Folding pathway dependence on energetic frustration and interaction heterogeneity for a three-dimensional hydrophobic protein model

Monte Carlo simulations of a hydrophobic protein model of 40 monomers in the cubic lattice are used to explore the effect of energetic frustration and interaction heterogeneity on its folding pathway. The folding pathway is described by the dependence of relevant conformational averages on an appropriate reaction coordinate, pfold, defined as the probability for a given conformation to reach the native structure before unfolding. We compare the energetically frustrated and heterogeneous hydrophobic potential, according to which individual monomers have a higher or lower tendency to form contacts unspecifically depending on their hydrophobicities, to an unfrustrated homogeneous Go-type potential with uniformly attractive native interactions and neutral non-native interactions (called Go1 in this study), and to an unfrustrated heterogeneous potential with neutral non-native interactions and native interactions having the same energy as the hydrophobic potential (called Go2 in this study). Folding kinetics are slowed down dramatically when energetic frustration increases, as expected and previously observed in a two-dimensional model. Contrary to our previous results in two dimensions, however, it appears that the folding pathway and transition state ensemble can be significantly dependent on the energy function used to stabilize the native structure. The sequence of events along the reaction coordinate, or the order along this coordinate in which different regions of the native conformation become structured, turns out to be similar for the hydrophobic and Go2 potentials, but with analogous events tending to occur at lower pfold values in the first case. In particular, the transition state obtained from the ensemble around pfold = 0.5 is more structured for the hydrophobic potential. For Go1, not only the transition state ensemble but the order of events itself is modified, suggesting that interaction heterogeneity, in addition to energetic frustration, can have significant effects on the folding mechanism, most likely by modifying the probability of different contacts in the unfolded state, the starting point for the folding reaction. Although based on a simple model, these results provide interesting insight into how sequence-dependent switching between folding pathways might occur in real proteins.     

Thermodynamics and Kinetics of Single-Chain Monellin Folding with Structural Insights into Specific Collapse in the Denatured State Ensemble

Proteins, which behave as random coils in high denaturant concentrations undergo collapse transition similar to polymers on denaturant dilution. We study collapse in the denatured ensemble of single-chain monellin (MNEI) using a coarse-grained protein model and molecular dynamics simulations. The model is validated by quantitatively comparing the computed guanidinium chloride and pH-dependent thermodynamic properties of MNEI folding with the experiments. The computed properties such as the fraction of the protein in the folded state and radius of gyration (R_g) as function of [GuHCl] are in good agreement with the experiments. The folded state of MNEI is destabilized with an increase in pH due to the deprotonation of the residues Glu24 and Cys42. On decreasing [GuHCl], the protein in the unfolded ensemble showed specific compaction. The R_g of the protein decreased steadily with [GuHCl] dilution due to increase in the number of native contacts in all the secondary structural elements present in the protein. MNEI folding kinetics is complex with multiple folding pathways and transiently stable intermediates are populated in these pathways. In strong stabilizing conditions, the protein in the unfolded ensemble showed transition to a more compact unfolded state where R_g decreased by ≈ 17% due to the formation of specific native contacts in the protein. The intermediate populated in the dominant MNEI folding pathway satisfies the structural features of the dry molten globule inferred from experiments.     

Analyzing the effect of homogeneous frustration in protein folding

The energy landscape theory has been an invaluable theoretical framework in the understanding of biological processes such as protein folding, oligomerization, and functional transitions. According to the theory, the energy landscape of protein folding is funneled toward the native state, a conformational state that is consistent with the principle of minimal frustration. It has been accepted that real proteins are selected through natural evolution, satisfying the minimum frustration criterion. However, there is evidence that a low degree of frustration accelerates folding. We examined the interplay between topological and energetic protein frustration. We employed a C_α structure‐based model for simulations with a controlled nonspecific energetic frustration added to the potential energy function. Thermodynamics and kinetics of a group of 19 proteins are completely characterized as a function of increasing level of energetic frustration. We observed two well‐separated groups of proteins: one group where a little frustration enhances folding rates to an optimal value and another where any energetic frustration slows down folding. Protein energetic frustration regimes and their mechanisms are explained by the role of non‐native contact interactions in different folding scenarios. These findings strongly correlate with the protein free‐energy folding barrier and the absolute contact order parameters. These computational results are corroborated by principal component analysis and partial least square techniques. One simple theoretical model is proposed as a useful tool for experimentalists to predict the limits of improvements in real proteins.Proteins 2013; 81:1727–1737. © 2013 Wiley Periodicals, Inc.     

