Direct molecular dynamics observation of protein folding transition state ensemble

Oligomer Formation by Physiologically Relevant C-Terminal Isoforms of Amyloid β-Protein

Alzheimer's disease (AD) is a neurological disorder associated with amyloid β-protein (Aβ) assembly into toxic oligomers. In addition to the two predominant alloforms, Aβ1-40 and Aβ1-42, other C-terminally truncated Aβ peptides, including Aβ1-38 and Aβ1-43, are produced in the brain. Here, we use discrete molecular dynamics (DMD) and a four-bead protein model with amino acid-specific hydropathic interactions, DMD4B-HYDRA, to examine oligomer formation of Aβ1-38, Aβ1-40, Aβ1-42, and Aβ1-43. Self-assembly of 32 unstructured monomer peptides into oligomers is examined using 32 replica DMD trajectories for each of the four peptides. In a quasi-steady state, Aβ1-38 and Aβ1-40 adopt similar unimodal oligomer size distributions with a maximum at trimers, whereas Aβ1-42 and Aβ1-43 oligomer size distributions are multimodal with the dominant maximum at trimers or tetramers, and additional maxima at hexamers and unidecamers (for Aβ1-42) or octamers and pentadecamers (for Aβ1-43). The free energy landscapes reveal isoform- and oligomer-order specific structural and morphological features of oligomer ensembles. Our results show that oligomers of each of the four isoforms have unique features, with Aβ1-42 alone resulting in oligomers with disordered and solvent-exposed N-termini. Our findings help unravel the structure-function paradigm governing oligomers formed by various Aβ isoforms.

A multi-functional genetic manipulation system and its use in high-level expression of a β-mannanase mutant with high specific activity in Pichia pastoris

To further extend the practical application of a thermostable and acidic resistance β-mannanase (ManAK) in animal feed additives, an effective strategy that combined directed evolution and metabolic engineering was developed. Four positive mutants (P191M, P194E, S199G and S268Q) with enhanced specific activity (25.5%-60.9%) were obtained. The S199G mutant exhibited 56.7% enhancement of specific activity at 37°C and good thermostability, and this was selected for high-level expression in P. pastoris X33. A multi-functional and scarless genetic manipulation system was proposed and functionally verified (gene deletion, substitution/insertion and point mutation). This was then subjected to Rox1p (an oxygen related transcription regulator) deletion and Vitreoscilla haemoglobin (VHb) co-expression for high enzyme productivity in P. pastoris X33VIIManAKS199G . An excellent strain, named X33VIIManAKS199G ∆rox1::VHb, was achieved by combining these two factors, and then the maximum enzymatic activity was further increased to 3753 U ml-1 , which was nearly twice as much as the maximum production of ManAK in P. pastoris. This work provides a systematic and effective method to improve the enzymatic yield of β-mannanase, promotes the application of ManAK in feed additives, and also demonstrated that a scarless genetic manipulation tool is useful in P. pastoris.

Improving the kinetic stability of a hyperthermostable β-mannanase by a rationally combined strategy

Feasible and easily accessible methods for the rational design of enzyme engineering strategies remain to be established. Thus, a new rationally combined strategy based on disulfide bond engineering and HotSpot Wizard 3.0 was proposed and experimentally demonstrated to be effective using a hyperthermostable β-mannanase. Ten of 42 mutants showed prominent enhancement of kinetic stability with 26.4%-39.9% increases in t_1/2 (75 °C) compared with the parent enzyme ManAKH. The best mutant, D273-V308, showed apparent increases in both optimal temperature (5 °C) and T₅₀ (6.8 °C), as well as advanced catalytic efficiency. The low rate of inactive mutants and the high rate of positive mutants indicated that newly introduced screening factors (distance from catalytic residues, Gibbs free energy term, molecular simulation, and visual inspections) greatly enhance the design of thermostable β-mannanase. Moreover, these findings further advance the industrial application of β-mannanase (ManAK) in food and food-related applications.

The effects of mutation and modification on the structure and stability of human lysozyme: A molecular link between carbamylation and atherosclerosis

Amino acid mutations in some proteins such as lysozyme lead to genetically disorder variants and adverse pathogenic consequences. Recently, amino acid modifications were known as a risk factor in many related diseases such as uremia and atherosclerosis, showing the importance of these surface-structure changes. Although the structural consequences of the hereditary proteins have been examined extensively, such effects for the protein modifications are known to a lesser extent. One drawback in the examination of protein modifications is hardness in experimental detection of modifications by techniques such as NMR and crystallography. Molecular modeling and simulation can help to understand such phenomena at the molecular levels. It is more rational that the effects of both mutation and modification can be compared in a single protein model. Here, molecular dynamics simulation is used to compare the effects of a disease-related carbamylation modification and an amyloidogenic mutation (D67H) in human lysozyme as a model protein. The results show that the carbamylation adversely effects on the tertiary structure, leading to the similar unfolding pathway to the hereditary amyloidogenic form. The carbamylation leads to the instability of the overall protein conformation, especially on the β-domain, which is a characteristic of hereditary amyloidosis in human lysozymes. The aggregation behaviors of both modified and mutant lysozyme were examined by molecular docking calculations. The results showed that the partially unfolded lysozyme might form tight protein aggregates upon carbamylation similar to the amyloidogenic variant. Both single and all-residues carbamylations impose serious conformational changes to the tertiary structure of lysozyme. It was obtained that carbamylation of lysozyme strongly effects on the stability of N-terminal β-sheet, which can produce a highly unstable conformation. The results of this study not only show the adverse structural consequences of a disease-associated post-translational modification, but it also may be very helpful to understand the molecular basis for many carbamylation-related diseases such as atherosclerosis in ESRD patients. The results show that non-native post-translational modifications may be as structurally important as hereditary mutations.

