An analysis of protein folding pathways

Fast closure of long loops at the initiation of the folding transition of globular proteins studied by time-resolved FRET-based methods

The protein folding problem would be considered “solved” when it will be possible to “read genes”, i.e., to predict the native fold of proteins, their dynamics, and the mechanism of fast folding based solely on sequence data. The long-term goal should be the creation of an algorithm that would simulate the stepwise mechanism of folding, which constrains the conformational space and in which random search for stable interactions is possible. Here, we focus attention on the initial phases of the folding transition starting with the compact disordered collapsed ensemble, in search of the initial sub-domain structural biases that direct the otherwise stochastic dynamics of the backbone. Our studies are designed to test the “loop hypothesis”, which suggests that fast closure of long loop structures by non-local interactions between clusters of mainly non-polar residues is an essential conformational step at the initiation of the folding transition of globular proteins. We developed and applied experimental methods based on time-resolved resonance excitation energy transfer (trFRET) measurements combined with fast mixing methods and studied the initial phases of the folding of

The loop hypothesis: contribution of early formed specific non-local interactions to the determination of protein folding pathways

The extremely fast and efficient folding transition (in seconds) of globular proteins led to the search for some unifying principles embedded in the physics of the folding polypeptides. Most of the proposed mechanisms highlight the role of local interactions that stabilize secondary structure elements or a folding nucleus as the starting point of the folding pathways, i.e., a "bottom-up" mechanism. Non-local interactions were assumed either to stabilize the nucleus or lead to the later steps of coalescence of the secondary structure elements. An alternative mechanism was proposed, an "up-down" mechanism in which it was assumed that folding starts with the formation of very few non-local interactions which form closed long loops at the initiation of folding. The possible biological advantage of this mechanism, the "loop hypothesis", is that the hydrophobic collapse is associated with ordered compactization which reduces the chance for degradation and misfolding. In the present review the experiments, simulations and theoretical consideration that either directly or indirectly support this mechanism are summarized. It is argued that experiments monitoring the time-dependent development of the formation of specifically targeted early-formed sub-domain structural elements, either long loops or secondary structure elements, are necessary. This can be achieved by the time-resolved FRET-based "double kinetics" method in combination with mutational studies. Yet, attempts to improve the time resolution of the folding initiation should be extended down to the sub-microsecond time regime in order to design experiments that would resolve the classes of proteins which first fold by local or non-local interactions.

Discriminating the native structure from decoys using scoring functions based on the residue packing in globular proteins

BACKGROUND

Setting the rules for the identification of a stable conformation of a protein is of utmost importance for the efficient generation of structures in computer simulation. For structure prediction, a considerable number of possible models are generated from which the best model has to be selected.

RESULTS

Two scoring functions, Rs and Rp, based on the consideration of packing of residues, which indicate if the conformation of an amino acid sequence is native-like, are presented. These are defined using the solvent accessible surface area (ASA) and the partner number (PN) (other residues that are within 4.5 A) of a particular residue. The two functions evaluate the deviation from the average packing properties (ASA or PN) of all residues in a polypeptide chain corresponding to a model of its three-dimensional structure. While simple in concept and computationally less intensive, both the functions are at least as efficient as any other energy functions in discriminating the native structure from decoys in a large number of standard decoy sets, as well as on models submitted for the targets of CASP7. Rs appears to be slightly more effective than Rp, as determined by the number of times the native structure possesses the minimum value for the function and its separation from the average value for the decoys.

CONCLUSION

Two parameters, Rs and Rp, are discussed that can very efficiently recognize the native fold for a sequence from an ensemble of decoy structures. Unlike many other algorithms that rely on the use of composite scoring function, these are based on a single parameter, viz., the accessible surface area (or the number of residues in contact), but still able to capture the essential attribute of the native fold.

A ternary nucleation model for the nucleation pathway of protein folding

Recently [Y. S. Djikaev and E. Ruckenstein, J. Phys. Chem. B 111, 886 (2007)], the authors proposed a kinetic model for the nucleation mechanism of protein folding where a protein was modeled as a heteropolymer consisting of hydrophobic and hydrophilic beads and the composition of the growing cluster of protein residues was assumed to be constant and equal to the overall protein composition. Here, they further develop the model by considering a protein as a three-component heteropolymer and by allowing the composition of the growing cluster of protein residues to vary independently of the overall one. All the bonds in the heteropolymer (now consisting of hydrophobic, hydrophilic, and neutral beads) have the same constant length, and all the bond angles are equal and fixed. As a crucial idea of the model, an overall potential around the cluster wherein a residue performs a chaotic motion is considered to be a combination of the average dihedral and average pairwise potentials assigned to the bead. The overall potential as a function of the distance from the cluster center has a double well shape which allows one to determine its emission and absorption rates by using a first passage time analysis. Knowing these rates as functions of three independent variables of a ternary cluster, one can develop a self-consistent kinetic theory for the nucleation mechanism of folding of a protein using a ternary nucleation formalism and evaluate the size and composition of the nucleus and the protein folding time. As an illustration, the model is applied to the folding of bovine pancreatic ribonuclease consisting of 124 amino acids whereof 40 are hydrophobic, 81 hydrophilic, and 3 neutral. With a reasonable choice of diffusion coefficients of the residues in the native state and potential parameters, the model predicts folding times in the range of 1-100 s.

