Consistency in structural energetics of protein folding and peptide recognition.

We report a new free energy decomposition that includes structure-derived atomic contact energies for the desolvation component, and show that it applies equally well to the analysis of single-domain protein folding and to the binding of flexible peptides to proteins. Specifically, we selected the 17 single-domain proteins for which the three-dimensional structures and thermodynamic unfolding free energies are available. By calculating all terms except the backbone conformational entropy change and comparing the result to the experimentally measured free energy, we estimated that the mean entropy gain by the backbone chain upon unfolding (delta Sbb) is 5.3 cal/K per mole of residue, and that the average backbone entropy for glycine is 6.7 cal/K. Both numbers are in close agreement with recent estimates made by entirely different methods, suggesting a promising degree of consistency between data obtained from disparate sources. In addition, a quantitative analysis of the folding free energy indicates that the unfavorable backbone entropy for each of the proteins is balanced predominantly by favorable backbone interactions. Finally, because the binding of flexible peptides to receptors is physically similar to folding, the free energy function should, in principle, be equally applicable to flexible docking. By combining atomic contact energies, electrostatics, and sequence-dependent backbone entropy, we calculated a priori the free energy changes associated with the binding of four different peptides to HLA-A2, 1 MHC molecule and found agreement with experiment to within 10% without parameter adjustment.     

A new computational model for protein folding based on atomic solvation.

A new model for calculating the solvation energy of proteins is developed and tested for its ability to identify the native conformation as the global energy minimum among a group of thousands of computationally generated compact non-native conformations for a series of globular proteins. In the model (called the WZS model), solvation preferences for a set of 17 chemically derived molecular fragments of the 20 amino acids are learned by a training algorithm based on maximizing the solvation energy difference between native and non-native conformations for a training set of proteins. The performance of the WZS model confirms the success of this learning approach; the WZS model misrecognizes (as more stable than native) only 7 of 8,200 non-native structures. Possible applications of this model to the prediction of protein structure from sequence are discussed.     

毛细管电泳及其在蛋白质折叠研究中的应用

简要介绍了毛细管电泳的常用分离模式及其原理,并对毛细管电泳在蛋白质化学领域中的新应用——研究蛋白质折叠和发展前景作了评述。     

Protein unfolding rates correlate as strongly as folding rates with native structure

Although the folding rates of proteins have been studied extensively, both experimentally and theoretically, and many native state topological parameters have been proposed to correlate with or predict these rates, unfolding rates have received much less attention. Moreover, unfolding rates have generally been thought either to not relate to native topology in the same manner as folding rates, perhaps depending on different topological parameters, or to be more difficult to predict. Using a dataset of 108 proteins including two-state and multistate folders, we find that both unfolding and folding rates correlate strongly, and comparably well, with well-established measures of native topology, the absolute contact order and the long range order, with correlation coefficient values of 0.75 or higher. In addition, compared to folding rates, the absolute values of unfolding rates vary more strongly with native topology, have a larger range of values, and correlate better with thermodynamic stability. Similar trends are observed for subsets of different protein structural classes. Taken together, these results suggest that choosing a scaffold for protein engineering may require a compromise between a simple topology that will fold sufficiently quickly but also unfold quickly, and a complex topology that will unfold slowly and hence have kinetic stability, but fold slowly. These observations, together with the established role of kinetic stability in determining resistance to thermal and chemical denaturation as well as proteases, have important implications for understanding fundamental aspects of protein unfolding and folding and for protein engineering and design.     

Direct observation of microscopic reversibility in single-molecule protein folding

Both folded and unfolded conformations should be observed for a protein at its melting temperature (T(m)), where DeltaG between these states is zero. In an all-atom molecular dynamics simulation of chymotrypsin inhibitor 2 (CI2) at its experimental T(m), the protein rapidly loses its low-temperature native structure; it then unfolds before refolding to a stable, native-like conformation. The initial unfolding follows the unfolding pathway described previously for higher-temperature simulations: the hydrophobic core is disrupted, the beta-sheet pulls apart and the alpha-helix unravels. The unfolded state reached under these conditions maintains a kernel of structure in the form of a non-native hydrophobic cluster. Refolding simply reverses this path, the side-chain interactions shift, the helix refolds, and the native packing and hydrogen bonds are recovered. The end result of this refolding is not the initial crystal structure; it contains the proper topology and the majority of the native contacts, but the structure is expanded and the contacts are long. We believe this to be the native state at elevated temperature, and the change in volume and contact lengths is consistent with experimental studies of other native proteins at elevated temperature and the chemical denaturant equivalent of T(m).     