Experimentally-driven protein structure modeling

Revolutions in natural and exact sciences started at the dawn of last century have led to the explosion of theoretical, experimental, and computational approaches to determine structures of molecules, complexes, as well as their rich conformational dynamics. Since different experimental methods produce information that is attributed to specific time and length scales, corresponding computational methods have to be tailored to these scales and experiments. These methods can be then combined and integrated in scales, hence producing a fuller picture of molecular structure and motion from the "puzzle pieces" offered by various experiments. Here, we describe a number of computational approaches to utilize experimental data to glance into structure of proteins and understand their dynamics. We will also discuss the limitations and the resolution of the constraints-based modeling approaches. SIGNIFICANCE: Experimentally-driven computational structure modeling and determination is a rapidly evolving alternative to traditional approaches for molecular structure determination. These new hybrid experimental-computational approaches are proving to be a powerful microscope to glance into the structural features of intrinsically or partially disordered proteins, dynamics of molecules and complexes. In this review, we describe various approaches in the field of experimentally-driven computational structure modeling.

A small single-domain protein folds through the same pathway on and off the ribosome

In vivo, proteins fold and function in a complex environment subject to many stresses that can modulate a protein's energy landscape. One aspect of the environment pertinent to protein folding is the ribosome, since proteins have the opportunity to fold while still bound to the ribosome during translation. We use a combination of force and chemical denaturant (chemomechanical unfolding), as well as point mutations, to characterize the folding mechanism of the src SH3 domain both as a stalled ribosome nascent chain and free in solution. Our results indicate that src SH3 folds through the same pathway on and off the ribosome. Molecular simulations also indicate that the ribosome does not affect the folding pathway for this small protein. Taken together, we conclude that the ribosome does not alter the folding mechanism of this small protein. These results, if general, suggest the ribosome may exert a bigger influence on the folding of multidomain proteins or protein domains that can partially fold before the entire domain sequence is outside the ribosome exit tunnel.

Accurate Protein-Folding Transition-Path Statistics from a Simple Free-Energy Landscape

A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths-the rare trajectories that transit between the folded and unfolded ensembles-using only thermodynamic information, such as a low-dimensional equilibrium free-energy landscape. However, commonly used one-dimensional landscapes typically fall short of this aim, because an empirical coordinate-dependent diffusion coefficient has to be fit to transition-path trajectory data in order to reproduce the transition-path dynamics. We show that an alternative, first-principles free-energy landscape predicts transition-path statistics that agree well with simulations and single-molecule experiments without requiring dynamical data as an input. This "topological configuration" model assumes that distinct, native-like substructures assemble on a time scale that is slower than native-contact formation but faster than the folding of the entire protein. Using only equilibrium simulation data to determine the free energies of these coarse-grained intermediate states, we predict a broad distribution of transition-path transit times that agrees well with the transition-path durations observed in simulations. We further show that both the distribution of finite-time displacements on a one-dimensional order parameter and the ensemble of transition-path trajectories generated by the model are consistent with the simulated transition paths. These results indicate that a landscape based on transient folding intermediates, which are often hidden by one-dimensional projections, can form the basis of a predictive model of protein-folding transition-path dynamics.

Islet Amyloid Polypeptide Promotes Amyloid-Beta Aggregation by Binding-Induced Helix-Unfolding of the Amyloidogenic Core

Amyloid aggregation of amyloid-beta (Aβ) and islet amyloid polypeptide (IAPP) is associated with Alzheimer's disease (AD) and type-2 diabetes (T2D), respectively. With T2D being the risk factor for AD and the ability of IAPP to cross the blood-brain barrier, the coaggregation of Aβ and IAPP has been explored to understand the cross-talk between the two diseases. Recent studies demonstrated that soluble IAPP could significantly accelerate the aggregation of Aβ while preformed amyloids of IAPP were poor "seeds" for Aβ aggregation. Here, we apply all-atom discrete molecular dynamics simulations to investigate possible molecular mechanisms for the accelerated coaggregation of IAPP and Aβ42 comparing to Aβ42 aggregation alone, which was confirmed by the complementary thioflavin-T fluorescence assay. Our simulation results suggest that peptides in the mixture tend to form heterodimers as the first step toward their coaggregation. Strong interpeptide interactions with IAPP in the heterodimer shift the helical conformation of Aβ42 in its amyloidogenic central hydrophobic core, residues 16-22 (Aβ16-22), to the extended conformation ready to form β-sheets. Our study suggests that the unfolding of Aβ16-22 helix contributes to the aggregation free-energy barrier and corresponds to the rate-limiting conformational change for Aβ42 aggregation. Therefore, we propose that soluble IAPP promotes the aggregation of Aβ42 by binding-induced conformational change of Aβ42 in its amyloidogenic core and thus reduced aggregation free-energy barrier.

Effects of force fields on the conformational and dynamic properties of amyloid β(1-40) dimer explored by replica exchange molecular dynamics simulations

The conformational space and structural ensembles of amyloid beta (Aβ) peptides and their oligomers in solution are inherently disordered and proven to be challenging to study. Optimum force field selection for molecular dynamics (MD) simulations and the biophysical relevance of results are still unknown. We compared the conformational space of the Aβ(1-40) dimers by 300 ns replica exchange MD simulations at physiological temperature (310 K) using: the AMBER-ff99sb-ILDN, AMBER-ff99sb*-ILDN, AMBER-ff99sb-NMR, and CHARMM22* force fields. Statistical comparisons of simulation results to experimental data and previously published simulations utilizing the CHARMM22* and CHARMM36 force fields were performed. All force fields yield sampled ensembles of conformations with collision cross sectional areas for the dimer that are statistically significantly larger than experimental results. All force fields, with the exception of AMBER-ff99sb-ILDN (8.8 ± 6.4%) and CHARMM36 (2.7 ± 4.2%), tend to overestimate the α-helical content compared to experimental CD (5.3 ± 5.2%). Using the AMBER-ff99sb-NMR force field resulted in the greatest degree of variance (41.3 ± 12.9%). Except for the AMBER-ff99sb-NMR force field, the others tended to under estimate the expected amount of β-sheet and over estimate the amount of turn/bend/random coil conformations. All force fields, with the exception AMBER-ff99sb-NMR, reproduce a theoretically expected β-sheet-turn-β-sheet conformational motif, however, only the CHARMM22* and CHARMM36 force fields yield results compatible with collapse of the central and C-terminal hydrophobic cores from residues 17-21 and 30-36. Although analyses of essential subspace sampling showed only minor variations between force fields, secondary structures of lowest energy conformers are different.