Model for the Nucleation Mechanism of Protein Folding

A nucleation-like pathway of protein folding involves the formation of a cluster containing native residues that grows by including residues from the unfolded part of the protein. This pathway is examined by using a heteropolymer as a protein model. The model heteropolymer consists of hydrophobic and hydrophilic beads with fixed bond lengths and bond angles. The total energy of the heteropolymer is determined by the pairwise repulsive/attractive interactions between nonlinked beads and by the contribution from the dihedral angles involved. The parameters of these interactions can be rigorously defined, unlike the ill-defined surface tension of a cluster of protein residues that constitutes the basis of a previous nucleation model. The main idea underlying the new model consists of averaging the dihedral potential of a selected residue over all possible configurations of all neighboring residues along the protein chain. The resulting average dihedral potential depends on the distance between the selected residue and the cluster center. Its combination with the average pairwise potential of the selected residue and with a confining potential caused by the bonds between the residues leads to an overall potential around the cluster that has a double-well shape. Residues in the inner (closer to the cluster) well are considered as belonging to the folded cluster, whereas those in the outer well are treated as belonging to the unfolded part of the protein. Transitions of residues from the inner well into the outer one and vice versa are considered as elementary emission and absorption events, respectively. The double-well character of the potential well around the cluster allows one to determine the rates of both emission and absorption of residues by the cluster using a first passage time analysis. Once these rates are found as functions of the cluster size, one can develop a self-consistent kinetic theory for the nucleation mechanism of folding of a protein. The model allows one to evaluate the size of the nucleus and the protein folding time. The latter is evaluated as the sum of the times necessary for the first nucleation event to occur and for the nucleus to grow to the maximum size (of the folded protein). Depending on the diffusion coefficients of the native residues in the range from 10(-6) to 10(-8) cm2/s, numerical calculations for a protein of 2500 residues suggest that the folding time ranges from several seconds to several hundreds of seconds.

The "first in-last out" hypothesis on protein folding revisited

We calculated profiles for mean residue depth, contact order, and number of contacts in the native structure of a series of proteins for which folding has been studied extensively, the chymotrypsin inhibitor 2, the SH3 module from the src tyrosine kinase, the small ribonuclease barnase, the bacterial immunity protein Im7, and apomyoglobin. We compared these profiles with experimental data from equilibrium or pulse labeling hydrogen-deuterium exchange obtained from NMR and phi values obtained from the protein engineering approach. We find a good qualitative agreement between the hierarchy of formation of topological elements during the folding process and the ranking of secondary structure elements in terms of residue depth. Residues that are most deeply buried in the core of the native protein usually belong to stretches of secondary structure elements that are formed early in the folding pathway. Residue depth can thus provide a useful and simple tool for the design of folding experiments.

Teaching computers to fold proteins

A new general algorithm for optimization of potential functions for protein folding is introduced. It is based upon gradient optimization of the thermodynamic stability of native folds of a training set of proteins with known structure. The iterative update rule contains two thermodynamic averages which are estimated by (generalized ensemble) Monte Carlo. We test the learning algorithm on a Lennard-Jones (LJ) force field with a torsional angle degrees-of-freedom and a single-atom side-chain. In a test with 24 peptides of known structure, none folded correctly with the initial potential functions, but two-thirds came within 3 A to their native fold after optimizing the potential functions.

Frequencies of amino acid strings in globular protein sequences indicate suppression of blocks of consecutive hydrophobic residues

Patterns of hydrophobic and hydrophilic residues play a major role in protein folding and function. Long, predominantly hydrophobic strings of 20-22 amino acids each are associated with transmembrane helices and have been used to identify such sequences. Much less attention has been paid to hydrophobic sequences within globular proteins. In prior work on computer simulations of the competition between on-pathway folding and off-pathway aggregate formation, we found that long sequences of consecutive hydrophobic residues promoted aggregation within the model, even controlling for overall hydrophobic content. We report here on an analysis of the frequencies of different lengths of contiguous blocks of hydrophobic residues in a database of amino acid sequences of proteins of known structure. Sequences of three or more consecutive hydrophobic residues are found to be significantly less common in actual globular proteins than would be predicted if residues were selected independently. The result may reflect selection against long blocks of hydrophobic residues within globular proteins relative to what would be expected if residue hydrophobicities were independent of those of nearby residues in the sequence.

Towards a complete description of the structural and dynamic properties of the denatured state of barnase and the role of residual structure in folding

The detailed characterization of denatured proteins remains elusive due to their mobility and conformational heterogeneity. NMR studies are beginning to provide clues regarding residual structure in the denatured state but the resulting data are too sparse to be transformed into molecular models using conventional techniques. Molecular dynamics simulations can complement NMR by providing detailed structural information for components of the denatured ensemble. Here, we describe three independent 4 ns high-temperature molecular dynamics simulations of barnase in water. The simulated denatured state was conformationally heterogeneous with respect to the conformations populated both within a single simulation and between simulations. Nonetheless, there were some persistent interactions that occurred to varying degrees in all simulations and primarily involved the formation of fluid hydrophobic clusters with participating residues changing over time. The region of the beta(3-4) hairpin contained a particularly high degree of such side-chain interactions but it lacked beta-structure in two of the three denatured ensembles: beta(3-4) was the only portion of the beta-structure to contain significant residual structure in the denatured state. The two principal alpha-helices (alpha1 and alpha2) adopted dynamic helical structure. In addition, there were persistent contacts that pinched off core 2 from the body of the protein. The rest of the protein was unstructured, aside from transient and mostly local side-chain interactions. Overall, the simulated denatured state contains residual structure in the form of dynamic, fluctuating secondary structure in alpha1 and alpha2, as well as fluctuating tertiary contacts in the beta(3-4) region, and between alpha1 and beta(3-4), in agreement with previous NMR studies. Here, we also show that these regions containing residual structure display impaired mobility by both molecular dynamics and NMR relaxation experiments. The residual structure was important in decreasing the conformational states available to the chain and in repairing disrupted regions. For example, tertiary contacts between beta(3-4) and alpha1 assisted in the refolding of alpha1. This contact-assisted helix formation was confirmed in fragment simulations of beta(3-4) and alpha1 alone and complexed, and, as such, alpha1 and beta(3-4) appear to be folding initiation sites. The role of these sites in folding was investigated by working backwards and considering the simulation in reverse, noting that earlier time-points from the simulations provide models of the major intermediate and transition states in quantitative agreement with data from both unfolding and refolding experiments. Both beta(3-4) and alpha1 are dynamic in the denatured state but when they collide and make enough contacts, they provide a loose structural scaffold onto which further beta-strands pack. The beta-structure condenses about beta(3-4), while alpha1 aids in stabilizing beta(3-4) and maintaining its orientation. The resulting beta-structure is relatively planar and loose in the major intermediate. Further packing ensues, and as a result the beta-sheet twists, leading to the major transition state. The structure is still expanded and loops are not well formed at this point. Fine-tuning of the packing interactions and the final condensation of the structure then occurs to yield the native state.

