Secondary structure length as a determinant of folding rate of proteins with two- and three-state kinetics

We present a simple method for determining the folding rates of two- and three-state proteins from the number of residues in their secondary structures (secondary structure length). The method is based on the hypothesis that two- and three-state foldings share a common pattern. Three-state proteins first condense into metastable intermediates, subsequent forming of alpha-helices, turns, and beta-sheets at slow rate-limiting step. The folding rate of such proteins anticorrelate with the length of these beta-secondary structures. It is also assumed that in two-state folding, rapidly folded alpha-helices and turns may facilitate formation of fleeting unobservable intermediates and thus show two-state behavior. There is an inverse relationship between the folding rate and the length of beta-sheets and loops. Our study achieves 94.0 and 88.1% correlations with folding rates determined experimentally for 21 three- and 38 two-state proteins, respectively, suggesting that protein-folding rates are determined by the secondary structure length. The kinetic kinds are selected on the basis of a competitive formation of hydrophobic collapse and alpha-structure in early intermediates.     

Chain length is the main determinant of the folding rate for proteins with three-state folding kinetics

We demonstrate that chain length is the main determinant of the folding rate for proteins with the three-state folding kinetics. The logarithm of their folding rate in water (k(f)) strongly anticorrelates with their chain length L (the correlation coefficient being -0.80). At the same time, the chain length has no correlation with the folding rate for two-state folding proteins (the correlation coefficient is -0.07). Another significant difference of these two groups of proteins is a strong anticorrelation between the folding rate and Baker's "relative contact order" for the two-state folders and the complete absence of such correlation for the three-state folders.     

Comparison between long-range interactions and contact order in determining the folding rate of two-state proteins: application of long-range order to folding rate prediction.

The contact order is believed to be an important factor for understanding protein folding mechanisms. In our earlier work, we have shown that the long-range interactions play a vital role in protein folding. In this work, we analyzed the contribution of long-range contacts to determine the folding rate of two-state proteins. We found that the residues that are close in space and are separated by at least ten to 15 residues in sequence are important determinants of folding rates, suggesting the presence of a folding nucleus at an interval of approximately 25 residues. A novel parameter "long-range order" has been proposed to predict protein folding rates. This parameter shows as good a relationship with the folding rate of two-state proteins as contact order. Further, we examined the minimum limit of residue separation to determine the long-range contacts for different structural classes. We observed an excellent correlation between long-range order and folding rate for all classes of globular proteins. We suggest that in mixed-class proteins, a larger number of residues can serve as folding nuclei compared to all-alpha and all-beta proteins. A simple statistical method has been developed to predict the folding rates of two-state proteins using the long-range order that produces an agreement with experimental results that is better or comparable to other methods in the literature.     

Bacterial proteins fold faster than eukaryotic proteins with simple folding kinetics

Protein domain frequency and distribution among kingdoms was statistically analyzed using the SCOP structural database. It appeared that among chosen protein domains with the best resolution, eukaryotic proteins more often belong to α-helical and β-structural proteins, while proteins of bacterial origin belong to α/β structural class. Statistical analysis of folding rates of 73 proteins with known experimental data revealed that bacterial proteins with simple kinetics (23 proteins) exhibit a higher folding rate compared to eukaryotic proteins with simple folding kinetics (27 proteins). Analysis of protein domain amino acid composition showed that the frequency of amino acid residues in proteins of eukaryotic and bacterial origin is different for proteins with simple and complex folding kinetics.     

Distinguishing between two-state and three-state models for ubiquitin folding

Conflicting results exist regarding whether the folding of mammalian ubiquitin at 25 degrees C is a simple, two-state kinetic process or a more complex, three-state process with a defined kinetic intermediate. We have measured folding rate constants up to about 1000 s(-1) using conventional rapid mixing methods in single-jump, double-jump, and continuous-flow modes. The linear dependence of folding rates on denaturant concentration and the lack of an unaccounted "burst-phase" change for the fluorescence signal indicate that a two-state folding model is adequate to describe the folding pathway. This behavior also is seen for folding in the presence of the stabilizing additives 0.23 M sodium sulfate and 1 M sodium chloride. These results stress the need for caution in interpreting deviations from ideal two-state "chevron" behavior when folding is heterogeneous or folding rate constants are near the detection limit.     

