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.     

Constraining local structure can speed up folding by promoting structural polarization of the folding pathway

The pathway which proteins take to fold can be influenced from the earliest events of structure formation. In this light, it was both predicted and confirmed that increasing the stiffness of a beta hairpin turn decreased the size of the transition state ensemble (TSE), while increasing the folding rate. Thus, there appears to be a relationship between conformationally restricting the TSE and increasing the folding rate, at least for beta hairpin turns. In this study, we hypothesize that the enormous sampling necessary to fold even two-state folding proteins in silico could be reduced if local structure constraints were used to restrict structural heterogeneity by polarizing folding pathways or forcing folding into preferred routes. Using a Gō model, we fold Chymotrypsin Inhibitor 2 (CI-2) and the src SH3 domain after constraining local sequence windows to their native structure by rigid body dynamics (RBD). Trajectories were monitored for any changes to the folding pathway and differences in the kinetics compared with unconstrained simulations. Constraining local structure decreases folding time two-fold for 41% of src SH3 windows and 45% of CI-2 windows. For both proteins, folding times are never significantly increased after constraining any window. Structural polarization of the folding pathway appears to explain these rate increases. Folding rate enhancements are consistent with the goal to reduce sampling time necessary to reach native structures during folding simulations. As anticipated, not all constrained windows showed an equal decrease in folding time. We conclude by analyzing these differences and explain why RBD may be the preferred way to constrain structure.     

Minimalist models for protein folding and design

Protein folding research during the past decade has emphasized the dominant role of native state topology in determining the speed and mechanism of folding for small proteins; this has been illustrated by simulations using minimalist protein models. The advantages of minimalist protein models lie in their ability to rapidly collect meaningful statistics about folding pathways and kinetics, their ease of characterization with coarse-grained order parameters and their concentration on the essential physics of the problem to connect with experimental observables for a target protein. The maturation of experimental protein folding has driven the need for more quantitative protein simulations to better understand the balance between sequence details and fold topology. In the past year, we have seen the emergence of more complex minimalist models, ranging from all-atom Gō potentials to coarse-grained bead models in which Gō interactions are replaced or supplemented by more physically motivated potentials. The reduced computational cost at the coarse-grained level of abstraction will potentially enable both folding studies on a genomic scale and systematic application in protein design.     

The family feud: do proteins with similar structures fold via the same pathway?

Theoretical and experimental studies of protein folding have suggested that the topology of the native state may be the most important factor determining the folding pathway of a protein, independent of its specific amino acid sequence. To test this concept, many experimental studies have been carried out with the aim of comparing the folding pathways of proteins that possess similar tertiary structures, but divergent sequences. Many of these studies focus on quantitative comparisons of folding transition state structures, as determined by Phi(f) value analysis of folding kinetic data. In some of these studies, folding transition state structures are found to be highly conserved, whereas in others they are not. We conclude that folds displaying more conserved transition state structures may have the most restricted number of possible folding pathways and that folds displaying low transition state structural conservation possess many potential pathways for reaching the native state.     

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.     

Diffusion-collision of foldons elucidates the kinetic effects of point mutations and suggests control strategies of the folding process of helical proteins

In this article we use mutation studies as a benchmark for a minimal model of the folding process of helical proteins. The model ascribes a pivotal role to the collisional dynamics of a few crucial residues (foldons) and predicts the folding rates by exploiting information drawn from the protein sequence. We show that our model rationalizes the effects of point mutations on the kinetics of folding. The folding times of two proteins and their mutants are predicted. Stability and location of foldons have a critical role as the determinants of protein folding. This allows us to elucidate two main mechanisms for the kinetic effects of mutations. First, it turns out that the mutations eliciting the most notable effects alter protein stability through stabilization or destabilization of the foldons. Secondly, the folding rate is affected via a modification of the foldon topology by those mutations that lead to the birth or death of foldons. The few mispredicted folding rates of some mutants hint at the limits of the current version of the folding model proposed in the present article. The performance of our folding model declines in case the mutated residues are subject to strong long-range forces. That foldons are the critical targets of mutation studies has notable implications for design strategies and is of particular interest to address the issue of the kinetic regulation of single proteins in the general context of the overall dynamics of the interactome.     

