Monte carlo simulations of protein folding. II. Application to protein A,ROP, and crambin

The hierarchy of lattice Monte Carlo models described in the accompanying paper (Kolinski, A., Skolnick, J. Monte Carlo simulations of protein folding. I. Lattice model and interaction scheme. Proteins 18:338–352, 1994) is applied to the simulation of protein folding and the prediction of 3-dimensional structure. Using sequence information alone, three proteins have been successfully folded: the B domain of staphylococcal protein A, a 120 residue, monomeric version of ROP dimer, and crambin. Starting from a random expanded conformation, the model proteins fold along relatively well-defined folding pathways. These involve a collection of early intermediates, which are followed by the final (and rate-determining) transition from compact intermediates closely resembling the molten globule state to the native-like state. The predicted structures are rather unique, with native-like packing of the side chains. The accuracy of the predicted native conformations is better than those obtained in previous folding simulations. The best (but by no means atypical) folds of protein A have a coordinate rms of 2.25 Å from the native Cα trace, and the best coordinate rms from crambin is 3.18 Å. For ROP monomer, the lowest coordinate rms from equivalent Cαs of ROP dimer is 3.65 Å. Thus, for two simple helical proteins and a small α/β protein, the ability to predict protein structure from sequence has been demonstrated. © 1994 John Wiley & Sons, Inc.     

A polar, solvent-exposed residue can be essential for native protein structure

BACKGROUND: A large energy gap between the native state and the non-native folded states is required for folding into a unique three-dimensional structure. The features that define this energy gap are not well understood, but can be addressed using de novo protein design. Previously, alpha(2)D, a dimeric four-helix bundle, was designed and shown to adopt a native-like conformation. The high-resolution solution structure revealed that this protein adopted a bisecting U motif. Glu7, a solvent-exposed residue that adopts many conformations in solution, might be involved in defining the unique three-dimensional structure of alpha(2)D. RESULTS: A variety of hydrophobic and polar residues were substituted for Glu7 and the dynamic and thermodynamic properties of the resulting proteins were characterized by analytical ultracentrifugation, circular dichroism spectroscopy, and nuclear magnetic resonance spectroscopy. The majority of substitutions at this solvent-exposed position had little affect on the ability to fold into a dimeric four-helix bundle. The ability to adopt a unique conformation, however, was profoundly modulated by the residue at this position despite the similar free energies of folding of each variant. CONCLUSIONS: Although Glu7 is not involved directly in stabilizing the native state of alpha(2)D, it is involved indirectly in specifying the observed fold by modulating the energy gap between the native state and the non-native folded states. These results provide experimental support for hypothetical models arising from lattice simulations of protein folding, and underscore the importance of polar interfacial residues in defining the native conformations of proteins.     

Structural characterization by computer experiments of the lipid-free LDL-receptor-binding domain of apolipoprotein E.

The structure and dynamics of the lipid-free LDL-receptor-binding domain of apolipoprotein E (apoE-RBD) has been investigated by Molecular Dynamics Simulations. ApoE-RBD in its monomeric lipid-free form is a singular four-helix bundle made up of four elongated amphipathic helices. Analysis of one 1.5 ns molecular dynamics trajectory of apoE-RBD performed in water indicates that the lipid-free domain adopts a structure that exhibits characteristics found in native proteins: it has very stable helices and presents a compact structure. Yet its interior exhibits a larger number of transient atomic-size cavities relative to that found in other proteins of similar size and its apolar side chains are more mobile. The latter features distinguish the elongated four-helix bundle as a slightly disordered structure, which shows a structural likeness with some de novo designed four-helix bundle proteins and shares with the latter a leucine-rich residue composition. We anticipate that these unique properties compared with other native helix bundles may be related to the postulated ability of apoE-RBD to undergo an opening of its bundle upon interaction with phospholipids. The distribution of empty cavities computed along the trajectory in the interface regions between the different pairs of helices reveals that the tertiary contacts in one of the interfaces are weaker suggesting that this particular interface could be more easily ruptured upon lipid association.     