Neural networks predict protein folding and structure: artificial intelligence faces biomolecular complexity

In the genomic era DNA sequencing is increasing our knowledge of the molecular structure of genetic codes from bacteria to man at a hyperbolic rate. Billions of nucleotides and millions of aminoacids are already filling the electronic files of the data bases presently available, which contain a tremendous amount of information on the most biologically relevant macromolecules, such as DNA, RNA and proteins. The most urgent problem originates from the need to single out the relevant information amidst a wealth of general features. Intelligent tools are therefore needed to optimise the search. Data mining for sequence analysis in biotechnology has been substantially aided by the development of new powerful methods borrowed from the machine learning approach. In this paper we discuss the application of artificial feedforward neural networks to deal with some fundamental problems tied with the folding process and the structure-function relationship in proteins.

The molten globule state of a chimera of human alpha-lactalbumin and equine lysozyme

The molten globule state of equine lysozyme is more stable than that of alpha-lactalbumin and is stabilized by non-specific hydrophobic interactions and native-like hydrophobic interactions. We constructed a chimeric protein which is produced by replacing the flexible loop (residues 105-110) in human alpha-lactalbumin with the helix D (residues 109-114) in equine lysozyme to investigate the possible role of the helix D for the high stability and native-like packing interaction in the molten globule state of equine lysozyme. The stability of the molten globule state formed by the chimeric protein to guanidine hydrochloride-induced unfolding is the same as that of equine lysozyme and is substantially greater than that of human alpha-lactalbumin, although only six residues come from equine lysozyme. Our results also suggest that the non-native interaction in the molten globule state of alpha-lactalbumin changes to the native-like packing interaction due to helix substitution. The solvent-accessibility of the Trp residues in the molten globule state of the chimeric protein is similar to that in the molten globule state of equine lysozyme in which packing interaction around the Trp residues in the native state is partially preserved. Therefore, the helix D in equine lysozyme is one of the contributing factors to the high stability and native-like packing interaction in the molten globule state of equine lysozyme. Our results indicate that the native-like packing interaction can stabilize the rudimentary intermediate which is stabilized by the non-specific hydrophobic interactions.

Cooperative folding units of escherichia coli tryptophan repressor

A previously published computational procedure was used to identify cooperative folding units within tryptophan repressor. The theoretical results predict the existence of distinct stable substructures in the protein chain for the monomer and the dimer. The predictions were compared with experimental data on structure and folding of the repressor and its proteolytic fragments and show excellent agreement for the dimeric form of the protein. The results suggest that the monomer, the structure of which is currently unknown, is likely to have a structure different from the one it has within the context of the highly intertwined dimer. Application of this method to the repressor monomer represents an extension of the computations into the realm of evaluating hypothetical structures such as those produced by threading.

Hierarchy of the interaction energy distribution in the spatial structure of globular proteins and the problem of domain definition

An algorithm for determining of protein domain structure is proposed. Domain structures resulted from the algorithm application have been obtained and compared with available data. The method is based on entirely physical model of van der Waals interactions that reflects as illustrated in this work the distribution of electron density. Various levels of hierarchy in the protein spatial structure are discerned by analysis of the energy interaction between structural units of different scales. Thus the level of energy hierarchy plays role of sole parameter, and the method obviates the use of complicated geometrical criteria with numerous fitting parameters. The algorithm readily and accurately locates domains formed by continuous segments of the protein chain as well as those comprising non-sequential segments, sets no limit to the number of segments in a domain. We have analyzed 309 protein structures. Among 277 structures for which our results could be compared with the domain definitions made in other works, 243 showed complete or partial coincidence, and only in 34 cases the domain structures proved substantially different. The domains delineated with our approach may coincide with reference definition at different levels of the globule hierarchy. Along with defining the domain structure, our approach allows one to consider the protein spatial structure in terms of the spatial distribution of the interaction energy in order to establish the correspondence between the hierarchy of energy distribution and the hierarchy of structural elements.

Independent nucleation and heterogeneous assembly of structure during folding of equine lysozyme

The refolding of equine lysozyme from guanidinium chloride has been studied using hydrogen exchange pulse labelling in conjunction with NMR spectroscopy and stopped flow optical methods. The stopped flow optical experiments indicate that extensive hydrophobic collapse occurs rapidly after the initiation of refolding. Pulse labelling experiments monitoring nearly 50 sites within the protein have enabled the subsequent formation of native-like structure to be followed in considerable detail. They reveal that an intermediate having persistent structure within three of the four helices of the alpha-domain of the protein is formed for the whole population of molecules within 4 ms. Subsequent to this event, however, the hydrogen exchange protection kinetics are complex and highly heterogeneous. Analysis of the results by fitting to stretched exponential functions shows that a series of other intermediates is formed as a consequence of the stepwise assembly of independently nucleated local regions of structure. In some molecules the next step in folding involves the stabilisation of the remaining helix in the alpha-domain, whilst in others persistent structure begins to form in the beta-domain. The formation of native-like structure throughout the beta-domain is itself heterogeneous, involving at least three kinetically distinguishable steps. Residues in loop regions throughout the protein attain persistent structure more slowly than regions of secondary structure. There is in addition evidence for locally misfolded regions of structure that reorganise on much longer timescales. The results reveal that the native state of the protein is generated by the heterogeneous assembly of a series of locally cooperative regions of structure. This observation has many features in common with the findings of recent theoretical simulations of protein folding.