Influence of denatured and intermediate states of folding on protein aggregation

We simulate the aggregation thermodynamics and kinetics of proteins L and G, each of which self-assembles to the same alpha/beta [corrected] topology through distinct folding mechanisms. We find that the aggregation kinetics of both proteins at an experimentally relevant concentration exhibit both fast and slow aggregation pathways, although a greater proportion of protein G aggregation events are slow relative to those of found for protein L. These kinetic differences are correlated with the amount and distribution of intrachain contacts formed in the denatured state ensemble (DSE), or an intermediate state ensemble (ISE) if it exists, as well as the folding timescales of the two proteins. Protein G aggregates more slowly than protein L due to its rapidly formed folding intermediate, which exhibits native intrachain contacts spread across the protein, suggesting that certain early folding intermediates may be selected for by evolution due to their protective role against unwanted aggregation. Protein L shows only localized native structure in the DSE with timescales of folding that are commensurate with the aggregation timescale, leaving it vulnerable to domain swapping or nonnative interactions with other chains that increase the aggregation rate. Folding experiments that characterize the structural signatures of the DSE, ISE, or the transition state ensemble (TSE) under nonaggregating conditions should be able to predict regions where interchain contacts will be made in the aggregate, and to predict slower aggregation rates for proteins with contacts that are dispersed across the fold. Since proteins L and G can both form amyloid fibrils, this work also provides mechanistic and structural insight into the formation of prefibrillar species.     

Small proteins fold through transition states with native-like topologies

The folding pathway of common-type acyl phosphatase (ctAcP) is characterized using psi-analysis, which identifies specific chain-chain contacts using bi-histidine (biHis) metal-ion binding sites. In the transition state ensemble (TSE), the majority of the protein is structured with a near-native topology, only lacking one beta-strand and an alpha-helix. psi-Values are zero or unity for all sites except one at the amino terminus of helix H2. This fractional psi-value remains unchanged when three metal ions of differing coordination geometries are used, indicating this end of the helix experiences microscopic heterogeneity through fraying in the TSE. Ubiquitin, the other globular protein characterized using psi-analysis, also exhibits a single consensus TSE structure. Hence, the TSE of both proteins have converged to a single configuration, albeit one that contains some fraying at the periphery. Models of the TSE of both proteins are created using all-atom Langevin dynamics simulations using distance constraints derived from the experimental psi-values. For both proteins, the relative contact order of the TS models is approximately 80% of the native value. This shared value viewed in the context of the known correlation between contact order and folding rates, suggests that other proteins will have a similarly high fraction of the native contact order. This constraint greatly limits the range of possible configurations at the rate-limiting step.     

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.     

Are residues in a protein folding nucleus evolutionarily conserved?

Protein is the working molecule of the cell, and evolution is the hallmark of life. It is important to understand how protein folding and evolution influence each other. Several studies correlating experimental measurement of residue participation in folding nucleus and sequence conservation have reached different conclusions. These studies are based on assessment of sequence conservation at folding nucleus sites using entropy or relative entropy measurement derived from multiple sequence alignment. Here we report analysis of conservation of folding nucleus using an evolutionary model alternative to entropy-based approaches. We employ a continuous time Markov model of codon substitution to distinguish mutation fixed by evolution and mutation fixed by chance. This model takes into account bias in codon frequency, bias-favoring transition over transversion, as well as explicit phylogenetic information. We measure selection pressure using the ratio omega of synonymous versus non-synonymous substitution at individual residue site. The omega-values are estimated using the PAML method, a maximum-likelihood estimator. Our results show that there is little correlation between the extent of kinetic participation in protein folding nucleus as measured by experimental phi-value and selection pressure as measured by omega-value. In addition, two randomization tests failed to show that folding nucleus residues are significantly more conserved than the whole protein, or the median omega value of all residues in the protein. These results suggest that at the level of codon substitution, there is no indication that folding nucleus residues are significantly more conserved than other residues. We further reconstruct candidate ancestral residues of the folding nucleus and suggest possible test tube mutation studies for testing folding behavior of ancient folding nucleus.     

