Loop folds in proteins and evolutionary conservation of folding nuclei

We show that loops of close contacts involving hydrophobic residues are important in protein folding. Contrary to Berezovsky Berezovsky and Trifonov (J Biomol Struct Dyn 20, 5-6, 2002) the loops important in protein folding usually are much larger in size than 23-31 residues, being instead comparable to the size of the protein for single domain proteins. Additionally what is important are not single loop contacts, but a highly interconnected network of such loop contacts, which provides extra stability to a protein fold and which leads to their conservation in evolution.     

Protein folding: looping from hydrophobic nuclei.

Protein structure can be viewed as a compact linear array of nearly standard size closed loops of 25-30 amino acid residues (Berezovsky et al., FEBS Letters 2000; 466: 283-286) irrespective of details of secondary structure. The end-to-end contacts in the loops are likely to be hydrophobic, which is a testable hypothesis. This notion could be verified by direct comparison of the loop maps with Kyte and Doolittle hydropathicity plots. This analysis reveals that most of the ends of the loops are hydrophobic, indeed. The same conclusion is reached on the basis of positional autocorrelation analysis of protein sequences of 23 fully sequenced bacterial genomes. Hydrophobic residues valine, alanine, glycine, leucine, and isoleucine appear preferentially at the 25-30 residues distance one from another. These observations open a new perspective in the understanding of protein structure and folding: a consecutive looping of the polypeptide chain with the loops ending primarily at hydrophobic nuclei.     

Kinetics of loop formation and breakage in the denatured state of iso-1-cytochrome c

The earliest events in protein folding involve the formation of simple loops. Observing the rates of loop closure under denaturing conditions can provide direct insight into the relative probability and sequence determinants for formation of loops of different sizes. The persistence of these initial contacts is equally important for efficient folding, so measurement of rates of loop breakage under denaturing conditions is also essential. We have used stopped-flow and continuous-flow methods to measure the rates of histidine-heme loop formation and breakage in the denatured state of iso-1-cytochrome c (in the presence of 3 M guanidine HCl). The data indicate that the mechanism for forming loops is a two-step process, the first step being the deprotonation of the histidine, and the second step being the binding of the histidine to the heme. This mechanism makes it possible to extract both the rate constants of formation, k(f), and breakage, k(b), of loops from the pH dependence of the observed rate constant, k(obs). To determine the dependence of k(f) and k(b) on loop size, we have carried out kinetic measurements for seven single surface histidine variants of iso-1-cytochrome c. A scaling factor (the dependence of k(f) on log[loop size]) of approximately -1.8 is observed for loop formation, similar to that observed in other systems. The magnitude of k(b) varies from 30 s(-1) to 300 s(-1), indicating that the stability of different loops varies considerably. The implications of the kinetics of loop formation and breakage in the denatured state for the mechanism of protein folding are discussed.     

Loop Fold Structure of Proteins: Resolution of Levinthal's Paradox

Abstract

According to Levinthal a protein chain of ordinary size would require enormous time to sort its conformational states before the final fold is reached. Experimentally observed time of folding suggests an estimate of the chain length for which the time would be sufficient. This estimate by order of magnitude fits to experimentally observed universal closed loop elements of globular proteins—25–30 residues.     

Sequence Structure of van der Waals Locks in Proteins

Abstract

Recent works has suggested that proteins in early evolution have gone through a stage of closed loop elements with a typical contour size of 25–35 residues. These closed loops are still the elementary protein units to these days, and can be used to spell out protein sequence/structure relationship through a relatively small number of protein prototypes. In this study we aimed to identify the sequences that are used to lock the loop ends to one another, and to show how an extensive dictionary of such locking pairs can be created using positional correlation data from a large proteome database, and structural data from PDB databases. Such a dictionary can be used in reconstructing the evolutionary pathway the modern proteins have gone through, and in identifying closed loop elements in modern proteins with yet unknown 3D structure.     