Exploring the folding funnel of a polypeptide chain by biophysical studies on protein fragments

We are examining possible roles of native and non-native interactions in early events in protein folding by a systematic analysis of the structures of fragments of proteins whose folding pathways are well characterised. Seven fragments of the 110-residue protein barnase, corresponding to the progressive elongation from its N terminus, have been characterised by a battery of biophysical and spectroscopic methods. Barnase is a multi-modular protein that folds via an intermediate in which the C-terminal region of its major alpha-helix (alpha-helix1, residues Thr6-His18) is substantially formed as is also its anti-parallel beta-sheet, centred around a beta-hairpin (residues Ser92-Leu95). Fragments up to, and including, residues 1-95 (fragment B95), appeared to be mainly disordered, although a small amount of helical secondary structure in each was inferred from far-UV CD experiments, and fluorescence studies indicated some native-like tertiary interactions in B95. The largest fragment (residues 1-105, B105) is compactly folded. The secondary structure in alpha-helix1 in the seven fragments was found by NMR to increase with increasing chain length faster than the build-up of tertiary interactions, indicating that alpha-helix1 is being stabilised by non-native interactions. This behaviour contrasts with that in fragments of the 64-residue chymotrypsin inhibitor 2 (CI2), in which tertiary and secondary structures build up in parallel with increasing length. CI2 consists of a single module of structure that folds without a detectable intermediate. The largest fragment of barnase, B105, has interactions that resemble its folding intermediate, whereas one of the largest fragments of CI2 (residues 1-60) resembles the folding transition state. The folding pathways of both proteins are consistent with a scheme in which there are low levels of native-like secondary structure in the denatured state that become stabilised by long-range interactions as folding proceeds. Neither protein forms a stable fold when lacking the last ten residues at the C terminus. Since at least 20 amino acid residues are bound to the ribosome during protein biosynthesis, these small proteins do not fold until they have left the ribosome, and so the studies of the folding of such proteins in vitro may be relevant to their folding in vivo, especially as the molecular chaperone GroEL binds only weakly to denatured CI2 and does not discernibly alter the folding mechanism of barnase.

Protein structure prediction and design

Proteins have a unique native conformation, which can be proven in many instances to be determined by the amino acid sequence alone. The folding problem, that is the understanding of how the amino acid sequence directs folding, is still unsolved, despite more than 30 years of effort. However, many new methods have appeared in the past few years. This chapter describes the different principles underlying them and tries to give an overview of their successes and pitfalls.

Peptide models of local and long-range interactions in the molten globule state of human alpha-lactalbumin

alpha-Lactalbumin, a small calcium-binding protein, forms an equilibrium molten globule state under a variety of conditions. A set of four peptides designed to probe the role of local interactions and the role of potential long-range interactions in stabilizing the molten globule of alpha-lactalbumin has been prepared. The first peptide consists of residues 20 through 36 of human alpha-lactalbumin and includes the entire B-helix. This peptide is unstructured in solution as judged by CD. The second peptide is derived from residues 101 through 120 and contains both the D and 310 helices. When this peptide is crosslinked via the native 28 to 111 disulfide to the B-helix peptide, a dramatic increase in helicity is observed. The crosslinked peptide is monomeric, as judged by analytical ultracentrifugation. The peptide binds 1-anilinonaphthalene-8-sulphonate (ANS) and the fluorescence emission maximum of the construct is consistent with partial solvent exposure of the tryptophan residues. The peptide corresponding to residues 101 to 120 adopts significant non-random structure in aqueous solution at low pH. Two hydrophobic clusters, one involving residues 101 through 104 and the other residues 115 through 119 have been identified and characterized by NMR. The hydrophobic cluster formed by residues 101 through 104 is still present in a smaller peptide containing only residues 101 to 111 of alpha-lactalbumin. The cluster also persists in 6 M urea. A non-native, pH-dependent interaction between the Y103 and H107 side-chains that was previously identified in the acid-denatured molten globule state was examined. This interaction was found to be more prevalent at low pH and may therefore be an example of a local interaction that stabilizes preferentially the acid-induced molten globule state.

Protein folding via binding and vice versa

The terms intermolecular and intramolecular recognition are often used when referring to binding and folding, highlighting the common ground between the two processes. Most studies, however, are aimed at either one process or the other. Here, we show how knowledge from binding can aid in understanding folding and vice versa.

Non-homology knowledge-based prediction of the papain prosegment folding pattern: a description of plausible folding and activation mechanisms

BACKGROUND

A detailed knowledge of three-dimensional conformations is necessary in order to understand the close relationship between protein structure and function. Among current methodologies, homology modeling is an important tool for obtaining reliable geometries and it provides a direct alternative to X-ray or NMR techniques. In contrast, predictive methods with no three-dimensional template (non-homology) still require further validation and systematization.

RESULTS

Here, we present a non-homology knowledge-based strategy for the structural prediction of the proregion of a cysteine proteinase zymogen. This method analyzes individual sequences and multiple alignments of homologous sequences, making use of different published algorithms and incorporating all available structure-related information to obtain improved predictions. Our strategy yielded acceptable secondary structure and general three-dimensional assignments when compared with crystallographic data from homologous proteins.

CONCLUSIONS

We discuss our successes and failures as a contribution to non-homology prediction development. In addition, based on the information analyzed and generated in this work, we propose plausible folding and activation mechanisms for thiol-proteinase precursors that attempt to shed light on the molecular basis of prosegment functions.

