Role of native topology investigated by multiple unfolding simulations of four SH3 domains

Protein-water interactions in MD simulations: POPS/POPSCOMP solvent accessibility analysis, solvation forces and hydration sites

The effects of solvation on molecular recognition are investigated from different perspectives, ranging from methods to analyse explicit solvent dynamical behaviour at the protein surface to methods for the implicit treatment of solvent effects associated with the conformational behaviour of biomolecules. The here presented implicit solvation method is based on an analytical approximation of the Solvent Accessible Surface Area (SASA) of solute molecules, which is computationally efficient and easy to parametrise. The parametrised SASA solvation method is discussed in the light of protein design and ligand binding studies. The POPS program for the SASA computation on single molecules and complex interfaces is described in detail. Explicit solvent behaviour is described here in the form of solvent density maps at the protein surface. We highlight the usefulness of that approach in defining the organisation of specific water molecules at functional sites and in determining hydrophobicity scores for the identification of potential interaction patches.

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

1 Abstract

Computational model for protein unfolding simulation

The protein folding problem is one of the fundamental and important questions in molecular biology. However, the all-atom molecular dynamics studies of protein folding and unfolding are still computationally expensive and severely limited by the time scale of simulation. In this paper, a simple and fast protein unfolding method is proposed based on the conformational stability analyses and structure modeling. In this method, two structure-based conditions are considered to identify the unstable regions of proteins during the unfolding processes. The protein unfolding trajectories are mimicked through iterative structure modeling according to conformational stability analyses. Two proteins, chymotrypsin inhibitor 2 (CI2) and α -spectrin SH3 domain (SH3) were simulated by this method. Their unfolding pathways are consistent with the previous molecular dynamics simulations. Furthermore, the transition states of the two proteins were identified in unfolding processes and the theoretical Φ values of these transition states showed significant correlations with the experimental data (the correlation coefficients are >0.8). The results indicate that this method is effective in studying protein unfolding. Moreover, we analyzed and discussed the influence of parameters on the unfolding simulation. This simple coarse-grained model may provide a general and fast approach for the mechanism studies of protein folding.

The folding transition-state ensemble of a four-helix bundle protein: helix propensity as a determinant and macromolecular crowding as a probe

The four-helix bundle protein Rd-apocyt b(562), a redesigned stable variant of apocytochrome b(562), exhibits two-state folding kinetics. Its transition-state ensemble has been characterized by Phi-value analysis. To elucidate the molecular basis of the transition-state ensemble, we have carried out high-temperature molecular dynamics simulations of the unfolding process. In six parallel simulations, unfolding started with the melting of helix I and the C-terminal half of helix IV, and followed by helix III, the N-terminal half of helix IV and helix II. This ordered melting of the helices is consistent with the conclusion from native-state hydrogen exchange, and can be rationalized by differences in intrinsic helix propensity. Guided by experimental Phi-values, a putative transition-state ensemble was extracted from the simulations. The residue helical probabilities of this transition-state ensemble show good correlation with the Phi-values. To further validate the putative transition-state ensemble, the effect of macromolecular crowding on the relative stability between the unfolded ensemble and the transition-state ensemble was calculated. The resulting effect of crowding on the folding kinetics agrees well with experimental observations. This study shows that molecular dynamics simulations combined with calculation of crowding effects provide an avenue for characterize the transition-state ensemble in atomic details.

Dynameomics: a consensus view of the protein unfolding/folding transition state ensemble across a diverse set of protein folds

The Dynameomics project aims to simulate a representative sample of all globular protein metafolds under both native and unfolding conditions. We have identified protein unfolding transition state (TS) ensembles from multiple molecular dynamics simulations of high-temperature unfolding in 183 structurally distinct proteins. These data can be used to study individual proteins and individual protein metafolds and to mine for TS structural features common across all proteins. Separating the TS structures into four different fold classes (all proteins, all-alpha, all-beta, and mixed alpha/beta and alpha +beta) resulted in no significant difference in the overall protein properties. The residues with the most contacts in the native state lost the most contacts in the TS ensemble. On average, residues beginning in an alpha-helix maintained more structure in the TS ensemble than did residues starting in beta-strands or any other conformation. The metafolds studied here represent 67% of all known protein structures, and this is, to our knowledge, the largest, most comprehensive study of the protein folding/unfolding TS ensemble to date. One might have expected broad distributions in the average global properties of the TS relative to the native state, indicating variability in the amount of structure present in the TS. Instead, the average global properties converged with low standard deviations across metafolds, suggesting that there are general rules governing the structure and properties of the TS.

Molecular dynamics simulation of phosphorylated KID post-translational modification

Background

Kinase-inducible domain (KID) as transcriptional activator can stimulate target gene expression in signal transduction by associating with KID interacting domain (KIX). NMR spectra suggest that apo-KID is an unstructured protein. After post-translational modification by phosphorylation, KID undergoes a transition from disordered to well folded protein upon binding to KIX. However, the mechanism of folding coupled to binding is poorly understood.

Methodology

To get an insight into the mechanism, we have performed ten trajectories of explicit-solvent molecular dynamics (MD) for both bound and apo phosphorylated KID (pKID). Ten MD simulations are sufficient to capture the average properties in the protein folding and unfolding.

