Role of non-covalent interactions for determining the folding rate of two-state proteins

Understanding the factors influencing the folding rate of proteins is a challenging problem. In this work, we have analyzed the role of non-covalent interactions for the folding rate of two-state proteins by free-energy approach. We have computed the free-energy terms, hydrophobic, electrostatic, hydrogen-bonding and van der Waals free energies. The hydrophobic free energy has been divided into the contributions from different atoms, carbon, neutral nitrogen and oxygen, charged nitrogen and oxygen, and sulfur. All the free-energy terms have been related with the folding rates of 28 two-state proteins with single and multiple correlation coefficients. We found that the hydrophobic free energy due to carbon atoms and hydrogen-bonding free energy play important roles to determine the folding rate in combination with other free energies. The normalized energies with total number of residues showed better results than the total energy of the protein. The comparison of amino acid properties with free-energy terms indicates that the energetic terms explain better the folding rate than amino acid properties. Further, the combination of free energies with topological parameters yielded the correlation of 0.91. The present study demonstrates the importance of topology for determining the folding rate of two-state proteins.     

Modulation of contact order effects in the two-state folding of stefins A and B

It is well established that contact order and folding rates are correlated for small proteins. The folding rates of stefins A and B differ by nearly two orders of magnitude despite sharing an identical native fold and hence contact order. We break down the determinants of this behavior and demonstrate that the modulation of contact order effects can be accounted for by the combined contributions of a framework-like mechanism, characterized by intrinsic helix stabilities, together with nonnative helical backbone conformation and nonnative hydrophobic interactions within the folding transition state. These contributions result in the formation of nonnative interactions in the transition state as evidenced by the opposing effects on folding rate and stability of these proteins.     

Influence of medium- and long-range interactions in different folding types of globular proteins

Recognition of protein fold from amino acid sequence is a challenging task. The structure and stability of proteins from different fold are mainly dictated by inter-residue interactions. In our earlier work, we have successfully used the medium- and long-range contacts for predicting the protein folding rates, discriminating globular and membrane proteins and for distinguishing protein structural classes. In this work, we analyze the role of inter-residue interactions in commonly occurring folds of globular proteins in order to understand their folding mechanisms. In the medium-range contacts, the globin fold and four-helical bundle proteins have more contacts than that of DNA-RNA fold although they all belong to all-alpha class. In long-range contacts, only the ribonuclease fold prefers 4-10 range and the other folding types prefer the range 21-30 in alpha/beta class proteins. Further, the preferred residues and residue pairs influenced by these different folds are discussed. The information about the preference of medium- and long-range contacts exhibited by the 20 amino acid residues can be effectively used to predict the folding type of each protein.     

Helix-coil transition theory including long-range electrostatic interactions: application to globular proteins

An extension of the Zimm–Bragg two-state theory for the helix–coil transition in polypeptides, which takes into account the effect of peptide charge–dipole interactions on helix stability, is presented. This new theory incorporates these interactions in an expression that is parameterized on recently obtained experimental data on polypeptides for which electrostatic effects are known to influence helix content. Unlike previous two-state or multistate models, which are parameterized on protein x-ray data, the present theoretical treatment in independent of such protein data. The theoretical model is applied to a series of peptides derived from the C-peptide of ribonuclease A, which have been the object of recent spectroscopic studies. The new theoretical approach can account for most of the structural information derived from studies of these C-peptides, and for overall average helix probabilities that are close in magnitude to those observed for these polypeptides in solution. An application of this new formulation for the prediction of the locations of α-helices in globular proteins from their amino acid sequence is also presented.     

Relationships between the folding rate constant and the topological parameters of small two-state proteins based on general random walk model

In this paper, we propose an analytically tractable model of protein folding based on one-dimensional general random walk. A second-order differential equation for the mean folding time of a single protein is constructed which can be used to derive the observed relationship between the folding rate constant and the number of native contacts. The parameters appearing in the model can be determined by fitting the theoretical prediction to the experimental result. In addition, taking into account the fact that the number of native contacts is almost proportional to the relative contact order, we can also explain the observed relationship between the folding rate constant and the relative contact order.     