A method for α-helical integral membrane protein fold prediction

Integral membrane proteins (of the α-helical class) are of central importance in a wide variety of vital cellular functions. Despite considerable effort on methods to predict the location of the helices, little attention has been directed toward developing an automatic method to pack the helices together. In principle, the prediction of membrane proteins should be easier than the prediction of globular proteins: there is only one type of secondary structure and all helices pack with a common alignment across the membrane. This allows all possible structures to be represented on a simple lattice and exhaustively enumerated. Prediction success lies not in generating many possible folds but in recognizing which corresponds to the native. Our evaluation of each fold is based on how well the exposed surface predicted from a multiple sequence alignment fits its allocated position. Just as exposure to solvent in globular proteins can be predicted from sequence variation, so exposure to lipid can be recognized by variable-hydrophobic (variphobic) positions. Application to both bacteriorhodopsin and the eukaryotic rhodopsin/opsin families revealed that the angular size of the lipid-exposed faces must be predicted accurately to allow selection of the correct fold. With the inherent uncertainties in helix prediction and parameter choice, this accuracy could not be guaranteed but the correct fold was typically found in the top six candidates. Our method provides the first completely automatic method that can proceed from a scan of the protein sequence databanks to a predicted three-dimensional structure with no intervention required from the investigator. Within the limited domain of the seven helix bundle proteins, a good chance can be given of selecting the correct structure. However, the limited number of sequences available with a corresponding known structure makes further characterization of the method difficult. © 1994 John Wiley & Sons, Inc.     

Structural class prediction: an application of residue distribution along the sequence

Deciphering the native conformation of proteins from their amino acid sequences is one of the most challenging problems in molecular biology. Information on the secondary structure of a protein can be helpful in understanding its native folded state. In our earlier work on molecular chaperones, we have analyzed the hydrophobic and charged patches, short-, medium- and long-range contacts and residue distributions along the sequence. In this article, we have made an attempt to predict the structural class of globular and chaperone proteins based on the information obtained from residue distributions. This method predicts the structural class with an accuracy of 93 and 96%, respectively, for the four- and three-state models in a training set of 120 globular proteins, and 90 and 96%, respectively, for a test set of 80 proteins. We have used this information and methodology to predict the structural classes of chaperones. Interestingly most of the chaperone proteins are predicted under alpha/beta or mixed folding type.     

The Roles of Entropy and Kinetics in Structure Prediction

Background

Here we continue our efforts to use methods developed in the folding mechanism community to both better understand and improve structure prediction. Our previous work demonstrated that Rosetta''s coarse-grained potentials may actually impede accurate structure prediction at full-atom resolution. Based on this work we postulated that it may be time to work completely at full-atom resolution but that doing so may require more careful attention to the kinetics of convergence.

Methodology/Principal Findings

To explore the possibility of working entirely at full-atom resolution, we apply enhanced sampling algorithms and the free energy theory developed in the folding mechanism community to full-atom protein structure prediction with the prominent Rosetta package. We find that Rosetta''s full-atom scoring function is indeed able to recognize diverse protein native states and that there is a strong correlation between score and Cα RMSD to the native state. However, we also show that there is a huge entropic barrier to folding under this potential and the kinetics of folding are extremely slow. We then exploit this new understanding to suggest ways to improve structure prediction.

Conclusions/Significance

Based on this work we hypothesize that structure prediction may be improved by taking a more physical approach, i.e. considering the nature of the model thermodynamics and kinetics which result from structure prediction simulations.     

Crystal structure and mutagenic analysis of a bacteriocin immunity protein,Mun-im

Bacteriocin-producing lactic acid bacteria (LAB) possess a self-protection factor, which is generally called an immunity protein. In this study, we determine the crystal structure of an immunity protein, designated Mun-im, which was classified into subgroup B immunity proteins for class IIa bacteriocins. The Mun-im protein takes a left-turning antiparallel four-helix bundle structure with the flexible N- and C-terminal parts. Although the amino acid sequences of the subgroup B immunity proteins are distinguished from those of the subgroup A, the core structure of Mun-im is well-superimposed with that of the subgroup A immunity protein, EntA-im, and the C-terminus of both proteins is flexible. However, the C-terminus of Mun-im is obviously shorter than that of the subgroup A. We found through mutagenic study of Mun-im that the C-terminus and the K86 residue on the helix 4 in the immunity protein molecule are important for expression of the immunity activity on the subgroup B immunity proteins.     

