Pathway Diversity and Concertedness in Protein Folding: An ab-initio Approach

Abstract

Making use of an ab-initio folding simulator, we generate in vitro pathways leading to the native fold in moderate size single-domain proteins. The assessment of pathway diversity is not biased by any a-priori information on the native fold. We focus on two study cases, hyperthermophile variant of protein G domain (1gb4) and ubiquitin (1ubi), with the same topology but different context dependence in their native folds. We demonstrate that a quenching of structural fluctuations is achieved once the proteins find 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 concerted event takes place generating a topology able to prevent water attack on a maximal number of hydrogen bonds. This result is consistent with the standard nucleation mechanism postulated for two-state folders. Pathway diversity is correlated with the extent of conflict between local structural propensity and large-scale context, rather than with contact order: In highly context-dependent proteins, the success of folding cannot rely on a single fortuitous event in which local propensity is overruled by large-scale effects. We predict mutational Φ values on individual pathways, compute ensemble averages and predict extent of surface burial and percentage of hydrogen bonding on each component of the transition state ensemble, thus deconvoluting individual folding-route contributions to the averaged two-state kinetic picture. Our predicted kinetic isotopic effects find experimental support and lead to further probes. Finally, the molecular redesign potentiality of the method, aimed at increasing folding expediency, is explored.     

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.     

Time-resolved backbone desolvation and mutational hot spots in folding proteins

A method is presented to identify hot mutational spots and predict the extent of surface burial at the transition state relative to the native fold in two-state folding proteins. The method is based on ab initio simulations of folding histories in which transitions between coarsely defined conformations and pairwise interactions are dependent on the solvent environments created by the chain. The highly conserved mammalian ubiquitin is adopted as a study case to make predictions. The evolution in time of the chain topology suggests a nucleation process with a critical point signaled by a sudden quenching of structural fluctuations. The occurrence of this nucleus is shown to be concurrent with a sudden escalation in the number of three-body correlations whereby hydrophobic units approach residue pairs engaged in amide-carbonyl hydrogen bonding. These correlations determine a pattern designed to structure the surrounding solvent, protecting intramolecular hydrogen bonds from water attack. Such correlations are shown to be required to stabilize the nucleus, with kinetic consequences for the folding process. Those nuclear residues that adopt the dual role of protecting and being protected while engaged in hydrogen bonds are predicted to be the hottest mutational spots. Some such residues are shown not to retain the same protecting role in the native fold. This kinetic treatment of folding nucleation is independently validated vis-a-vis a Phi-value analysis on chymotrypsin inhibitor 2, a protein for which extensive mutational data exists.     

Multiple folding pathways of the SH3 domain

Experimental observations suggest that proteins follow different folding pathways under different environmental conditions. We perform molecular dynamics simulations of a model of the c-Crk SH3 domain over a broad range of temperatures, and identify distinct pathways in the folding transition. We determine the kinetic partition temperature-the temperature for which the c-Crk SH3 domain undergoes a rapid folding transition with minimal kinetic barriers-and observe that below this temperature the model protein may undergo a folding transition by multiple folding pathways via only one or two intermediates. Our findings suggest the hypothesis that the SH3 domain, a protein fold for which only two-state folding kinetics was observed in previous experiments, may exhibit intermediate states under conditions that strongly stabilize the native state.     

Protein unfolding rates correlate as strongly as folding rates with native structure

Although the folding rates of proteins have been studied extensively, both experimentally and theoretically, and many native state topological parameters have been proposed to correlate with or predict these rates, unfolding rates have received much less attention. Moreover, unfolding rates have generally been thought either to not relate to native topology in the same manner as folding rates, perhaps depending on different topological parameters, or to be more difficult to predict. Using a dataset of 108 proteins including two-state and multistate folders, we find that both unfolding and folding rates correlate strongly, and comparably well, with well-established measures of native topology, the absolute contact order and the long range order, with correlation coefficient values of 0.75 or higher. In addition, compared to folding rates, the absolute values of unfolding rates vary more strongly with native topology, have a larger range of values, and correlate better with thermodynamic stability. Similar trends are observed for subsets of different protein structural classes. Taken together, these results suggest that choosing a scaffold for protein engineering may require a compromise between a simple topology that will fold sufficiently quickly but also unfold quickly, and a complex topology that will unfold slowly and hence have kinetic stability, but fold slowly. These observations, together with the established role of kinetic stability in determining resistance to thermal and chemical denaturation as well as proteases, have important implications for understanding fundamental aspects of protein unfolding and folding and for protein engineering and design.     