An entropy criterion to detect minimally frustrated intermediates in native proteins

The analysis of the information flow in a feed-forward neural network suggests that the output of the network can be used to compute a structural entropy for the sequence-to-secondary structure mapping. On this basis, we formulate a minimum entropy criterion for the identification of minimally frustrated traits with helical conformation that correspond to initiation sites of protein folding. The entropy of protein segments can be viewed as a nucleation propensity that is useful to characterize putative regions where folding is likely to be initiated with the formation of stretches of alpha-helices under the predominant influence of local interactions. Our procedure is successfully tested in the search for initiation sites of protein folding for which independent experimental and computational evidence exists. Our results lend support to the view that folding is a hierarchical event in which, in harmony with the minimal frustration principle, the final conformation preserves structural modules formed in the early stages of the process.

A graph-theoretic algorithm for comparative modeling of protein structure

The interconnected nature of interactions in protein structures appears to be the major hurdle in preventing the construction of accurate comparative models. We present an algorithm that uses graph theory to handle this problem. Each possible conformation of a residue in an amino acid sequence is represented using the notion of a node in a graph. Each node is given a weight based on the degree of the interaction between its side-chain atoms and the local main-chain atoms. Edges are then drawn between pairs of residue conformations/nodes that are consistent with each other (i.e. clash-free and satisfying geometrical constraints). The edges are weighted based on the interactions between the atoms of the two nodes. Once the entire graph is constructed, all the maximal sets of completely connected nodes (cliques) are found using a clique-finding algorithm. The cliques with the best weights represent the optimal combinations of the various main-chain and side-chain possibilities, taking the respective environments into account. The algorithm is used in a comparative modeling scenario to build side-chains, regions of main chain, and mix and match between different homologs in a context-sensitive manner. The predictive power of this method is assessed by applying it to cases where the experimental structure is not known in advance.

Characterisation of urea-denatured states of an immunoglobulin superfamily domain by heteronuclear NMR

The structural and dynamic properties of an immunoglobulin superfamily domain (IgSF), Ig 18', have been characterised by NMR at 285 K, in the presence of 4.2 M and 6.0 M urea, respectively. Analysis of chemical shift deviations, 3JHNHalpha coupling constants, sequential NOE pattern, and 15N relaxation data reveals that although the two urea-denatured states are highly disordered, some local turn-like residual structures do exist. Moreover, some distinct differences between the properties of the two denatured states are observed. In 4.2 M urea-denatured Ig 18', regions 80-83 and 86-92 adopt turn-like conformations, furthermore, region 84-93 is involved in slow exchange processes that occur on a micro- to millisecond time-scale. In the 6.0 M urea-denatured state, these turn-like conformations are less occupied, and chemical exchange processes in region 84-93 are largely reduced. In contrast, region 32-36 has persistent turn-like structures in both urea-denatured states. Some correlation between the spectral density function at 0 frequency, Jeff(0), for the urea-denatured states and the secondary structure elements of the folded state have been observed. Except for the terminal regions, residues corresponding to beta-strands have higher Jeff(0) values compared to residues corresponding to loops. The characterisation and comparison of the two urea-denatured states highlight residues that possess properties that may be crucial for the initiation of folding of this domain.

Molecular dynamics simulations of hydrophobic collapse of ubiquitin

Nine nonnative conformations of ubiquitin, generated during two different thermal denaturation trajectories, were simulated under nearly native conditions (62 degrees C). The simulations included all protein and solvent atoms explicitly, and simulation times ranged from 1-2.4 ns. The starting structures had alpha-carbon root-mean-square deviations (RMSDs) from the crystal structure of 4-12 A and radii of gyration as high as 1.3 times that of the native state. In all but one case, the protein collapsed when the temperature was lowered and sampled conformations as compact as those reached in a control simulation beginning from the crystal structure. In contrast, the protein did not collapse when simulated in a 60% methanol:water mixture. The behavior of the protein depended on the starting structure: during simulation of the most native-like starting structures (<5 A RMSD to the crystal structure) the RMSD decreased, the number of native hydrogen bonds increased, and the secondary and tertiary structure increased. Intermediate starting structures (5-10 A RMSD) collapsed to the radius of gyration of the control simulation, hydrophobic residues were preferentially buried, and the protein acquired some native contacts. However, the protein did not refold. The least native starting structures (10-12 A RMSD) did not collapse as completely as the more native-like structures; instead, they experienced large fluctuations in radius of gyration and went through cycles of expansion and collapse, with improved burial of hydrophobic residues in successive collapsed states.

Homology modeling with low sequence identity

The field of protein structure prediction is evolving rapidly and in the last few years a number of new methods have been developed and evaluated. However, comparative modeling, or modeling by homology, is still the method of choice when the unknown protein shares any significant sequence similarity with a protein of known structure. The accuracy of the method is highly dependent on the degree of similarity between the target protein and that used as a template. Nevertheless, careful consideration of all the steps performed in the modeling procedure allows useful information to be obtained also from a model based on very low sequence identity.

An all-atom distance-dependent conditional probability discriminatory function for protein structure prediction

We present a formalism to compute the probability of an amino acid sequence conformation being native-like, given a set of pairwise atom-atom distances. The formalism is used to derive three discriminatory functions with different types of representations for the atom-atom contacts observed in a database of protein structures. These functions include two virtual atom representations and one all-heavy atom representation. When applied to six different decoy sets containing a range of correct and incorrect conformations of amino acid sequences, the all-atom distance-dependent discriminatory function is able to identify correct from incorrect more often than the discriminatory functions using approximate representations. We illustrate the importance of using a detailed atomic description for obtaining the most accurate discrimination, and the necessity for testing discriminatory functions against a wide variety of decoys. The discriminatory function is also shown to be capable of capturing the fine details of atom-atom preferences. These results suggest that the all-atom distance-dependent discriminatory function will be useful for protein structure prediction and model refinement.

