (2) We use constrained dynamics to perform a formal free-energy calculation for each fragment and collect the values together to provide the entire free-energy profile. This method avoids the requirement to explicitly define reaction coordinates in Cartesian coordinates and provides a novel strategy to perform free-energy calculations for biomolecules along any complex transition path.

Turn-directed folding dynamics of β-hairpin-forming de novo decapeptide Chignolin

Realistic mechanistic pictures of β-hairpin formation, offering valuable insights into some of the key early events in protein folding, are accessible through short designed polypeptides as they allow atomic-level scrutiny through simulations. Here, we present a detailed picture of the dynamics and mechanism of β-hairpin formation of Chignolin, a de novo decapeptide, using extensive, unbiased molecular dynamics simulations. The results provide clear evidence for turn-directed broken-zipper folding and reveal details of turn nucleation and cooperative progression of turn growth, hydrogen-bond formations, and eventual packing of the hydrophobic core. Further, we show that, rather than driving folding through hydrophobic collapse, cross-strand side-chain packing could in fact be rate-limiting as packing frustrations can delay formation of the native hydrophobic core prior to or during folding and even cause relatively long-living misfolded or partially folded states that may nucleate aggregative events in more complex situations. The results support the increasing evidence for turn-centric folding mechanisms for β-hairpin formation suggested recently for GB1 and Peptide 1 based on experiments and simulations but also point to the need for similar examinations of polypeptides with larger numbers of cross-strand hydrophobic residues.

Hydrophobic interactions in the formation of secondary structures in small peptides

Effects of the attractive and repulsive parts of hydrophobic interactions on α helices and β sheets in small peptides are investigated using a simple atomic potential. Typically, a physical spatial range of attraction tends to favor β sheets, but α helices would be favored if the attractive range were more extended. We also found that desolvation barriers favor β sheets in collapsed conformations of polyalanine, polyvaline, polyleucine, and three fragments of amyloid peptides tested in this study. Our results provide insight into the multifaceted role of hydrophobicity in secondary structure formation, including the α to β transitions in certain amyloid peptides.

Microscopic events in β-hairpin folding from alternative unfolded ensembles

We have performed the first unbiased folding simulations of the GB1 hairpin in explicit solvent, using hundreds of microsecond-long molecular dynamics simulations (total time: 0.7 ms). Our simulations are initiated from two sets of structures. Starting from an equilibrium unfolded state, we obtain single-exponential folding kinetics with rate coefficients in good agreement (T=350 K) or within an order of magnitude (T=300 K) of the experimental values. However, simulations initiated from unfolded configurations lacking secondary structure result in biexponential kinetics with an additional fast nanosecond kinetic mode. This mode can strongly bias the folding rate estimated from the mean first passage time, when the trials are much shorter than the folding time. We find that the mechanism of the hairpin folding is insensitive to the details of the initial unfolded ensemble and is initiated by correct formation of the turn of the hairpin, followed by the formation of the native hydrogen bonds and hydrophobic contacts, consistent with experimental -value analysis. Subsequent native interactions can be formed either from the turn or from the hairpin termini, helping to explain an apparent discrepancy in experimental results. From our simulations, we also obtain the transition path durations, a critical parameter for single molecule experiments aiming to resolve events along folding pathways. The lengths of transition paths span a wide range, from 50 ps to 140 ns, at 300 K.

A chirality-based metrics for free-energy calculations in biomolecular systems

In this work, we exploit the chirality index introduced in (Pietropaolo et al., Proteins 2008, 70, 667) as an effective descriptor of the secondary structure of proteins to explore their complex free-energy landscape. We use the chirality index as an alternative metrics in the path collective variables (PCVs) framework and we show in the prototypical case of the C-terminal domain of immunoglobulin binding protein GB1 that relevant configurations can be efficiently sampled in combination with well-tempered metadynamics. While the projections of the configurations found onto a variety of different descriptors are fully consistent with previously reported calculations, this approach provides a unifying perspective of the folding mechanism which was not possible using metadynamics with the previous formulation of PCVs.

Free-energy landscape of the GB1 hairpin in all-atom explicit solvent simulations with different force fields: Similarities and differences

Although it is now possible to fold peptides and miniproteins in molecular dynamics simulations, it is well appreciated that force fields are not all transferable to different proteins. Here, we investigate the influence of the protein force field and the solvent model on the folding energy landscape of a prototypical two-state folder, the GB1 hairpin. We use extensive replica-exchange molecular dynamics simulations to characterize the free-energy surface as a function of temperature. Most of these force fields appear similar at a global level, giving a fraction folded at 300 K between 0.2 and 0.8 in all cases, which is a difference in stability of 2.8 kT, and are generally consistent with experimental data at this temperature. The most significant differences appear in the unfolded state, where there are different residual secondary structures which are populated, and the overall dimensions of the unfolded states, which in most of the force fields are too collapsed relative to experimental Förster Resonance Energy Transfer (FRET) data.