Conclusions

Room-temperature MD simulations suggest that pKID becomes more rigid and stable upon the KIX-binding. Kinetic analysis of high-temperature MD simulations shows that bound pKID and apo-pKID unfold via a three-state and a two-state process, respectively. Both kinetics and free energy landscape analyses indicate that bound pKID folds in the order of KIX access, initiation of pKID tertiary folding, folding of helix α_B, folding of helix α_A, completion of pKID tertiary folding, and finalization of pKID-KIX binding. Our data show that the folding pathways of apo-pKID are different from the bound state: the foldings of helices α_A and α_B are swapped. Here we also show that Asn139, Asp140 and Leu141 with large Φ-values are key residues in the folding of bound pKID. Our results are in good agreement with NMR experimental observations and provide significant insight into the general mechanisms of binding induced protein folding and other conformational adjustment in post-translational modification.

Binding induced folding in p53-MDM2 complex

The MDM2 N-terminal domain can bind to the transactivation domain of p53 and downregulate its ability to activate transcription. It was found that binding with p53 stabilizes the MDM2 N-terminal domain. Thus the coupling between binding and folding is essential in the normal functional interactions between p53 and MDM2. We have performed explicit-solvent molecular dynamics simulations (MD) for both bound MDM2(N) and apo-MDM2 to study the interdependence of binding and folding in the p53-MDM2 complex. Kinetic analysis of high-temperature MD simulations shows that both bound MDM2(N) and apo-MDM2 unfold via a two-state process. Both kinetics and free energy landscape analyses indicate that bound MDM2 unfolds in the order of p53 unbinding, tertiary unfolding, and finally secondary structure unfolding. Our data show that the unfolding pathways are different between bound MDM2(N) and apo-MDM2: the unfolding order of unstable helices and tertiary contacts is reversed. Transition state analysis shows that the transition state of bound MDM2 is more nativelike and more heterogeneous than that of apo-MDM2. The predicted Phi-values suggest that the stable helices are more nativelike than other regions in both bound MDM2(N) and apo-MDM2. Within the stable helices, helix II in bound MDM2 is more nativelike than that in apo-MDM2. However, helix I and IV in bound MDM2 are less nativelike than those in apo-MDM2.

Transition state of a SH3 domain detected with principle component analysis and a charge-neutralized all-atom protein model

The src SH3 domain has been known to be a two-state folder near room temperature. However, in a previous study with an all-atom model simulation near room temperature, the transition state of this protein was not successfully detected on a free-energy profile using two axes: the radius of gyration (R(g)) and native contact reproduction ratio (Q value). In this study, we focused on an atom packing effect to characterize the transition state and tried another analysis to detect it. To explore the atom packing effect more efficiently, we introduced a charge-neutralized all-atom model, where all of the atoms in the protein and water molecules were treated explicitly, but their partial atomic charges were set to zero. Ten molecular dynamics simulations were performed starting from the native structure at 300 K, where the simulation length of each run was 90 ns, and the protein unfolded in all runs. The integrated trajectories (10 x 90 = 900 ns) were analyzed by a principal component analysis (PCA) and showed a clear free-energy barrier between folded- and unfolded-state conformational clusters in a conformational space generated by PCA. There were segments that largely deformed when the conformation passed through the free-energy barrier. These segments correlated well with the structural core regions characterized by large phi-values, and the atom-packing changes correlated with the conformational deformations. Interestingly, using the same simulation data, no significant barrier was found in a free-energy profile using the R(g) and Q values for the coordinate axes. These results suggest that the atom packing effect may be one of the most important determinants of the transition state.

Substructural cooperativity and parallel versus sequential events during protein unfolding

According to the "old view," proteins fold along well-defined sequential pathways, whereas the "new view" sees protein folding as a highly parallel stochastic process on funnel-shaped energy landscapes. We have analyzed parallel and sequential processes on a large number of molecular dynamics unfolding trajectories of the protein CI2 at high temperatures. Using rigorous statistical measures, we quantify the degree of sequentiality on two structural levels. The unfolding process is highly parallel on the microstructural level of individual contacts. On a coarser, macrostructural level of contact clusters, characteristic parallel and sequential events emerge. These characteristic events can be understood from loop-closure dependencies between the contact clusters. A correlation analysis of the unfolding times of the contacts reveals a high degree of substructural cooperativity within the contact clusters.

Similarity and difference in the unfolding of thermophilic and mesophilic cold shock proteins studied by molecular dynamics simulations

Molecular dynamics simulations were performed to unfold a homologous pair of thermophilic and mesophilic cold shock proteins at high temperatures. The two proteins differ in just 11 of 66 residues and have very similar structures with a closed five-stranded antiparallel beta-barrel. A long flexible loop connects the N-terminal side of the barrel, formed by three strands (beta1-beta3), with the C-terminal side, formed by two strands (beta4-beta5). The two proteins were found to follow the same unfolding pathway, but with the thermophilic protein showing much slower unfolding. Unfolding started with the melting of C-terminal strands, leading to exposure of the hydrophobic core. Subsequent melting of beta3 and the beta-hairpin formed by the first two strands then resulted in unfolding of the whole protein. The slower unfolding of the thermophilic protein could be attributed to ion pair formation of Arg-3 with Glu-46, Glu-21, and the C-terminal. These ion pairs were also found to be important for the difference in folding stability between the pair of proteins. Thus electrostatic interactions appear to play similar roles in the difference in folding stability and kinetics between the pair of proteins.