Prediction of folding pathway and kinetics among plant hemoglobins using an average distance map method

Computational methods, such as the ADM (average distance map) method, have been developed to predict folding of homologous proteins. In this work we used the ADM method to predict the folding pathway and kinetics among selected plant nonsymbiotic (nsHb), symbiotic (Lb), and truncated (tHb) hemoglobins (Hbs). Results predicted that (1) folding of plant Hbs occurs throughout the formation of compact folding modules mostly formed by helices A, B, and C, and E, F, G, and H (folding modules A/C and E/H, respectively), and (2) primitive (moss) nsHbs fold in the C-->N direction, evolved (monocot and dicot) nsHbs fold either in the C-->N or N-->C direction, and Lbs and plant tHbs fold in the C-->N direction. We also predicted relative folding rates of plant Hbs from qualitative analyses of the stability of subdomains and classified plant Hbs into fast and moderate folding. ADM analysis of nsHbs predicted that prehelix A plays a role during folding of the N-terminal domain of Ceratodon nsHb, and that CD-loop plays a role in folding of primitive (Physcomitrella and Ceratodon) but not evolved nsHbs. Modeling of the rice Hb1 A/C and E/H modules showed that module E/H overlaps to the Mycobacterium tuberculosis HbO two-on-two folding. This observation suggests that module E/H is an ancient tertiary structure in plant Hbs.     

Analysis of the kinetics of folding of proteins and peptides using circular dichroism

Circular dichroism (CD) is a useful spectroscopic technique for studying the secondary structure, folding and binding properties of proteins. This protocol covers how to use the intrinsic circular dichroic properties of proteins to follow their folding and unfolding as a function of time. Included are methods of obtaining data and for analyzing the folding and unfolding data to determine the rate constants and the order of the folding and unfolding reactions. The protocol focuses on the use of CD to follow folding when it is relatively slow, on the order of minutes to days. The methods for analyzing the data, however, can also be applied to data collected with a CD machine equipped with stopped-flow accessories in the range of milliseconds to seconds and folding analyzed by other spectroscopic methods including changes in absorption or fluorescence spectra as a function of time.     

Amino acid sequence predicts folding rate for middle-size two-state proteins

The significant correlation between protein folding rates and the sequence-predicted secondary structure suggests that folding rates are largely determined by the amino acid sequence. Here, we present a method for predicting the folding rates of proteins from sequences using the intrinsic properties of amino acids, which does not require any information on secondary structure prediction and structural topology. The contribution of residue to the folding rate is expressed by the residue's Omega value. For a given residue, its Omega depends on the amino acid properties (amino acid rigidity and dislike of amino acid for secondary structures). Our investigation achieves 82% correlation with folding rates determined experimentally for simple, two-state proteins studied until the present, suggesting that the amino acid sequence of a protein is an important determinant of the protein-folding rate and mechanism.     

In silico chaperonin-like cycle helps folding of proteins for structure prediction

Currently, one of the most serious problems in protein-folding simulations for de novo structure prediction is conformational sampling of medium-to-large proteins. In vivo, folding of these proteins is mediated by molecular chaperones. Inspired by the functions of chaperonins, we designed a simple chaperonin-like simulation protocol within the framework of the standard fragment assembly method: in our protocol, the strength of the hydrophobic interaction is periodically modulated to help the protein escape from misfolded structures. We tested this protocol for 38 proteins and found that, using a certain defined criterion of success, our method could successfully predict the native structures of 14 targets, whereas only those of 10 targets were successfully predicted using the standard protocol. In particular, for non-α-helical proteins, our method yielded significantly better predictions than the standard approach. This chaperonin-inspired protocol that enhanced de novo structure prediction using folding simulations may, in turn, provide new insights into the working principles underlying the chaperonin system.     

The dual role of a loop with low loop contact distance in folding and domain swapping

Alpha helices, beta strands, and loops are the basic building blocks of protein structure. The folding kinetics of alpha helices and beta strands have been investigated extensively. However, little is known about the formation of loops. Experimental studies show that for some proteins, the formation of a single loop is the rate-determining step for folding, whereas for others, a loop (or turn) can misfold to serve as the hinge loop region for domain-swapped species. Computer simulations of an all-atom model of fragment B of Staphylococcal protein A found that the formation of a single loop initiates the dominant folding pathway. On the other hand, the stability analysis of intermediates suggests that the same loop is a likely candidate to serve as a hinge loop for domain swapping. To interpret the simulation result, we developed a simple structural parameter: the loop contact distance (LCD), or the sequence distance of contacting residues between a loop and the rest of the protein. The parameter is applied to a number of other proteins, including SH3 domains and prion protein. The results suggest that a locally interacting loop (low LCD) can either promote folding or serve as the hinge region for domain swapping. Thus, there is an intimate connection between folding and domain swapping, a possible cause of misfolding and aggregation.     