Transition state contact orders correlate with protein folding rates

We have used molecular dynamics simulations restrained by experimental phi values derived from protein engineering experiments to determine the structures of the transition state ensembles of ten proteins that fold with two-state kinetics. For each of these proteins we then calculated the average contact order in the transition state ensemble and compared it with the corresponding experimental folding rate. The resulting correlation coefficient is similar to that computed for the contact orders of the native structures, supporting the use of native state contact orders for predicting folding rates. The native contacts in the transition state also correlate with those of the native state but are found to be about 30% lower. These results show that, despite the high levels of heterogeneity in the transition state ensemble, the large majority of contributing structures have native-like topologies and that the native state contact order captures this phenomenon.     

A survey of flexible protein binding mechanisms and their transition states using native topology based energy landscapes

Many cellular functions rely on interactions between protein pairs and higher oligomers. We have recently shown that binding mechanisms are robust and owing to the minimal frustration principle, just as for protein folding, are governed primarily by the protein's native topology, which is characterized by the network of non-covalent residue-residue interactions. The detailed binding mechanisms of nine dimers, a trimer, and a tetramer, each involving different degrees of flexibility and plasticity during assembly, are surveyed here using a model that is based solely on the protein topology, having a perfectly funneled energy landscape. The importance of flexibility in binding reactions is manifested by the fly-casting effect, which is diminished in magnitude when protein flexibility is removed. Many of the grosser and finer structural aspects of the various binding mechanisms (including binding of pre-folded monomers, binding of intrinsically unfolded monomers, and binding by domain-swapping) predicted by the native topology based landscape model are consistent with the mechanisms found in the laboratory. An asymmetric binding mechanism is often observed for the formation of the symmetric homodimers where one monomer is more structured at the binding transition state and serves as a template for the folding of the other monomer. Phi values were calculated to show how the structure of the binding transition state ensemble would be manifested in protein engineering studies. For most systems, the simulated Phi values are reasonably correlated with the available experimental values. This agreement suggests that the overall binding mechanism and the nature of the binding transition state ensemble can be understood from the network of interactions that stabilize the native fold. The Phi values for the formation of an antibody-antigen complex indicate a possible role for solvation of the interface in biomolecular association of large rigid proteins.     

Topological and energetic factors: what determines the structural details of the transition state ensemble and "en-route" intermediates for protein folding? An investigation for small globular proteins

Recent experimental results suggest that the native fold, or topology, plays a primary role in determining the structure of the transition state ensemble, at least for small, fast-folding proteins. To investigate the extent of the topological control of the folding process, we studied the folding of simplified models of five small globular proteins constructed using a Go-like potential to retain the information about the native structures but drastically reduce the energetic frustration and energetic heterogeneity among residue-residue native interactions. By comparing the structure of the transition state ensemble (experimentally determined by Phi-values) and of the intermediates with those obtained using our models, we show that these energetically unfrustrated models can reproduce the global experimentally known features of the transition state ensembles and "en-route" intermediates, at least for the analyzed proteins. This result clearly indicates that, as long as the protein sequence is sufficiently minimally frustrated, topology plays a central role in determining the folding mechanism.     