The equilibrium properties and folding kinetics of an all-atom Go model of the Trp-cage

The ultrafast-folding 20-residue Trp-cage protein is quickly becoming a new benchmark for molecular dynamics studies. Already several all-atom simulations have probed its equilibrium and kinetic properties. In this work an all-atom Go model is used to accurately represent the side-chain packing and native atomic contacts of the Trp-cage. The model reproduces the hallmark thermodynamics cooperativity of small proteins. Folding simulations observe that in the fast-folding dominant pathway, partial alpha-helical structure forms before hydrophobic core collapse. In the slow-folding secondary pathway, partial core collapse occurs before helical structure. The slow-folding rate of the secondary pathway is attributed to the loss of side-chain rotational freedom, due to the early core collapse, which impedes the helix formation. A major finding is the observation of a low-temperature kinetic intermediate stabilized by a salt bridge between residues Asp-9 and Arg-16. Similar observations [R. Zhou, Proc. Natl. Acad. Sci. U.S.A. 100, 13280 (2003)] were reported in a recent study using an all-atom model of the Trp-cage in explicit water, in which the salt-bridge stabilized intermediate was hypothesized to be the origin of the ultrafast-folding mechanism. A theoretical mutation that eliminates the Asp-9-Arg-16 salt bridge, but leaves the residues intact, is performed. Folding simulations of the mutant Trp-cage observe a two-state free-energy landscape with no kinetic intermediate and a significant decrease in the folding rate, in support of the hypothesis.

A detailed unfolding pathway of a (beta/alpha)8-barrel protein as studied by molecular dynamics simulations

The (beta/alpha)(8)-barrel is the most common protein fold. Similar structural properties for folding intermediates of (beta/alpha)(8)-barrel proteins involved in tryptophan biosynthesis have been reported in a number of experimental studies; these intermediates have the last two beta-strands and three alpha-helices partially unfolded, with other regions of the polypeptide chain native-like in conformation. To investigate the detailed folding/unfolding pathways of these (beta/alpha)(8)-barrel proteins, temperature-induced unfolding simulations of N-(5'-phosphoribosyl)anthranilate isomerase from Escherichia coli were carried out using a special-purpose parallel computer system. Unfolding simulations at five different temperatures showed a sequential unfolding pathway comprised of several events. Early events in unfolding involved disruption of the last two strands and three helices, producing an intermediate ensemble similar to those detected in experimental studies. Then, denaturation of the first two betaalpha units and separation of the sixth strand from the fifth took place independently. The remaining central betaalphabetaalphabeta module persisted the longest during all simulations, suggesting an important role for this module as the incipient folding scaffold. Our simulations also predicted the presence of a nucleation site, onto which several hydrophobic residues condensed forming the foundation for the central betaalphabetaalphabeta module.

Protein conformational transitions coupled to binding in molecular recognition of unstructured proteins: deciphering the effect of intermolecular interactions on computational structure prediction of the p27Kip1 protein bound to the cyclin A-cyclin-dependent kinase 2 complex

The relationship between folding mechanism coupled to binding and structure prediction of the tertiary complexes is studied for the p27(Kip) (1) protein which has an intrinsically disordered unbound form and undergoes a functional folding transition during complex formation with the phosphorylated cyclin A-cyclin-dependent kinase 2 (Cdk2) binary complex. Hierarchy of p27(Kip1) structural loss determined in our earlier studies from temperature-induced Monte Carlo simulations and subsequent characterization of the transition state ensemble (TSE) for the folding reaction have shown that simultaneous ordering of the p27(Kip1) native intermolecular interface for the beta-hairpin and beta-strand secondary structure elements is critical for nucleating a rapid kinetic transition to the native tertiary complex. In the present study, we investigate the effect of forming specific intermolecular interactions on structure prediction of the p27(Kip1) tertiary complex. By constraining different secondary structure elements of p27(Kip1) in their native bound conformations and conducting multiple simulated annealing simulations, we analyze differences in the success rate of predicting the native structure of p27(Kip1) in the tertiary complex. In accordance with the nucleation-condensation mechanism, we have found that further stabilization of the native intermolecular interface for the beta-hairpin and beta-strand elements of p27(Kip1), that become ordered in the TSE, but are hardly populated in the unbound state, results in a consistent acquisition of the native bound structure. Conversely, the excessive stablization of the local secondary structure elements, which are rarely detected in the TSE, has a detrimental effect on convergence to the native bound structure.

Loop-closure events during protein folding: rationalizing the shape of Phi-value distributions

In the past years, the folding kinetics of many small single-domain proteins has been characterized by mutational Phi-value analysis. In this article, a simple, essentially parameter-free model is introduced which derives folding routes from native structures by minimizing the entropic loop-closure cost during folding. The model predicts characteristic folding sequences of structural elements such as helices and beta-strand pairings. Based on few simple rules, the kinetic impact of these structural elements is estimated from the routes and compared to average experimental Phi-values for the helices and strands of 15 small, well-characterized proteins. The comparison leads on average to a correlation coefficient of 0.62 for all proteins with polarized Phi-value distributions, and 0.74 if distributions with negative average Phi-values are excluded. The diffuse Phi-value distributions of the remaining proteins are reproduced correctly. The model shows that Phi-value distributions, averaged over secondary structural elements, can often be traced back to entropic loop-closure events, but also indicates energetic preferences in the case of a few proteins governed by parallel folding processes.