Pathways for protein folding: is a new view needed?

Theoretical studies using simplified models of proteins have shed light on the general heteropolymeric aspects of the folding problem. Recent work has emphasized the statistical aspects of folding pathways. In particular, progress has been made in characterizing the ensemble of transition state conformations and elucidating the role of intermediates. These advances suggest a reconciliation between the new ensemble approaches and the classical view of a folding pathway.

Molecular dynamics simulation of the unfolding of barnase: characterization of the major intermediate

The folding/unfolding pathway of barnase has been studied extensively using the protein engineering method, which has provided indirect structural information for the transition state and the major folding intermediate. To further characterize the structural properties of the intermediate, we have simulated the thermal denaturation of barnase beginning from the average NMR structure. Our results indicate that there are at least two intermediates on the unfolding pathway. The three hydrophobic cores are partially formed in the major intermediate (I1), with core1 and core3 being slightly stronger than core2. Helix alpha 1 is substantially formed, with the center being stronger than the termini. The first turn of alpha 2 is lost and alpha 3 is unfolded. The center of the beta-sheet is substantially formed, but the edges are disrupted. These structural characteristics are in good qualitative agreement with the experimental data. For semi-quantitative comparison with experimental data, the extent of native structure of individual residues is characterized by a structure index, S, that reflects both secondary and tertiary structure. There is good agreement between S and the experimentally measured phi values, which are based on energetics, except for three residues. These residues are polar and non-conservative mutations were made to obtain phi values, which can complicate structural interpretations. These residues make strong side-chain interactions in I1, but the backbone structure is disrupted, leading to low S values. Thus, this discordance highlights possible limitations in both the phi value and S value analyses: strong polar interactions in the intermediate may give rise to high phi values that are not reflective of structure per se; however, due to sampling limitations, any one simulation is not expected to capture all of the features of the true conformational ensemble. In any case, these simulations provide an experimentally testable, atomic-level structural model for the major folding intermediate of barnase, as well as the detailed pathway from the native to the intermediate state.

The nucleation-collapse mechanism in protein folding: evidence for the non-uniqueness of the folding nucleus

BACKGROUND

Recent experimental and theoretical studies have shown that several small proteins reach the native state by a nucleation-collapse mechanism. Studies based on lattice models have been used to suggest that the critical nucleus is specific, leading to the notion that the transition state may be unique. On the other hand, results of studies using off-lattice models show that the critical nuclei should be viewed as fluctuating mobile structures, thus implying non-unique transition states.

RESULTS

The microscopic underpinnings of the nucleation-collapse mechanism in protein folding are probed using minimal off-lattice models and Langevin dynamics. We consider a 46-mer continuum model which has a native beta-barrel-like structure. The fast-folding trajectories reach the native state by a nucleation-collapse process. An algorithm based on the self-organized neural nets is used to identify the critical nuclei for a large number of rapidly folding trajectories. This method, which reduces the determination of the critical nucleus to one of 'pattern recognition', unambiguously shows that the folding nucleus is not unique. The only common characteristics of the mobile critical nuclei are that they are small (containing on average 15-22 residues) and are largely composed of residues near the loop regions of the molecule. The structures of the transition states, corresponding to the critical nuclei, show the existence of spatially localized ordered regions that are largely made up of residues that are close to each other. These structures are stabilized by a few long-range contacts. The structures in the ensemble of transition states exhibit a rather diverse degree of similarity to the native conformation.

CONCLUSIONS

The multiplicity of delocalized nucleation regions can explain the two-state folding by a nucleation-collapse mechanism for small single-domain proteins (such as chymotrypsin inhibitor 2) and their mutants. Because there are many distinct critical nuclei, we predict that the folding kinetics of fast-folding proteins will not be drastically changed even if some of the residues in a 'typical' nucleus are altered.

Characterization of residual structure in the thermally denatured state of barnase by simulation and experiment: description of the folding pathway

Residual structure in the denatured state of a protein may contain clues about the early events in folding. We have simulated by molecular dynamics the denatured state of barnase, which has been studied by NMR spectroscopy. An ensemble of 10(4) structures was generated after 2 ns of unfolding and following for a further 2 ns. The ensemble was heterogeneous, but there was nonrandom, residual structure with persistent interactions. Helical structure in the C-terminal portion of helix alpha1 (residues 13-17) and in helix alpha2 as well as a turn and nonnative hydrophobic clustering between beta3 and beta4 were observed, consistent with NMR data. In addition, there were tertiary contacts between residues in alpha1 and the C-terminal portion of the beta-sheet. The simulated structures allow the rudimentary NMR data to be fleshed out. The consistency between simulation and experiment inspires confidence in the methods. A description of the folding pathway of barnase from the denatured to the native state can be constructed by combining the simulation with experimental data from phi value analysis and NMR.

Hydrophobic folding units at protein-protein interfaces: implications to protein folding and to protein-protein association

A hydrophobic folding unit cutting algorithm, originally developed for dissecting single-chain proteins, has been applied to a dataset of dissimilar two-chain protein-protein interfaces. Rather than consider each individual chain separately, the two-chain complex has been treated as a single chain. The two-chain parsing results presented in this work show hydrophobicity to be a critical attribute of two-state versus three-state protein-protein complexes. The hydrophobic folding units at the interfaces of two-state complexes suggest that the cooperative nature of the two-chain protein folding is the outcome of the hydrophobic effect, similar to its being the driving force in a single-chain folding. In analogy to the protein-folding process, the two-chain, two-state model complex may correspond to the formation of compact, hydrophobic nuclei. On the other hand, the three-state model complex involves binding of already folded monomers, similar to the association of the hydrophobic folding units within a single chain. The similarity between folding entities in protein cores and in two-state protein-protein interfaces, despite the absence of some chain connectivities in the latter, indicates that chain linkage does not necessarily affect the native conformation. This further substantiates the notion that tertiary, non-local interactions play a critical role in protein folding. These compact, hydrophobic, two-chain folding units, derived from structurally dissimilar protein-protein interfaces, provide a rich set of data useful in investigations of the role played by chain connectivity and by tertiary interactions in studies of binding and of folding. Since they are composed of non-contiguous pieces of protein backbones, they may also aid in defining folding nuclei.

