Reducing the computational complexity of protein folding via fragment folding and assembly

Understanding, and ultimately predicting, how a 1-D protein chain reaches its native 3-D fold has been one of the most challenging problems during the last few decades. Data increasingly indicate that protein folding is a hierarchical process. Hence, the question arises as to whether we can use the hierarchical concept to reduce the practically intractable computational times. For such a scheme to work, the first step is to cut the protein sequence into fragments that form local minima on the polypeptide chain. The conformations of such fragments in solution are likely to be similar to those when the fragments are embedded in the native fold, although alternate conformations may be favored during the mutual stabilization in the combinatorial assembly process. Two elements are needed for such cutting: (1) a library of (clustered) fragments derived from known protein structures and (2) an assignment algorithm that selects optimal combinations to "cover" the protein sequence. The next two steps in hierarchical folding schemes, not addressed here, are the combinatorial assembly of the fragments and finally, optimization of the obtained conformations. Here, we address the first step in a hierarchical protein-folding scheme. The input is a target protein sequence and a library of fragments created by clustering building blocks that were generated by cutting all protein structures. The output is a set of cutout fragments. We briefly outline a graph theoretic algorithm that automatically assigns building blocks to the target sequence, and we describe a sample of the results we have obtained.     

Cotranslational Folding of Proteins

We suppose that folding of proteins occurs cotranslationally by the following scheme. The polypeptide chains enter the folding sites from protein translocation complexes (ribosome, translocation machinery incorporated in membranes) directionally with the N-terminus and gradually. The chain starts to fold as soon as its N-terminal residue enters the folding site from the translocation complex. The folding process accompanies the translocation of the chain to its folding site and is completed after the C-terminal residue leaves the translocation complex. Proteins fold in sequential stages, by translocation of their polypeptide into folding compartments. At each stage a particular conformation of the N-terminal part of the chain that has emerged from the translocation complex is formed. The formation of both the particular conformations of the N-terminal chain segment at each folding stage and the final native protein conformation at the last stage occurs in a time that does not exceed the duration of the fastest elongation cycle on the ribosome.     

Hierarchical protein folding pathways: a computational study of protein fragments

We have previously presented a building block folding model. The model postulates that protein folding is a hierarchical top-down process. The basic unit from which a fold is constructed, referred to as a hydrophobic folding unit, is the outcome of combinatorial assembly of a set of "building blocks." Results obtained by the computational cutting procedure yield fragments that are in agreement with those obtained experimentally by limited proteolysis. Here we show that as expected, proteins from the same family give very similar building blocks. However, different proteins can also give building blocks that are similar in structure. In such cases the building blocks differ in sequence, stability, contacts with other building blocks, and in their 3D locations in the protein structure. This result, which we have repeatedly observed in many cases, leads us to conclude that while a building block is influenced by its environment, nevertheless, it can be viewed as a stand-alone unit. For small-sized building blocks existing in multiple conformations, interactions with sister building blocks in the protein will increase the population time of the native conformer. With this conclusion in hand, it is possible to develop an algorithm that predicts the building block assignment of a protein sequence whose structure is unknown. Toward this goal, we have created sequentially nonredundant databases of building block sequences. A protein sequence can be aligned against these, in order to be matched to a set of potential building blocks.     

Evidence for sequential barriers and obligatory intermediates in apparent two-state protein folding

Many small proteins fold fast and without detectable intermediates. This is frequently taken as evidence against the importance of partially folded states, which often transiently accumulate during folding of larger proteins. To get insight into the properties of free energy barriers in protein folding we analyzed experimental data from 23 proteins that were reported to show non-linear activation free-energy relationships. These non-linearities are generally interpreted in terms of broad transition barrier regions with a large number of energetically similar states. Our results argue against the presence of a single broad barrier region. They rather indicate that the non-linearities are caused by sequential folding pathways with consecutive distinct barriers and a few obligatory high-energy intermediates. In contrast to a broad barrier model the sequential model gives a consistent picture of the folding barriers for different variants of the same protein and when folding of a single protein is analyzed under different solvent conditions. The sequential model is also able to explain changes from linear to non-linear free energy relationships and from apparent two-state folding to folding through populated intermediates upon single point mutations or changes in the experimental conditions. These results suggest that the apparent discrepancy between two-state and multi-state folding originates in the relative stability of the intermediates, which argues for the importance of partially folded states in protein folding.     

