Importance of sequence specificity for predicting protein folding pathways: perturbed Gaussian chain model

Recent experimental and theoretical studies suggest that rates and pathways of protein folding are largely decided by topology of the native structures, at least for small proteins. However, some exceptions are known; for example, protein L and protein G have the same topology, but exhibit different characteristics of the TSE. Thus, folding pathways of some proteins are critically affected by detailed information on amino acid sequences. To investigate the sequence specificity, we calculate folding pathways of 20 small proteins using the perturbed Gaussian chain model developed by Portman et al. (Phys Rev Lett 1998;81:5237-5240; J Chem Phys 2001;114:5069-5081). Characteristics of the TSE predicted by the model are in good agreement with experimental phi-value data for many proteins at coarse-grained level. Especially, estimation of folding TSE for protein G and protein L based on both topology and additional sequence information are consistent with experimental phi-value data. With only topology information, however, the model predicts the TSE of protein G incorrectly. Moreover, the model that uses topology and sequence information describes free energy profiles of two-state and three-state folders consistently with experiment, whereas the topology only model predicts free energy profiles of some proteins incorrectly. This indicates that sequence specificity also has critical roles in determining the folding pathways for some proteins.     

The origins of asymmetry in the folding transition states of protein L and protein G

Topology has been shown to be an important determinant of many features of protein folding; however, the delineation of sequence effects on folding remains obscure. Furthermore, differentiation between the two influences proves difficult due to their intimate relationship. To investigate the effect of sequence in the absence of significant topological differences, we examined the folding mechanisms of segment B1 peptostreptococcal protein L and segment B1 of streptococcal protein G. These proteins share the same highly symmetrical topology. Despite this symmetry, neither protein folds through a symmetrical transition state. We analyzed the origins of this difference using theoretical models. We found that the strength of the interactions present in the N-terminal hairpin of protein L causes this hairpin to form ahead of the C-terminal hairpin. The difference in chain entropy associated with the formation of the hairpins of protein G proves sufficient to beget initiation of folding at the shorter C-terminal hairpin. Our findings suggest that the mechanism of folding may be understood by examination of the free energy associated with the formation of partially folded microstates.     

Intermediates and the folding of proteins L and G

We use a minimalist protein model, in combination with a sequence design strategy, to determine differences in primary structure for proteins L and G, which are responsible for the two proteins folding through distinctly different folding mechanisms. We find that the folding of proteins L and G are consistent with a nucleation-condensation mechanism, each of which is described as helix-assisted beta-1 and beta-2 hairpin formation, respectively. We determine that the model for protein G exhibits an early intermediate that precedes the rate-limiting barrier of folding, and which draws together misaligned secondary structure elements that are stabilized by hydrophobic core contacts involving the third beta-strand, and presages the later transition state in which the correct strand alignment of these same secondary structure elements is restored. Finally, the validity of the targeted intermediate ensemble for protein G was analyzed by fitting the kinetic data to a two-step first-order reversible reaction, proving that protein G folding involves an on-pathway early intermediate, and should be populated and therefore observable by experiment.     

Designing cooperativity into the designed protein Top7

The topology of the designed protein Top7 is not found in natural proteins. Top7 shows signatures of non‐cooperative folding in both experimental studies and computer simulations. In particular, molecular dynamics of coarse‐grained structure‐based models of Top7 show a well‐populated C‐terminal folding‐intermediate. Since most similarly sized globular proteins are cooperative folders, the non‐natural topology of Top7 has been suggested as a reason for its non‐cooperative folding. Here, we computationally examine the folding of Top7 with the intent of making it cooperative. We find that its folding cooperativity can be increased in two ways: (a) Optimization of packing interactions in the N‐terminal half of the protein enables further folding of the C‐terminal intermediate. (b) Reduction in the packing density of the C‐terminal region destabilizes the intermediate. In practice, these strategies are implemented in our Top7 model through modifications to the contact‐map. These modifications do not alter the topology of Top7 but result in cooperative folding. Amino‐acid mutations that mimic these modifications also lead to a significant increase in folding cooperativity. Finally, we devise a method to randomize the sizes of amino‐acids within the same topology, and confirm that the structure of Top7 makes its folding sensitive to packing interactions. In contrast, the ribosomal protein S6, which has secondary structure similar to Top7, has folding which is much less sensitive to packing perturbations. Thus, it should be possible to make a sequence fold cooperatively to the structure of Top7, but to do so its side‐chain packing needs to be carefully designed. Proteins 2014; 82:364–374. © 2013 Wiley Periodicals, Inc.     