A molecular dynamics approach to the structural characterization of amyloid aggregation

A novel computational approach to the structural analysis of ordered beta-aggregation is presented and validated on three known amyloidogenic polypeptides. The strategy is based on the decomposition of the sequence into overlapping stretches and equilibrium implicit solvent molecular dynamics (MD) simulations of an oligomeric system for each stretch. The structural stability of the in-register parallel aggregates sampled in the implicit solvent runs is further evaluated using explicit water simulations for a subset of the stretches. The beta-aggregation propensity along the sequence of the Alzheimer's amyloid-beta peptide (Abeta(42)) is found to be highly heterogeneous with a maximum in the segment V(12)HHQKLVFFAE(22) and minima at S(8)G(9), G(25)S(26), G(29)A(30), and G(38)V(39), which are turn-like segments. The simulation results suggest that these sites may play a crucial role in determining the aggregation tendency and the fibrillar structure of Abeta(42). Similar findings are obtained for the human amylin, a 37-residue peptide that displays a maximal beta-aggregation propensity at Q(10)RLANFLVHSSNN(22) and two turn-like sites at G(24)A(25) and G(33)S(34). In the third application, the MD approach is used to identify beta-aggregation "hot-spots" within the N-terminal domain of the yeast prion Ure2p (Ure2p(1-94)) and to design a double-point mutant (Ure2p-N4748S(1-94)) with lower beta-aggregation propensity. The change in the aggregation propensity of Ure2p-N4748S(1-94) is verified in vitro using the thioflavin T binding assay.

Reconstruction of the src-SH3 Protein Domain Transition State Ensemble using Multiscale Molecular Dynamics Simulations

We use an integrated computational approach to reconstruct accurately the transition state ensemble (TSE) for folding of the src-SH3 protein domain. We first identify putative TSE conformations from free energy surfaces generated by importance sampling molecular dynamics for a fully atomic, solvated model of the src-SH3 protein domain. These putative TSE conformations are then subjected to a folding analysis using a coarse-grained representation of the protein and rapid discrete molecular dynamics simulations. Those conformations that fold to the native conformation with a probability (P(fold)) of approximately 0.5, constitute the true transition state. Approximately 20% of the putative TSE structures were found to have a P(fold) near 0.5, indicating that, although correct TSE conformations are populated at the free energy barrier, there is a critical need to refine this ensemble. Our simulations indicate that the true TSE conformations are compact, with a well-defined central beta sheet, in good agreement with previous experimental and theoretical studies. A structured central beta sheet was found to be present in a number of pre-TSE conformations, however, indicating that this element, although required in the transition state, does not define it uniquely. An additional tight cluster of contacts between highly conserved residues belonging to the diverging turn and second beta-sheet of the protein emerged as being critical elements of the folding nucleus. A number of commonly used order parameters to identify the transition state for folding were investigated, with the number of native Cbeta contacts displaying the most satisfactory correlation with P(fold) values.

Estimation of protein folding probability from equilibrium simulations

The assumption that similar structures have similar folding probabilities (p(fold)) leads naturally to a procedure to evaluate p(fold) for every snapshot saved along an equilibrium folding-unfolding trajectory of a structured peptide or protein. The procedure utilizes a structurally homogeneous clustering and does not require any additional simulation. It can be used to detect multiple folding pathways as shown for a three-stranded antiparallel beta-sheet peptide investigated by implicit solvent molecular dynamics simulations.

Replica exchange molecular dynamics simulations of amyloid peptide aggregation

The replica exchange molecular dynamics (REMD) approach is applied to four oligomeric peptide systems. At physiologically relevant temperature values REMD samples conformation space and aggregation transitions more efficiently than constant temperature molecular dynamics (CTMD). During the aggregation process the energetic and structural properties are essentially the same in REMD and CTMD. A condensation stage toward disordered aggregates precedes the beta-sheet formation. Two order parameters, borrowed from anisotropic fluid analysis, are used to monitor the aggregation process. The order parameters do not depend on the peptide sequence and length and therefore allow to compare the amyloidogenic propensity of different peptides

Formation of the folding nucleus of an SH3 domain investigated by loosely coupled molecular dynamics simulations

The experimentally well-established folding mechanism of the src-SH3 domain, and in particular the phi-value analysis of its transition state, represents a sort of testing table for computational investigations of protein folding. Here, parallel molecular dynamics simulations of the src-SH3 domain have been performed starting from denatured conformations. By rescuing and restarting only trajectories approaching the folding transition state, an ensemble of conformations was obtained with a completely structured central beta-sheet and a native-like packing of residues Ile-110, Ala-121, and Ile-132. An analysis of the trajectories shows that there are several pathways leading to the formation of the central beta-sheet whereas its two hairpins form in a different but consistent way.

The protein folding network

The conformation space of a 20 residue antiparallel beta-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Snapshots saved along the trajectory are grouped according to secondary structure into nodes of the network and the transitions between them are links. The conformation space network describes the significant free energy minima and their dynamic connectivity without requiring arbitrarily chosen reaction coordinates. As previously found for the Internet and the World-Wide Web as well as for social and biological networks, the conformation space network is scale-free and contains highly connected hubs like the native state which is the most populated free energy basin. Furthermore, the native basin exhibits a hierarchical organization, which is not found for a random heteropolymer lacking a predominant free-energy minimum. The network topology is used to identify conformations in the folding transition state (TS) ensemble, and provides a basis for understanding the heterogeneity of the TS and denatured state ensemble as well as the existence of multiple pathways.