Populating partially unfolded forms by hydrogen exchange-directed protein engineering

The native-state hydrogen exchange of a redesigned apocytochrome b(562) suggests that at least two partially unfolded forms (PUFs) exist for this four-helix bundle protein under native conditions. The more stable PUF has the N-terminal helix unfolded. To verify the conclusion further and obtain more detailed structural information about this PUF, five hydrophobic core residues in the N-terminal helix were mutated to Gly and Asp to destabilize the native state selectively and populate the PUF for structural studies. The secondary structure and the backbone dynamics of this mutant were characterized using multidimensional NMR. Consistent with the prediction, the N-terminal region of the mutant was found to be unfolded while other parts of the proteins remained folded. These results suggest that native-state hydrogen exchange-directed protein engineering can be a useful approach to populating partially unfolded forms for detailed structural studies.     

Easily Searched Protein Folding Potentials

In order to calculate the tertiary structure of a protein from its amino acid sequence, the thermodynamic approach requires a potential function of sequence and conformation that has its global minimum at the native conformation for many different proteins. Here we study the behavior of such functions for the simplest model system that still has the essential features of the protein folding problem, namely two-dimensional square lattice chain configurations involving two residue types. First we demonstrate a method for accurately recovering the given contact potential from only a knowledge of which sequences fold to which structures and what the non-native structures are. Second, we show how to derive from the same information more general potential functions having much better positive correlations between potential function value and conformational deviation from the native. These functions consequently permit faster and more reliable searches for the native conformation, given the native sequence. Furthermore, the method for finding such potentials is easily applied to more realistic protein models.     

Role of evolutionary information in prediction of aromatic-backbone NH interactions in proteins

In this study, an attempt has been made to develop a neural network-based method for predicting segments in proteins containing aromatic-backbone NH (Ar-NH) interactions using multiple sequence alignment. We have analyzed 3121 segments seven residues long containing Ar-NH interactions, extracted from 2298 non-redundant protein structures where no two proteins have more than 25% sequence identity. Two consecutive feed-forward neural networks with a single hidden layer have been trained with standard back-propagation as learning algorithm. The performance of the method improves from 0.12 to 0.15 in terms of Matthews correlation coefficient (MCC) value when evolutionary information (multiple alignment obtained from PSI-BLAST) is used as input instead of a single sequence. The performance of the method further improves from MCC 0.15 to 0.20 when secondary structure information predicted by PSIPRED is incorporated in the prediction. The final network yields an overall prediction accuracy of 70.1% and an MCC of 0.20 when tested by five-fold cross-validation. Overall the performance is 15.2% higher than the random prediction. The method consists of two neural networks: (i) a sequence-to-structure network which predicts the aromatic residues involved in Ar-NH interaction from multiple alignment of protein sequences and (ii) a structure-to structure network where the input consists of the output obtained from the first network and predicted secondary structure. Further, the actual position of the donor residue within the 'potential' predicted fragment has been predicted using a separate sequence-to-structure neural network. Based on the present study, a server Ar_NHPred has been developed which predicts Ar-NH interaction in a given amino acid sequence. The web server Ar_NHPred is available at and (mirror site).     

Use of residual dipolar couplings as restraints in ab initio protein structure prediction

NMR residual dipolar couplings (RDCs), in the form of the projection angles between the respective internuclear bond vectors, are used as structural restraints in the ab initio structure prediction of a test set of six proteins. The restraints are applied using a recently developed SICHO (SIde-CHain-Only) lattice protein model that employs a replica exchange Monte Carlo (MC) algorithm to search conformational space. Using a small number of RDC restraints, the quality of the predicted structures is improved as reflected by lower RMSD/dRMSD (root mean square deviation/distance root mean square deviation) values from the corresponding native structures and by the higher correlation of the most cooperative mode of motion of each predicted structure with that of the native structure. The latter, in particular, has possible implications for the structure-based functional analysis of predicted structures.     