A model study of protein nascent chain and cotranslational folding using hydrophobic-polar residues

To study protein nascent chain folding during biosynthesis, we investigate the folding behavior of models of hydrophobic and polar (HP) chains at growing length using both two-dimensional square lattice model and an optimized three-dimensional 4-state discrete off-lattice model. After enumerating all possible sequences and conformations of HP heteropolymers up to length N = 18 and N = 15 in two and three-dimensional space, respectively, we examine changes in adopted structure, stability, and tolerance to single point mutation as the nascent chain grows. In both models, we find that stable model proteins have fewer folded nascent chains during growth, and often will only fold after reaching full length. For the few occasions where partial chains of stable proteins fold, these partial conformations on average are very similar to the corresponding parts of the final conformations at full length. Conversely, we find that sequences with fewer stable nascent chains and sequences with native-like folded nascent chains are more stable. In addition, these stable sequences in general can have many more point mutations and still fold into the same conformation as the wild type sequence. Our results suggest that stable proteins are less likely to be trapped in metastable conformations during biosynthesis, and are more resistant to point-mutations. Our results also imply that less stable proteins will require the assistance of chaperone and other factors during nascent chain folding. Taken together with other reported studies, it seems that cotranslational folding may not be a general mechanism of in vivo protein folding for small proteins, and in vitro folding studies are still relevant for understanding how proteins fold biologically.     

Potential folding-function interrelationship in proteins

The possibility is addressed that protein folding and function may be related via regions that are critical for both folding and function. This approach is based on the building blocks folding model that describes protein folding as binding events of conformationally fluctuating building blocks. Within these, we identify building block fragments that are critical for achieving the native fold. A library of such critical building blocks (CBBs) is constructed. Then, it is asked whether the functionally important residues fall in these CBB fragments. We find that for over two-thirds of the proteins in our library with available functional information, the catalytic or binding site residues lie within the CBB regions. From the evolutionary standpoint, a folding-function relationship is advantageous, since the need to guard against mutations is limited to one region. Furthermore, conformationally similar CBBs are found in globally unrelated proteins with different functions. Hence, substituting CBBs may lead to designed proteins with altered functions. We further find that the CBBs in our library are conformationally unstable.     

Comparison of protein fragments identified by limited proteolysis and by computational cutting of proteins

Here we present a comparison between protein fragments produced by limited proteolysis and those identified by computational cutting based on the building block folding model. The principles upon which the two methods are based are different. Limited proteolysis of natively folded proteins occurs at flexible sites and never at the level of chain segments of regular secondary structure such as alpha-helices. Therefore, the targets for limited proteolysis are locally unfolded regions. In contrast, the computational cutting algorithm considers the compactness of the fragments, their nonpolar buried surface area, and their isolatedness, that is, the surface area which was buried prior to the cutting and becomes exposed subsequently. Despite the different criteria, there is an overall correspondence between sites or regions of limited proteolysis with those identified by computational cutting. The computational cutting method has been applied to several model proteins for which detailed limited proteolysis data are available, namely apomyoglobin, cytochrome c, ribonuclease A, alpha-lactalbumin, and thermolysin. As expected, more cuts are obtained computationally than experimentally and the agreement is better when a number of proteolytic enzymes are used. For example, cytochrome c is cleaved by thermolysin at 56-57, 45-46, and at 80-81, and by proteinase K at 48-49 and 50-51. Incubation of the noncovalent and native-like complex of cytochrome c fragments 1-56 and 57-104 with proteinase K yielded the gapped protein species 1-48/57-104 and finally 1-40/57-104. Computational cutting of cytochrome c reproduced the major experimental observations, with cuts at 47, 64-65 or 65-66 and 80-81 and an unstable 32-47 region not assigned to any building block. The next step, not addressed in this work, is to probe the ability of the generated fragments to fold independently. Since both the computational algorithm and limited proteolysis attempt to dissect the protein folding problem, the general agreement between the two procedures is gratifying. This consistency allows us to propose the use of limited proteolysis to produce protein fragments that can adopt an independent folding and, therefore, to study folding intermediates. The results of the present study appear to validate the building block folding model and are in line with the proposal that protein folding is a hierarchical process, where parts constituting local minima of energy fold first, with their subsequent association and mutual stabilization to finally yield the global fold.     