Balance between alpha and beta structures in ab initio protein folding

Despite initial successes in folding of proteins by molecular simulation, it is becoming increasingly evident that current energy functions (force fields) tend to favor either alpha or beta secondary structure, such that the choice of force field is governed by the structural class of the protein. Here, we study the folding of peptides with either predominantly alpha (Trp cage) or beta (GB1 hairpin) structure with a modified version of the Amber ff03 force field, optimized to reproduce structural propensity in a helix-forming peptide. Using extensive replica exchange molecular dynamics simulations starting from completely unfolded configurations, we obtain the correct folded structure for each peptide, in close agreement with the experimental native structure (<1.5 A all-atom root-mean-square deviation). We obtain converged equilibrium distributions, with folded populations at standard conditions (approximately 300 K), in remarkable accord with experiment. Further comparison to experimental data from NMR spectroscopy and FRET suggests that although the folded structures are accurately reproduced, the unfolded state remains too structured and compact. Our results suggest that the backbone correction results in a force field that is transferable to the folding of proteins from different structural classes.

Structural classification of the amide I sites of a beta-hairpin with isotope label 2DIR spectroscopy

We present a theoretical study of the possibility to use isotope label two-dimensional infrared (2DIR) spectroscopy to obtain site specific structural information in trpzip2. This small beta-hairpin peptide was designed as a model system for studying protein folding in beta-sheet structures. In order to unravel the folding mechanism, the surroundings of local sites should be characterized, which in principle is possible by using 2DIR in combination with isotope labeling. This requires a classification that correlates local structures to two-dimensional spectra. To this end, we provide the first spectral simulation of the isotope label spectra of all the amide I sites in trpzip2. We find that the anti-diagonal width of the 2DIR peak associated with a labelled site is a good measure of solvent exposure and the key parameter to distinguish between solvent exposed and internal sites. The diagonal widths are not particularly sensitive to this, but they do reveal the presence of slowly interconverting turn structures.

Common folding mechanism of a beta-hairpin peptide via non-native turn formation revealed by unbiased molecular dynamics simulations

The folding of a 15-residue beta-hairpin peptide (Peptide 1) is characterized using multiple unbiased, atomistic molecular dynamics (MD) simulations. Fifteen independent MD trajectories, each 2.5 micros-long for a total of 37.5 micros, are performed of the peptide in explicit solvent, at room temperature, and without the use of enhanced sampling techniques. The computed folding time of 1-1.5 micros obtained from the simulations is in good agreement with experiment [Xu, Y.; et al. J. Am. Chem. Soc. 2003, 125, 15388-15394]. A common folding mechanism is observed, in which the turn is always found to be the major determinant in initiating the folding process, followed by cooperative formation of the interstrand hydrogen bonds and the side-chain packing. Furthermore, direct transition to the folded state from fully unstructured conformations does not take place. Instead, the peptide is always observed to form partially structured conformations involving a non-native (ESYI) turn from which the native (NPDG) turn forms, triggering the folding to the beta-hairpin.

Recovering kinetics from a simplified protein folding model using replica exchange simulations: a kinetic network and effective stochastic dynamics

We present an approach to recover kinetics from a simplified protein folding model at different temperatures using the combined power of replica exchange (RE), a kinetic network, and effective stochastic dynamics. While RE simulations generate a large set of discrete states with the correct thermodynamics, kinetic information is lost due to the random exchange of temperatures. We show how we can recover the kinetics of a 2D continuous potential with an entropic barrier by using RE-generated discrete states as nodes of a kinetic network. By choosing the neighbors and the microscopic rates between the neighbors appropriately, the correct kinetics of the system can be recovered by running a kinetic simulation on the network. We fine-tune the parameters of the network by comparison with the effective drift velocities and diffusion coefficients of the system determined from short-time stochastic trajectories. One of the advantages of the kinetic network model is that the network can be built on a high-dimensional discretized state space, which can consist of multiple paths not consistent with a single reaction coordinate.

A coarse-grained protein force field for folding and structure prediction

We have revisited the protein coarse-grained optimized potential for efficient structure prediction (OPEP). The training and validation sets consist of 13 and 16 protein targets. Because optimization depends on details of how the ensemble of decoys is sampled, trial conformations are generated by molecular dynamics, threading, greedy, and Monte Carlo simulations, or taken from publicly available databases. The OPEP parameters are varied by a genetic algorithm using a scoring function which requires that the native structure has the lowest energy, and the native-like structures have energy higher than the native structure but lower than the remote conformations. Overall, we find that OPEP correctly identifies 24 native or native-like states for 29 targets and has very similar capability to the all-atom discrete optimized protein energy model (DOPE), found recently to outperform five currently used energy models.

Folding mechanism of β-hairpin trpzip2: heterogeneity, transition state and folding pathways

We review the studies on the folding mechanism of the β-hairpin tryptophan zipper 2 (trpzip2) and present some additional computational results to refine the picture of folding heterogeneity and pathways. We show that trpzip2 can have a two-state or a multi-state folding pattern, depending on whether it folds within the native basin or through local state basins on the high-dimensional free energy surface; Trpzip2 can fold along different pathways according to the packing order of tryptophan pairs. We also point out some important problems related to the folding mechanism of trpzip2 that still need clarification, e.g., a wide distribution of the computed conformations for the transition state ensemble.