Probing possible downhill folding: native contact topology likely places a significant constraint on the folding cooperativity of proteins with approximately 40 residues

Experiments point to appreciable variations in folding cooperativity among natural proteins with approximately 40 residues, indicating that the behaviors of these proteins are valuable for delineating the contributing factors to cooperative folding. To explore the role of native topology in a protein's propensity to fold cooperatively and how native topology might constrain the degree of cooperativity achievable by a given set of physical interactions, we compared folding/unfolding kinetics simulated using three classes of native-centric C^α chain models with different interaction schemes. The approach was applied to two homologous 45-residue fragments from the peripheral subunit-binding domain family and a 39-residue fragment of the N-terminal domain of ribosomal protein L9. Free-energy profiles as functions of native contact number were computed to assess the heights of thermodynamic barriers to folding. In addition, chevron plots of folding/unfolding rates were constructed as functions of native stability to facilitate comparison with available experimental data. Although common Gō-like models with pairwise Lennard-Jones-type interactions generally fold less cooperatively than real proteins, the rank ordering of cooperativity predicted by these models is consistent with experiment for the proteins investigated, showing increasing folding cooperativity with increasing nonlocality of a protein's native contacts. Models that account for water-expulsion (desolvation) barriers and models with many-body (nonadditive) interactions generally entail higher degrees of folding cooperativity indicated by more linear model chevron plots, but the rank ordering of cooperativity remains unchanged. A robust, experimentally valid rank ordering of model folding cooperativity independent of the multiple native-centric interaction schemes tested here argues that native topology places significant constraints on how cooperatively a protein can fold.     

Coarse-grained strategy for modeling protein stability in concentrated solutions

We present a coarse-grained approach for modeling the thermodynamic stability of single-domain globular proteins in concentrated aqueous solutions. Our treatment derives effective protein-protein interactions from basic structural and energetic characteristics of the native and denatured states. These characteristics, along with the intrinsic (i.e., infinite dilution) thermodynamics of folding, are calculated from elementary sequence information using a heteropolymer collapse theory. We integrate this information into Reactive Canonical Monte Carlo simulations to investigate the connections between protein sequence hydrophobicity, protein-protein interactions, protein concentration, and the thermodynamic stability of the native state. The model predicts that sequence hydrophobicity can affect how protein concentration impacts native-state stability in solution. In particular, low hydrophobicity proteins are primarily stabilized by increases in protein concentration, whereas high hydrophobicity proteins exhibit richer nonmonotonic behavior. These trends appear qualitatively consistent with the available experimental data. Although factors such as pH, salt concentration, and protein charge are also important for protein stability, our analysis suggests that some of the nontrivial experimental trends may be driven by a competition between destabilizing hydrophobic protein-protein attractions and entropic crowding effects.     

Matching simulation and experiment: a new simplified model for simulating protein folding.

Simulations of simplified protein folding models have provided much insight into solving the protein folding problem. We propose here a new off-lattice bead model, capable of simulating several different fold classes of small proteins. We present the sequence for an alpha/beta protein resembling the IgG-binding proteins L and G. The thermodynamics of the folding process for this model are characterized using the multiple multihistogram method combined with constant-temperature Langevin simulations. The folding is shown to be highly cooperative, with chain collapse nearly accompanying folding. Two parallel folding pathways are shown to exist on the folding free energy landscape. One pathway contains an intermediate--similar to experiments on protein G, and one pathway contains no intermediates-similar to experiments on protein L. The folding kinetics are characterized by tabulating mean-first passage times, and we show that the onset of glasslike kinetics occurs at much lower temperatures than the folding temperature. This model is expected to be useful in many future contexts: investigating questions of the role of local versus nonlocal interactions in various fold classes, addressing the effect of sequence mutations affecting secondary structure propensities, and providing a computationally feasible model for studying the role of solvation forces in protein folding.     

Improved Gō-like models demonstrate the robustness of protein folding mechanisms towards non-native interactions

The use of simple theoretical models has provided a considerable contribution to our present understanding of the means by which proteins adopt their native fold from the plethora of available unfolded states. A common assumption in building computationally tractable models has been the neglect of stabilizing non-native interactions in the class of models described as "Gō-like." The focus of this study is the characterization of the folding of a number of proteins via a Gō-like model, which aims to map a maximal amount of information reflecting the protein sequence onto a "minimalist" skeleton. This model is shown to contain sufficient information to reproduce the folding transition states of a number of proteins, including topologically analogous proteins that fold via different transition states. Remarkably, these models also demonstrate consistency with the general features of folding transition states thought to be stabilized by non-native interactions. This suggests that native interactions are the primary determinant of most protein folding transition states, and that non-native interactions lead only to local structural perturbations. A prediction is also included for an asymmetrical folding transition state of bacteriophage lambda protein W, which has yet to be subjected to experimental characterization.     