A captured folding intermediate involved in dimerization and domain-swapping of GB1

Immunoglobulin binding domain B1 of streptococcal protein G (GB1), a small (56 residues), stable, single domain protein, is one of the most extensively used model systems in the area of protein folding and design. The recently determined NMR structure of a quadruple mutant (HS#124F26A, L5V/F30V/Y33F/A34F) revealed a domain-swapped dimer that dissociated into a partially folded, monomeric species at low micromolar protein concentrations. Here, we have characterized this monomeric, partially folded species by NMR and show that extensive conformational heterogeneity for a substantial portion of the polypeptide chain exists. Exchange between the conformers within the monomer ensemble on the microsecond to millisecond timescale renders the majority of backbone amide resonances broadened beyond detection. Despite these extensive temporal and spatial fluctuations, the overall architecture of the monomeric mutant protein resembles that of wild-type GB1 and not the monomer unit of the domain-swapped dimer.     

Inter-residue interactions in protein folding and stability

During the process of protein folding, the amino acid residues along the polypeptide chain interact with each other in a cooperative manner to form the stable native structure. The knowledge about inter-residue interactions in protein structures is very helpful to understand the mechanism of protein folding and stability. In this review, we introduce the classification of inter-residue interactions into short, medium and long range based on a simple geometric approach. The features of these interactions in different structural classes of globular and membrane proteins, and in various folds have been delineated. The development of contact potentials and the application of inter-residue contacts for predicting the structural class and secondary structures of globular proteins, solvent accessibility, fold recognition and ab initio tertiary structure prediction have been evaluated. Further, the relationship between inter-residue contacts and protein-folding rates has been highlighted. Moreover, the importance of inter-residue interactions in protein-folding kinetics and for understanding the stability of proteins has been discussed. In essence, the information gained from the studies on inter-residue interactions provides valuable insights for understanding protein folding and de novo protein design.     

Mechanical unfoldons as building blocks of maltose-binding protein

Identifying independently folding cores or substructures is important for understanding and assaying the structure, function and assembly of large proteins. Here, we suggest mechanical stability as a criterion to identify building blocks of the 366 amino acid maltose-binding protein (MBP). We find that MBP, when pulled at its termini, unfolds via three (meta-) stable unfolding intermediates. Consequently, the MBP structure consists of four structural blocks (unfoldons) that detach sequentially from the folded structure upon force application. We used cysteine cross-link mutations to characterize the four unfoldons structurally. We showed that many MBP constructs composed of those building blocks indeed form stably folded structures in solution. Mechanical unfoldons may provide a new tool for a systematic search for stable substructures of large proteins.     

The importance of explicit chain representation in protein folding models: an examination of Ising-like models

A class of models that represents a protein chain as a sequence of "folded" and "unfolded" residues has recently been used to correlate rates and mechanisms of protein folding with the protein native structure. In order to better understand the conditions under which these "Ising-like" models apply, we compare results from this model to those obtained from an off-lattice model which uses the same potential function. We find that Ising-like models by construction impose folding via a highly sequential nucleation-condensation mechanism, which in turn leads to more rugged energy landscapes, fewer "pathways" to the native state, and in the specific case examined here, the cold shock protein A from Escherichia coli, a qualitative difference in the most likely order of events in folding.     