Sequence determinants of protein folding rates: positive correlation between contact energy and contact range indicates selection for fast folding

In comparison with intense investigation of the structural determinants of protein folding rates, the sequence features favoring fast folding have received little attention. Here, we investigate this subject using simple models of protein folding and a statistical analysis of the Protein Data Bank (PDB). The mean-field model by Plotkin and coworkers predicts that the folding rate is accelerated by stronger-than-average interactions at short distance along the sequence. We confirmed this prediction using the Finkelstein model of protein folding, which accounts for realistic features of polymer entropy. We then tested this prediction on the PDB. We found that native interactions are strongest at contact range l = 8. However, since short range contacts tend to be exposed and they are frequently formed in misfolded structures, selection for folding stability tends to make them less attractive, that is, stability and kinetics may have contrasting requirements. Using a recently proposed model, we predicted the relationship between contact range and contact energy based on buriedness and contact frequency. Deviations from this prediction induce a positive correlation between contact range and contact energy, that is, short range contacts are stronger than expected, for 2/3 of the proteins. This correlation increases with the absolute contact order (ACO), as expected if proteins that tend to fold slowly due to large ACO are subject to stronger selection for sequence features favoring fast folding. Our results suggest that the selective pressure for fast folding is detectable only for one third of the proteins in the PDB, in particular those with large contact order.     

Exploring the effects of sparse restraints on protein structure prediction

One of the main barriers to accurate computational protein structure prediction is searching the vast space of protein conformations. Distance restraints or inter‐residue contacts have been used to reduce this search space, easing the discovery of the correct folded state. It has been suggested that about 1 contact for every 12 residues may be sufficient to predict structure at fold level accuracy. Here, we use coarse‐grained structure‐based models in conjunction with molecular dynamics simulations to examine this empirical prediction. We generate sparse contact maps for 15 proteins of varying sequence lengths and topologies and find that given perfect secondary‐structural information, a small fraction of the native contact map (5%‐10%) suffices to fold proteins to their correct native states. We also find that different sparse maps are not equivalent and we make several observations about the type of maps that are successful at such structure prediction. Long range contacts are found to encode more information than shorter range ones, especially for α and αβ‐proteins. However, this distinction reduces for β‐proteins. Choosing contacts that are a consensus from successful maps gives predictive sparse maps as does choosing contacts that are well spread out over the protein structure. Additionally, the folding of proteins can also be used to choose predictive sparse maps. Overall, we conclude that structure‐based models can be used to understand the efficacy of structure‐prediction restraints and could, in future, be tuned to include specific force‐field interactions, secondary structure errors and noise in the sparse maps.     

Exploring the factors determining the dynamics of different protein folds

Normal mode analyses of homologous proteins at the family and superfamily level show that slow dynamics are similar and are preserved through evolution. This study investigates how the slow dynamics of proteins is affected by variation in the protein architecture and fold. For this purpose, we have used computer-generated protein models based on idealized protein structures with varying folds. These are shown to be protein-like in their behavior, and they are used to investigate the influence of architecture and fold on the slow dynamics. We compared the dynamics of models having different folds but similar architecture and found the architecture to be the dominant factor for the slow dynamics.     

Continuous and discontinuous domains: an algorithm for the automatic generation of reliable protein domain definitions.

An algorithm is presented for the fast and accurate definition of protein structural domains from coordinate data without prior knowledge of the number or type of domains. The algorithm explicitly locates domains that comprise one or two continuous segments of protein chain. Domains that include more than two segments are also located. The algorithm was applied to a nonredundant database of 230 protein structures and the results compared to domain definitions obtained from the literature, or by inspection of the coordinates on molecular graphics. For 70% of the proteins, the derived domains agree with the reference definitions, 18% show minor differences and only 12% (28 proteins) show very different definitions. Three screens were applied to identify the derived domains least likely to agree with the subjective definition set. These screens revealed a set of 173 proteins, 97% of which agree well with the subjective definitions. The algorithm represents a practical domain identification tool that can be run routinely on the entire structural database. Adjustment of parameters also allows smaller compact units to be identified in proteins.     

Comparing folding codes for proteins and polymers

Proteins fold to unique compact native structures. Perhaps other polymers could be designed to fold in similar ways. The chemical nature of the monomer “alphabet” determines the “energy matrix” of monomer interactions—which defines the folding code, the relationship between sequence and structure. We study two properties of energy matrices using two-dimensional lattice models: uniqueness, the number of sequences that fold to only one structure, and encodability, the number of folds that are unique lowest-energy structures of certain monomer sequences. For the simplest model folding code, involving binary sequences of H (hydrophobic) and P (polar) monomers, only a small fraction of sequences fold uniquely, and not all structures can be encoded. Adding strong repulsive interactions results in a folding code with more sequences folding uniquely and more designable folds. Some theories suggest that the quality of a folding code depends only on the number of letters in the monomer alphabet, but we find that the energy matrix itself can be at least as important as the size of the alphabet. Certain multi-letter codes, including some with 20 letters, may be less physical or protein-like than codes with smaller numbers of letters because they neglect correlations among inter-residue interactions, treat only maximally compact conformations, or add arbitrary energies to the energy matrix.     