Switching two-state to three-state kinetics in the helical protein Im9 via the optimisation of stabilising non-native interactions by design

The four-helix protein Im7 folds through an on-pathway intermediate at pH 7.0 and 10 degrees C. By contrast, under these conditions there is no evidence for a populated intermediate in the folding of its more stable homologue, Im9, even in the presence of 0.4 M sodium sulphate. Previous studies using phi-value analysis have shown that the Im7 intermediate is misfolded, in that three of its four native helices are formed, but are docked in a non-native manner. Using knowledge of the structure of the intermediate of Im7, we have used rational design to stabilise an intermediate formed during the folding of Im9 by the introduction of specific stabilising interactions at positions known to stabilise the Im7 folding intermediate through non-native interactions. We show that the redesigned Im9 sequence folds with three-state kinetics at pH 7.0 and have used phi-value analysis to demonstrate that this species resembles the misfolded intermediate populated during Im7 folding. The redesigned Im9 sequence folds 20-fold faster than the wild-type protein under conditions in which folding is two-state. The data show that intermediate formation is an important feature of folding, even for small proteins such as Im9 for which these partially folded states do not become significantly populated. In addition, they show that the introduction of stabilising interactions can lead to rapid refolding, even when the contacts introduced are non-native.     

Folding mechanisms of proteins with high sequence identity but different folds

The problem of how a protein folds from a linear chain of amino acids to the three-dimensional structure necessary for function is often investigated using proteins with a low degree of sequence identity that adopt different folds. The design of pairs of proteins with a high degree of sequence identity but different folds offers the opportunity for a complementary study; in two highly similar sequences, which residues are the most important in directing folding to a particular structure? Here we use molecular dynamics simulations to characterize the folding-unfolding pathways of a pair of proteins designed by Bryan and co-workers [Alexander, P. A., et al. (2005) Biochemistry 44, 14045-14054; He, Y. N., et al. (2005) Biochemistry 44, 14055-14061]. Despite being 59% identical, the two protein sequences fold to two different structures. The first sequence folds to the alpha+beta protein G structure and the second to the all-alpha-helical protein A structure. We show that the final protein structure is determined early along the folding pathway. In folding to the protein G structure, the single alpha-helix (alpha1) and the beta3-beta4 turn fold early. Formation of the hairpin turn essentially prevents folding to helical structure in this region of the protein. This early structure is then consolidated by formation of long-range hydrophobic interactions between alpha1 and the beta3-beta4 turn. The protein A sequence differs both in the residues that form the beta3-beta4 turn and also in many of the residues that form the early hydrophobic interactions in the protein G structure. Instead, in the protein A sequence, a more hierarchical mechanism is observed, with helices folding before many of the tertiary interactions are formed. We find that small, but critical, sequence differences determine the topology of the protein early along the folding pathway, which help to explain the process by which one fold can evolve into another.     

The Limited Role of Nonnative Contacts in the Folding Pathways of a Lattice Protein

Models of protein energetics that neglect interactions between amino acids that are not adjacent in the native state, such as the Gō model, encode or underlie many influential ideas on protein folding. Implicit in this simplification is a crucial assumption that has never been critically evaluated in a broad context: Detailed mechanisms of protein folding are not biased by nonnative contacts, typically argued to be a consequence of sequence design and/or topology. Here we present, using computer simulations of a well-studied lattice heteropolymer model, the first systematic test of this oft-assumed correspondence over the statistically significant range of hundreds of thousands of amino acid sequences that fold to the same native structure. Contrary to previous conjectures, we find a multiplicity of folding mechanisms, suggesting that Gō-like models cannot be justified by considerations of topology alone. Instead, we find that the crucial factor in discriminating among topological pathways is the heterogeneity of native contact energies: The order in which native contacts accumulate is profoundly insensitive to omission of nonnative interactions, provided that native contact heterogeneity is retained. This robustness holds over a surprisingly wide range of folding rates for our designed sequences. Mirroring predictions based on the principle of minimum frustration, fast-folding sequences match their Gō-like counterparts in both topological mechanism and transit times. Less optimized sequences dwell much longer in the unfolded state and/or off-pathway intermediates than do Gō-like models. For dynamics that bridge unfolded and unfolded states, however, even slow folders exhibit topological mechanisms and transit times nearly identical with those of their Gō-like counterparts. Our results do not imply a direct correspondence between folding trajectories of Gō-like models and those of real proteins, but they do help to clarify key topological and energetic assumptions that are commonly used to justify such caricatures.