Identification and ab initio simulations of early folding units in proteins

The location of protein subunits that form early during folding, constituted of consecutive secondary structure elements with some intrinsic stability and favorable tertiary interactions, is predicted using a combination of threading algorithms and local structure prediction methods. Two folding units are selected among the candidates identified in a database of known protein structures: the fragment 15-55 of 434 cro, an all-alpha protein, and the fragment 1-35 of ubiquitin, an alpha/beta protein. These units are further analyzed by means of Monte Carlo simulated annealing using several database-derived potentials describing different types of interactions. Our results suggest that the local interactions along the chain dominate in the first folding steps of both fragments, and that the formation of some of the secondary structures necessarily occurs before structure compaction. These findings led us to define a prediction protocol, which is efficient to improve the accuracy of the predicted structures. It involves a first simulation with a local interaction potential only, whose final conformation is used as a starting structure of a second simulation that uses a combination of local interaction and distance potentials. The root mean square deviations between the coordinates of predicted and native structures are as low as 2-4 A in most trials. The possibility of extending this protocol to the prediction of full proteins is discussed. Proteins 2001;42:164-176.     

Sequence specific resonance assignment via Multicanonical Monte Carlo search using an ABACUS approach

ABACUS [Grishaev et al. (2005) Proteins 61:36-43] is a novel protocol for automated protein structure determination via NMR. ABACUS starts from molecular fragments defined by unassigned J-coupled spin-systems and involves a Monte Carlo stochastic search in assignment space, probabilistic sequence selection, and assembly of fragments into structures that are used to guide the stochastic search. Here, we report further development of the two main algorithms that increase the flexibility and robustness of the method. Performance of the BACUS [Grishaev and Llinás (2004) J Biomol NMR 28:1-101] algorithm was significantly improved through use of sequential connectivities available from through-bond correlated 3D-NMR experiments, and a new set of likelihood probabilities derived from a database of 56 ultra high resolution X-ray structures. A Multicanonical Monte Carlo procedure, Fragment Monte Carlo (FMC), was developed for sequence-specific assignment of spin-systems. It relies on an enhanced assignment sampling and provides the uncertainty of assignments in a quantitative manner. The efficiency of the protocol was validated on data from four proteins of between 68-116 residues, yielding 100% accuracy in sequence specific assignment of backbone and side chain resonances.     

Some fundamental aspects of building protein structures from fragment libraries

We have investigated some of the basic principles that influence generation of protein structures using a fragment-based, random insertion method. We tested buildup methods and fragment library quality for accuracy in constructing a set of known structures. The parameters most influential in the construction procedure are bond and torsion angles with minor inaccuracies in bond angles alone causing >6 A CalphaRMSD for a 150-residue protein. Idealization to a standard set of values corrects this problem, but changes the torsion angles and does not work for every structure. Alternatively, we found using Cartesian coordinates instead of torsion angles did not reduce performance and can potentially increase speed and accuracy. Under conditions simulating ab initio structure prediction, fragment library quality can be suboptimal and still produce near-native structures. Using various clustering criteria, we created a number of libraries and used them to predict a set of native structures based on nonnative fragments. Local CalphaRMSD fit of fragments, library size, and takeoff/landing angle criteria weakly influence the accuracy of the models. Based on a fragment's minimal perturbation upon insertion into a known structure, a seminative fragment library was created that produced more accurate structures with fragments that were less similar to native fragments than the other sets. These results suggest that fragments need only contain native-like subsections, which when correctly overlapped, can recreate a native-like model. For fragment-based, random insertion methods used in protein structure prediction and design, our findings help to define the parameters this method needs to generate near-native structures.     

Ab initio protein structure assembly using continuous structure fragments and optimized knowledge-based force field

Ab initio protein folding is one of the major unsolved problems in computational biology owing to the difficulties in force field design and conformational search. We developed a novel program, QUARK, for template-free protein structure prediction. Query sequences are first broken into fragments of 1-20 residues where multiple fragment structures are retrieved at each position from unrelated experimental structures. Full-length structure models are then assembled from fragments using replica-exchange Monte Carlo simulations, which are guided by a composite knowledge-based force field. A number of novel energy terms and Monte Carlo movements are introduced and the particular contributions to enhancing the efficiency of both force field and search engine are analyzed in detail. QUARK prediction procedure is depicted and tested on the structure modeling of 145 nonhomologous proteins. Although no global templates are used and all fragments from experimental structures with template modeling score >0.5 are excluded, QUARK can successfully construct 3D models of correct folds in one-third cases of short proteins up to 100 residues. In the ninth community-wide Critical Assessment of protein Structure Prediction experiment, QUARK server outperformed the second and third best servers by 18 and 47% based on the cumulative Z-score of global distance test-total scores in the FM category. Although ab initio protein folding remains a significant challenge, these data demonstrate new progress toward the solution of the most important problem in the field.     