Temperature dependence of the free energy landscape of the src-SH3 protein domain

The temperature dependence of the free energy landscape of the src-SH3 protein domain is investigated through fully atomic simulations in explicit solvent. Simulations are performed above and below the folding transition temperature, enabling an analysis of both protein folding and unfolding. The transition state for folding and unfolding, identified from the free energy surfaces, is found to be very similar, with structure in the central hydrophobic sheet and little structure throughout the rest of the protein. This is a result of a polarized folding (unfolding) mechanism involving early formation (late loss) of the central hydrophobic sheet at the transition state. Unfolding simulations map qualitatively well onto low-temperature free energy surfaces but appear, however, to miss important features observed in folding simulations. In particular, details of the folding mechanism involving the opening and closing of the hydrophobic core are not captured by unfolding simulations performed under strongly denaturing conditions. In addition, free energy surfaces at high temperatures do not display a desolvation barrier found at lower temperatures, involving the expulsion of water molecules from the hydrophobic core.

Transition states for folding of circular-permuted proteins

To explore the role of entropy and chain connectivity in protein folding, a particularly interesting scheme, namely, the circular permutation, has been used. Recently, experimental observations showed that there are large differences in the folding mechanisms between the wild-type proteins and their circular permutants. These differences are strongly related to the change in the intrachain connectivity. Some results obtained by molecular dynamics simulations also showed a good agreement with the experimental findings. Here, we use a topology-based free-energy functional method to study the role of the chain connectivity in folding by comparing features of transition states of the wild-type proteins with those of their circular permutants. We concentrate our study on 3 small globular proteins, namely, the alpha-spectrin SH3 domain (SH3), the chymotrypsin inhibitor 2 (CI2), and the ribosomal protein S6, and obtain exciting results that are consistent with the available experimental and simulation results. A heterogeneity of the interaction energies between contacts for protein CI2 and for protein S6 is also introduced, which characterizes the strong interactions between contacts with long loops, as speculated from experiments for protein S6. The comparison between the folding nucleus of the wild-type proteins and those of their circular permutants indicates that chain connectivity affects remarkably the shapes of the energy profiles and thus the folding mechanism. Further comparisons between our theoretical calculated phi(th) values and the experimental observed phi(exp) values for the 3 proteins and their permutants show that our results are in good agreement with experimental ones and that correlations between them are high. These indicate that the free-energy functional method really provides a way to analyze the folding behavior of the circular-permuted proteins and therefore the folding mechanism of the wild-type proteins.

Does native state topology determine the RNA folding mechanism?

Recent studies in protein folding suggest that native state topology plays a dominant role in determining the folding mechanism, yet an analogous statement has not been made for RNA, most likely due to the strong coupling between the ionic environment and conformational energetics that make RNA folding more complex than protein folding. Applying a distributed computing architecture to sample nearly 5000 complete tRNA folding events using a minimalist, atomistic model, we have characterized the role of native topology in tRNA folding dynamics: the simulated bulk folding behavior predicts well the experimentally observed folding mechanism. In contrast, single-molecule folding events display multiple discrete folding transitions and compose a largely diverse, heterogeneous dynamic ensemble. This both supports an emerging view of heterogeneous folding dynamics at the microscopic level and highlights the need for single-molecule experiments and both single-molecule and bulk simulations in interpreting bulk experimental measurements.

Roles of physical interactions in determining protein-folding mechanisms: molecular simulation of protein G and alpha spectrin SH3

Protein-folding mechanisms of two small globular proteins, IgG binding domain of protein G and alpha spectrin SH3 domain are investigated via Brownian dynamics simulations with a model made of coarse-grained physical energy functions responsible for sequence-specific interactions and weak Gō-like energies. The folding pathways of alpha spectrin SH3 are known to be mainly controlled by the native topology, while protein G folding is anticipated to be more sensitive to the sequence-specific effects than native topology. We found in the folding of protein G that the C terminal beta hairpin is formed earlier and is rigid, once ordered, in the presence of an intact C terminal turn. The alpha helix is found to exhibit repeated partial formations/deformations during folding and to be stabilized via the tertiary contact with preformed beta sheets. This predicted scenario is fully consistent with experimental phi value data. Moreover, we found that the folding route is critically affected when the hydrophobic interaction is excluded from physical energy terms, suggesting that the hydrophobicity critically contributes to the folding propensity of protein G. For the folding of alpha spectrin SH3, we found that the distal beta hairpin and diverging turn are parts formed early, fully in harmony with previous results of simple Gō-like and experimental analysis, supporting that the folding route of SH3 domain is robust and coded by the native topology. The hybrid method provides useful tools for analyzing roles of physical interactions in determining folding mechanisms.

Unfolding of the cold shock protein studied with biased molecular dynamics

The cold shock protein from Bacillus caldolyticus is a small beta-barrel protein that folds in a two-state mechanism. For the native protein and for several mutants, a wealth of experimental data are available on stability and folding, so that it is an optimal system to study this process. We compare data from unfolding simulations (trajectories of 5 and up to 12 ns) obtained with a bias potential at room temperature and from unbiased thermal unfolding simulations with experimental data. The unfolding patterns derived from the trajectories starting from different native-like conformations and subject to different unfolding conditions agree. The transition state found in the simulations of unfolding is close to the native structure in agreement with experiment. Moreover, a lower value of the free energy barrier of unfolding was found for the mutant R3E than for the mutant E46A and the native protein, as indicated by experimental data. The first unfolding event involves the three-stranded beta-sheet whose decomposition corresponds to the transition state. In contrast to conclusions drawn from experiments, we found that the two-stranded beta-strand forms the most stable substructure, which decomposes very late in the unfolding process. However, assuming that this structure forms very early in the folding process, our findings would not contradict the experiments but require a different interpretation of them.