K-Fold: a tool for the prediction of the protein folding kinetic order and rate

K-Fold is a tool for the automatic prediction of the protein folding kinetic order and rate. The tool is based on a support vector machine (SVM) that was trained on a data set of 63 proteins, whose 3D structure and folding mechanism are known from experiments already described in the literature. The method predicts whether a protein of known atomic structure folds according to a two-state or a multi-state kinetics and correctly classifies 81% of the folding mechanisms when tested over the training set of the 63 proteins. It also predicts as a further option the logarithm of the folding rate. To the best of our knowledge, the tool discriminates for the first time whether a protein is characterized by a two state or a multiple state kinetics, during the folding process, and concomitantly estimates also the value of the constant rate of the process. When used to predict the logarithm of the folding rate, K-Fold scores with a correlation value to the experimental data of 0.74 (with a SE of 1.2). Availability: http://gpcr.biocomp.unibo.it/cgi/predictors/K-Fold/K-Fold.cgi. Supplementary Information: http://gpcr.biocomp.unibo.it/~emidio/K-Fold/K-Fold_help.html.     

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.     

Role of hydrophobic clusters and long-range contact networks in the folding of (alpha/beta)8 barrel proteins

Analysis on the three dimensional structures of (alpha/beta)(8) barrel proteins provides ample light to understand the factors that are responsible for directing and maintaining their common fold. In this work, the hydrophobically enriched clusters are identified in 92% of the considered (alpha/beta)(8) barrel proteins. The residue segments with hydrophobic clusters have high thermal stability. Further, these clusters are formed and stabilized through long-range interactions. Specifically, a network of long-range contacts connects adjacent beta-strands of the (alpha/beta)(8) barrel domain and the hydrophobic clusters. The implications of hydrophobic clusters and long-range networks in providing a feasible common mechanism for the folding of (alpha/beta)(8) barrel proteins are proposed.     

Energetics of multihelix interactions in protein folding: application to myoglobin

Conformational-energy calculations have been carried out in order to determine favorable packing arrangements within a group of α-helices. The influence of side chains and of the number of interacting α-helices on the mode of packing was analyzed. In this work, our earlier methods for computing the packing energy of a pair of α-helices [Chou, K.-C., Némethy, G. & Scheraga, H. A. (1984) J. Am. Chem. Soc. 106 , 3161–3170] have been extended to treat the interactions among several helices. Also, new algorithms allow the matching of standard peptide geometry to x-ray coordinates of helical complexes and the analysis of interrelations between several helices. As a specific test case, the packing of three neighboring α-helices, viz., the A, G, and H helices of sperm whale myoglobin, was considered. Minimum-energy arrangements were computed for the separate A-H and the G-H α-helix pairs as well as for the A-G-H three-helix complex. For the packing of the nearly antiparallel G and H α-helices, the same optimal structure was obtained in two- and three-helix complexes, indicating that a single packing arrangement is specifically favored by interhelix interactions. For the pair of nearly perpendicular A and H α-helices, interactions are less specific, so that there is no unique optimal structure in the two-helix complex; in the three-helix complex, however, a specific mode of packing is favored even for the A-H pair. This result indicates that the presence of other nearby α-helices can influence the packing of a given α-helix pair. The computed arrangement of the A-G-H complex is very close to that of the crystallographically determined structure. These results can be used to make deductions about the likely sequence of events in protein folding, where, in this particular case, it appears that the G-H helix pair may form first and then induce proper orientation of the A helix.     

Role of medium--and long-range interactions in discriminating globular and membrane proteins.

The analysis of inter-residue interactions in protein structures provides considerable insight to understand their folding and stability. We have previously analyzed the role of medium- and long-range interactions in the folding of globular proteins. In this work, we study the distinct role of such interactions in the three-dimensional structures of membrane proteins. We observed a higher number of long-range contacts in the termini of transmembrane helical (TMH) segments, implying their role in the stabilization of helix-helix interactions. The transmembrane strand (TMS) proteins are having appreciably higher long-range contacts than that in all-beta class of globular proteins, indicating closer packing of the strands in TMS proteins. The residues in membrane spanning segments of TMH proteins have 1.3 times higher medium-range contacts than long-range contacts whereas that of TMS proteins have 14 times higher long-range contacts than medium-range contacts. Residue-wise analysis indicates that in TMH proteins, the residues Cys, Glu, Gly, Pro, Gln, Ser and Tyr have higher long-range contacts than medium-range contacts in contrast with all-alpha class of globular proteins. The charged residue pairs have higher medium-range contacts in all-alpha proteins, whereas hydrophobic residue pairs are dominant in TMH proteins. The information on the preference of residue pairs to form medium-range contacts has been successfully used to discriminate the TMH proteins from all-alpha proteins. The statistical significance of the results obtained from the present study has been verified using randomized structures of TMH and TMS protein templates.     

Logical analysis of the mechanism of protein folding III. Prediction of the strong long-range interactions.