The posttranslational concept of protein folding: how valid is it?

Two concepts of protein folding are known. One of them, the cotranslational concept, states that a protein folds during the synthesis of the polypeptide chain on the ribosome. According to the other, the posttranslational concept, the protein starts to fold just after the synthesis of its polypeptide chain. This article attempts to show that the posttranslational concept is hardly suited to solve the problem of protein folding. In our opinion, polypeptide chains cannot be represented as random coils. They are stiff chain-like macromolecules rather than flexible ones: the single bond rotational barriers of a polypeptide substantially exceed the accepted standard values; even in strong denaturing conditions, a protein possesses a considerable amount of residual folded structures. We believe that the popular "hierarchical" models for the protein folding mechanism are not realistic because the formation of secondary and tertiary structures of proteins occurs simultaneously and cooperatively. The time for the elongation of a polypeptide chain by one amino acid residue during biosynthesis exceeds considerably the time of the formation of alpha-helices and beta-sheets in proteins as well as the time supposed for the spatial structure formation of a native protein during renaturation. Thus, we believe that the mechanism of protein folding in vivo cannot be clarified by denaturation-renaturation experiments. In our opinion, the phenomenon of protein renaturation is no more than the restoration of native protein conformation (which initially forms cotranslationally) disrupted during denaturation, and thus denaturation-renaturation experiments cannot serve as a model to clarify the mechanism of protein folding.     

Buried hydrophobic side-chains essential for the folding of the parallel beta-helix domains of the P22 tailspike

The processive beta-strands and turns of a polypeptide parallel beta-helix represent one of the topologically simplest beta-sheet folds. The three subunits of the tailspike adhesin of phage P22 each contain 13 rungs of a parallel beta-helix followed by an interdigitated section of triple-stranded beta-helix. Long stacks of hydrophobic residues dominate the elongated buried core of these two beta-helix domains and extend into the core of the contiguous triple beta-prism domain. To test whether these side-chain stacks represent essential residues for driving the chain into the correct fold, each of three stacked phenylalanine residues within the buried core were substituted with less bulky amino acids. The mutant chains with alanine in place of phenylalanine were defective in intracellular folding. The chains accumulated exclusively in the aggregated inclusion body state regardless of temperature of folding. These severe folding defects indicate that the stacked phenylalanine residues are essential for correct parallel beta-helix folding. Replacement of the same phenylalanine residues with valine or leucine also impaired folding in vivo, but with less severity. Mutants were also constructed in a second buried stack that extends into the intertwined triple-stranded beta-helix and contiguous beta-prism regions of the protein. These mutants exhibited severe defects in later stages of chain folding or assembly, accumulating as misfolded but soluble multimeric species. The results indicate that the formation of the buried hydrophobic stacks is critical for the correct folding of the parallel beta-helix, triple-stranded beta-helix, and beta-prism domains in the tailspike protein.     

Molecular simulations of cotranslational protein folding: fragment stabilities, folding cooperativity, and trapping in the ribosome