NanoEHS beyond Toxicity - Focusing on Biocorona

The first phase of environmental health and safety of nanomaterials (nanoEHS) studies has been mainly focused on evidence-based investigations that probe the impact of nanoparticles, nanomaterials and nano-enabled products on biological and ecological systems. The integration of multiple disciplines, including colloidal science, nanomaterial science, chemistry, toxicology/immunology and environmental science, is necessary to understand the implications of nanotechnology for both human health and the environment. While strides have been made in connecting the physicochemical properties of nanomaterials with their hazard potential in tiered models, fundamental understanding of nano-biomolecular interactions and their implications for nanoEHS is largely absent from the literature. Research on nano-biomolecular interactions within the context of natural systems not only provides important clues for deciphering nanotoxicity and nanoparticle-induced pathology, but also presents vast new opportunities for screening beneficial material properties and designing greener products from bottom up. This review highlights new opportunities concerning nano-biomolecular interactions beyond the scope of toxicity.

Failure and recovery in dynamical networks

Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between spontaneous damage, induced failure and recovery in both embedded and non-embedded networks. In our model the network's components follow three realistic processes that capture these features: (i) spontaneous failure of a component independent of the neighborhood (internal failure), (ii) failure induced by failed neighboring nodes (external failure) and (iii) spontaneous recovery of a component. We identify a metastable domain in the global network phase diagram spanned by the model's control parameters where dramatic hysteresis effects and random switching between two coexisting states are observed. This dynamics depends on the characteristic link length of the embedded system. For the Euclidean lattice in particular, hysteresis and switching only occur in an extremely narrow region of the parameter space compared to random networks. We develop a unifying theory which links the dynamics of our model to contact processes. Our unifying framework may help to better understand controllability in spatially embedded and random networks where spontaneous recovery of components can mitigate spontaneous failure and damage spread in dynamical networks.

Controlling Allosteric Networks in Proteins

Allosteric transition, defined as conformational changes induced by ligand binding, is one of the fundamental properties of proteins. Allostery has been observed and characterized in many proteins, and has been recently utilized to control protein function via regulation of protein activity. Here, we review the physical and evolutionary origin of protein allostery, as well as its importance to protein regulation, drug discovery, and biological processes in living systems. We describe recently developed approaches to identify allosteric pathways, connected sets of pairwise interactions that are responsible for propagation of conformational change from the ligand-binding site to a distal functional site. We then present experimental and computational protein engineering approaches for control of protein function by modulation of allosteric sites. As an example of application of these approaches, we describe a synergistic computational and experimental approach to rescue the cystic-fibrosis-associated protein cystic fibrosis transmembrane conductance regulator, which upon deletion of a single residue misfolds and causes disease. This example demonstrates the power of allosteric manipulation in proteins to both elucidate mechanisms of molecular function and to develop therapeutic strategies that rescue those functions. Allosteric control of proteins provides a tool to shine a light on the complex cascades of cellular processes and facilitate unprecedented interrogation of biological systems.

Contrasting effects of nanoparticle-protein attraction on amyloid aggregation

Nanoparticles (NPs) have been experimentally found to either promote or inhibit amyloid aggregation of proteins, but the molecular mechanisms for such complex behaviors remain unknown. Using coarse-grained molecular dynamics simulations, we investigated the effects of varying the strength of nonspecific NP-protein attraction on amyloid aggregation of a model protein, the amyloid-beta peptide implicated in Alzheimer's disease. Specifically, with increasing NP-peptide attraction, amyloid aggregation on the NP surface was initially promoted due to increased local protein concentration on the surface and destabilization of the folded state. However, further increase of NP-peptide attraction decreased the stability of amyloid fibrils and reduced their lateral diffusion on the NP surface necessary for peptide conformational changes and self-association, thus prohibiting amyloid aggregation. Moreover, we found that the relative concentration between protein and NPs also played an important role in amyloid aggregation. With a high NP/protein ratio, NPs that intrinsically promote protein aggregation may display an inhibitive effect by depleting the proteins in solution while having a low concentration of the proteins on each NP's surface. Our coarse-grained molecular dynamics simulation study offers a molecular mechanism for delineating the contrasting and seemingly conflicting effects of NP-protein attraction on amyloid aggregation and highlights the potential of tailoring anti-aggregation nanomedicine against amyloid diseases.

Direct observation of a single nanoparticle-ubiquitin corona formation

The advancement of nanomedicine and the increasing applications of nanoparticles in consumer products have led to administered biological exposure and unintentional environmental accumulation of nanoparticles, causing concerns over the biocompatibility and sustainability of nanotechnology. Upon entering physiological environments, nanoparticles readily assume the form of a nanoparticle-protein corona that dictates their biological identity. Consequently, understanding the structure and dynamics of a nanoparticle-protein corona is essential for predicting the fate, transport, and toxicity of nanomaterials in living systems and for enabling the vast applications of nanomedicine. Here we combined multiscale molecular dynamics simulations and complementary experiments to characterize the silver nanoparticle-ubiquitin corona formation. Notably, ubiquitins competed with citrates for the nanoparticle surface, governed by specific electrostatic interactions. Under a high protein/nanoparticle stoichiometry, ubiquitins formed a multi-layer corona on the particle surface. The binding exhibited an unusual stretched-exponential behavior, suggesting a rich binding kinetics. Furthermore, the binding destabilized the α-helices while increasing the β-sheet content of the proteins. This study revealed the atomic and molecular details of the structural and dynamic characteristics of nanoparticle-protein corona formation.