All-atom folding of the three-helix HIV accessory protein with an adaptive parallel tempering method

All-atom protein structure prediction from the amino acid sequence alone remains an important goal of biophysical chemistry. Recent progress in force field development and validation suggests that the PFF01 free-energy force field correctly predicts the native conformation of various helical proteins as the global optimum of its free-energy surface. Reproducible protein structure prediction requires the availability of efficient optimization methods to locate the global minima of such complex potentials. Here we investigate an adapted version of the parallel tempering method as an efficient parallel stochastic optimization method for protein structure prediction. Using this approach we report the reproducible all-atom folding of the three-helix 40 amino acid HIV accessory protein from random conformations to within 2.4 A backbone RMS deviation from the experimental structure with modest computational resources.     

TOUCHSTONE II: a new approach to ab initio protein structure prediction

We have developed a new combined approach for ab initio protein structure prediction. The protein conformation is described as a lattice chain connecting C(alpha) atoms, with attached C(beta) atoms and side-chain centers of mass. The model force field includes various short-range and long-range knowledge-based potentials derived from a statistical analysis of the regularities of protein structures. The combination of these energy terms is optimized through the maximization of correlation for 30 x 60,000 decoys between the root mean square deviation (RMSD) to native and energies, as well as the energy gap between native and the decoy ensemble. To accelerate the conformational search, a newly developed parallel hyperbolic sampling algorithm with a composite movement set is used in the Monte Carlo simulation processes. We exploit this strategy to successfully fold 41/100 small proteins (36 approximately 120 residues) with predicted structures having a RMSD from native below 6.5 A in the top five cluster centroids. To fold larger-size proteins as well as to improve the folding yield of small proteins, we incorporate into the basic force field side-chain contact predictions from our threading program PROSPECTOR where homologous proteins were excluded from the data base. With these threading-based restraints, the program can fold 83/125 test proteins (36 approximately 174 residues) with structures having a RMSD to native below 6.5 A in the top five cluster centroids. This shows the significant improvement of folding by using predicted tertiary restraints, especially when the accuracy of side-chain contact prediction is >20%. For native fold selection, we introduce quantities dependent on the cluster density and the combination of energy and free energy, which show a higher discriminative power to select the native structure than the previously used cluster energy or cluster size, and which can be used in native structure identification in blind simulations. These procedures are readily automated and are being implemented on a genomic scale.     

First principles prediction of protein folding rates

Experimental studies have demonstrated that many small, single-domain proteins fold via simple two-state kinetics. We present a first principles approach for predicting these experimentally determined folding rates. Our approach is based on a nucleation-condensation folding mechanism, where the rate-limiting step is a random, diffusive search for the native tertiary topology. To estimate the rates of folding for various proteins via this mechanism, we first determine the probability of randomly sampling a conformation with the native fold topology. Next, we convert these probabilities into folding rates by estimating the rate that a protein samples different topologies during diffusive folding. This topology-sampling rate is calculated using the Einstein diffusion equation in conjunction with an experimentally determined intra-protein diffusion constant. We have applied our prediction method to the 21 topologically distinct small proteins for which two-state rate data is available. For the 18 beta-sheet and mixed alpha-beta native proteins, we predict folding rates within an average factor of 4, even though the experimental rates vary by a factor of approximately 4 x 10(4). Interestingly, the experimental folding rates for the three four-helix bundle proteins are significantly underestimated by this approach, suggesting that proteins with significant helical content may fold by a faster, alternative mechanism. This method can be applied to any protein for which the structure is known and hence can be used to predict the folding rates of many proteins prior to experiment.     

Potential for assessing quality of protein structure based on contact number prediction

We developed a novel knowledge-based residue environment potential for assessing the quality of protein structures in protein structure prediction. The potential uses the contact number of residues in a protein structure and the absolute contact number of residues predicted from its amino acid sequence using a new prediction method based on a support vector regression (SVR). The contact number of an amino acid residue in a protein structure is defined by the number of residues around a given residue. First, the contact number of each residue is predicted using SVR from an amino acid sequence of a target protein. Then, the potential of the protein structure is calculated from the probability distribution of the native contact numbers corresponding to the predicted ones. The performance of this potential is compared with other score functions using decoy structures to identify both native structure from other structures and near-native structures from nonnative structures. This potential improves not only the ability to identify native structures from other structures but also the ability to discriminate near-native structures from nonnative structures.     