Evidence concerning rate-limiting steps in protein folding from the effects of trifluoroethanol

The refolding kinetics of 13 proteins have been studied in the presence of 2,2,2-trifluoroethanol (TFE). Low concentrations of TFE increased the folding rates of all the proteins, whereas higher concentrations have the opposite effect. The extent of deceleration of folding correlates closely with similar effects of guanidine hydrochloride and can be related to the burial of accessible surface area during folding. For those proteins folding in a two-state manner, the extent of acceleration of folding correlates closely with the number of local backbone hydrogen bonds in the native structure. For those proteins that fold in a multistate manner, however, the extent of acceleration is much smaller than that predicted from the data for two-state proteins. These results support the concept that for two-state proteins the search for native-like contacts is a key aspect of the folding reaction, whereas the rate-determining steps for folding of multistate proteins are associated with the reorganization of stable structure within a collapsed state or with the search for native-like interactions within less structured regions.     

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.     

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.     

An expanded view of the protein folding landscape of PDZ domains

Most protein domains fold in an apparently co-operative and two-state manner with only the native and denatured states significantly populated at any experimental condition. However, the protein folding energy landscape is often rugged and different transition states may be rate limiting for the folding reaction under different conditions, as seen for the PDZ protein domain family. We have here analyzed the folding kinetics of two PDZ domains and found that a previously undetected third transition state is rate limiting under conditions that stabilize the native state relative to the denatured state. In light of these results, we have re-analyzed previous folding data on PDZ domains and present a unified folding mechanism with three distinct transition states separated by two high-energy intermediates. Our data show that sequence composition tunes the relative stabilities of folding transition states within the PDZ family, while the overall mechanism is determined by topology. This model captures the kinetic folding mechanism of all PDZ domains studied to date.     

First principles prediction of protein folding rates

Experimental studies have demonstrated that many small, single-domain proteins fold via simple two-state kinetics. We present a first principles approach for predicting these experimentally determined folding rates. Our approach is based on a nucleation-condensation folding mechanism, where the rate-limiting step is a random, diffusive search for the native tertiary topology. To estimate the rates of folding for various proteins via this mechanism, we first determine the probability of randomly sampling a conformation with the native fold topology. Next, we convert these probabilities into folding rates by estimating the rate that a protein samples different topologies during diffusive folding. This topology-sampling rate is calculated using the Einstein diffusion equation in conjunction with an experimentally determined intra-protein diffusion constant. We have applied our prediction method to the 21 topologically distinct small proteins for which two-state rate data is available. For the 18 beta-sheet and mixed alpha-beta native proteins, we predict folding rates within an average factor of 4, even though the experimental rates vary by a factor of approximately 4 x 10(4). Interestingly, the experimental folding rates for the three four-helix bundle proteins are significantly underestimated by this approach, suggesting that proteins with significant helical content may fold by a faster, alternative mechanism. This method can be applied to any protein for which the structure is known and hence can be used to predict the folding rates of many proteins prior to experiment.     

Towards a consistent modeling of protein thermodynamic and kinetic cooperativity: how applicable is the transition state picture to folding and unfolding?

To what extent do general features of folding/unfolding kinetics of small globular proteins follow from their thermodynamic properties? To address this question, we investigate a new simplified protein chain model that embodies a cooperative interplay between local conformational preferences and hydrophobic burial. The present four-helix-bundle 55mer model exhibits protein-like calorimetric two-state cooperativity. It rationalizes native-state hydrogen exchange observations. Our analysis indicates that a coherent, self-consistent physical account of both the thermodynamic and kinetic properties of the model leads naturally to the concept of a native state ensemble that encompasses considerable conformational fluctuations. Such a multiple-conformation native state is seen to involve conformational states similar to those revealed by native-state hydrogen exchange. Many of these conformational states are predicted to lie below native baselines commonly used in interpreting calorimetric data. Folding and unfolding kinetics are studied under a range of intrachain interaction strengths as in experimental chevron plots. Kinetically determined transition midpoints match well with their thermodynamic counterparts. Kinetic relaxations are found to be essentially single-exponential over an extended range of model interaction strengths. This includes the entire unfolding regime and a significant part of a folding regime with a chevron rollover, as has been observed for real proteins that fold with non-two-state kinetics. The transition state picture of protein folding and unfolding is evaluated by comparing thermodynamic free energy profiles with actual kinetic rates. These analyses suggest that some chevron rollovers may arise from an internal frictional effect that increasingly impedes chain motions with more native conditions, rather than being caused by discrete deadtime folding intermediates or shifts of the transition state peak as previously posited.     