Building native protein conformation from NMR backbone chemical shifts using Monte Carlo fragment assembly

We have been analyzing the extent to which protein secondary structure determines protein tertiary structure in simple protein folds. An earlier paper demonstrated that three-dimensional structure can be obtained successfully using only highly approximate backbone torsion angles for every residue. Here, the initial information is further diluted by introducing a realistic degree of experimental uncertainty into this process. In particular, we tackle the practical problem of determining three-dimensional structure solely from backbone chemical shifts, which can be measured directly by NMR and are known to be correlated with a protein's backbone torsion angles. Extending our previous algorithm to incorporate these experimentally determined data, clusters of structures compatible with the experimentally determined chemical shifts were generated by fragment assembly Monte Carlo. The cluster that corresponds to the native conformation was then identified based on four energy terms: steric clash, solvent-squeezing, hydrogen-bonding, and hydrophobic contact. Currently, the method has been applied successfully to five small proteins with simple topology. Although still under development, this approach offers promise for high-throughput NMR structure determination.     

A stochastic method for the reconstruction of protein structures from one-dimensional structural profiles

We discuss a computational approach for reconstructing the native structures of proteins from the knowledge of a structural profile - the first eigenvector of the contact map of the native structure itself. The procedure consists in carrying out Monte Carlo simulations of a tube model of the protein structure with an energy bias towards the target structural profile. We present the reconstruction of two small proteins and address problems arising in the reconstruction of larger proteins. Our results indicate that an accurate physico-chemical energy function should be used in conjunction with the structural profile bias in order to achieve accurate reconstructions.     

Assembly of protein structure from sparse experimental data: An efficient Monte Carlo model

A new, efficient method for the assembly of protein tertiary structure from known, loosely encoded secondary structure restraints and sparse information about exact side chain contacts is proposed and evaluated. The method is based on a new, very simple method for the reduced modeling of protein structure and dynamics, where the protein is described as a lattice chain connecting side chain centers of mass rather than Cαs. The model has implicit built-in multibody correlations that simulate short- and long-range packing preferences, hydrogen bonding cooperativity and a mean force potential describing hydrophobic interactions. Due to the simplicity of the protein representation and definition of the model force field, the Monte Carlo algorithm is at least an order of magnitude faster than previously published Monte Carlo algorithms for structure assembly. In contrast to existing algorithms, the new method requires a smaller number of tertiary restraints for successful fold assembly; on average, one for every seven residues as compared to one for every four residues. For example, for smaller proteins such as the B domain of protein G, the resulting structures have a coordinate root mean square deviation (cRMSD), which is about 3 Å from the experimental structure; for myoglobin, structures whose backbone cRMSD is 4.3 Å are produced, and for a 247-residue TIM barrel, the cRMSD of the resulting folds is about 6 Å. As would be expected, increasing the number of tertiary restraints improves the accuracy of the assembled structures. The reliability and robustness of the new method should enable its routine application in model building protocols based on various (very sparse) experimentally derived structural restraints. Proteins 32:475–494, 1998. © 1998 Wiley-Liss, Inc.     

Understanding protein folding: small proteins in silico

Recent improvements in methodology and increased computer power now allow atomistic computer simulations of protein folding. We briefly review several advanced Monte Carlo algorithms that have contributed to this development. Details of folding simulations of three designed mini proteins are shown. Adding global translations and rotations has allowed us to handle multiple chains and to simulate the aggregation of six beta-amyloid fragments. In a different line of research we have developed several algorithms to predict local features from sequence. In an outlook we sketch how such biasing could extend the application spectrum of Monte Carlo simulations to structure prediction of larger proteins.     

Small libraries of protein fragments model native protein structures accurately

Prediction of protein structure depends on the accuracy and complexity of the models used. Here, we represent the polypeptide chain by a sequence of rigid fragments that are concatenated without any degrees of freedom. Fragments chosen from a library of representative fragments are fit to the native structure using a greedy build-up method. This gives a one-dimensional representation of native protein three-dimensional structure whose quality depends on the nature of the library. We use a novel clustering method to construct libraries that differ in the fragment length (four to seven residues) and number of representative fragments they contain (25-300). Each library is characterized by the quality of fit (accuracy) and the number of allowed states per residue (complexity). We find that the accuracy depends on the complexity and varies from 2.9A for a 2.7-state model on the basis of fragments of length 7-0.76A for a 15-state model on the basis of fragments of length 5. Our goal is to find representations that are both accurate and economical (low complexity). The models defined here are substantially better in this regard: with ten states per residue we approximate native protein structure to 1A compared to over 20 states per residue needed previously.For the same complexity, we find that longer fragments provide better fits. Unfortunately, libraries of longer fragments must be much larger (for ten states per residue, a seven-residue library is 100 times larger than a five-residue library). As the number of known protein native structures increases, it will be possible to construct larger libraries to better exploit this correlation between neighboring residues. Our fragment libraries, which offer a wide range of optimal fragments suited to different accuracies of fit, may prove to be useful for generating better decoy sets for ab initio protein folding and for generating accurate loop conformations in homology modeling.     