Dynamic Monte Carlo simulations of globular protein folding/unfolding pathways. II. Alpha-helical motifs

Dynamic Monte Carlo simulations of the folding pathways of alpha-helical protein motifs have been undertaken in the context of a diamond lattice model of globular proteins. The first question addressed in the nature of the assembly process of an alpha-helical hairpin. While the hairpin could, in principle, be formed via the diffusion-collision-adhesion of isolated performed helices, this is not the dominant mechanism of assembly found in the simulations. Rather, the helices that form native hairpins are constructed on-site, with folding initiating at or near the turn in almost all cases. Next, the folding/unfolding pathways of four-helix bundles having tight bends and one and two long loops in the native state are explored. Once again, an on-site construction mechanism of folding obtains, with a hairpin forming first, followed by the formation of a three-helix bundle, and finally the fourth helix of the native bundle assembles. Unfolding is essentially the reverse of folding. A simplified analytic theory is developed that reproduces the equilibrium folding transitions obtained from the simulations remarkably well and, for the dominant folding pathway, correctly identifies the intermediates seen in the simulations. The analytic theory provides the free energy along the reaction co-ordinate and identifies the transition state for all three motifs as being quite close to the native state, with three of the four helices assembled, and approximately one turn of the fourth helix in place. The transition state is separated from the native conformation by a free-energy barrier of mainly energetic origin and from the denatured state by a barrier of mainly entropic origin. The general features of the folding pathway seen in all variants of the model four-helix bundles are similar to those observed in the folding of beta-barrel, Greek key proteins; this suggests that many of the qualitative aspects of folding are invariant to the particular native state topology and secondary structure.     

Large-scale prediction of protein geometry and stability changes for arbitrary single point mutations

We have developed a method to both predict the geometry and the relative stability of point mutants that may be used for arbitrary mutations. The geometry optimization procedure was first tested on a new benchmark of 2141 ordered pairs of X-ray crystal structures of proteins that differ by a single point mutation, the largest data set to date. An empirical energy function, which includes terms representing the energy contributions of the folded and denatured proteins and uses the predicted mutant side chain conformation, was fit to a training set consisting of half of a diverse set of 1816 experimental stability values for single point mutations in 81 different proteins. The data included a substantial number of small to large residue mutations not considered by previous prediction studies. After removing 22 (approximately 2%) outliers, the stability calculation gave a standard deviation of 1.08 kcal/mol with a correlation coefficient of 0.82. The prediction method was then tested on the remaining half of the experimental data, giving a standard deviation of 1.10 kcal/mol and covariance of 0.66 for 97% of the test set. A regression fit of the energy function to a subset of 137 mutants, for which both native and mutant structures were available, gave a prediction error comparable to that for the complete training set with predicted side chain conformations. We found that about half of the variation is due to conformation-independent residue contributions. Finally, a fit to the experimental stability data using these residue parameters exclusively suggests guidelines for improving protein stability in the absence of detailed structure information.     

Structural characterization of a novel Cbl phosphotyrosine recognition motif in the APS family of adapter proteins

The Cbl adapter proteins typically function to down-regulate activated protein tyrosine kinases and other signaling proteins by coupling them to the ubiquitination machinery for degradation by the proteasome. Cbl proteins bind to specific tyrosine-phosphorylated sequences in target proteins via the tyrosine kinase-binding (TKB) domain, which comprises a four-helix bundle, an EF-hand calcium-binding domain, and a non-conventional Src homology-2 domain. The previously derived consensus sequence for phosphotyrosine recognition by the Cbl TKB domain is NXpY(S/T)XXP (X denotes lesser residue preference), wherein specificity is conferred primarily by residues C-terminal to the phosphotyrosine. Cbl is recruited to and phosphorylated by the insulin receptor in adipose cells through the adapter protein APS. APS is phosphorylated by the insulin receptor on a C-terminal tyrosine residue, which then serves as a binding site for the Cbl TKB domain. Using x-ray crystallography, site-directed mutagenesis, and calorimetric studies, we have characterized the interaction between the Cbl TKB domain and the Cbl recruitment site in APS, which contains a sequence motif, RA(V/I)XNQpY(S/T), that is conserved in the related adapter proteins SH2-B and Lnk. These studies reveal a novel mode of phosphopeptide interaction with the Cbl TKB domain, in which N-terminal residues distal to the phosphotyrosine directly contact residues of the four-helix bundle of the TKB domain.