Single-Molecule Studies of the Im7 Folding Landscape

Under appropriate conditions, the four-helical Im7 (immunity protein 7) folds from an ensemble of unfolded conformers to a highly compact native state via an on-pathway intermediate. Here, we investigate the unfolded, intermediate, and native states populated during folding using diffusion single-pair fluorescence resonance energy transfer by measuring the efficiency of energy transfer (or proximity or P ratio) between pairs of fluorophores introduced into the side chains of cysteine residues placed in the center of helices 1 and 4, 1 and 3, or 2 and 4. We show that while the native states of each variant give rise to a single narrow distribution with high P values, the distributions of the intermediates trapped at equilibrium (denoted I^eqm) are fitted by two Gaussian distributions. Modulation of the folding conditions from those that stabilize the intermediate to those that destabilize the intermediate enabled the distribution of lower P value to be assigned to the population of the unfolded ensemble in equilibrium with the intermediate state. The reduced stability of the I^eqm variants allowed analysis of the effect of denaturant concentration on the compaction and breadth of the unfolded state ensemble to be quantified from 0 to 6 M urea. Significant compaction is observed as the concentration of urea is decreased in both the presence and absence of sodium sulfate, as previously reported for a variety of proteins. In the presence of Na₂SO₄ in 0 M urea, the P value of the unfolded state ensemble approaches that of the native state. Concurrent with compaction, the ensemble displays increased peak width of P values, possibly reflecting a reduction in the rate of conformational exchange among iso-energetic unfolded, but compact conformations. The results provide new insights into the initial stages of folding of Im7 and suggest that the unfolded state is highly conformationally constrained at the outset of folding.     

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.     

Thermodynamics and folding kinetics analysis of the SH3 domain form discrete molecular dynamics

We perform a detailed analysis of the thermodynamics and folding kinetics of the SH3 domain fold with discrete molecular dynamic simulations. We propose a protein model that reproduces some of the experimentally observed thermodynamic and folding kinetic properties of proteins. Specifically, we use our model to study the transition state ensemble of the SH3 fold family of proteins, a set of unstable conformations that fold to the protein native state with probability 1/2. We analyze the participation of each secondary structure element formed at the transition state ensemble. We also identify the folding nucleus of the SH3 fold and test extensively its importance for folding kinetics. We predict that a set of amino acid contacts between the RT-loop and the distal hairpin are the critical folding nucleus of the SH3 fold and propose a hypothesis that explains this result.     

Energetic Frustrations in Protein Folding at Residue Resolution: A Homologous Simulation Study of Im9 Proteins

Energetic frustration is becoming an important topic for understanding the mechanisms of protein folding, which is a long-standing big biological problem usually investigated by the free energy landscape theory. Despite the significant advances in probing the effects of folding frustrations on the overall features of protein folding pathways and folding intermediates, detailed characterizations of folding frustrations at an atomic or residue level are still lacking. In addition, how and to what extent folding frustrations interact with protein topology in determining folding mechanisms remains unclear. In this paper, we tried to understand energetic frustrations in the context of protein topology structures or native-contact networks by comparing the energetic frustrations of five homologous Im9 alpha-helix proteins that share very similar topology structures but have a single hydrophilic-to-hydrophobic mutual mutation. The folding simulations were performed using a coarse-grained Gō-like model, while non-native hydrophobic interactions were introduced as energetic frustrations using a Lennard-Jones potential function. Energetic frustrations were then examined at residue level based on φ-value analyses of the transition state ensemble structures and mapped back to native-contact networks. Our calculations show that energetic frustrations have highly heterogeneous influences on the folding of the four helices of the examined structures depending on the local environment of the frustration centers. Also, the closer the introduced frustration is to the center of the native-contact network, the larger the changes in the protein folding. Our findings add a new dimension to the understanding of protein folding the topology determination in that energetic frustrations works closely with native-contact networks to affect the protein folding.     

Use of MM-PB/SA in estimating the free energies of proteins: application to native, intermediates, and unfolded villin headpiece

