Analyses of the folding properties of ferredoxin‐like fold proteins by means of a coarse‐grained Gō model: Relationship between the free energy profiles and folding cores

The folding mechanisms of proteins with multi‐state transitions, the role of the intermediate states, and the precise mechanism how each transition occurs are significant on‐going research issues. In this study, we investigate ferredoxin‐like fold proteins which have a simple topology and multi‐state transitions. We analyze the folding processes by means of a coarse‐grained Gō model. We are able to reproduce the differences in the folding mechanisms between U1A, which has a high‐free‐energy intermediate state, and ADA2h and S6, which fold into the native structure through two‐state transitions. The folding pathways of U1A, ADA2h, S6, and the S6 circular permutant, S6_p54‐55, are reproduced and compared with experimental observations. We show that the ferredoxin‐like fold contains two common regions consisting folding cores as predicted in other studies and that U1A produces an intermediate state due to the distinct cooperative folding of each core. However, because one of the cores of S6 loses its cooperativity and the two cores of ADA2h are tightly coupled, these proteins fold into the native structure through a two‐state mechanism. Proteins 2014; 82:954–965. © 2013 Wiley Periodicals, Inc.     

Studying the folding process of the acylphosphatase from Sulfolobus solfataricus. A comparative analysis with other proteins from the same superfamily

The folding process of the acylphosphatase from Sulfolobus solfataricus (Sso AcP) has been followed, starting from the fully unfolded state, using a variety of spectroscopic probes, including intrinsic fluorescence, circular dichroism, and ANS binding. The results indicate that an ensemble of partially folded or misfolded species form rapidly on the submillisecond time scale after initiation of folding. This conformational ensemble produces a pronounced downward curvature in the Chevron plot, appears to possess a content of secondary structure similar to that of the native state, as revealed by far-UV circular dichroism, and appears to have surface-exposed hydrophobic clusters, as indicated by the ability of this ensemble to bind to 8-anilino-1-naphthalenesulfonic acid (ANS). Sso AcP folds from this conformational state with a rate constant of ca. 5 s(-1) at pH 5.5 and 37 degrees C. A minor slow exponential phase detected during folding (rate constant of 0.2 s(-1) under these conditions) is accelerated by cyclophilin A and is absent in a mutant of Sso AcP in which alanine replaces the proline residue at position 50. This indicates that for a lower fraction of Sso AcP molecules the folding process is rate-limited by the cis-trans isomerism of the peptide bond preceding Pro50. A comparative analysis with four other homologous proteins from the acylphosphatase superfamily shows that sequence hydrophobicity is an important determinant of the conformational stability of partially folded states that may accumulate during folding of a protein. A low net charge and a high propensity to form alpha-helical structure also emerge as possibly important determinants of the stability of partially folded states. A significant correlation is also observed between folding rate and hydrophobic content of the sequence within this superfamily, lending support to the idea that sequence hydrophobicity, in addition to relative contact order and conformational stability of the native state, is a key determinant of folding rate.     

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.     

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

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

The SH3-fold family: experimental evidence and prediction of variations in the folding pathways

To investigate the relationships between protein topology, amino acid sequence and folding mechanisms, the folding transition state of the Sso7d protein has been characterised both experimentally and theoretically. Although Sso7d protein has a similar topology to that of the SH3 domains, the structure of its transition state is different from that of alpha-spectrin and src SH3 domains previously studied. The folding algorithm, Fold-X, including an energy function with specific sequence features, accounts for these differences and reproduces with a good agreement the set of experimental phi(double dagger-U) values obtained for the three proteins. Our analysis shows that taking into account sequence features underlying protein topology is critical for an accurate prediction of the folding process.     

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.     

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.     

Sensitivity of the Folding Pathway to the Details of Amino Acid Sequence

Experimental data on the structure of the transition state demonstrate that proteins with the same topology as a rule have similar folding nuclei (the structured formed part of the transition state). In this review discussed are the experimental works showing that the position of folding nuclei is different among proteins with the same topology. These facts emphasize that the folding pathway is sensitive to the details of amino acid sequence.     

raf RBD and ubiquitin proteins share similar folds, folding rates and mechanisms despite having unrelated amino acid sequences