Prediction of the three-dimensional structure of proteins using the electrostatic screening model and hierarchic condensation

We describe a method for predicting the three-dimensional (3-D) structure of proteins from their sequence alone. The method is based on the electrostatic screening model for the stability of the protein main-chain conformation. The free energy of a protein as a function of its conformation is obtained from the potentials of mean force analysis of high-resolution x-ray protein structures. The free energy function is simple and contains only 44 fitted coefficients. The minimization of the free energy is performed by the torsion space Monte Carlo procedure using the concept of hierarchic condensation. The Monte Carlo minimization procedure is applied to predict the secondary, super-secondary, and native 3-D structures of 12 proteins with 28–110 amino acids. The 3-D structures of the majority of local secondary and super-secondary structures are predicted accurately. This result suggests that control in forming the native-like local structure is distributed along the entire protein sequence. The native 3-D structure is predicted correctly for 3 of 12 proteins composed mainly from the α-helices. The method fails to predict the native 3-D structure of proteins with a predominantly β secondary structure. We suggest that the hierarchic condensation is not an appropriate procedure for simulating the folding of proteins made up primarily from β-strands. The method has been proved accurate in predicting the local secondary and super-secondary structures in the blind ab initio 3-D prediction experiment. Proteins 31:74–96, 1998. © 1998 Wiley-Liss, Inc.     

Separating true positive predicted residue contacts from false positive ones in mainly alpha proteins, using constrained Metropolis MC simulations

We present a method that significantly improves the accuracy of predicted proximal residue pairs in protein molecules. Computational methods for predicting pairs of amino acids that are distant in the protein sequence but close in the protein 3D structure can benefit attempts to in silico recognize the fold of a protein molecule. Unfortunately, currently available methods suffer from low predictive accuracy. In this work, we use Monte Carlo simulations to fold protein molecules with proximal pair predictions used as additional energy constraints. To test our methods, we study molecules with known tertiary structures. With Monte Carlo, we generate ensembles of structures for each set of residues constraints. The distribution of the root mean square deviation of the folded structures from the known native structure reveals clear information about the accuracy of the constraint sets used. With recursive substitutions of constraints, false positive predictions are identified and filtered out and significant improvements in accuracy are observed.     

Computer simulations aimed at structure prediction of supersecondary motifs in proteins

It is well established that protein structures are more conserved than protein sequences. One-third of all known protein structures can be classified into ten protein folds, which themselves are composed mainly of alpha-helical hairpin, beta hairpin, and betaalphabeta supersecondary structural elements. In this study, we explore the ability of a recent Monte Carlo-based procedure to generate the 3D structures of eight polypeptides that correspond to units of supersecondary structure and three-stranded antiparallel beta sheet. Starting from extended or misfolded compact conformations, all Monte Carlo simulations show significant success in predicting the native topology using a simplified chain representation and an energy model optimized on other structures. Preliminary results on model peptides from nucleotide binding proteins suggest that this simple protein folding model can help clarify the relation between sequence and topology.     

Protein structure prediction based on fragment assembly and parameter optimization

We propose a novel method for ab-initio prediction of protein tertiary structures based on the fragment assembly and global optimization. Fifteen residue long fragment libraries are constructed using the secondary structure prediction method PREDICT, and fragments in these libraries are assembled to generate full-length chains of a query protein. Tertiary structures of 50 to 100 conformations are obtained by minimizing an energy function for proteins, using the conformational space annealing method that enables one to sample diverse low-lying local minima of the energy. Then in order to enhance the performance of the prediction method, we optimize the linear parameters of the energy function, so that the native-like conformations become energetically more favorable than the non-native ones for proteins with known structures. We test the feasibility of the parameter optimization procedure by applying it to the training set consisting of three proteins: the 10-55 residue fragment of staphylococcal protein A (PDB ID 1bdd), a designed protein betanova, and 1fsd.     

Monte Carlo refinement of rigid-body protein docking structures with backbone displacement and side-chain optimization

Structures of hitherto unknown protein complexes can be predicted by docking the solved protein monomers. Here, we present a method to refine initial docking estimates of protein complex structures by a Monte Carlo approach including rigid-body moves and side-chain optimization. The energy function used is comprised of van der Waals, Coulomb, and atomic contact energy terms. During the simulation, we gradually shift from a novel smoothed van der Waals potential, which prevents trapping in local energy minima, to the standard Lennard-Jones potential. Following the simulation, the conformations are clustered to obtain the final predictions. Using only the first 100 decoys generated by a fast Fourier transform (FFT)-based rigid-body docking method, our refinement procedure is able to generate near-native structures (interface RMSD <2.5 A) as first model in 14 of 59 cases in a benchmark set. In most cases, clear binding funnels around the native structure can be observed. The results show the potential of Monte Carlo refinement methods and emphasize their applicability for protein-protein docking.     