Nucleation‐based prediction of the protein folding rate and its correlation with the folding nucleus size

The problem of protein self‐organization is in the focus of current molecular biology studies. Although the general principles are understood, many details remain unclear. Specifically, protein folding rates are of interest because they dictate the rate of protein aggregation which underlies many human diseases. Here we offer predictions of protein folding rates and their correlation with folding nucleus sizes. We calculated free energies of the transition state and sizes of folding nuclei for 84 proteins and peptides whose other parameters were measured at the point of thermodynamic equilibrium between their unfolded and native states. We used the dynamic programming method where each residue was considered to be either as folded as in its native state or completely disordered. The calculated and measured folding rates showed a good correlation at the temperature mid‐transition point (the correlation coefficient was 0.75). Also, we pioneered in demonstrating a moderate (‐0.57) correlation coefficient between the calculated sizes of folding nuclei and the folding rates. Predictions made by different methods were compared. The established good correlation between the estimated free energy barrier and the experimentally found folding rate of each studied protein/peptide indicates that our model gives reliable results for the considered data set. Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Folding thermodynamics and kinetics of YNMG RNA hairpins: specific incorporation of 8-bromoguanosine leads to stabilization by enhancement of the folding rate

Modified nucleotides allow fundamental energetic and kinetic properties of nucleic acids to be probed. Here, we demonstrate that an RNA hairpin containing the nucleotide analogue 8-bromoguanosine (8BrG or G), gcUUCGgc, has enhanced stability relative to the unmodified hairpin, with DeltaDeltaG(37)(degrees)= -0.69 +/- 0.15 kcal mol(-1) and DeltaT(M) = +6.8 +/- 1.4 degrees C. NMR spectroscopic data suggest that the enhanced stability of gcUUCGgc does not arise from the native state; laser temperature-jump experiments support this notion, as gcUUCGgc and gcUUCGgc have similar unfolding rate constants, but the folding rate constant of gcUUCGgc is 4.1-fold faster at 37.5 degrees C and 2.8-fold faster under isoenergetic conditions. On the basis of these findings, we propose that 8BrG reduces the conformational entropy of the denatured state, resulting in an accelerated conformational search for the native state and enhanced stability.     

Strategies for folding of affinity tagged proteins using GroEL and osmolytes

Obtaining a proper fold of affinity tagged chimera proteins can be difficult. Frequently, the protein of interest aggregates after the chimeric affinity tag is cleaved off, even when the entire chimeric construct is initially soluble. If the attached protein is incorrectly folded, chaperone proteins such as GroEL bind to the misfolded construct and complicate both folding and affinity purification. Since chaperonin/osmolyte mixtures facilitate correct folding from the chaperonin, we explored the possibility that we could use this intrinsic binding reaction to advantage to refold two difficult-to-fold chimeric constructs. In one instance, we were able to recover activity from a properly folded construct after the construct was released from the chaperonin in the presence of osmolytes. As an added advantage, we have also found that this method involving chaperonins can enable researchers to decide (1) if further stabilization of the folded product is required and (2) if the protein construct in question will ever be competent to fold with osmolytes.     

Folding kinetics of the outer membrane proteins OmpA and FomA into phospholipid bilayers

The folding mechanism of outer membrane proteins (OMPs) of Gram-negative bacteria into lipid bilayers has been studied using OmpA of E. coli and FomA of F. nucleatum as examples. Both, OmpA and FomA are soluble in unfolded form in urea and insert and fold into phospholipid bilayers upon strong dilution of the denaturant urea. OmpA is a structural protein and forms a small ion channel, composed of an 8-stranded transmembrane beta-barrel domain. FomA is a voltage-dependent porin, predicted to form a 14 stranded beta-barrel. Both OMPs fold into a range of model membranes of very different phospholipid compositions. Three membrane-bound folding intermediates of OmpA were discovered in folding studies with dioleoylphosphatidylcholine bilayers that demonstrated a highly synchronized mechanism of secondary and tertiary structure formation of beta-barrel membrane proteins. A study on FomA folding into lipid bilayers indicated the presence of parallel folding pathways for OMPs with larger transmembrane beta-barrels.     

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.     

Ab initio fold prediction of small helical proteins using distance geometry and knowledge-based scoring functions.

The problem of protein tertiary structure prediction from primary sequence can be separated into two subproblems: generation of a library of possible folds and specification of a best fold given the library. A distance geometry procedure based on random pairwise metrization with good sampling properties was used to generate a library of 500 possible structures for each of 11 small helical proteins. The input to distance geometry consisted of sets of restraints to enforce predicted helical secondary structure and a generic range of 5 to 11 A between predicted contact residues on all pairs of helices. For each of the 11 targets, the resulting library contained structures with low RMSD versus the native structure. Near-native sampling was enhanced by at least three orders of magnitude compared to a random sampling of compact folds. All library members were scored with a combination of an all-atom distance-dependent function, a residue pair-potential, and a hydrophobicity function. In six of the 11 cases, the best-ranking fold was considered to be near native. Each library was also reduced to a final ab initio prediction via consensus distance geometry performed over the 50 best-ranking structures from the full set of 500. The consensus results were of generally higher quality, yielding six predictions within 6.5 A of the native fold. These favorable predictions corresponded to those for which the correlation between the RMSD and the scoring function were highest. The advantage of the reported methodology is its extreme simplicity and potential for including other types of structural restraints.