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.     

Monomer topology defines folding speed of heptamer

Small monomeric proteins often fold in apparent two-state processes with folding speeds dictated by their native-state topology. Here we test, for the first time, the influence of monomer topology on the folding speed of an oligomeric protein: the heptameric cochaperonin protein 10 (cpn10), which in the native state has seven beta-barrel subunits noncovalently assembled through beta-strand pairing. Cpn10 is a particularly useful model because equilibrium-unfolding experiments have revealed that the denatured state in urea is that of a nonnative heptamer. Surprisingly, refolding of the nonnative cpn10 heptamer is a simple two-state kinetic process with a folding-rate constant in water (2.1 sec(-1); pH 7.0, 20 degrees C) that is in excellent agreement with the prediction based on the native-state topology of the cpn10 monomer. Thus, the monomers appear to fold as independent units, with a speed that correlates with topology, although the C and N termini are trapped in beta-strand pairing with neighboring subunits. In contrast, refolding of unfolded cpn10 monomers is dominated by a slow association step.     

Cooperative folding of the isolated alpha-helical domain of hen egg-white lysozyme.

Proteins in the alpha-lactalbumin and c-type lysozyme family have been studied extensively as model systems in protein folding. Early formation of the alpha-helical domain is observed in both alpha-lactalbumin and c-type lysozyme; however, the details of the kinetic folding pathways are significantly different. The major folding intermediate of hen egg-white lysozyme has a cooperatively formed tertiary structure, whereas the intermediate of alpha-lactalbumin exhibits the characteristics of a molten globule. In this study, we have designed and constructed an isolated alpha-helical domain of hen egg-white lysozyme, called Lyso-alpha, as a model of the lysozyme folding intermediate that is stable at equilibrium. Disulfide-exchange studies show that under native conditions, the cysteine residues in Lyso-alpha prefer to form the same set of disulfide bonds as in the alpha-helical domain of full-length lysozyme. Under denaturing conditions, formation of the nearest-neighbor disulfide bonds is strongly preferred. In contrast to the isolated alpha-helical domain of alpha-lactalbumin, Lyso-alpha with two native disulfide bonds exhibits a well-defined tertiary structure, as indicated by cooperative thermal unfolding and a well-dispersed NMR spectrum. Thus, the determinants for formation of the cooperative side-chain interactions are located mainly in the alpha-helical domain. Our studies suggest that the difference in kinetic folding pathways between alpha-lactalbumin and lysozyme can be explained by the difference in packing density between secondary structural elements and support the hypothesis that the structured regions in a protein folding intermediate may correspond to regions that can fold independently.     

Elucidating quantitative stability/flexibility relationships within thioredoxin and its fragments using a distance constraint model

Numerous quantitative stability/flexibility relationships, within Escherichia coli thioredoxin (Trx) and its fragments are determined using a minimal distance constraint model (DCM). A one-dimensional free energy landscape as a function of global flexibility reveals Trx to fold in a low-barrier two-state process, with a voluminous transition state. Near the folding transition temperature, the native free energy basin is markedly skewed to allow partial unfolded forms. Under native conditions the skewed shape is lost, and the protein forms a compact structure with some flexibility. Predictions on ten Trx fragments are generally consistent with experimental observations that they are disordered, and that complementary fragments reconstitute. A hierarchical unfolding pathway is uncovered using an exhaustive computational procedure of breaking interfacial cross-linking hydrogen bonds that span over a series of fragment dissociations. The unfolding pathway leads to a stable core structure (residues 22-90), predicted to act as a kinetic trap. Direct connection between degree of rigidity within molecular structure and non-additivity of free energy is demonstrated using a thermodynamic cycle involving fragments and their hierarchical unfolding pathway. Additionally, the model provides insight about molecular cooperativity within Trx in its native state, and about intermediate states populating the folding/unfolding pathways. Native state cooperativity correlation plots highlight several flexibly correlated regions, giving insight into the catalytic mechanism that facilitates access to the active site disulfide bond. Residual native cooperativity correlations are present in the core substructure, suggesting that Trx can function when it is partly unfolded. This natively disordered kinetic trap, interpreted as a molten globule, has a wide temperature range of metastability, and it is identified as the "slow intermediate state" observed in kinetic experiments. These computational results are found to be in overall agreement with a large array of experimental data.     