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.     

Contact order revisited: influence of protein size on the folding rate

Guided by the recent success of empirical model predicting the folding rates of small two-state folding proteins from the relative contact order (CO) of their native structures, by a theoretical model of protein folding that predicts that logarithm of the folding rate decreases with the protein chain length L as L(2/3), and by the finding that the folding rates of multistate folding proteins strongly correlate with their sizes and have very bad correlation with CO, we reexamined the dependence of folding rate on CO and L in attempt to find a structural parameter that determines folding rates for the totality of proteins. We show that the Abs_CO = CO x L, is able to predict rather accurately folding rates for both two-state and multistate folding proteins, as well as short peptides, and that this Abs_CO scales with the protein chain length as L(0.70 +/- 0.07) for the totality of studied single-domain proteins and peptides.     

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.     

Critical role of beta-hairpin formation in protein G folding

Comparison of the folding mechanisms of proteins with similar structures but very different sequences can provide fundamental insights into the determinants of protein folding mechanisms. Despite very little sequence similarity, the approximately 60 residue IgG binding domains of protein G and protein L both consist of a single helix packed against a four-stranded sheet formed by two symmetrically disposed beta-hairpins. We demonstrate that, as in the case of protein L, one of the two beta-turns of protein G is formed and the other disrupted in the folding transition state. Unlike protein L, however, in protein G it is the second beta-turn that is formed in the folding transition state ensemble. Substitution of an Asp residue by Ala in protein G that eliminates an i,i+2 side chain-main chain hydrogen bond in the second beta-turn slows the folding rate approximately 20-fold but has virtually no effect on the unfolding rate. Taken together with previous results, these findings suggest that the presence of an intact beta-turn in the folding transition state is a consequence of the overall topology of protein L and protein G, but the particular hairpin that is formed is determined by the detailed interatomic interactions that determine the free energies of formation of the isolated beta-hairpins.     

Protein aggregation determinants from a simplified model: cooperative folders resist aggregation

Two-chain aggregation simulations using minimalist models of proteins G, L, and mutants were used to investigate the fundamentals of protein aggregation. Mutations were selected to break up repeats of hydrophobic beads in the sequence while maintaining native topology and folding ability. Data are collected under conditions in which all chain types have similar folded populations and after equilibrating the separated chains to minimize competition between folding and aggregation. Folding cooperativity stands out as the best single-chain determinant under these conditions and for these simple models. It can be experimentally measured by the width of the unfolding transition during thermal denaturation and loosely related to population of intermediate-like states during folding. Additional measures of cooperativity and other properties such as radius of gyration fluctuations and patterning of hydrophobic residues are also examined. Initial contact system states with transition-state characteristics can be identified and are more expanded than average initial contact states. Two-chain minimalist model aggregates are considerably less structured than their native states and have minimal domain-swapping features.     

Unification of the folding mechanisms of non-two-state and two-state proteins

We have collected the kinetic folding data for non-two-state and two-state globular proteins reported in the literature, and investigated the relationships between the folding kinetics and the native three-dimensional structure of these proteins. The rate constants of formation of both the intermediate and the native state of non-two-state folders were found to be significantly correlated with protein chain length and native backbone topology, which is represented by the absolute contact order and sequence-distant native pairs. The folding rate of two-state folders, which is known to be correlated with the native backbone topology, apparently does not correlate significantly with protein chain length. On the basis of a comparison of the folding rates of the non-two-state and two-state folders, it was found that they are similarly dependent on the parameters that reflect the native backbone topology. This suggests that the mechanisms behind non-two-state and two-state folding are essentially identical. The present results lead us to propose a unified mechanism of protein folding, in which folding occurs in a hierarchical manner, reflecting the hierarchy of the native three-dimensional structure, as embodied in the case of non-two-state folding with an accumulation of the intermediate. Apparently, two-state folding is merely a simplified version of hierarchical folding caused either by an alteration in the rate-limiting step of folding or by destabilization of the intermediate.     