Microcanonical thermostatistics of coarse-grained proteins with amyloidogenic propensity

The formation of fibrillar aggregates seems to be a common characteristic of polypeptide chains, although the observation of these aggregates may depend on appropriate experimental conditions. Partially folded intermediates seem to have an important role in the generation of protein aggregates, and a mechanism for this fibril formation considers that these intermediates also correspond to metastable states with respect to the fibrillar ones. Here, using a coarse-grained (CG) off-lattice model, we carry out a comparative analysis of the thermodynamic aspects characterizing the folding transition with respect to the propensity for aggregation of four different systems: two isoforms of the amyloid β-protein, the Src SH3 domain, and the human prion proteins (hPrP). Microcanonical analysis of the data obtained from replica exchange method is conducted to evaluate the free-energy barrier and latent heat in these models. The simulations of the amyloid β isoforms and Src SH3 domain indicated that the folding process described by this CG model is related to a negative specific heat, a phenomenon that can only be verified in the microcanonical ensemble in first-order phase transitions. The CG simulation of the hPrP heteropolymer yielded a continuous folding transition. The absence of a free-energy barrier and latent heat favors the presence of partially unfolded conformations, and in this context, this thermodynamic aspect could explain the reason why the hPrP heteropolymer is more aggregation-prone than the other heteropolymers considered in this study. We introduced the hydrophobic radius of gyration as an order parameter and found that it can be used to obtain reliable information about the hydrophobic packing and the transition temperatures in the folding process.

Network approach to identify the folding transition states of peptides and proteins

Folding transition states and their structures are crucial in understanding protein folding pathways and folding dynamics. As they cannot be detected directly by experiments due to their instability, many computational methods have been proposed to solve this problem. However, each of these methods can give only one part of the transition state ensemble for a peptide or protein. Here we present a folding-network approach to identify the transition states of peptides or proteins and test it on the β-hairpin peptide trpzip2, with the result that we identify all the folding transition states of tripzip2, which may only be determined separately by other methods. This suggests that the network approach can provide more complete information about the folding transition states, at least for peptides.

Discrete molecular dynamics distinguishes nativelike binding poses from decoys in difficult targets

Virtual screening is one of the major tools used in computer-aided drug discovery. In structure-based virtual screening, the scoring function is critical to identifying the correct docking pose and accurately predicting the binding affinities of compounds. However, the performance of existing scoring functions has been shown to be uneven for different targets, and some important drug targets have proven especially challenging. In these targets, scoring functions cannot accurately identify the native or near-native binding pose of the ligand from among decoy poses, which affects both the accuracy of the binding affinity prediction and the ability of virtual screening to identify true binders in chemical libraries. Here, we present an approach to discriminating native poses from decoys in difficult targets for which several scoring functions failed to correctly identify the native pose. Our approach employs Discrete Molecular Dynamics simulations to incorporate protein-ligand dynamics and the entropic effects of binding. We analyze a collection of poses generated by docking and find that the residence time of the ligand in the native and nativelike binding poses is distinctly longer than that in decoy poses. This finding suggests that molecular simulations offer a unique approach to distinguishing the native (or nativelike) binding pose from decoy poses that cannot be distinguished using scoring functions that evaluate static structures. The success of our method emphasizes the importance of protein-ligand dynamics in the accurate determination of the binding pose, an aspect that is not addressed in typical docking and scoring protocols.

Local unfolding of Cu, Zn superoxide dismutase monomer determines the morphology of fibrillar aggregates

Aggregation of Cu, Zn superoxide dismutase (SOD1) is often found in amyotrophic lateral sclerosis patients. The fibrillar aggregates formed by wild type and various disease-associated mutants have recently been found to have distinct cores and morphologies. Previous computational and experimental studies of wild-type SOD1 suggest that the apo-monomer, highly aggregation prone, displays substantial local unfolding dynamics. The residual folded structure of locally unfolded apoSOD1 corresponds to peptide segments forming the aggregation core as identified by a combination of proteolysis and mass spectroscopy. Therefore, we hypothesize that the destabilization of apoSOD1 caused by various mutations leads to distinct local unfolding dynamics. The partially unfolded structure, exposing the hydrophobic core and backbone hydrogen bond donors and acceptors, is prone to aggregate. The peptide segments in the residual folded structures form the "building block" for aggregation, which in turn determines the morphology of the aggregates. To test this hypothesis, we apply a multiscale simulation approach to study the aggregation of three typical SOD1 variants: wild type, G37R, and I149T. Each of these SOD1 variants has distinct peptide segments forming the core structure and features different aggregate morphologies. We perform atomistic molecular dynamics simulations to study the conformational dynamics of apoSOD1 monomer and coarse-grained molecular dynamics simulations to study the aggregation of partially unfolded SOD1 monomers. Our computational studies of monomer local unfolding and the aggregation of different SOD1 variants are consistent with experiments, supporting the hypothesis of the formation of aggregation "building blocks" via apo-monomer local unfolding as the mechanism of SOD1 fibrillar aggregation.