Structural analysis of the rate-limiting transition states in the folding of Im7 and Im9: similarities and differences in the folding of homologous proteins

The bacterial immunity proteins Im7 and Im9 fold with mechanisms of different kinetic complexity. Whilst Im9 folds in a two-state transition at pH 7.0 and 10 degrees C, Im7 populates an on-pathway intermediate under these conditions. In order to assess the role of sequence versus topology in the folding of these proteins, and to analyse the effect of populating an intermediate on the landscape for folding, we have determined the conformational properties of the rate-limiting transition state for Im9 folding/unfolding using Phi(F)-value analysis and have compared the results with similar data obtained previously for Im7. The data show that the rate-limiting transition states for Im9 and Im7 folding/unfolding are similar: both are compact (beta(T)=0.94 and 0.89, respectively) and contain three of the four native helices docked around a specific hydrophobic core. Significant differences are observed, however, in the magnitude of the Phi(F)-values obtained for the two proteins. Of the 20 residues studied in both proteins, ten have Phi(F)-values in Im7 that exceed those in Im9 by more than 0.2, and of these five differ by more than 0.4. The data suggest that the population of an intermediate in Im7 results in folding via a transition state ensemble that is conformationally restricted relative to that of Im9. The data are consistent with the view that topology is an important determinant of folding. Importantly, however, they also demonstrate that while the folding transition state may be conserved in homologous proteins that fold with two and three-state kinetics, the population of an intermediate can have a significant effect on the breadth of the transition state ensemble.     

Kinetic partitioning mechanism governs the folding of the third FnIII domain of tenascin-C: evidence at the single-molecule level

Statistical mechanics and molecular dynamics simulations proposed that the folding of proteins can follow multiple parallel pathways on a rugged energy landscape from unfolded state en route to their folded native states. Kinetic partitioning mechanism is one of the possible mechanisms underlying such complex folding dynamics. Here, we use single-molecule atomic force microscopy technique to directly probe the multiplicity of the folding pathways of the third fibronectin type III domain from the extracellular matrix protein tenascin-C (TNfn3). By stretching individual (TNfn3)₈ molecules, we forced TNfn3 domains to undergo mechanical unfolding and refolding cycles, allowing us to directly observe the folding pathways of TNfn3. We found that, after being mechanically unraveled and then relaxed to zero force, TNfn3 follows multiple parallel pathways to fold into their native states. The majority of TNfn3 fold into the native state in a simple two-state fashion, while a small percentage of TNfn3 were found to be trapped into kinetically stable folding intermediate states with well-defined three-dimensional structures. Furthermore, the folding of TNfn3 was also influenced by its neighboring TNfn3 domains. Complex misfolded states of TNfn3 were observed, possibly due to the formation of domain-swapped dimeric structures. Our studies revealed the ruggedness of the folding energy landscape of TNfn3 and provided direct experimental evidence that the folding dynamics of TNfn3 are governed by the kinetic partitioning mechanism. Our results demonstrated the unique capability of single-molecule AFM to probe the folding dynamics of proteins at the single-molecule level.     

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.     

Characterizing the unstructured intermediates in oxidative folding

A recently developed method is used here to characterize some of the folding intermediates, and the oxidative folding processes, of RNase A. This method is based on the ability of trans-[Pt(en)(2)Cl(2)](2+) to oxidize cysteine residues to form disulfide bonds faster than the disulfide bonds can be rearranged by reshuffling or reduction. Variations of this method have enabled us to address three issues. (i) How the nature of the residual structure and/or conformational order that is present, or develops, during the initial stages of folding can be elucidated. It is shown here that there is a 10-fold increase in the propensity of the unfolded reduced forms of RNase A to form the native set of disulfides directly, compared to the propensity under strongly denaturing conditions (4-6 M GdnHCl). Thus, the unfolded reduced forms of RNase A are not statistical coils with a more condensed form than in the GdnHCl-denatured state; rather, it is suggested that reduced RNase A has a little bias toward a native topology. (ii) The structural characterization of oxidative folding intermediates in terms of disulfide pairing is demonstrated; specifically, a lower-limit estimate is made of the percentage of native disulfide-containing molecules in the two-disulfide ensemble of RNase A. (iii) The critical role of structured intermediate species in determining the oxidative folding pathways of proteins was shown previously. Here, we demonstrate that the presence of a structured intermediate in the oxidative folding of proteins can be revealed by this method.