Recent experimental and theoretical studies in protein folding suggest that the rates and underlying mechanisms by which proteins attain the native state are largely determined by the topological complexity of a specific fold rather than by the fine details of the amino acid sequences. However, such arguments are based upon the examination of a limited number of protein folds. To test this view, we sought to investigate whether proteins belonging to the ubiquitin superfamily display similar folding behavior. To do so, we compared the folding-unfolding transitions of mammalian ubiquitin (mUbi) with those of its close yeast homologue (yUbi), and to those of the structurally related Ras binding domain (RBD) of the serine/threonine kinase raf that displays no apparent sequence homology with the ubiquitin family members. As demonstrated for mUbi [Krantz, B. A., and Sosnick, T. R. (2000) Biochemistry 39, 11696-11701], we show that a two-state transition model with no burst phase intermediate can describe folding of both yUbi and raf RBD. We further demonstrate that (1) all three proteins refold at rates that are within 1 order of magnitude (1800, 1100, and 370 s(-1) for mUbi, raf RBD, and yUbi, respectively), (2) both mUbi and raf RBD display similar refolding heterogeneity, and (3) the folding free energy barriers of both mUbi and raf RBD display a similar temperature dependence and sensitivity to a stabilizing agent or to mutations of a structurally equivalent central core residue. These findings are consistent with the view that rates and mechanisms for protein folding depend mostly on the complexity of the native structure topology rather than on the fine details of the amino acid sequence.     

Sensitivity of the folding pathway to the details of amino acid sequence

Experimental data on the structure of transition state demonstrate that the proteins with the same topology as a rule have similar folding nuclei (the structured formed part of the transition state). In this review we discuss the experimental works which show that the position of folding nuclei is different among proteins with the same topology. These facts underline that the folding pathway is sensitive to the details of amino-acid sequence.     

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.     

Mechanisms of protein folding

The strong correlation between protein folding rates and the contact order suggests that folding rates are largely determined by the topology of the native structure. However, for a given topology, there may be several possible low free energy paths to the native state and the path that is chosen (the lowest free energy path) may depend on differences in interaction energies and local free energies of ordering in different parts of the structure. For larger proteins whose folding is assisted by chaperones, such as the Escherichia coli chaperonin GroEL, advances have been made in understanding both the aspects of an unfolded protein that GroEL recognizes and the mode of binding to the chaperonin. The possibility that GroEL can remove non-native proteins from kinetic traps by unfolding them either during polypeptide binding to the chaperonin or during the subsequent ATP-dependent formation of folding-active complexes with the co-chaperonin GroES has also been explored.     

Local and non-local native topologies reveal the underlying folding landscape of proteins

Due to Plaxco, Simons, Baker and others, it is now well known that the two-state single domain protein folding rate is fairly well predicted from knowledge of the topology of the native structure. Plaxco et al found that the folding rates of two-state proteins correlate with the average degree to which native contacts are 'local' within the chain sequence: fast-folders usually have mostly local structures. Here, we dissected the native topology further by focusing on non-local and local contacts using lower and upper bounds of allowable sequence separation in computing the average contact order. We analyzed non-local and local contacts of 82 two-state proteins whose experimental folding rates span over six orders of magnitude. We observed that both the number of non-local contacts and the average sequence separation of non-local contacts (non-local CO) are both negatively correlated with the folding rate, showing that the non-local contacts dominate the barrier-crossing process. Surprisingly, the local contact orders of the proteins also correlate with the folding rates. However, this correlation shows a strong positive trend indicating the role of a diffusive search in the denatured basin.     

Why Do Protein Folding Rates Correlate with Metrics of Native Topology?

For almost 15 years, the experimental correlation between protein folding rates and the contact order parameter has been under scrutiny. Here, we use a simple simulation model combined with a native-centric interaction potential to investigate the physical roots of this empirical observation. We simulate a large set of circular permutants, thus eliminating dependencies of the folding rate on other protein properties (e.g. stability). We show that the rate-contact order correlation is a consequence of the fact that, in high contact order structures, the contact order of the transition state ensemble closely mirrors the contact order of the native state. This happens because, in these structures, the native topology is represented in the transition state through the formation of a network of tertiary interactions that are distinctively long-ranged.     