Back to Units of Protein Folding

Abstract

In response to the criticism by A. Finkelstein (J. Biomol. Struct. Dyn. 20, 311–314, 2002) of our Communication (J. Biomol. Struct. Dyn. 20, 5–6, 2002) several issues are dealt with. Importance of the notion of elementary folding unit, its size and structure, and the necessity of further characterization of the units for the elucidation of the protein folding in vivo are discussed. The criticism (J. Biomol. Struct. Dyn. 20, 311–314, 2002) on the hierarchical protein folding is also briefly addressed.     

mRNA环结构对蛋白质折叠速率的影响

前期的相关研究发现mRNA二级结构中存在对蛋白质折叠速率的重要影响因素.而mRNA二级结构中普遍存在着各种复杂的环结构,这些环结构是否对蛋白质折叠速率也有重要的影响呢?不同的环结构对蛋白质折叠速率的影响是否相同呢?基于此想法,建立了一个包含mRNA内部环、发夹环、膨胀环和多分支环等环结构信息和相应蛋白质折叠速率的数据库.对于数据库中的每一个蛋白质,计算了mRNA二级结构中各种环结构碱基含量、配对碱基含量及单链碱基含量等参量,分析了各参量与相应蛋白质折叠速率的相关性.结果显示,各种环结构碱基含量与蛋白质折叠速率均呈极显著或显著正相关.说明mRNA环结构对蛋白质折叠速率有重要的影响.进一步,把蛋白质按照不同折叠类型或不同二级结构类型分组后,对每一组蛋白质重复上述的分析工作.结果表明,对不同类蛋白质,mRNA的各种环结构对其相应蛋白质折叠速率的影响存在着显著差异.上述研究将为进一步开展有关mRNA和蛋白质折叠速率的研究奠定理论基础.     

Structure of a partially unfolded form of Escherichia coli dihydrofolate reductase provides insight into its folding pathway

Proteins frequently fold via folding intermediates that correspond to local minima on the conformational energy landscape. Probing the structure of the partially unfolded forms in equilibrium under native conditions can provide insight into the properties of folding intermediates. To elucidate the structures of folding intermediates of Escherichia coli dihydrofolate reductase (DHFR), we investigated transient partial unfolding of DHFR under native conditions. We probed the structure of a high‐energy conformation susceptible to proteolysis (cleavable form) using native‐state proteolysis. The free energy for unfolding to the cleavable form is clearly less than that for global unfolding. The dependence of the free energy on urea concentration (m‐value) also confirmed that the cleavable form is a partially unfolded form. By assessing the effect of mutations on the stability of the partially unfolded form, we found that native contacts in a hydrophobic cluster formed by the F‐G and Met‐20 loops on one face of the central β‐sheet are mostly lost in the partially unfolded form. Also, the folded region of the partially unfolded form is likely to have some degree of structural heterogeneity. The structure of the partially unfolded form is fully consistent with spectroscopic properties of the near‐native kinetic intermediate observed in previous folding studies of DHFR. The findings suggest that the last step of the folding of DHFR involves organization in the structure of two large loops, the F‐G and Met‐20 loops, which is coupled with compaction of the rest of the protein.     

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.     

Backbone entropy of loops as a measure of their flexibility: Application to a Ras protein simulated by molecular dynamics

The flexibility of surface loops plays an important role in protein–protein and protein–peptide recognition; it is commonly studied by Molecular Dynamics or Monte Carlo simulations. We propose to measure the relative backbone flexibility of loops by the difference in their backbone conformational entropies, which are calculated here with the local states (LS) method of Meirovitch. Thus, one can compare the entropies of loops of the same protein or, under certain simulation conditions, of different proteins. These loops should be equal in size but can differ in their sequence of amino acids residues. This methodology is applied successfully to three segments of 10 residues of a Ras protein simulated by the stochastic boundary molecular dynamics procedure. For the first time estimates of backbone entropy differences are obtained, and their correlation with B factors is pointed out; for example, the segments which consist of residues 60–65 and 112–117 have average B factors of 67 and 18 Ų, respectively, and entropy difference T ΔS = 5.4 ± 0.1 kcal/mol at T = 300 K. In a large number of recent publications the entropy due to the fast motions (on the ps-ns time scale) of N–H and C–H vectors has been obtained from their order parameter, measured in nuclear magnetic resonance spin relaxation experiments. This enables one to estimate differences in the entropy of protein segments due to folding–unfolding transitions, for example. However, the vectors are assumed to be independent, and the effect of the neglected correlations is unknown; our method is expected to become an important tool for assessing this approximation. The present calculations, obtained with the LS method, suggest that the errors involved in experimental entropy differences might not be large; however, this should be verified in each case. Potential applications of entropy calculations to rational drug design are discussed. Proteins 29:127–140, 1997. © 1997 Wiley-Liss, Inc.     