Structural and dynamic effects of α-Helix deletion in Sso7d: Implications for protein thermal stability

Sso7d is a 62-residue protein from the hyperthemophilic archaeon Sulfolobus solfataricus with a denaturation temperature close to 100 degrees C around neutral pH. An engineered form of Sso7d truncated at leucine 54 (L54Delta) is significantly less stable, with a denaturation temperature of 53 degrees C. Molecular dynamics (MD) studies of Sso7d and its truncated form at two different temperatures have been performed. The results of the MD simulations at 300 K indicate that: (1) the flexibility of Sso7d chain at 300 K agrees with that detected from X-ray and NMR structural studies; (2) L54Delta remains stable in the native folded conformation and possesses an overall dynamic behavior similar to that of the parent protein. MD simulations performed at 500 K, 10 ns long, indicate that, while Sso7d is in-silico resistant to high temperature, the truncated variant partially unfolds, revealing the early phases of the thermal unfolding pathway of the protein. Analysis of the trajectories of L54Delta suggests that the unzipping of the N-terminal and C-terminal beta-strands should be the first event of the unfolding pathway, and points out the regions more resistant to thermal unfolding. These findings allow one to understand the role played by specific interactions connecting the two ends of the chain for the high thermal stability of Sso7d, and support recent hypotheses on its folding mechanism emerged from site-directed mutagenesis studies.

A binding event converted into a folding event

We have designed a chimeric protein by connecting a circular permutant of the alpha-spectrin SH3 domain to the proline-rich decapeptide APSYSPPPPP with a three-residue link. Our aim was to obtain a single-chain protein with a tertiary fold that would mimic the binding between SH3 domains and proline-rich peptides. A comparison of the circular-dichroism and fluorescence spectra of the purified chimera and the SH3 circular permutant showed that the proline-rich sequence occupies the putative SH3 binding site in a similar conformation and with comparable interactions to those found in complexes between SH3 and proline-rich peptides. Differential scanning calorimetry indicated that the interactions in the binding motif interface are highly cooperative with the rest of the structure and thus the protein unfolds in a two-state process. The chimera is more stable than the circular permutant SH3 by 6-8 kJ mol(-1) at 25 degrees C and the difference in their unfolding enthalpy is approximately 32 kJ mol(-1), which coincides with the values found for the binding of proline-rich peptides to SH3 domains. This type of chimeric protein may be useful in designing SH3 peptide ligands with improved affinity and specificity.

Insights into nucleic acid conformational dynamics from massively parallel stochastic simulations

The helical hairpin is one of the most ubiquitous and elementary secondary structural motifs in nucleic acids, capable of serving functional roles and participating in long-range tertiary contacts. Yet the self-assembly of these structures has not been well-characterized at the atomic level. With this in mind, the dynamics of nucleic acid hairpin formation and disruption have been studied using a novel computational tool: large-scale, parallel, atomistic molecular dynamics simulation employing an inhomogeneous distributed computer consisting of more than 40,000 processors. Using multiple methodologies, over 500 micro s of atomistic simulation time has been collected for a large ensemble of hairpins (sequence 5'-GGGC[GCAA]GCCU-3'), allowing characterization of rare events not previously observable in simulation. From uncoupled ensemble dynamics simulations in unperturbed folding conditions, we report on 1), competing pathways between the folded and unfolded regions of the conformational space; 2), observed nonnative stacking and basepairing traps; and 3), a helix unwinding-rewinding mode that is differentiated from the unfolding and folding dynamics. A heterogeneous transition state ensemble is characterized structurally through calculations of conformer-specific folding probabilities and a multiplexed replica exchange stochastic dynamics algorithm is used to derive an approximate folding landscape. A comparison between the observed folding mechanism and that of a peptide beta-hairpin analog suggests that although native topology defines the character of the folding landscape, the statistical weighting of potential folding pathways is determined by the chemical nature of the polymer.

Fast protein folding on downhill energy landscape

Proteins fold in a time range of microseconds to minutes despite the large amount of possible conformers. Molecular dynamics simulations of a three-stranded antiparallel beta-sheet peptide (for a total of 12.6 microsec and 72 folding events) show that at the melting temperature the unfolded state ensemble contains many more conformers than those sampled during a folding event.

Circular permutation of 5-aminolevulinate synthase: effect on folding, conformational stability, and structure

The first and regulatory step of heme biosynthesis in mammals begins with the pyridoxal 5'-phosphate-dependent condensation reaction catalyzed by 5-aminolevulinate synthase. The enzyme functions as a homodimer with the two active sites at the dimer interface. Previous studies demonstrated that circular permutation of 5-aminolevulinate synthase does not prevent folding of the polypeptide chain into a structure amenable to binding of the pyridoxal 5'-phosphate cofactor and assembly of the two subunits into a functional enzyme. However, while maintaining a wild type-like three-dimensional structure, active, circularly permuted 5-aminolevulinate synthase variants possess different topologies. To assess whether the aminolevulinate synthase overall structure can be reached through alternative or multiple folding pathways, we investigated the guanidine hydrochloride-induced unfolding, conformational stability, and structure of active, circularly permuted variants in relation to those of the wild type enzyme using fluorescence, circular dichroism, activity, and size exclusion chromatography. Aminolevulinate synthase and circularly permuted variants folded reversibly; the equilibrium unfolding/refolding profiles were biphasic and, in all but one case, protein concentration-independent, indicating a unimolecular process with the presence of at least one stable intermediate. The formation of this intermediate was preceded by the disruption of the dimeric interface or dissociation of the dimer without significant change in the secondary structural content of the subunits. In contrast to the similar stabilities associated with the dimeric interface, the energy for the unfolding of the intermediate as well as the overall conformational stabilities varied among aminolevulinate synthase and variants. The unfolding of one functional permuted variant was protein concentration-dependent and had a potentially different folding mechanism. We propose that the order of the ALAS secondary structure elements does not determine the ability of the polypeptide chain to fold but does affect its folding mechanism.