The redundancy of NMR restraints can be used to accelerate the unfolding behavior of an SH3 domain during molecular dynamics simulations

1 Abstract

Structured pathway across the transition state for peptide folding revealed by molecular dynamics simulations

Small globular proteins and peptides commonly exhibit two-state folding kinetics in which the rate limiting step of folding is the surmounting of a single free energy barrier at the transition state (TS) separating the folded and the unfolded states. An intriguing question is whether the polypeptide chain reaches, and leaves, the TS by completely random fluctuations, or whether there is a directed, stepwise process. Here, the folding TS of a 15-residue β-hairpin peptide, Peptide 1, is characterized using independent 2.5 μs-long unbiased atomistic molecular dynamics (MD) simulations (a total of 15 μs). The trajectories were started from fully unfolded structures. Multiple (spontaneous) folding events to the NMR-derived conformation are observed, allowing both structural and dynamical characterization of the folding TS. A common loop-like topology is observed in all the TS structures with native end-to-end and turn contacts, while the central segments of the strands are not in contact. Non-native sidechain contacts are present in the TS between the only tryptophan (W11) and the turn region (P7-G9). Prior to the TS the turn is found to be already locked by the W11 sidechain, while the ends are apart. Once the ends have also come into contact, the TS is reached. Finally, along the reactive folding paths the cooperative loss of the W11 non-native contacts and the formation of the central inter-strand native contacts lead to the peptide rapidly proceeding from the TS to the native state. The present results indicate a directed stepwise process to folding the peptide.

The folding dynamics of many small protein/peptides investigated recently are in terms of simple two-state model in which only two populations exist (folded and unfolded), separated by a single free energy barrier with only one kinetically important transition state (TS). However, dynamical characterization of the folding TS is challenging. We have used independent unbiased atomistic molecular dynamics simulations with clear folding-unfolding transitions to characterize structural and dynamical features of transition state ensemble of Peptide 1. A common loop-like topology is observed in all TS structures extracted from multiple simulations. The trajectories were used to examine the mechanism by which the TS is reached and subsequent events in folding pathways. The folding TS is reached and crossed in a directed stagewise process rather than through random fluctuations. Specific structures are formed before, during, and after the transition state, indicating a clear structured folding pathway.

Effectiveness of Φ-value analysis in the binding process of Arc repressor dimer

Φ-value analysis has proved to be a powerful technique in protein folding studies. It has been used to study the transition state structures, to infer microscopic folding pathways, and to identify key residues in the protein folding process. However, its effectiveness in protein binding reaction has not been tested, especially when a fly-casting mechanism is involved. In this article we attempt to answer this question through a coarse-grained study of the binding reaction of Arc repressor dimer. Our simulations show that its binding process proceeds through a fly-casting mechanism, consistent with previous results. We then estimate the importance of the residues for the fly-casting binding by computationally mutating each of them into glycine and calculating their respective effects on the capture radius. It is found that (1) the residues with high Φ values may not be responsible for the large capture radius in the fly-casting binding; (2) mutation of residues with low Φ values may destabilize the denatured states and then increase the capture radius, presumably further increasing the binding rate. Based on our simulations, we conclude that Φ values do not reflect well the importance of residues in the fly-casting binding reaction and need to be combined with other techniques to provide a complete picture.

Macromolecular crowding induces polypeptide compaction and decreases folding cooperativity

A cell's interior is comprised of macromolecules that can occupy up to 40% of its available volume. Such crowded environments can influence the stability of proteins and their rates of reaction. Using discrete molecular dynamics simulations, we investigate how both the size and number of neighboring crowding reagents affect the thermodynamic and folding properties of structurally diverse proteins. We find that crowding induces higher compaction of proteins. We also find that folding becomes less cooperative with the introduction of crowders into the system. The crowders may induce alternative non-native protein conformations, thus creating barriers for protein folding in highly crowded media.

Nucleation process in the folding of a domain-swapped dimer

Nucleation processes are important for the understanding in protein dynamics. To evaluate the effect of nucleation mechanism in dimerization process, a domain-swapped dimer (Esp8) is simulated with the symmetrized Gō model and the classical Gō model. The pathways of the dimerization are analyzed with computational phi -analysis method. It is found out that some nuclei are observed in the kinetic steps of the dimeric association though the whole pathway is a process with multiple intermediate states. The key residues in the nuclei are rather similar to those observed in the monomeric folding. The differences with the monomeric cases are also discussed. These differences illustrate the effects of dimeric feature on the nucleation process. Besides, manual mutations are carried out to illustrate the importance of the interactions related to the nuclei. It is observed that the mutations in the nuclei-related interactions apparently change the dynamics while other mutations have little effect on the kinetics. All of these results outline a picture that the nucleation processes act as the fundamental steps of high-order organization of protein systems.

N-terminal strands of filamin Ig domains act as a conformational switch under biological forces

Conformational changes of filamin A under stress have been postulated to play crucial roles in signaling pathways of cell responses. Direct observation of conformational changes under stress is beyond the resolution of current experimental techniques. On the other hand, computational studies are mainly limited to either traditional molecular dynamics simulations of short durations and high forces or simulations of simplified models. Here we perform all-atom discrete molecular dynamics (DMD) simulations to study thermally and force-induced unfolding of filamin A. The high conformational sampling efficiency of DMD allows us to observe force-induced unfolding of filamin A Ig domains under physiological forces. The computationally identified critical unfolding forces agree well with experimental measurements. Despite a large heterogeneity in the population of force-induced intermediate states, we find a common initial unfolding intermediate in all the Ig domains of filamin, where the N-terminal strand unfolds. We also study the thermal unfolding of several filamin Ig-like domains. We find that thermally induced unfolding features an early-stage intermediate state similar to the one observed in force-induced unfolding and characterized by the N-terminal strand being unfurled. We propose that the N-terminal strand may act as a conformational switch that unfolds under physiological forces leading to exposure of cryptic binding sites, removal of native binding sites, and modulating the quaternary structure of domains.