Protein folding simulations with genetic algorithms and a detailed molecular description

We have explored the application of genetic algorithms (GA) to the determination of protein structure from sequence, using a full atom representation. A free energy function with point charge electrostatics and an area based solvation model is used. The method is found to be superior to previously investigated Monte Carlo algorithms. For selected fragments, up to 14 residues long, the lowest free energy structures produced by the GA are similar in conformation to the corresponding experimental structures in most cases. There are three main conclusions from these results. First, the genetic algorithm is an effective method for searching amongst the compact conformations of a polypeptide chain. Second, the free energy function is generally able to select native-like conformations. However, some deficiencies are identified, and further development is proposed. Third, the selection of native-like conformations for some protein fragments establishes that in these cases the conformation observed in the full protein structure is largely context independent. The implications for the nature of protein folding pathways are discussed.

Structural characterisation and comparison of the native and A-states of equine lysozyme

Native state 1H NMR resonance assignments for 125 of the 129 residues of equine lysozyme have enabled measurement of the hydrogen exchange kinetics for over 60 backbone amide and three tryptophan indole hydrogen atoms in the native state. Native holo equine lysozyme hydrogen exchange protection factors are as large as 10(6), the most protected residues being located in elements of secondary structure. High exchange protection in the domain interface correlates with the binding of Ca2+ in this region. Equine lysozyme differs from most non-Ca2+ binding lysozymes in forming a highly populated partially folded state at low pH. The protein in this A-state at pH 2.0 has been found to bind 1-anilino-naphthalene-8-sulphonate with the enhancement of fluorescent intensity and blue shift in the spectral maximum characteristic of molten globules. NMR spectra indicate that the A-state is globally much less ordered than native equine lysozyme but does not contain significant regions of random coil structure. The amides most protected against hydrogen exchange in the A-state (protection factors up to 10(2) at 5 degrees C) correspond to residues of three of the four alpha-helices of the native state; the side-chains of these residues form a hydrophobic cluster that includes five aromatic residues. Circular dichroism and tryptophan fluorescence indicate that these residues are substantially more constrained than similar residues in "classical" molten globules. Taken together, the data suggest a model for the A-state of equine lysozyme in which a more ordered core is surrounded by a less ordered but still compact polypeptide chain.

The tryptophan/histidine interaction in alpha-helices

Contacts between aromatic and charged residues are often found in proteins. Mutational studies have shown that a tryptophan/charged histidine pair can stabilise a protein by more than 1 kcal mol(-1). We have used circular dichroism and nuclear magnetic resonance to study the helical content of several peptides in which a tryptophan/histidine pair was placed at i, i + 3 or i, i + 4 in either the N to C or the C to N orientation. Our data indicate that the WH i, i + 4 geometry is the most stabilising one (when the histidine is protonated) and gives rise to the highest helical content. Little preference is observed among the three other orientations. The energy of the WH+ i, i + 4 interaction (calculated with AGADIR and SCINT) is about 1 kcal mol(-1). A statistical analysis of the occurrence of tryptophan/histidine pairs in alpha-helices of natural proteins reveals that, although the WH i, i + 4 pairs are not more abundant than the others, in most of the WH i, i + 4 pairs the two side-chains are in contact, but not in the other three orientations. These results suggest that the conformational stability of proteins could be increased by means of solvent-exposed intrahelical i, i + 4 tryptophan-histidine bridges and that these bridges could be useful to tailor the stability of helical peptides at physiological pH.

Theoretical studies of protein-folding thermodynamics and kinetics

Recently, protein-folding models have advanced to the point where folding simulations of protein-like chains of reasonable length (up to 125 amino acids) are feasible, and the major physical features of folding proteins, such as cooperativity in thermodynamics and nucleation mechanisms in kinetics, can be reproduced. This has allowed deep insight into the physical mechanism of folding, including the solution of the so-called 'Levinthal paradox'.

Hydrophobic folding units derived from dissimilar monomer structures and their interactions

We have designed an automated procedure to cut a protein into compact hydrophobic folding units. The hydrophobic units are large enough to contain tertiary non-local interactions, reflecting potential nucleation sites during protein folding. The quality of a hydrophobic folding unit is evaluated by four criteria. The first two correspond to visual characterization of a structural domain, namely, compactness and extent of isolation. We use the definition of Zehfus and Rose (Zehfus MH, Rose GD, 1986, Biochemistry 25:35-340) to calculate the compactness of a cut protein unit. The isolation of a unit is based on the solvent accessible surface area (ASA) originally buried in the interior and exposed to the solvent after cutting. The third quantity is the hydrophobicity, equivalent to the fraction of the buried non-polar ASA with respect to the total non-polar ASA. The last criterion in the evaluation of a folding unit is the number of segments it includes. To conform with the rationale of obtaining hydrophobic units, which may relate to early folding events, the hydrophobic interactions are implicitly and explicitly applied in their generation and assessment. We follow Holm and Sander (Holm L, Sander C, 1994, Proteins 19:256-268) to reduce the multiple cutting-point problem to a one-dimensional search for all reasonable trial cuts. However, as here we focus on the hydrophobic cores, the contact matrix used to obtain the first non-trivial eigenvector contains only hydrophobic contracts, rather than all, hydrophobic and hydrophilic, interactions. This dataset of hydrophobic folding units, derived from structurally dissimilar single chain monomers, is particularly useful for investigations of the mechanism of protein folding. For cases where there are kinetic data, the one or more hydrophobic folding units generated for a protein correlate with the two or with the three-state folding process observed. We carry out extensive amino acid sequence order independent structural comparisons to generate a structurally non-redundant set of hydrophobic folding units for fold recognition and for statistical purposes.