Analysis of the distributed computing approach applied to the folding of a small beta peptide

In the recently proposed distributed computing approach to protein folding a very large number of short independent simulations is performed. Using this method, folding events on a time scale orders of magnitude shorter than the experimental one have been reported. However, it has also been observed that the folding process is not an elementary kinetic step and that the presence of initial lag phases can bias short simulations toward atypical pathways. We study here a 20-residue three-stranded antiparallel beta-sheet peptide whose equilibrium properties can be characterized by atomistic molecular dynamics simulations. We found that the folding rate of this peptide is estimated correctly by the distributed computing approach when trajectories > approximately 1/100 of the equilibrium folding time are considered. We also found that the fastest folding events occur through high-energy pathways, which are unlikely under equilibrium conditions. These very fast folding pathways do not relax within the equilibrium denatured state that is stabilized by the transient presence of both native and non-native interactions, and they are characterized by the nearly simultaneous formation of the two beta-hairpins and a very small number of non-native contacts.

Folding rates and low-entropy-loss routes of two-state proteins

We develop a simple model for computing the rates and routes of folding of two-state proteins from the contact maps of their native structures. The model is based on the graph-theoretical concept of effective contact order (ECO). The model predicts that proteins fold by "zipping up" in a sequence of small-loop-closure events, depending on the native chain fold. Using a simple equation, with a few physical rate parameters, we obtain a good correlation with the folding rates of 24 two-state folding proteins. The model rationalizes data from Phi-value analysis that have been interpreted in terms of delocalized or polarized transition states. This model indicates how much of protein folding may take place in parallel, not along a single reaction coordinate or with a single transition state.

The role of side-chain interactions in the early steps of aggregation: Molecular dynamics simulations of an amyloid-forming peptide from the yeast prion Sup35

Understanding the early steps of aggregation at atomic detail might be crucial for the rational design of therapeutics preventing diseases associated with amyloid deposits. In this paper, aggregation of the heptapeptide GNNQQNY, from the N-terminal prion-determining domain of the yeast protein Sup35, was studied by 20 molecular dynamics runs for a total simulation time of 20 micros. The simulations generate in-register parallel packing of GNNQQNY beta-strands that is consistent with x-ray diffraction and Fourier transform infrared data. The statistically preferred aggregation pathway does not correspond to a purely downhill profile of the energy surface because of the presence of enthalpic barriers that originate from out-of-register interactions. The parallel beta-sheet arrangement is favored over the antiparallel because of side-chain contacts; in particular, stacking interactions of the tyrosine rings and hydrogen bonds between amide groups. No ordered aggregation was found in control simulations with the mutant sequence SQNGNQQRG in accord with experimental data and the strong sequence dependence of aggregation.

Thermal unfolding simulations of apo-calmodulin using leap-dynamics

The simulation method leap-dynamics (LD) has been applied to protein thermal unfolding simulations to investigate domain-specific unfolding behavior. Thermal unfolding simulations of the 148-residue protein apo-calmodulin with implicit solvent were performed at temperatures 290 K, 325 K, and 360 K and compared with the corresponding molecular dynamics trajectories in terms of a number of calculated conformational parameters. The main experimental results of unfolding are reproduced in showing the lower stability of the C-domain: at 290 K, both the N- and C-domains are essentially stable; at 325 K, the C-domain unfolds, whereas the N-domain remains folded; and at 360 K, both domains unfold extensively. This behavior could not be reproduced by molecular dynamics simulations alone under the same conditions. These results show an encouraging degree of convergence between experiment and LD simulation. The simulations are able to describe the overall plasticity of the apo-calmodulin structure and to reveal details such as reversible folding/unfolding events within single helices. The results show that by using the combined application of a fast and efficient sampling routine with a detailed molecular dynamics force field, unfolding simulations of proteins at atomic resolution are within the scope of current computational power.

Molecular dynamics simulation reveals a surface salt bridge forming a kinetic trap in unfolding of truncated Staphylococcal nuclease

Surface salt bridges are ubiquitous in globular proteins. Their contribution to protein stability has been extensively debated in the past decade. Here, molecular dynamics simulations are performed starting from a non-equilibrium state of Staphylococcal nuclease (SNase) with C-terminal truncation (SNaseDelta). The results indicate a key role in the unfolding of the surface salt bridge between arginine 105 and glutamate 135. Experimentally, SNaseDelta is known to be partially unfolded. However, in simulations over 1 ns at 300 K and over 500 ps at 400 K, SNaseDelta remains stable in the native-like folded conformation, the salt bridge hindering unfolding. When the potential function is altered so as to selectively weaken the salt bridge, which then breaks rapidly at 430 K, the protein starts to unfold. The results suggest that breaking of this salt bridge presents a significant barrier to the unfolding transition of SNaseDelta from a native-like state to the unfolded state. Potential of mean force calculations indicate that the barrier height for this transition is approximately 7 kcal/mol.