Allosteric Conformational Transition in Adenylate Kinase: Dynamic Correlations and Implication for Allostery

An essential aspect of protein science is to determine the deductive relationship between structure, dynamics, and various sets of functions. The role of dynamics is currently challenging our understanding of protein functions, both experimentally and theoretically. To verify the internal fluctuations and dynamics correlations in an enzyme protein undergoing conformational transitions, we have applied a coarse-grained dynamics algorithm using the elastic network model for adenylate kinase. Normal mode analysis reveals possible dynamical and allosteric pathways for the transition between the open and the closed states of adenylate kinase. As the ligands binding induces significant flexibility changes of the nucleotides monophosphate (NMP) domain and adenosine triphosphate (ATP) domain, the diagonalized correlation between different structural transition states shows that most correlated motions occur between the NMP domain and the helices surrounding the ATP domain. The simultaneous existence of positive and negative correlations indicates that the conformational changes of adenylate kinase take place in an allosteric manner. Analyses of the cumulated normal mode overlap coefficients and long-range correlated motion provide new insights of operating mechanisms and dynamics of adenylate kinase. They also suggest a quantitative dynamics criterion for determining the allosteric cooperativity, which may be applicable to other proteins.

Prediction of the protein folding core: application to the immunoglobulin fold

We propose an algorithm that allows predicting residues important for the formation of the structure of globular proteins. It relies on a simulation that detects the amino acids presenting a maximum number of neighbours during the early steps of the folding process. They have been called MIR (Most Interacting Residues). Independently, description of the protein structures in fragments with closed ends shows the correlation between these extremities and the core of the globules. These fragments are of rather constant length, typically between 20 and 25 amino acids, and we have previously shown that their extremities are preferentially occupied by MIR. Introduction of rules derived from this fragment analysis of tertiary structures allows to smooth the distribution of MIR, for a better match between TEF ends and MIR. In order to assess this prediction of the folding core, a large family of structures has been used, with sequences as different as possible. A dataset of 56 immunoglobulin structures of various functions but common fold has been used in this study. This fold was chosen because it is one of the most populated with a large amount of data available on its nucleus. In the immunoglobulin domain, "functional and structural load is clearly separated: loops are responsible for binding and recognition while interactions between several residues of the buried core provide stability and fast folding"[1]. We then determined the positions susceptible of high importance for the folding process to occur and compared them to published data, either to High Throw Out Order (HTOO), Conservatism of Conservatism (CoC) or Phi value experiments. It results a reasonable agreement between the positions that we predict and experimental data. Besides, our prediction goes beyond the simple use of a null solvent accessibility of amino acids as a criterion to predict the core. We find the same quality of our prediction on the flavodoxin like superfamily.

Analysis of the free-energy surface of proteins from reversible folding simulations

Computer generated trajectories can, in principle, reveal the folding pathways of a protein at atomic resolution and possibly suggest general and simple rules for predicting the folded structure of a given sequence. While such reversible folding trajectories can only be determined ab initio using all-atom transferable force-fields for a few small proteins, they can be determined for a large number of proteins using coarse-grained and structure-based force-fields, in which a known folded structure is by construction the absolute energy and free-energy minimum. Here we use a model of the fast folding helical λ-repressor protein to generate trajectories in which native and non-native states are in equilibrium and transitions are accurately sampled. Yet, representation of the free-energy surface, which underlies the thermodynamic and dynamic properties of the protein model, from such a trajectory remains a challenge. Projections over one or a small number of arbitrarily chosen progress variables often hide the most important features of such surfaces. The results unequivocally show that an unprojected representation of the free-energy surface provides important and unbiased information and allows a simple and meaningful description of many-dimensional, heterogeneous trajectories, providing new insight into the possible mechanisms of fast-folding proteins.

The process of protein folding is a complex transition from a disordered to an ordered state. Here, we simulate a specific fast-folding protein at the point at which the native and denatured states are at equilibrium and show that obtaining an accurate description of the mechanisms of folding and unfolding is far from trivial. Using simple quantities which quantify the degree of native order is, in the case of this protein, clearly misleading. We show that an unbiased representation of the free-energy surface can be obtained; using such a representation we are able to redesign the landscape and thus modify, upon site-specific “mutations”, the folding and unfolding rates. This leads us to formulate a hypothesis to explain the very fast folding of many proteins.

Multiscale approaches for studying energy transduction in dynein

Cytoplasmic dynein is an important motor that drives all minus-end directed movement along microtubules. Dynein is a complex motor whose processive motion is driven by ATP-hydrolysis. Dynein's run length has been measured to be several millimetres with typical velocities in the order of a few nanometres per second. Therefore, the average time between steps is a fraction of a second. When this time scale is compared with typical time scales for protein side chain and backbone movements (approximately 10(-9) s and approximately 10(-5) s, respectively), it becomes clear that a multi-timescale modelling approach is required to understand energy transduction in this protein. Here, we review recent efforts to use computational and mathematical modelling to understand various aspects of dynein's chemomechanical cycle. First, we describe a structural model of dynein's motor unit showing a heptameric organization of the motor subunits. Second, we describe our molecular dynamics simulations of the motor unit that are used to investigate the dynamics of the various motor domains. Third, we present a kinetic model of the coordination between the two dynein heads. Lastly, we investigate the various potential geometries of the dimer during its hydrolytic and stepping cycle.

Coarse-grained dynamics of the receiver domain of NtrC: fluctuations, correlations and implications for allosteric cooperativity

Receiver domains are key molecular switches in bacterial signaling. Structural studies have shown that the receiver domain of the nitrogen regulatory protein C (NtrC) exists in a conformational equilibrium encompassing both inactive and active states, with phosphorylation of Asp54 allosterically shifting the equilibrium towards the active state. To analyze dynamical fluctuations and correlations in NtrC as it undergoes activation, we have applied a coarse-grained dynamics algorithm using elastic network models. Normal mode analysis reveals possible dynamical pathways for the transition of NtrC from the inactive state to the active state. The diagonalized correlation between the inactive and the active (phosphorylated) state shows that most correlated motions occur around the active site of Asp54 and in the region Thr82 to Tyr101. This indicates a coupled correlation of dynamics in the "Thr82-Tyr101" motion. With phosphorylation inducing significant flexibility changes around the active site and alpha3 and alpha4 helices, we find that this activation makes the active-site region and the loops of alpha3/beta4 and alpha4/beta5 more stable. This means that phosphorylation entropically favors the receiver domain in its active state, and the induced conformational changes occur in an allosteric manner. Analyses of the local flexibility and long-range correlated motion also suggest a dynamics criterion for determining the allosteric cooperativity of NtrC, and may be applicable to other proteins.