Stability and folding of a mutant ribose-binding protein ofEscherichia coli

A mature mutant ribose-binding protein (RBP) ofEscherichia coli was obtained by site-directed mutagenesis, replacing Thr-3 in the N-domain of wild-type mature RBP (WT-mRBP) with a Trp residue (N-Trp-mRBP). The equilibrium unfolding properties and the refolding kinetics of this protein were monitored by fluorescence and circular dichroism (CD). The stability of N-Trp-mRBP appears to be the same as that of C-Trp-mRBP, another mutant obtained by replacing Phe-187 with a Trp, and lower than that of WT-mRBP. The overall refolding rate of N-Trp-mRBP is much smaller than that of C-Trp-mRBP, which, in turn, is similar to that of WT-mRBP. For the case of WT-mRBP, the rate constant obtained by Tyr fluorescence is identical to the value obtained by CD. But with C-Trp-mRBP, the rate constant from CD is smaller than the value from the Trp fluorescence and this difference in the rate constants is much greater with the N-TrpmRBP.     

Conformational subspace in simulation of early-stage protein folding

A probability calculus was used to simulate the early stages of protein folding in ab initio structure prediction. The probabilities of particular phi and psi angles for each of 20 amino acids as they occur in crystal forms of proteins were used to calculate the amount of information necessary for the occurrence of given phi and psi angles to be predicted. It was found that the amount of information needed to predict phi and psi angles with 5 degrees precision is much higher than the amount of information actually carried by individual amino acids in the polypeptide chain. To handle this problem, a limited conformational space for the preliminary search for optimal polypeptide structure is proposed based on a simplified geometrical model of the polypeptide chain and on the probability calculus. These two models, geometric and probabilistic, based on different sources, yield a common conclusion concerning how a limited conformational space can represent an early stage of polypeptide chain-folding simulation. The ribonuclease molecule was used to test the limited conformational space as a tool for modeling early-stage folding.     

Structure of stable protein folding intermediates by equilibrium phi-analysis: the apoflavodoxin thermal intermediate

Protein intermediates in equilibrium with native states may play important roles in protein dynamics but, in cases, can initiate harmful aggregation events. Investigating equilibrium protein intermediates is thus important for understanding protein behaviour (useful or pernicious) but it is hampered by difficulties in gathering structural information. We show here that the phi-analysis techniques developed to investigate transition states of protein folding can be extended to determine low-resolution three-dimensional structures of protein equilibrium intermediates. The analysis proposed is based solely on equilibrium data and is illustrated by determination of the structure of the apoflavodoxin thermal unfolding intermediate. In this conformation, a large part of the protein remains close to natively folded, but a 40 residue region is clearly unfolded. This structure is fully consistent with the NMR data gathered on an apoflavodoxin mutant designed specifically to stabilise the intermediate. The structure shows that the folded region of the intermediate is much larger than the proton slow-exchange core at 25 degrees C. It also reveals that the unfolded region is made of elements whose packing surface is more polar than average. In addition, it constitutes a useful guide to rationally stabilise the native state relative to the intermediate state, a far from trivial task.     

Transition state contact orders correlate with protein folding rates

We have used molecular dynamics simulations restrained by experimental phi values derived from protein engineering experiments to determine the structures of the transition state ensembles of ten proteins that fold with two-state kinetics. For each of these proteins we then calculated the average contact order in the transition state ensemble and compared it with the corresponding experimental folding rate. The resulting correlation coefficient is similar to that computed for the contact orders of the native structures, supporting the use of native state contact orders for predicting folding rates. The native contacts in the transition state also correlate with those of the native state but are found to be about 30% lower. These results show that, despite the high levels of heterogeneity in the transition state ensemble, the large majority of contributing structures have native-like topologies and that the native state contact order captures this phenomenon.     

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.     