Probing the folding free energy landscape of the Src-SH3 protein domain

The mechanism and thermodynamics of folding of the Src homology 3 (SH3) protein domain are characterized at an atomic level through molecular dynamics with importance sampling. This methodology enables the construction of the folding free energy landscape of the protein as a function of representative reaction coordinates. We observe that folding proceeds in a downhill manner under native conditions, with early compaction and structure formation in the hydrophobic sheet consisting of the three central beta strands of the protein. This state bears considerable resemblance to the experimentally determined transition state for folding. Folding proceeds further with the formation of the second hydrophobic sheet consisting of the terminal strands and the RT loop. The final stages of folding appear to involve the formation of the hydrophobic core through the expulsion of water molecules bridging the two hydrophobic sheets. This work sheds new light on the complementary roles of sequence and topology in governing the folding mechanism of small proteins and provides further support for the role of water in facilitating the late stages in folding.

Folding pathways of prion and doppel

The relevance of various residue positions for the stability and the folding characteristics of the prion protein in its normal cellular form are investigated by using molecular dynamics simulations of models exploiting the topology of the native state. These models allow for reproducing the experimentally validated two-state behavior of the normal prion isoform. Highly significant correlations are found between the most topologically relevant sites in our analysis and the single point mutations known to be associated with the arousal of the genetic forms of prion disease. Insight into the conformational change is provided by comparing the folding process of cellular prion and doppel that share a similar native state topology: the folding pathways of the former can be grouped in two main classes according to which tertiary structure contacts are formed first enroute to the native state. For the latter a single class of pathways leads to the native state again through a two-state process. Our results are consistent and supportive of the recent experimental findings that doppel lacks the scrapie isoform and that such remarkably different behavior involves residues in the region containing the two beta-strands and the intervening helix.

Pathways and intermediates in forced unfolding of spectrin repeats

Spectrin repeats are triple-helical coiled-coil domains found in many proteins that are regularly subjected to mechanical stress. We used atomic force microscopy technique and steered molecular dynamics simulations to study the behavior of a wild-type spectrin repeat and two mutants. The experiments indicate that spectrin repeats can form stable unfolding intermediates when subjected to external forces. In the simulations the unfolding proceeded via a variety of pathways. Stable intermediates were associated to kinking of the central helix close to a proline residue. A mutant stabilizing the central helix showed no intermediates in experiments, in agreement with simulation. Spectrin repeats may thus function as elastic elements, extendable to intermediate states at various lengths.

Parameter optimized surfaces (POPS): analysis of key interactions and conformational changes in the ribosome

We present a new method for the calculation of solvent accessible surface areas at the atomic and residue levels, which we call parameter optimized surfaces (POPS-A and POPS-R ). Atomic and residue areas (the latter simulated with a single sphere centered at the C(alpha)s atom for amino acids and at the P atom for nucleotides) have been optimized versus accurate all-atoms methods. We concentrated on an analytical formula for the approximation of solvent accessibilities. The formula is simple, easily derivable and fast to compute, therefore it is practical for use in molecular dynamics simulations as an approximation to the first solvation shell. The residue based approach POPS-R has been derived as a useful tool for the analysis of large macromolecular assemblies like the ribosome, and is especially suited for use in refinement of low resolution structures. The structures of the 70S, 50S and 30S ribosomes have been analyzed in detail and most of the interactions within the subunits and at their interfaces were clearly identified. Some interesting differences between 30S alone and within the 70S have been highlighted. Owing to the presence of the P-tRNA in the 70S ribosome, localized conformational rearrangements occur within the subunits, exposing Arg and Lys residues to negatively charged binding sites of P-tRNA. POPS-R also allows for estimates of the loss of free energy of solvation upon complex formation, particularly useful in designing new protein-RNA complexes and in suggesting more focused experimental work.

Molecular dynamics simulations of protein folding from the transition state

Putative transition-state ensemble (TSE) conformations of src SH3 were identified by monitoring the deviation from the experimental phi values along molecular dynamics (MD) simulations of unfolding. Sixty MD trajectories (for a total of about 7 micros) were then started from the putative TSE. About one-half of the 60 runs reached the folded state while unfolding was observed in the remaining half of the runs. This result validates phi-value analysis as an approach to obtain structural information on the transition state. It also demonstrates that an atomic resolution description of the TSE can be extracted from MD simulations. All conformations in the TSE have the central three-stranded beta-sheet formed in agreement with experimental data. An elongation of strand beta 2 as well as non-native side-chain interactions between the diverging turn and the distal hairpin are observed. The simulation results indicate that the tight packing of the side chains between the diverging turn and the distal hairpin is a necessary condition for rapid folding. Contacts between residues in the most structured element of the TSE, the central beta-sheet, are kinetically more important than those between the N- and C-terminal strands.

Evaluation of a fast implicit solvent model for molecular dynamics simulations

A solvation term based on the solvent accessible surface area (SASA) is combined with the CHARMM polar hydrogen force field for the efficient simulation of peptides and small proteins in aqueous solution. Only two atomic solvation parameters are used: one is negative for favoring the direct solvation of polar groups and the other positive for taking into account the hydrophobic effect on apolar groups. To approximate the water screening effects on the intrasolute electrostatic interactions, a distance-dependent dielectric function is used and ionic side chains are neutralized. The use of an analytical approximation of the SASA renders the model extremely efficient (i.e., only about 50% slower than in vacuo simulations). The limitations and range of applicability of the SASA model are assessed by simulations of proteins and structured peptides. For the latter, the present study and results reported elsewhere show that with the SASA model it is possible to sample a significant amount of folding/unfolding transitions, which permit the study of the thermodynamics and kinetics of folding at an atomic level of detail.