Crystal contact-free conformation of an intrinsically flexible loop in protein crystal: Tim21 as the case study

BackgroundIn protein crystals, flexible loops are frequently deformed by crystal contacts, whereas in solution, the large motions result in the poor convergence of such flexible loops in NMR structure determinations. We need an experimental technique to characterize the structural and dynamic properties of intrinsically flexible loops of protein molecules.MethodsWe designed an intended crystal contact-free space (CCFS) in protein crystals, and arranged the flexible loop of interest in the CCFS. The yeast Tim 21 protein was chosen as the model protein, because one of the loops (loop 2) is distorted by crystal contacts in the conventional crystal.ResultsYeast Tim21 was fused to the MBP protein by a rigid α-helical linker. The space created between the two proteins was used as the CCFS. The linker length provides adjustable freedom to arrange loop 2 in the CCFS. We re-determined the NMR structure of yeast Tim21, and conducted MD simulations for comparison. Multidimensional scaling was used to visualize the conformational similarity of loop 2. We found that the crystal contact-free conformation of loop 2 is located close to the center of the ensembles of the loop 2 conformations in the NMR and MD structures.ConclusionsLoop 2 of yeast Tim21 in the CCFS adopts a representative, dominant conformation in solution.General significanceNo single powerful technique is available for the characterization of flexible structures in protein molecules. NMR analyses and MD simulations provide useful, but incomplete information. CCFS crystallography offers a third route to this goal.     

Protein structure and folding: a new start.

Standard building blocks of proteins--closed loops of 25-30 amino acid residues--have been recently discovered and further characterized by combined efforts of several laboratories. New challenging views on the protein structure, folding, and evolution are introduced by these studies. In particular, the role of van der Waals contacts in protein stability is better understood. They can be considered as locks closing the polypeptide chain returns and forming the loop-n-lock elements. The linearity of the arrangement of the standard loops in the proteins has important evolutionary implications. Selection pressure to maintain the loops of nearly standard size is reflected in the protein sequences as characteristic distance between hydrophobic residues, equal to the loop end-to-end distance. Further characterization of the loop-n-lock units reveals several sequence/structure prototypes, which suggests a new basis for protein classification. The following is a review of these studies.     

Identifying folding nucleus based on residue contact networks of proteins

In the native structure of a protein, all the residues are tightly parked together in a specific order following its folding and every residue contacts with some spatially neighbor residues. A residue contact network can be constructed by defining the residues as nodes and the native contacts as edges. During the folding of small single-domain proteins, there is a set of contacts (or bonds), defined as the folding nucleus (FN), which is formed around the transition state, i.e., a rate-limiting barrier located at about the middle between the unfolded states and the native state on the free energy landscape. Such a FN plays an essential role in the folding dynamics and the residues, which form the related contacts called as folding nucleus residues (FNRs). In this work, the FNRs in proteins are identified by using quantities which characterize the topology of residue contact networks of proteins. By comparing the specificities of residues with the network quantities K(R), L(R), and D(R), up to 90% FNRs of six typical proteins found experimentally are identified. It is found that the FNRs behave the full-closeness centrals rather than degree or closeness centers in the residue contact network, implying that they are important to the folding cooperativity of proteins. Our study shows that the FNRs can be identified solely from the native structures of proteins based on the analysis of residue contact network without any knowledge of the transition state ensemble.     

Cunning Simplicity of a Hierarchical Folding

Abstract

A hierarchic scheme of protein folding does not solve the Levinthal paradox since it cannot provide a simultaneous explanation for major features observed for protein folding: (i) folding within non-astronomical time, (ii) independence of the native structure on large variations in the folding rates of given protein under different conditions, and (iii) co-existence, in a visible quantity, of only the native and the unfolded molecules during folding of moderate size (single-domain) proteins. On the contrary, a nucleation mechanism can account for all these major features simultaneously and resolves the Levinthal paradox.     