One- and two-body decomposable Poisson-Boltzmann methods for protein design calculations

Successfully modeling electrostatic interactions is one of the key factors required for the computational design of proteins with desired physical, chemical, and biological properties. In this paper, we present formulations of the finite difference Poisson-Boltzmann (FDPB) model that are pairwise decomposable by side chain. These methods use reduced representations of the protein structure based on the backbone and one or two side chains in order to approximate the dielectric environment in and around the protein. For the desolvation of polar side chains, the two-body model has a 0.64 kcal/mol RMSD compared to FDPB calculations performed using the full representation of the protein structure. Screened Coulombic interaction energies between side chains are approximated with an RMSD of 0.13 kcal/mol. The methods presented here are compatible with the computational demands of protein design calculations and produce energies that are very similar to the results of traditional FDPB calculations.     

Role of electrostatic interactions for the stability and folding behavior of cold shock protein

The impacts of three charged‐residue‐involved mutations, E46A, R3E, and R3E/L66E, on the thermostability and folding behavior of the cold shock protein from the themophile Bacillus caldolyticus (Bc‐Csp) were investigated by using a modified Gō‐like model, in which the nonspecific electrostatic interactions of charged residues were taken into account. Our simulation results show that the wild‐type Bc‐Csp and its three mutants are all two‐sate folders, which is consistent with the experimental observations. It is found that these three mutations all lead to a decrease of protein thermodynamical stability, and the effect of R3E mutation is the strongest. The lower stability of these three mutants is due to the increase of the enthalpy of the folded state and the entropy of the unfolded state. Using this model, we also studied the folding kinetics and the folding/unfolding pathway of the wild‐type Bc‐Csp as well as its three mutants and then discussed the effects of electrostatic interactions on the folding kinetics. The results indicate that the substitutions at positions 3 and 46 largely decrease the folding kinetics, whereas the mutation of residue 66 only slightly decreases the folding rate. This result agrees well with the experimental observations. It is also found that these mutations have little effects on the folding transition state and the folding pathway, in which the N‐terminal β sheet folds earlier than the C‐terminal region. We also investigated the detailed unfolding pathway and found that it is really the reverse of the folding pathway, providing the validity of our simulation results. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Interaction potentials for protein folding

We outline a general strategy for determining the effective coarse-grained interactions between the amino acids of a protein from the experimentally derived native-state structures. The method is, in principle, free from any adjustable or empirically determined parameters, and it is tested on simple models and compared with other existing approaches. Proteins 30:244–248, 1998. © 1998 Wiley-Liss, Inc.     

Simulated folding in polypeptides of diversified molecular tacticity: implications for protein folding and de novo design

Stereochemistry could be a powerful variable for conformational tune up of polypeptides for de novo design. It may be also useful probe of possible role of interamide energetics in selection and stabilization of conformation. The homopolypeptides Ac-Xxx30-NHMe, with Xxx = Ala, Val, and Leu, of diversified stereochemical structure are generated by simulated racemization with a modified GROMOS-96 force field. The polypeptides, and other systematic stereochemical variants, are folded by simulated annealing with another modified GROMOS-96 force field under the dielectric constant values 1, 4, and 10. The resultant 15,000 molecular folds of isotactic (poly-L-chiral), syndiotactic (alternating L,D-chiral), and heterotactic (random-L,D-chiral) stereochemical structure, belonging to three polypeptide series, achieved under three different folding conditions, are assessed statistically for structure-to-energy-to-conformation relationship. The results suggest that interamide electrostatics could be a major factor in secondary-structure selection in polypeptides while main-chain stereochemistry could dictate molecular packing and therefore the relative magnitude of hydrogen-bond and Lennard-Jones (LJ) contributions in conformational energy. A method for computational design of heterotactic molecular folds in polypeptide structure has been developed, and the first road map for a chiral tune up of polypeptide structure based on stereochemical engineering has been laid down. Broad implications for protein structure, folding, and de novo design are briefly discussed.     

Sub-microsecond protein folding

We have investigated the structure, equilibria, and folding kinetics of an engineered 35-residue subdomain of the chicken villin headpiece, an ultrafast-folding protein. Substitution of two buried lysine residues by norleucine residues stabilizes the protein by 1 kcal/mol and increases the folding rate sixfold, as measured by nanosecond laser T-jump. The folding rate at 300 K is (0.7 micros)(-1) with little or no temperature dependence, making this protein the first sub-microsecond folder, with a rate only twofold slower than the theoretically predicted speed limit. Using the 70 ns process to obtain the effective diffusion coefficient, the free energy barrier height is estimated from Kramers theory to be less than approximately 1 kcal/mol. X-ray crystallographic determination at 1A resolution shows no significant change in structure compared to the single-norleucine-substituted molecule and suggests that the increased stability is electrostatic in origin. The ultrafast folding rate, very accurate X-ray structure, and small size make this engineered villin subdomain an ideal system for simulation by atomistic molecular dynamics with explicit solvent.