We investigated the stability of three different ensembles of the 36-mer villin headpiece subdomain, the native, a compact folding intermediate, and the random coil. Structures were taken from a 1-micros molecular dynamics folding simulation and a 100-ns control simulation on the native structure. Our approach for each conformation is to first determine the solute internal energy from the molecular mechanics potential and then to add the change resulting from solvation (DeltaG(solv)). Explicit water was used to run the simulation, and a continuum model was used to estimate DeltaG(solv) with the finite difference Poisson-Boltzmann model accounting for the polarization part and a linearly surface area-dependent term for the non-polar part. We leave out the solute vibrational entropy from these values but demonstrate that there is no statistical difference among the native, folding intermediate, and random coil ensembles. We find the native ensemble to be approximately 26 kcal/mol more stable than the folding intermediate and approximately 39 kcal/mol more stable than the random coil ensemble. With an experimental estimate for the free energy of denaturation equal to 3 kcal/mol, we approximate the non-native degeneracy to lie between 10(16) and 10.(25) We also present a possible scheme for the mechanism of folding, first-order exponential decay of a putative transition state, with an estimate for the t(1/2) of folding of approximately 1 micros.     

Nucleation and the transition state of the SH3 domain

We present a verified computational model of the SH3 domain transition state (TS) ensemble. This model was built for three separate SH3 domains using experimental phi-values as structural constraints in all-atom protein folding simulations. While averaging over all conformations incorrectly considers non-TS conformations as transition states, quantifying structures as pre-TS, TS, and post-TS by measurement of their transmission coefficient ("probability to fold", or p(fold)) allows for rigorous conclusions regarding the structure of the folding nucleus and a full mechanistic analysis of the folding process. Through analysis of the TS, we observe a highly polarized nucleus in which many residues are solvent-exposed. Mechanistic analysis suggests the hydrophobic core forms largely after an early nucleation step. SH3 presents an ideal system for studying the nucleation-condensation mechanism and highlights the synergistic relationship between experiment and simulation in the study of protein folding.     

Structural comparison of the two alternative transition states for folding of TI I27

TI I27, a beta-sandwich domain from the human muscle protein titin, has been shown to fold via two alternative pathways, which correspond to a change in the folding mechanism. Under physiological conditions, TI I27 folds by a classical nucleation-condensation mechanism (diffuse transition state), whereas at extreme conditions of temperature and denaturant it switches to having a polarized transition state. We have used experimental Phi-values as restraints in ensemble-averaged molecular dynamics simulations to determine the ensembles of structures representing the two transition states. The comparison of these ensembles indicates that when native interactions are substantially weakened, a protein may still be able to fold if it can access an alternative transition state characterized by a much larger entropic contribution. Analysis of the probability distribution of Phi-values derived from ensemble averaged simulations, enables us to identify residues that form contacts in some members of the ensemble but not in others illustrating that many interactions present in transition states are not strictly required for the successful completion of the folding process.     

Experiment and theory highlight role of native state topology in SH3 folding.

We use a combination of experiments, computer simulations and simple model calculations to characterize, first, the folding transition state ensemble of the src SH3 domain, and second, the features of the protein that determine its folding mechanism. Kinetic analysis of mutations at 52 of the 57 residues in the src SH3 domain revealed that the transition state ensemble is even more polarized than suspected earlier: no single alanine substitution in the N-terminal 15 residues or the C-terminal 9 residues has more than a two-fold effect on the folding rate, while such substitutions at 15 sites in the central three-stranded beta-sheet cause significant decreases in the folding rate. Molecular dynamics (MD) unfolding simulations and ab initio folding simulations on the src SH3 domain exhibit a hierarchy of folding similar to that observed in the experiments. The similarity in folding mechanism of different SH3 domains and the similar hierarchy of structure formation observed in the experiments and the simulations can be largely accounted for by a simple native state topology-based model of protein folding energy landscapes.     

Commitment and nucleation in the protein G transition state

An accurate characterization of the transition state ensemble (TSE) is central to furthering our understanding of the protein folding reaction. We have extensively tested a recently reported method for studying a protein's TSE, utilizing phi-value data from protein engineering experiments and computational studies as restraints in all-atom Monte Carlo (MC) simulations. The validity of interpreting experimental phi-values as the fraction of native contacts made by a residue in the TSE was explored, revealing that this definition is unable to uniquely specify a TSE. The identification of protein G's second hairpin, in both pre and post-transition conformations demonstrates that high experimental phi-values do not guarantee a residue's importance in the TSE. An analysis of simulations based on structures restrained by experimental phi-values is necessary to yield this result, which is not obvious from a simplistic interpretation of individual phi-values. The TSE that we obtain corresponds to a single, specific nucleation event, characterized by six residues common to all three observed, convergent folding pathways. The same specific nucleus was independently identified from computational and experimental data, and "Conservation of Conservation" analysis in the protein G fold. When associated strictly with complete nucleus formation and concomitant chain collapse, folding is a well-defined two state event. Once the nucleus has formed, the folding reaction enters a slow relaxation process associated with side-chain packing and small, local backbone rearrangements. A detailed analysis of phi-values and their relationship to the transition state ensemble allows us to construct a unified theoretical model of protein G folding.     