Investigating the Effect of Chain Connectivity on the Folding of a Beta-Sheet Protein On and Off the Ribosome

Determining the relationship between protein folding pathways on and off the ribosome remains an important area of investigation in biology. Studies on isolated domains have shown that alteration of the separation of residues in a polypeptide chain, while maintaining their spatial contacts, may affect protein stability and folding pathway. Due to the vectorial emergence of the polypeptide chain from the ribosome, chain connectivity may have an important influence upon cotranslational folding. Using MATH, an all β-sandwich domain, we investigate whether the connectivity of residues and secondary structure elements is a key determinant of when cotranslational folding can occur on the ribosome. From Φ-value analysis, we show that the most structured region of the transition state for folding in MATH includes the N and C terminal strands, which are located adjacent to each other in the structure. However, arrest peptide force-profile assays show that wild-type MATH is able to fold cotranslationally, while some C-terminal residues remain sequestered in the ribosome, even when destabilized by 2–3?kcal?mol^?1. We show that, while this pattern of Φ-values is retained in two circular permutants in our studies of the isolated domains, one of these permutants can fold only when fully emerged from the ribosome. We propose that in the case of MATH, onset of cotranslational folding is determined by the ability to form a sufficiently stable folding nucleus involving both β-sheets, rather than by the location of the terminal strands in the ribosome tunnel.     

Conformational properties of the iso-1-cytochrome C denatured state: dependence on guanidine hydrochloride concentration

Production of seven single surface histidine variants of yeast iso-1-cytochrome c allowed measurement of the apparent pK(a), pK(a)(obs), for histidine-heme loop formation for loops of nine to 83 amino acid residues under varying denaturing conditions (2 M to 6 M guanidine hydrochloride, gdnHCl). A linear correlation between pK(a)(obs) and the log of the loop size is expected for a random coil, pK(a)(obs) proportional to k log(n), where k is a scaling factor and n is the number of monomers in the loop. For small loops of nine, 16, and 22 monomers, no dependence of pK(a)(obs) on loop size was observed at any denaturant concentration indicating effects from chain stiffness. For larger loops of 37, 56, 72, and 83 monomers, the dependence of pK(a)(obs) on log(n) was linear and the slope of that dependence decreased with increasing concentration of denaturant. The scaling factor obtained at 5 M and 6 M gdnHCl for the larger loop sizes was approximately -2.0, close to the value of -2.2 expected for a random coil with excluded volume. However, scaling factors obtained under less harsh denaturing conditions (2 M to 4.5 M gdnHCl) deviated strongly from that expected for a random coil, being in the range -3 to -4. The gdnHCl dependence of pK(a)(obs) at each loop size was also evaluated to obtain denaturant m-values. Short loops where chain stiffness dominates had similar m-values of approximately 0.25 kcal/mol M. For larger loops m-values decrease with increasing loop size indicating that less hydrophobic area is sequestered when larger loops form. It is known that the earliest events in protein folding involve the formation of simple loops. The data from these studies provide direct insight into the relative probability with which loops of different sizes will form, as well as the factors which affect loop formation.     

Visualization of the nature of protein folding by a study of a distance constraint approach in two-dimensional models

A distance constraint approach is applied to two-dimensional models of proteins in order to visualize the nature of protein folding and to examine the relative roles of different ranges of interaction. Three different native structures (I, II, and III) are considered; they have two different kinds of residues, viz., hydrophobic and hydrophilic, and different sequences of these residues. We examine how the distance constraint approach functions in the prediction of protein folding when we know the sequence of the residues, the (fixed) bond lengths, the mean distances between residues i and i + 2, and i and i + 3, and the mean distances for hydrophobic–hydrophobic, hydrophobic–hydrophilic, and hydrophilic–hydrophilic contacts between residues i and i + j, where j ≥ 4. This approach involves optimization of an object function with respect to 98 variables and is not free of the multiple-minimum problem. The optimization is always terminated if the chain is entangled and/or the segments (residues) are packed too compactly to move. In order to escape from such situations and to take the excluded-volume effect into account, a Monte Carlo method is used after the optimization is trapped in local minima. Success in the prediction of folding is found to depend on the starting conformations and on the native conformations. Fair success is obtained in predicting the helix-like structure in protein I and the overall structure of protein III, but not the β-like structures of proteins I and II. Insofar as the prediction of the structure of protein III is reasonable, it appears that some sequences of residues produce greater constraints on their conformations than others, if one considers only the hydrophobic and hydrophilic nature of the residues. These results imply that, in the folding of real proteins in three dimensions, the competition for hydrophobic (and hydrophilic) residues for inside (outside) positions in the molecule probably constitutes a necessary but not a sufficient condition to form and stabilize the native structure. The failure to predict the structure of protein II, and part of that of protein I, suggests that there are two types of long-range interactions. One (which we considered here) is nonspecific (i.e., is defined only in terms of contacts between residues of the same or different polarity) and acts at any stage of protein folding; the other (which we did not consider here) is a specific interaction between residues in pairs and contributes only when the residues in the specific pair take on the native conformation. Presumably, incorporation of such specific long-range interactions, together with the nonspecific ones, is necessary for successful protein folding, using the distance constraint approach.     