Replica exchange molecular dynamics simulations of coarse-grained proteins in implicit solvent

Current approaches aimed at determining the free energy surface of all-atom medium-size proteins in explicit solvent are slow and are not sufficient to converge to equilibrium properties. To ensure a proper sampling of the configurational space, it is preferable to use reduced representations such as implicit solvent and/or coarse-grained protein models, which are much lighter computationally. Each model must be verified, however, to ensure that it can recover experimental structures and thermodynamics. Here we test the coarse-grained implicit solvent OPEP model with replica exchange molecular dynamics (REMD) on six peptides ranging in length from 10 to 28 residues: two alanine-based peptides, the second beta-hairpin from protein G, the Trp-cage and zinc-finger motif, and a dimer of a coiled coil peptide. We show that REMD-OPEP recovers the proper thermodynamics of the systems studied, with accurate structural description of the beta-hairpin and Trp-cage peptides (within 1-2 A from experiments). The light computational burden of REMD-OPEP, which enables us to generate many hundred nanoseconds at each temperature and fully assess convergence to equilibrium ensemble, opens the door to the determination of the free energy surface of larger proteins and assemblies.

The unfolded ensemble and folding mechanism of the C-terminal GB1 beta-hairpin

In this work, we shed new light on a much-studied case of beta-hairpin folding by means of advanced molecular dynamics simulations. A fully atomistic description of the protein and the solvent molecule is used, together with metadynamics, to accelerate the sampling and estimate free-energy landscapes. This is achieved using the path collective variables approach, which provides an adaptive description of the mechanism under study. We discover that the folding mechanism is a multiscale process where the turn region conformation leads to two different energy pathways that are connected by elongated structures. The former displays a stable 2:4 native-like structure in which an optimal hydrophobic packing and hydrogen bond pattern leads to 8 kcal/mol of stabilization. The latter shows a less-structured 3:5 beta-sheet, where hydrogen bonds and hydrophobic packing provide only 2.5 kcal/mol of stability. This perspective is fully consistent with experimental evidence that shows this to be a prototypical two-state folder, while it redefines the nature of the unfolded state.

Folding mechanisms of individual beta-hairpins in a Go model of Pin1 WW domain by all-atom molecular dynamics simulations

This paper examines the folding mechanism of an individual beta-hairpin in the presence of other hairpins by using an off-lattice model of a small triple-stranded antiparallel beta-sheet protein, Pin1 WW domain. The turn zipper model and the hydrophobic collapse model originally developed for a single beta-hairpin in literature is confirmed to be useful in describing beta-hairpins in model Pin1 WW domain. We find that the mechanism for folding a specific hairpin is independent of whether it folds first or second, but the formation process are significantly dependent on temperature. More specifically, beta1-beta2 hairpin folds via the turn zipper model at a low temperature and the hydrophobic collapse model at a high temperature, while the folding of beta2-beta3 hairpin follows the turn zipper model at both temperatures. The change in folding mechanisms is interpreted by the interplay between contact stability (enthalpy) and loop lengths (entropy), the effect of which is temperature dependent.

Energy landscapes of the monomer and dimer of the Alzheimer's peptide Abeta(1-28)

The cytotoxicity of Alzheimer's disease has been linked to the self-assembly of the 4042 amino acid of the amyloid-beta (Abeta) peptide into oligomers. To understand the assembly process, it is important to characterize the very first steps of aggregation at an atomic level of detail. Here, we focus on the N-terminal fragment 1-28, known to form fibrils in vitro. Circular dichroism and NMR experiments indicate that the monomer of Abeta(1-28) is alpha-helical in a membranelike environment and random coil in aqueous solution. Using the activation-relaxation technique coupled with the OPEP coarse grained force field, we determine the structures of the monomer and of the dimer of Abeta(1-28). In agreement with experiments, we find that the monomer is predominantly random coil in character, but displays a non-negligible beta-strand probability in the N-terminal region. Dimerization impacts the structure of each chain and leads to an ensemble of intertwined conformations with little beta-strand content in the region Leu17-Ala21. All these structural characteristics are inconsistent with the amyloid fibril structure and indicate that the dimer has to undergo significant rearrangement en route to fibril formation.

The complex folding pathways of protein A suggest a multiple-funnelled energy landscape

Folding proteins into their native states requires the formation of both secondary and tertiary structures. Many questions remain, however, as to whether these form into a precise order, and various pictures have been proposed that place the emphasis on the first or the second level of structure in describing folding. One of the favorite test models for studying this question is the B domain of protein A, which has been characterized by numerous experiments and simulations. Using the activation-relaxation technique coupled with a generic energy model (optimized potential for efficient peptide structure prediction), we generate more than 50 folding trajectories for this 60-residue protein. While the folding pathways to the native state are fully consistent with the funnel-like description of the free energy landscape, we find a wide range of mechanisms in which secondary and tertiary structures form in various orders. Our nonbiased simulations also reveal the presence of a significant number of non-native beta and alpha conformations both on and off pathway, including the visit, for a non-negligible fraction of trajectories, of fully ordered structures resembling the native state of nonhomologous proteins.