Probing protein aggregation using discrete molecular dynamics

Understanding the role of biomolecular dynamics in cellular processes leading to human diseases and the ability to rationally manipulate these processes is of fundamental importance in scientific research. The last decade has witnessed significant progress in probing biophysical behavior of proteins. However, we are still limited in understanding how changes in protein dynamics and inter-protein interactions occurring in short length- and time-scales lead to aberrations in their biological function. Bridging this gap in biology probed using computer simulations marks a challenging frontier in computational biology. Here we examine hypothesis-driven simplified protein models in conjunction with discrete molecular dynamics in the study of protein aggregation, implicated in series of neurodegenerative diseases, such as Alzheimer's and Huntington's diseases. Discrete molecular dynamics simulations of simplified protein models have emerged as a powerful methodology with its ability to bridge the gap in time and length scales from protein dynamics to aggregation, and provide an indispensable tool for probing protein aggregation.

Coarse-grained models reveal functional dynamics--II. Molecular dynamics simulation at the coarse-grained level--theories and biological applications

Molecular dynamics (MD) simulation has remained the most indispensable tool in studying equilibrium/non-equilibrium conformational dynamics since its advent 30 years ago. With advances in spectroscopy accompanying solved biocomplexes in growing sizes, sampling their dynamics that occur at biologically interesting spatial/temporal scales becomes computationally intractable; this motivated the use of coarse-grained (CG) approaches. CG-MD models are used to study folding and conformational transitions in reduced resolution and can employ enlarged time steps due to the absence of some of the fastest motions in the system. The Boltzmann-Inversion technique, heavily used in parameterizing these models, provides a smoothed-out effective potential on which molecular conformation evolves at a faster pace thus stretching simulations into tens of microseconds. As a result, a complete catalytic cycle of HIV-1 protease or the assembly of lipid-protein mixtures could be investigated by CG-MD to gain biological insights. In this review, we survey the theories developed in recent years, which are categorized into Folding-based and Molecular-Mechanics-based. In addition, physical bases in the selection of CG beads/time-step, the choice of effective potentials, representation of solvent, and restoration of molecular representations back to their atomic details are systematically discussed.

Geometrical features of the protein folding mechanism are a robust property of the energy landscape: a detailed investigation of several reduced models

The concept of a funneled energy landscape and the principle of minimal frustration are the theoretical foundation justifying the applicability of structure-based models. In simulations, a protein is commonly reduced to a C(alpha)-bead representation. These simulations are sufficient to predict the geometrical features of the folding mechanism observed experimentally utilizing a concise formulation of the Hamiltonian with low computational costs. Toward a better understanding of the interplay between energetic and geometrical features in folding, the side chain is now explicitly included in the simulations. The simplest choice is the addition of C(beta)-beads at the center-of-mass position of the side chains. While one varies the energetic parameters of the model, the geometric aspects of the folding mechanism remain robust for a broad range of parameters. Energetic properties like folding barriers and protein stability are sensitive to the details of simulations. This robustness to geometry and sensitivity to energetic properties provide flexibility in choosing different parameters to represent changes in sequences, environments, stability or folding rate effects. Therefore, minimal frustration and the funnel concept guarantee that the geometrical features are robust properties of the folding landscape, while mutations and/or changes in the environment easily influence energy-dependent properties like folding rates or stability.

Protein folding: then and now

Over the past three decades the protein folding field has undergone monumental changes. Originally a purely academic question, how a protein folds has now become vital in understanding diseases and our abilities to rationally manipulate cellular life by engineering protein folding pathways. We review and contrast past and recent developments in the protein folding field. Specifically, we discuss the progress in our understanding of protein folding thermodynamics and kinetics, the properties of evasive intermediates, and unfolded states. We also discuss how some abnormalities in protein folding lead to protein aggregation and human diseases.

Folding and unfolding of gammaTIM monomers and dimers

Kinetic simulations of the folding and unfolding of triosephosphate isomerase (TIM) from yeast were conducted using a single monomer gammaTIM polypeptide chain that folds as a monomer and two gammaTIM chains that fold to the native dimer structure. The basic protein model used was a minimalist Gō model using the native structure to determine attractive energies in the protein chain. For each simulation type--monomer unfolding, monomer refolding, dimer unfolding, and dimer refolding--thirty simulations were conducted, successfully capturing each reaction in full. Analysis of the simulations demonstrates four main conclusions. First, all four simulation types have a similar "folding order", i.e., they have similar structures in intermediate stages of folding between the unfolded and folded state. Second, despite this similarity, different intermediate stages are more or less populated in the four different simulations, with 1), no intermediates populated in monomer unfolding; 2), two intermediates populated with beta(2)-beta(4) and beta(1)-beta(5) regions folded in monomer refolding; 3), two intermediates populated with beta(2)-beta(3) and beta(2)-beta(4) regions folded in dimer unfolding; and 4), two intermediates populated with beta(1)-beta(5) and beta(1)-beta(5) + beta(6) + beta(7) + beta(8) regions folded in dimer refolding. Third, simulations demonstrate that dimer binding and unbinding can occur early in the folding process before complete monomer-chain folding. Fourth, excellent agreement is found between the simulations and MPAX (misincorporation proton alkyl exchange) experiments. In total, this agreement demonstrates that the computational Gō model is accurate for gammaTIM and that the energy landscape of gammaTIM appears funneled to the native state.