A simple measure of native-state topology and chain connectivity predicts the folding rates of two-state proteins with and without crosslinks

The folding rates of two-state proteins have been found to correlate with simple measures of native-state topology. The most prominent among these measures is the relative contact order (CO), which is the average CO, or localness, of all contacts in the native protein structure, divided by the chain length. Here, we test whether such measures can be generalized to capture the effect of chain crosslinks on the folding rate. Crosslinks change the chain connectivity and therefore also the localness of some of the native contacts. These changes in localness can be taken into account by the graph-theoretical concept of effective contact order (ECO). The relative ECO, however, the natural extension of the relative CO for proteins with crosslinks, overestimates the changes in the folding rates caused by crosslinks. We suggest here a novel measure of native-state topology, the relative logCO, and its natural extension, the relative logECO. The relative logCO is the average value for the logarithm of the CO of all contacts, divided by the logarithm of the chain length. The relative log(E)CO reproduces the folding rates of a set of 26 two-state proteins without crosslinks with essentially the same high correlation coefficient as the relative CO. In addition, it also captures the folding rates of eight two-state proteins with crosslinks.     

Novel approach for alpha-helical topology prediction in globular proteins: generation of interhelical restraints

The protein folding problem represents one of the most challenging problems in computational biology. Distance constraints and topology predictions can be highly useful for the folding problem in reducing the conformational space that must be searched by deterministic algorithms to find a protein structure of minimum conformational energy. We present a novel optimization framework for predicting topological contacts and generating interhelical distance restraints between hydrophobic residues in alpha-helical globular proteins. It should be emphasized that since the model does not make assumptions about the form of the helices, it is applicable to all alpha-helical proteins, including helices with kinks and irregular helices. This model aims at enhancing the ASTRO-FOLD protein folding approach of Klepeis and Floudas (Journal of Computational Chemistry 2003;24:191-208), which finds the structure of global minimum conformational energy via a constrained nonlinear optimization problem. The proposed topology prediction model was evaluated on 26 alpha-helical proteins ranging from 2 to 8 helices and 35 to 159 residues, and the best identified average interhelical distances corresponding to the predicted contacts fell below 11 A in all 26 of these systems. Given the positive results of applying the model to several protein systems, the importance of interhelical hydrophobic-to-hydrophobic contacts in determining the folding of alpha-helical globular proteins is highlighted.     

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.     

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.     

Pathway heterogeneity in protein folding

We generate ab initio folding pathways in two single-domain proteins, hyperthermophile variant of protein G domain (1gb4) and ubiquitin (1ubi), both presumed to be two-state folders. Both proteins are endowed with the same topology but, as shown in this work, rely to a different extent on large-scale context to find their native folds. First, we demonstrate a generic feature of two-state folders: A downsizing of structural fluctuations is achieved only when the protein reaches a stationary plateau maximizing the number of highly protected hydrogen bonds. This enables us to identify the folding nucleus and show that folding does not become expeditious until a topology is generated that is able to protect intramolecular hydrogen bonds from water attack. Pathway heterogeneity is shown to be dependent on the extent to which the protein relies on large-scale context to fold, rather than on contact order: Proteins that can only stabilize native secondary structure by packing it against scaffolding hydrophobic moieties are meant to have a heterogeneous transition-state ensemble if they are to become successful folders (otherwise, successful folding would be too fortuitous an event.) We estimate mutational Phi values as ensemble averages and deconvolute individual-route contributions to the averaged two-state kinetic picture. Our results find experimental corroboration in the well-studied chymotrypsin inhibitor (CI2), while leading to verifiable predictions for the other two study cases.     