It has been found that strong long-range interactions occur in regions having large β-structural potentials. As has been described previously (Nagano, 1974), interactions among regions having both helical and β-structural potentials (αβ-gaβ interactions) are also very important. Accordingly, an idea is presented in this paper that the relative stability of a protein conformation could be estimated by a relatively simple mathematical function of sequence and conformation. The function P(p,q) is called the non-energy part of pseudo-free energy, because minimization of the sum of P(p,q) and energy functions (cf. Levitt, 1974; Warme &; Scheraga, 1974) can be expected to lead to a plausible model of a protein. A merit of the function is that it can help us decide which way to go in manipulating a temporarily built model, e.g. towards a helix-rich protein or towards a β-structure-rich protein. The estimation of P(p,q) as an artificial potential does not use much computer time because only the co-ordinates of the β-carbon atoms (α-carbon atoms if the residue is Gly) are used. It is composed of terms of the long-range interactions P_L and short-range interactions P_S. The term P_L represents the relative strength of helix-helix interactions, helix-β-candidate interactions and β-candidate-β-candidate interactions. It is assumed that both helical and β-structural potentials can be measured as the differences between the predicted function for helix and β-structure, respectively, as defined previously (Nagano, 1973), and the corresponding largest values ever found. A hypothesis that two residues distantly separated in the primary sequence contribute less to the stability of the whole molecule is finally discarded because the true conformation of concanavalin A becomes very unstable compared with its false conformation folded like the main part of subtilisin. The parameters thus determined indicate that the helix-β-candidate interactions are almost as important as the β-candidate-β-candidate interactions. Both helix and loop prediction functions are combined to give the short-range interactions term, P_S, according to whether the region is really helical or not, and to whether it is really looped or not. The function P(p,q) can be used as a criterion for judging whether the predicted conformation is realistic or false, because the parameters can be adjusted to give, within limits, reasonable values of −10 kcal/residue for true conformations and higher than −5 kcal/residue for false conformations.As an application of the present theory of protein folding, the tertiary structure of bacteriophage T4 lysozyme is predicted and presented in Figure 1, prior to the X-ray structure becoming available.     

Mutational analysis of acylphosphatase suggests the importance of topology and contact order in protein folding.

Muscle acylphosphatase (AcP) is a small protein that folds very slowly with two-state behavior. The conformational stability and the rates of folding and unfolding have been determined for a number of mutants of AcP in order to characterize the structure of the folding transition state. The results show that the transition state is an expanded version of the native protein, where most of the native interactions are partially established. The transition state of AcP turns out to be remarkably similar in structure to that of the activation domain of procarboxypeptidase A2 (ADA2h), a protein having the same overall topology but sharing only 13% sequence identity with AcP. This suggests that transition states are conserved between proteins with the same native fold. Comparison of the rates of folding of AcP and four other proteins with the same topology, including ADA2h, supports the concept that the average distance in sequence between interacting residues (that is, the contact order) is an important determinant of the rate of protein folding.     

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.     

Analysing the origin of long-range interactions in proteins using lattice models

Background  

Long-range communication is very common in proteins but the physical basis of this phenomenon remains unclear. In order to gain insight into this problem, we decided to explore whether long-range interactions exist in lattice models of proteins. Lattice models of proteins have proven to capture some of the basic properties of real proteins and, thus, can be used for elucidating general principles of protein stability and folding.     

Protein folding: from the levinthal paradox to structure prediction.

This article is a personal perspective on the developments in the field of protein folding over approximately the last 40 years. In addition to its historical aspects, the article presents a view of the principles of protein folding with particular emphasis on the relationship of these principles to the problem of protein structure prediction. It is argued that despite much that is new, the essential elements of our current understanding of protein folding were anticipated by researchers many years ago. These elements include the recognition of the central importance of the polypeptide backbone as a determinant of protein conformation, hierarchical protein folding, and multiple folding pathways. Important areas of progress include a detailed characterization of the folding pathways of a number of proteins and a fundamental understanding of the physical chemical forces that determine protein stability. Despite these developments, fold prediction algorithms still encounter difficulties in identifying the correct fold for a given sequence. This may be due to the possibility that the free energy differences between at least a few alternate conformations of many proteins are not large. Significant progress in protein structure prediction has been due primarily to the explosive growth of sequence and structural databases. However, further progress is likely to depend in part on the ability to combine information available from databases with principles and algorithms derived from physical chemical studies of protein folding. An approach to the integration of the two areas is outlined with specific reference to the PrISM program that is a fully integrated sequence/structural-analysis/fold-recognition/homology model building software system.