Structural analysis of kinetic folding intermediates for a TIM barrel protein, indole-3-glycerol phosphate synthase, by hydrogen exchange mass spectrometry and Gō model simulation

The structures of partially folded states appearing during the folding of a (betaalpha)(8) TIM barrel protein, the indole-3-glycerol phosphate synthase from Sulfolobus solfataricus (sIGPS), was assessed by hydrogen exchange mass spectrometry (HX-MS) and Gō model simulations. HX-MS analysis of the peptic peptides derived from the pulse-labeled product of the sub-millisecond folding reaction from the urea-denatured state revealed strong protection in the (betaalpha)(4) region, modest protection in the neighboring (betaalpha)(1-3) and (betaalpha)(5)beta(6) segments and no significant protection in the remaining N and C-terminal segments. These results demonstrate that this species is not a collapsed form of the unfolded state under native-favoring conditions nor is it the native state formed via fast-track folding. However, the striking contrast of these results with the strong protection observed in the (betaalpha)(2-5)beta(6) region after 5 s of folding demonstrates that these species represent kinetically distinct folding intermediates that are not identical as previously thought. A re-examination of the kinetic folding mechanism by chevron analysis of fluorescence data confirmed distinct roles for these two species: the burst-phase intermediate is predicted to be a misfolded, off-pathway intermediate, while the subsequent 5 s intermediate corresponds to an on-pathway equilibrium intermediate. Comparison with the predictions using a C(alpha) Gō model simulation of the kinetic folding reaction for sIGPS shows good agreement with the core of the structure offering protection against exchange in the on-pathway intermediate(s). Because the native-centric Gō model simulations do not explicitly include sequence-specific information, the simulation results support the hypothesis that the topology of TIM barrel proteins is a primary determinant of the folding free energy surface for the productive folding reaction. The early misfolding reaction must involve aspects of non-native structure not detected by the Gō model simulation.

Multiscale Coarse-Graining of Monosaccharides

A systematic multiscale coarse-graining (MS-CG) algorithm is applied to build coarse-grained models for monosaccharides in aqueous solution. The methodology is demonstrated for the example of alpha-D-glucopyranose. The nonbonded interactions are directly derived from the force-matching approach, whereas the bonded interactions are obtained through Boltzmann statistical analyses of the underlying atomistic trajectory. The MS-CG model is shown to reproduce many structural and thermodynamic properties in the constant NPT ensemble. Although the model is derived at a single temperature, pressure, and concentration, it is shown to be reasonably transferable to other thermodynamic states. In this model, long-range interactions are effectively mapped into short-range forces with a moderate cutoff and are evaluated by table look-up. As a result, molecular dynamics employing the MS-CG model is approximately 3 orders of magnitude more efficient than its atomistic counterpart. Consequently, the model is particularly suitable for simulating carbohydrate systems at large length and long time scales. Results for an alpha-(1-->4)-d-glucan with 14 glucose units are also presented, demonstrating that the MS-CG algorithm is also applicable to the coarse-graining of other saccharide systems.

Parallel folding pathways in the SH3 domain protein

The transition-state ensemble (TSE) is the set of protein conformations with an equal probability to fold or unfold. Its characterization is crucial for an understanding of the folding process. We determined the TSE of the src-SH3 domain protein by using extensive molecular dynamics simulations of the Go model and computing the folding probability of a generated set of TSE candidate conformations. We found that the TSE possesses a well-defined hydrophobic core with variable enveloping structures resulting from the superposition of three parallel folding pathways. The most preferred pathway agrees with the experimentally determined TSE, while the two least preferred pathways differ significantly. The knowledge of the different pathways allows us to design the interactions between amino acids that guide the protein to fold through the least preferred pathway. This particular design is akin to a circular permutation of the protein. The finding motivates the hypothesis that the different experimentally observed TSEs in homologous proteins and circular permutants may represent potentially available pathways to the wild-type protein.

Energy and Enthalpy Distribution Functions for a Few Physical Systems

The present work is devoted to extracting the energy or enthalpy distribution function of a physical system from the moments of the distribution using the maximum entropy method. This distribution theory has the salient traits that it utilizes only the experimental thermodynamic data. The calculated distribution functions provide invaluable insight into the state or phase behavior of the physical systems under study. As concrete evidence, we demonstrate the elegance of the distribution theory by studying first a test case of a two-dimensional six-state Potts model for which simulation results are available for comparison, then the biphasic behavior of the binary alloy Na-K whose excess heat capacity, experimentally observed to fall in a narrow temperature range, has yet to be clarified theoretically, and finally, the thermally induced state behavior of a collection of 16 proteins.

The length dependence of the polyQ-mediated protein aggregation

Polyglutamine (polyQ) repeat disorders are caused by the expansion of CAG tracts in certain genes, resulting in transcription of proteins with abnormally long polyQ inserts. When these inserts expand beyond 35-45 glutamines, affected proteins form toxic aggregates, leading to neuron death. Chymotrypsin inhibitor 2 (CI2) with an inserted glutamine repeat has previously been used to model polyQ-mediated aggregation in vitro. However, polyQ insertion lengths in these studies have been kept below the pathogenic threshold. We perform molecular dynamics simulations to study monomer folding dynamics and dimer formation in CI2-polyQ chimeras with insertion lengths of up to 80 glutamines. Our model recapitulates the experimental results of previous studies of chimeric CI2 proteins, showing high folding cooperativity of monomers as well as protein association via domain swapping. Surprisingly, for chimeras with insertion lengths above the pathogenic threshold, monomer folding cooperativity decreases and the dominant mode for dimer formation becomes interglutamine hydrogen bonding. These results support a mechanism for pathogenic polyQ-mediated aggregation, in which expanded polyQ tracts destabilize affected proteins and promote the formation of partially unfolded intermediates. These unfolded intermediates form aggregates through associations by interglutamine interactions.