Although molecular simulation methods have yielded valuable insights into mechanistic aspects of protein refolding in vitro, they have up to now not been used to model the folding of proteins as they are actually synthesized by the ribosome. To address this issue, we report here simulation studies of three model proteins: chymotrypsin inhibitor 2 (CI2), barnase, and Semliki forest virus protein (SFVP), and directly compare their folding during ribosome-mediated synthesis with their refolding from random, denatured conformations. To calibrate the methodology, simulations are first compared with in vitro data on the folding stabilities of N-terminal fragments of CI2 and barnase; the simulations reproduce the fact that both the stability and thermal folding cooperativity increase as fragments increase in length. Coupled simulations of synthesis and folding for the same two proteins are then described, showing that both fold essentially post-translationally, with mechanisms effectively identical to those for refolding. In both cases, confinement of the nascent polypeptide chain within the ribosome tunnel does not appear to promote significant formation of native structure during synthesis; there are however clear indications that the formation of structure within the nascent chain is sensitive to location within the ribosome tunnel, being subject to both gain and loss as the chain lengthens. Interestingly, simulations in which CI2 is artificially stabilized show a pronounced tendency to become trapped within the tunnel in partially folded conformations: non-cooperative folding, therefore, appears in the simulations to exert a detrimental effect on the rate at which fully folded conformations are formed. Finally, simulations of the two-domain protease module of SFVP, which experimentally folds cotranslationally, indicate that for multi-domain proteins, ribosome-mediated folding may follow different pathways from those taken during refolding. Taken together, these studies provide a first step toward developing more realistic methods for simulating protein folding as it occurs in vivo.     

Absence of a stable intermediate on the folding pathway of protein A.

The B-domain of protein A has one of the simplest protein topologies, a three-helix bundle. Its folding has been studied as a model for elementary steps in the folding of larger proteins. Earlier studies suggested that folding might occur by way of a helical hairpin intermediate. Equilibrium hydrogen exchange measurements indicate that the C-terminal helical hairpin could be a potential folding intermediate. Kinetic refolding experiments were performed using stopped-flow circular dichroism and NMR hydrogen-deuterium exchange pulse labeling. Folding of the entire molecule is essentially complete within the 6 ms dead time of the quench-flow apparatus, indicating that the intermediate, if formed, progresses rapidly to the final folded state. Site-directed mutagenesis of the isoleucine residue at position 16 was used to generate a variant protein containing tryptophan (the 116 W mutant). The formation of the putative folding intermediate was expected to be favored in this mutant at the expense of the native folded form, due to predicted unfavorable steric interactions of the bulky tryptophan side chain in the folded state. The 116 W mutant refolds completely within the dead time of a stopped-flow fluorescence experiment. No partly folded intermediate could be detected by either kinetic or equilibrium measurements. Studies of peptide fragments suggest that the protein A sequence has an intrinsic propensity to form a helix II/helix III hairpin. However, its stability appears to be marginal (of the order of 1/2 kT) and it could not be an obligatory intermediate on a defined folding pathway. These results explicitly demonstrate that the protein A B domain folds extremely rapidly by an apparent two-state mechanism without formation of stable partly folded intermediates. Similar mechanisms may also be involved in the rapid folding of subdomains of larger proteins to form the compact molten globule intermediates that often accumulate during the folding process.     

Monte Carlo simulation of protein folding in the presence of residue-specific binding sites

Ensemble growth Monte Carlo (EGMC) and dynamic Monte Carlo (DMC) simulations are used to study sequential folding and thermodynamic stability of hydrophobic-polar (HP) chains that fold to a compact structure. Molecularly imprinted cavities are modeled as hard walls having sites that are attractive to specific polar residues on the chain. Using EGMC simulation, we find that the folded conformation can be stabilized using a small number of carefully selected residue-specific sites while a random selection of surface-bound residues may only slightly contribute toward stabilizing the folded conformation, and in some cases may hinder the folding of the chain. DMC simulations of the surface-bound chain confirm increased stability of the folded conformation over a free chain. However, a different trend of the equilibrium population of folded chains as a function of residue-external site interactions is predicted with the two simulation methods.     