Relationship between energy distribution and fold stability: Insights from molecular dynamics simulations of native and mutant proteins

Most proteins must fold to a well-defined structure with a minimal stability to perform their function. Here we use a simple, molecular dynamics-based, energy decomposition approach to map the principal energetic interactions in a set of proteins representative of different folds. This work involves the all-atom simulation and analysis of the native structures and mutants of five different proteins representative of an all-alpha (yACPB, Protein A), all-beta (SH3), and a mixed alpha/beta fold (Proteins G and L). Given a certain structure, a native sequence and a set of mutants, we show that our model discriminates the ability of a mutation to yield a more or less stable protein, in agreement with experimental data, catching the principal energetic determinants of protein stabilization. Our approach identifies the interaction determinants responsible to define a fold and shows that mutations can either modulate the strength of pair-wise coupling between residues important for folding, or modify the profile of the principal interactions. Furthermore, we address the question of how to evaluate the fitness of a sequence to a given structure by comparing the information contained in the energy map, which recapitulates the chemistry of the sequence, to that contained in the contact map, which recapitulates the fold topology. The results show that the better fit between the energetic properties of the sequence and the fold topology corresponds to a higher stabilization of the protein. We discuss the relevance of these observations to the analysis of protein designability and to the rational evolution of new sequences.     

Unstructured intermediate states in single protein force experiments

Recent single-molecule force measurements on single-domain proteins have highlighted a three-state folding mechanism where a stabilized intermediate state (I) is observed on the folding trajectory between the stretched state and the native state. Here we investigate on-lattice protein-like heteropolymer models that lead to a three-state mechanism and show that force experiments can be useful to determine the structure of I. We have mostly found that I is composed of a core stabilized by a high number of native contacts, plus an unstructured extended chain. The lifetime of I is shown to be sensitive to modifications of the protein that spoil the core. We then propose three types of modifications--point mutations, cuts, and circular permutations--aiming at: (1) confirming the presence of the core and (2) determining its location, within one amino acid accuracy, along the polypeptide chain. We also propose force jump protocols aiming to probe the on/off-pathway nature of I.     

A model study of protein nascent chain and cotranslational folding using hydrophobic-polar residues

To study protein nascent chain folding during biosynthesis, we investigate the folding behavior of models of hydrophobic and polar (HP) chains at growing length using both two-dimensional square lattice model and an optimized three-dimensional 4-state discrete off-lattice model. After enumerating all possible sequences and conformations of HP heteropolymers up to length N = 18 and N = 15 in two and three-dimensional space, respectively, we examine changes in adopted structure, stability, and tolerance to single point mutation as the nascent chain grows. In both models, we find that stable model proteins have fewer folded nascent chains during growth, and often will only fold after reaching full length. For the few occasions where partial chains of stable proteins fold, these partial conformations on average are very similar to the corresponding parts of the final conformations at full length. Conversely, we find that sequences with fewer stable nascent chains and sequences with native-like folded nascent chains are more stable. In addition, these stable sequences in general can have many more point mutations and still fold into the same conformation as the wild type sequence. Our results suggest that stable proteins are less likely to be trapped in metastable conformations during biosynthesis, and are more resistant to point-mutations. Our results also imply that less stable proteins will require the assistance of chaperone and other factors during nascent chain folding. Taken together with other reported studies, it seems that cotranslational folding may not be a general mechanism of in vivo protein folding for small proteins, and in vitro folding studies are still relevant for understanding how proteins fold biologically.     

Class-specific correlations between protein folding rate, structure-derived, and sequence-derived descriptors

Small single-domain proteins that fold by simple two-state kinetics have been shown to exhibit a wide variation in their folding rates. It has been proposed that folding mechanisms in these proteins are largely determined by the native-state topology, and a significant correlation between folding rate and measures of the average topological complexity, such as relative contact order (RCO), has been reported. We perform a statistical analysis of folding rate and RCO in all three major structural classes (alpha, beta, and alpha/beta) of small two-state proteins and of RCO in groups of analogous and homologous small single-domain proteins with the same topology. We also study correlation between folding rate and the average physicochemical properties of amino acid sequences in two-state proteins. Our results indicate that 1) helical proteins have statistically distinguishable, class-specific folding rates; 2) RCO accounts for essentially all the variation of folding rate in helical proteins, but for only a part of the variation in beta-sheet-containing proteins; and 3) only a small fraction of the protein topologies studied show a topology-specific RCO. We also report a highly significant correlation between the folding rate and average intrinsic structural propensities of protein sequences. These results suggest that intrinsic structural propensities may be an important determinant of the rate of folding in small two-state proteins.