Kinetics of internal-loop formation in polypeptide chains: a simulation study

The speed of simple diffusional motions, such as the formation of loops in the polypeptide chain, places one physical limit on the speed of protein folding. Many experimental studies have explored the kinetics of formation of end-to-end loops in polypeptide chains; however, protein folding more often requires the formation of contacts between interior points on the chain. One expects that, for loops of fixed contour length, interior loops will form more slowly than end-to-end loops, owing to the additional excluded volume associated with the "tails". We estimate the magnitude of this effect by generating ensembles of randomly coiled, freely jointed chains, and then using the theory of Szabo, Schulten, and Schulten to calculate the corresponding contact formation rates for these ensembles. Adding just a few residues, to convert an end-to-end loop to an internal loop, sharply decreases the contact rate. Surprisingly, the relative change in rate increases for a longer loop; sufficiently long tails, however, actually reverse the effect and accelerate loop formation slightly. Our results show that excluded volume effects in real, full-length polypeptides may cause the rates of loop formation during folding to depart significantly from the values derived from recent loop-formation experiments on short peptides.     

Importance of Contact Persistence in Denatured State Loop Formation: Kinetic Insights into Sequence Effects on Nucleation Early in Folding

Protein folding is dependent on the formation and persistence of simple loops early in folding. Ease of loop formation and persistence is believed to be dependent on the steric interactions of the residues involved in loop formation. We have previously investigated this factor in the denatured state of iso-1-cytochrome c using a five-amino-acid insert in front of a unique histidine in the N-terminal region of the protein. Previously, we reported that the apparent pK_a values of loop formation for the most flexible (all Gly) and least flexible (all Ala) insert were, within error, the same. We evaluate whether this observation is due to differences in the persistence of loop contacts or due to effects of local sequence sterics and main-chain hydration on the persistence length of the chain. We also test whether sequence order affects loop formation. Here, we report kinetic results coupled to further mutagenesis of the insert to discern between these possibilities.We find that the amino acid—glycine versus alanine—next to the loop forming histidine has a dominant effect on loop kinetics and equilibria. A glycine in this position speeds loop breakage relative to alanine, resulting in less stable loops. At high percentage of Gly in the insert, rates of loop formation and breakage exactly compensate, leading to a leveling out in loop stability. Loop formation rates also increase with glycine content, inconsistent with poly-Gly segments being more extended than previously suspected due to main-chain hydration or local sterics. Unlike loop breakage rates, loop formation rates are insensitive to local sequence. Together, these observations suggest that contact persistence plays a more important role in defining the “folding code” than rates of loop formation.     

Prolyl isomerization: How significant for in vivo protein folding?

Suggestive but not decisive evidence indicates that in vivo peptide chain folding is completed in a time not much longer than that required for covalent peptide synthesis. Extrapolation of model peptide rates of the cis–trans prolyl isomerization leads to the prediction tht protein folding should be much slower than the apparent in vivo rates. On the assumption that rapid protein folding in vivo is the rule, three routes are suggested by which a protein undergoing biosynthesis can avoid a strongly slowed folding rate: (1) by a peptide chain-elongation process that adds only trans peptide bonds, follwed by a rapid folding process that incorporates them into a three-dimensional structure, raising the energy barrier to isomerization; (2) by folding to produce three dimensional structures that position prolyl residues largely in chain turns on the protein surface, where the residue may be either cis or trans without large effects on the protein structure and function; (3) prolyl cis–trans isomerization may be speeded by the formation of peptide loops.