Transient structure formation in unfolded acyl-coenzyme A-binding protein observed by site-directed spin labelling

Paramagnetic relaxation has been used to monitor the formation of structure in the folding peptide chain of guanidinium chloride-denatured acyl-coenzyme A-binding protein. The spin label (1-oxyl-2,2,5,5-tetramethyl-3-pyrroline-3-methyl)methanesulfonate (MTSL) was covalently bound to a single cysteine residue introduced into five different positions in the amino acid sequence. It was shown that the formation of structure in the folding peptide chain at conditions where 95% of the sample is unfolded brings the relaxation probe close to a wide range of residues in the peptide chain, which are not affected in the native folded structure. It is suggested that the experiment is recording the formation of many discrete and transient structures in the polypeptide chain in the preface of protein folding. Analysis of secondary chemical shifts shows a high propensity for alpha-helix formation in the C-terminal part of the polypeptide chain, which forms an alpha-helix in the native structure and a high propensity for turn formation in two regions of the polypeptide that form turns in the native structure. The results contribute to the idea that native-like structural elements form transiently in the unfolded state, and that these may be of importance to the initiation of protein folding.     

Stability and folding kinetics of structurally characterized cytochrome c-b562

The four-helix-bundle protein fold can be constructed from a wide variety of primary amino acid sequences. Proteins with this structure are excellent candidates for investigations of the relationship between folding mechanism and topology. The folding of cytochrome b(562), a four-helix-bundle heme protein, is hampered by heme dissociation. To overcome this complication, we have engineered a variant of cytochrome b(562) (cyt c-b(562)) featuring a c-type linkage between the heme and the polypeptide chain. The replacement of the native cyt b(562) leader sequence in this protein with that of a c-type cytochrome (cyt c(556)) led to high yields of fully matured and correctly folded cyt c-b(562). We have determined the X-ray crystal structure of cyt c-b(562) at 2.25 A and characterized its physical, chemical, and folding properties. These measurements reveal that the c-type linkage does not perturb the protein fold or reduction potential of the heme group. The covalent attachment of the porphyrin to the polypeptide does, however, produce a substantial change in protein stability and folding kinetics.     

Backbones of Folded Proteins Reveal Novel Invariant Amino Acid Neighborhoods

Abstract

Folding of naturally occurring proteins has eluded a universal molecular level explanation till date. Rather, there is an abundance of diverse views on dominant factors governing protein folding. Through rigorous analyses of several thousand crystal structures, we observe that backbones of folded proteins display some remarkable invariant features. Folded proteins are characterized by spatially well-defined, distance dependent, and universal, neighborhoods of amino acids which defy any of the conventionally prevalent views. These findings present a compelling case for a newer view of protein folding which takes into account solvent mediated and amino acid shape and size assisted optimization of the tertiary structure of the polypeptide chain to make a functional protein.     

The cross-road between the mechanisms of protein folding and aggregation; study of human stefin B and its H75W mutant

The role of the aromatic residue at site 75 to protein stability, the mechanism of folding and the mechanism of amyloid-fibril formation were investigated for the human stefin B variant (bearing Y at site 31) and its point mutation H75W. With an aim to reveal the conformation at the cross-road between folding and aggregation, first, the kinetics of folding and oligomer formation by human stefin B(Y31) variant were studied. It was found to fold in three kinetic phases at pH 4.8 and 10% TFE; the pH and solvent conditions that transform the protein into amyloid fibrils at longer times. The same pH leads to the formation of native-like intermediate (known from previous studies of this variant), meaning that the process of folding and amyloid-fibril formation share the same structural intermediate, which is in this case native-like and dimeric. At pH 5.8 and 7.0 stefin B folded to the native state in four kinetic phases over two intermediates. In distinction, the mutant H75W did not fold to completion, ending in intermediate states at all pH values studied: 4.8, 5.8 and 7.0. At pH 4.8 and 5.8, the mutant folded in one kinetic phase to the intermediate of the “molten globule” type, which leads to the conclusion that its mechanism of folding differs from the one of the parent stefin B at the same pH. At pH 7.0 the mutant H75W folded in three kinetic phases to a native-like intermediate, analogous to folding of stefin B at pH 4.8.