Kinetic traps in the folding of beta alpha-repeat proteins: CheY initially misfolds before accessing the native conformation

The βα-repeat class of proteins, represented by the (βα)₈ barrel and the α/β/α sandwich, are among the most common structural platforms in biology. Previous studies on the folding mechanisms of these motifs have revealed or suggested that the initial event involves the submillisecond formation of a kinetically trapped species that must at least partially unfold before productive folding to the respective native conformation can occur. To test the generality of these observations, CheY, a bacterial response regulator, was subjected to an extensive analysis of its folding reactions. Although earlier studies had proposed the formation of an off-pathway intermediate, the data available were not sufficient to rule out an alternative on-pathway mechanism. A global analysis of single- and double-jump kinetic data, combined with equilibrium unfolding data, was used to show that CheY folds and unfolds through two parallel channels defined by the state of isomerization of a prolyl peptide bond in the active site. Each channel involves a stable, highly structured folding intermediate whose kinetic properties are better described as the properties of an off-pathway species. Both intermediates subsequently flow through the unfolded state ensemble and adopt the native cis-prolyl isomer prior to forming the native state. Initial collapse to off-pathway folding intermediates is a common feature of the folding mechanisms of βα-repeat proteins, perhaps reflecting the favored partitioning to locally determined substructures that cannot directly access the native conformation. Productive folding requires the dissipation of these prematurely folded substructures as a prelude to forming the larger-scale transition state that leads to the native conformation. Results from Gō-modeling studies in the accompanying paper elaborate on the topological frustration in the folding free-energy landscape of CheY.     

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-α, all-β, and mixed α/β and α + β) 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 α-helix maintained more structure in the TS ensemble than did residues starting in β-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.     

Determination of the transition state ensemble for the folding of ubiquitin from a combination of Phi and Psi analyses

Protein engineering techniques have emerged as powerful tools for characterizing transition states (TSs) for protein folding. Recently, the Ψ analysis, in which double-histidine mutations create the possibility of reversible crosslinking in the native state, has been proposed as an additional approach to the well-established Φ analysis. We present here a combination of these two procedures for defining the structure of the TS of ubiquitin, a small α/β protein that has been used extensively as a model system for both experimental and computational studies of the protein-folding process. We performed a series of molecular dynamics simulations in which Φ and Ψ values were used as ensemble-averaged structural restraints to determine an ensemble of structures representing the TS of ubiquitin. Although the available Ψ values for ubiquitin did not, by themselves, generate well-defined TS ensembles, the inclusion of the restricted set of zero or unity values, but not fractional ones, provided useful complementary information to the Φ analysis. Our results show that the TS of ubiquitin is formed by a relatively narrow ensemble of structures exhibiting an overall native-like topology in which the N-terminal and C-terminal regions are in close proximity.     

Transition states for protein folding have native topologies despite high structural variability

We present a structural analysis of the folding transition states of three SH3 domains. Our results reveal that the secondary structure is not yet fully formed at this stage of folding and that the solvent is only partially excluded from the interior of the protein. Comparison of the members of the transition state ensemble with a database of native folds shows that, despite substantial local variability, the transition state structures can all be classified as having the topology characteristic of an SH3 domain. Our results suggest a mechanism for folding in which the formation of a network of interactions among a subset of hydrophobic residues ensures that the native topology is generated. Such a mechanism enables high fidelity in folding while minimizing the need to establish a large number of specific interactions in the conformational search.