Critical nucleation size in the folding of small apparently two-state proteins

For apparently two-state proteins, we found that the size (number of folded residues) of a transition state is mostly encoded by the topology, defined by total contact distance (TCD) of the native state, and correlates with its folding rate. This is demonstrated by using a simple procedure to reduce the native structures of the 41 two-state proteins with native TCD as a constraint, and is further supported by analyzing the results of eight proteins from protein engineering studies. These results support the hypothesis that the major rate-limiting process in the folding of small apparently two-state proteins is the search for a critical number of residues with the topology close to that of the native state.     

Comparison of the folding processes of distantly related proteins. Importance of hydrophobic content in folding

The N-terminal domain of HypF from Escherichia coli (HypF-N) is a 91 residue protein module sharing the same folding topology and a significant sequence identity with two extensively studied human proteins, muscle and common-type acylphosphatases (mAcP and ctAcP). With the aim of learning fundamental aspects of protein folding from the close comparison of so similar proteins, the folding process of HypF-N has been studied using stopped-flow fluorescence. While mAcP and ctAcP fold in a two-state fashion, HypF-N was found to collapse into a partially folded intermediate before reaching the fully folded conformation. Formation of a burst-phase intermediate is indicated by the roll over in the Chevron plot at low urea concentrations and by the large jump of intrinsic and 8-anilino-1-naphtalenesulphonic acid-derived fluorescence immediately after removal of denaturant. Furthermore, HypF-N was found to fold rapidly with a rate constant that is approximately two and three orders of magnitudes faster than ctAcP and mAcP, respectively. Differences between the bacterial protein and the two human counterparts were also found as to the involvement of proline isomerism in their respective folding processes. The results clearly indicate that features that are often thought to be relevant in protein folding are not highly conserved in the evolution of the acylphosphatase superfamily. The large difference in folding rate between mAcP and HypF-N cannot be entirely accounted for by the difference in relative contact order or related topological metrics. The analysis shows that the higher folding rate of HypF-N is in part due to the relatively high hydrophobic content of this protein. This conclusion, which is also supported by the highly significant correlation found between folding rate and hydrophobic content within a group of proteins displaying the topology of HypF-N and AcPs, suggests that the average hydrophobicity of a protein sequence is an important determinant of its folding rate.     

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.     

Comparison of the transition states for folding of two Ig-like proteins from different superfamilies

In the "fold approach" proteins with a similar fold but different sequences are compared in order to investigate the relationship between native state structure and folding behaviour. Here we compare the properties of the transition states for folding of TI I27, the 27th immunoglobulin domain from human cardiac titin, and that of TNfn3, the third fibronectin type III domain from human tenascin. Experimental phi-values were used as restraints in molecular dynamics simulations to determine the structures that make up the transition state ensembles (TSEs) for folding of the two proteins. The restrained simulations that we present allow a detailed structural comparison of the two TSEs to be made. Further calculations show explicitly that for both proteins the formation of the interactions involving the residues in the folding nucleus is sufficient for the establishment of the topology of the Ig-like fold. We found that, although the folding nuclei of the two proteins are similar, the packing of the folding nucleus of TI I27 is much tighter than that of TNfn3, reflecting the higher experimental phi-values and beta(T) (Tanford Beta) of TI I27. These results suggest that the folding nucleus can be significantly deformed to accommodate extensive sequence variation while conserving the same folding mechanism.     

Shortening a loop can increase protein native state entropy

Protein loops are essential structural elements that influence not only function but also protein stability and folding rates. It was recently reported that shortening a loop in the AcP protein may increase its native state conformational entropy. This effect on the entropy of the folded state can be much larger than the lower entropic penalty of ordering a shorter loop upon folding, and can therefore result in a more pronounced stabilization than predicted by polymer model for loop closure entropy. In this study, which aims at generalizing the effect of loop length shortening on native state dynamics, we use all‐atom molecular dynamics simulations to study how gradual shortening a very long or solvent‐exposed loop region in four different proteins can affect their stability. For two proteins, AcP and Ubc7, we show an increase in native state entropy in addition to the known effect of the loop length on the unfolded state entropy. However, for two permutants of SH3 domain, shortening a loop results only with the expected change in the entropy of the unfolded state, which nicely reproduces the observed experimental stabilization. Here, we show that an increase in the native state entropy following loop shortening is not unique to the AcP protein, yet nor is it a general rule that applies to all proteins following the truncation of any loop. This modification of the loop length on the folded state and on the unfolded state may result with a greater effect on protein stability. Proteins 2015; 83:2137–2146. © 2015 Wiley Periodicals, Inc.