Residual helical and turn structure in the denatured state of staphylococcal nuclease: analysis of peptide fragments

BACKGROUND

Previous NMR studies of the denatured state of staphylococcal nuclease identified three significantly populated native-like secondary structures: the second alpha-helix, alpha 2 (residues 98-106), estimated to be present 30% of the time, and two highly populated beta-turns, a type I turn (residues 83-86) and a type I' turn (residues 94-97). In the absence of detectable beta-structure or long-range interactions in this low-density denatured state, these three secondary structures appeared to be stabilized exclusively by local interactions.

RESULTS

To quantitate the intrinsic stability of these secondary structures, three synthetic peptides corresponding in sequence to these chain segments, plus 2-4 flanking residues, have been analyzed by NMR and CD spectroscopy. Neither of the turn peptides showed significant evidence of residual structure. The data for the alpha 2 peptide suggest that this alpha-helix remains approximately 30% helical when separated from the rest of the protein. However, the type I' turn and the Schellman motif, at the amino and carboxyl termini, respectively, observed in both the native and the denatured state, do not form in this peptide. Instead, the helix appears to propagate to the ends of the peptide, overriding both of these helix-stop signals.

CONCLUSIONS

The presence of a native-like secondary structure in a denatured protein does not necessarily imply that it has a high intrinsic stability. beta-turns in particular can be stabilized by long-range interactions in the absence of stable beta-strands. In addition, so-called helix-stop signals, such as the Schellman motif, may not contribute actively to helix stability. As for turns, these local interactions at the ends of helices may be passive structures that form in response to longer-range interactions.

Properties of the protein matrix revealed by the free energy of cavity formation

BACKGROUND

The classical picture of the hydrophobic stabilization of proteins invokes a resemblance between the protein interior and nonpolar solvents, but the extent to which this is the case has often been questioned. The protein interior is believed to be at least as tightly packed as organic crystals, and was shown to have very low compressibility. There is also evidence that these properties are not uniform throughout the protein, and conflicting views exist on the nature of sidechain packing and on its influence on the properties of the protein.

RESULTS

In order to probe the physical properties of the protein, the free energy associated with the formation of empty cavities has been evaluated for two proteins: barnase and T4 lysozyme. To this end, the likelihood of encountering such cavities was computed from room temperature molecular dynamics trajectories of these proteins in water. The free energy was evaluated in each protein taken as a whole and in submolecular regions. The computed free energies yielded information on the manner in which empty space is distributed in the system, while the latter undergoes thermal motion, a property hitherto not analyzed in heterogeneous media such as proteins. Our results showed that the free energy of cavity formation is higher in proteins than in both water and hexane, providing direct evidence that the native protein medium differs in fundamental ways from the two liquids. Furthermore, although the packing density was found to be higher in nonpolar regions of the protein than in polar ones, the free energy cost of forming atomic size cavities is significantly lower in nonpolar regions, implying that these regions contain larger chunks of empty space, thereby increasing the likelihood of containing atomic size packing defects. These larger empty spaces occur preferentially where buried hydrophobic sidechains belonging to secondary structures meet one another. These particular locations also appear to be more compressible than other parts of the core or surface of the protein.

CONCLUSIONS

The cavity free energy calculations described here provide a much more detailed physical picture of the protein matrix than volume and packing calculations. According to this picture, the packing of hydrophobic sidechains is tight in the interior of the protein, but far from uniform. In particular, the packing is tighter in regions where the backbone forms less regular hydrogen-bonding interactions than at interfaces between secondary structure elements, where such interactions are fully developed. This may have important implications on the role of sidechain packing in protein folding and stability.

Evolutionary algorithms in computer-aided molecular design

In recent years, search and optimisation algorithms inspired by evolutionary processes have been applied with marked success to a wide variety of problems in diverse fields of study. In this review, we survey the growing application of these 'evolutionary algorithms' in one such area: computer-aided molecular design. In the course of the review, we seek to summarise the work to date and to indicate where evolutionary algorithms have met with success and where they have not fared so well. In addition to this, we also attempt to discern some future trends in both the basic research concerning these algorithms and their application to the elucidation, design and modelling of chemical and biochemical structures.

Protein folding for realists: a timeless phenomenon

Future research on protein folding must confront two serious dilemmas. (1) It may never be possible to observe at high resolution the very important structures that form in the first few milliseconds of the refolding reaction. (2) The energy functions used to predict structure from sequence will always be approximations of the true energy function. One strategy to resolve both dilemmas is to view protein folding from a different perspective, one that no longer emphasizes time and unique trajectories through conformation space. Instead, free energy replaces time as the reaction coordinate, and ensembles of equilibrium states of partially folded proteins are analyzed in place of trajectories of one protein chain through conformation space, either in vitro or in silico. Initial characterization of the folding of staphylococcal nuclease within this alternative conceptual framework has led to an equilibrium folding pathway with several surprising features. In addition to the finding of two bundles of four hydrophobic segments containing both native and non-native interactions, a gradient in relative stability of different substructures has been identified, with the most stable interactions located toward the amino terminus and the least stable toward the carboxy terminus. Hydrophobic bundles with up-down topology and stability gradients may be two examples of numerous tactics used by proteins to facilitate rapid folding and minimize aggregation. As NMR methods for structural analysis of partially folded proteins are refined, higher resolution descriptions of the structure and dynamics of the polypeptide chain outside the native state may provide many insights into the processes and energetics underlying the self-assembly of folded structure.