Reactivity-based analysis of domain structures in native replication protein A

Replication protein A (RPA) is an essential heterotrimeric ssDNA binding protein that participates in DNA repair, replication, and recombination. Though X-ray and NMR experiments have been used to determine three-dimensional structure models of the protein's domain fragments, a complete RPA structural model has not been reported. To test whether the fragment structures faithfully represent the same portions in the native solution-state protein, we have examined the structure of RPA under biologically relevant conditions. We have probed the location of multiple amino acids within the native RPA three-dimensional structure using reactivity of these amino acids toward proteolytic and chemical modification reagents. In turn, we evaluated different structural models by comparing the observed native RPA reactivities with anticipated reactivities based on candidate structural models. Our results show that our reactivity analysis approach is capable of critically assessing structure models and can be a basis for selecting the most relevant from among alternate models of a protein structure. Using this analytical approach, we verified the relevance of RPA fragment models to the native protein structure. Our results further indicate several important features of native RPA's structure in solution, such as flexibility at specific locations in RPA, particularly in the C-terminal region of RPA70. Our findings are consistent with reported DNA-free structural models and support the role of conformational change in the ssDNA binding mechanism of RPA.     

Prediction of protein tertiary structure using PROFESY, a novel method based on fragment assembly and conformational space annealing

A novel method for ab initio prediction of protein tertiary structures, PROFESY (PROFile Enumerating SYstem), is proposed. This method utilizes the secondary structure prediction information of a query sequence and the fragment assembly procedure based on global optimization. Fifteen-residue-long fragment libraries are constructed using the secondary structure prediction method PREDICT, and fragments in these libraries are assembled to generate full-length chains of a query protein. Tertiary structures of 50 to 100 conformations are obtained by minimizing an energy function for proteins, using the conformational space annealing method that enables one to sample diverse low-lying local minima of the energy. We apply PROFESY for benchmark tests to proteins with known structures to demonstrate its feasibility. In addition, we participated in CASP5 and applied PROFESY to four new-fold targets for blind prediction. The results are quite promising, despite the fact that PROFESY was in its early stages of development. In particular, PROFESY successfully provided us the best model-one structure for the target T0161.     

Fragment-based local statistical potentials derived by combining an alphabet of protein local structures with secondary structures and solvent accessibilities

General and transferable statistical potentials to quantify the compatibility between local structures and local sequences of peptide fragments in proteins were derived. In the derivation, structure clusters of fragments are obtained by clustering five-residue fragments in native proteins based on their conformations represented by a local structure alphabet (de Brevern et al., Proteins 2000;41:271-287), secondary structure states, and solvent accessibilities. On the basis of the native sequences of the structurally clustered fragments, the probabilities of different amino acid sequences were estimated for each structure cluster. From the sequence probabilities, statistical energies as a function of sequence for a given structure were directly derived. The same sequence probabilities were employed in a database-matching approach to derive statistical energies as a function of local structure for a given sequence. Compared with prior models of local statistical potentials, we provided an integrated approach in which local conformations and local environments are treated jointly, structures are treated in units of fragments instead of individual residues so that coupling between the conformations of adjacent residues is included, and strong interdependences between the conformations of overlapping or neighboring fragment units are also considered. In tests including fragment threading, pseudosequence design, and local structure predictions, the potentials performed at least comparably and, in most cases, better than a number of existing models applicable to the same contexts indicating the advantages of such an integrated approach for deriving local potentials and suggesting applicability of the statistical potentials derived here in sequence designs and structure predictions.     

Dihedral angle and secondary structure database of short amino acid fragments

Dihedral angles of amino acids are of considerable importance in protein tertiary structure prediction as they define the backbone of a protein and hence almost define the protein's entire conformation. Most ab initio protein structure prediction methods predict the secondary structure of a protein before predicting the tertiary structure because three-dimensional fold consists of repeating units of secondary structures. Hence, both dihedral angles and secondary structures are important in tertiary structure prediction of proteins. Here we describe a database called DASSD (Dihedral Angle and Secondary Structure Database of Short Amino acid Fragments) that contains dihedral angle values and secondary structure details of short amino acid fragments of lengths 1, 3 and 5. Information stored in this database was extracted from a set of 5,227 non-redundant high resolution (less than 2-angstroms) protein structures. In total, DASSD stores details for about 733,000 fragments. This database finds application in the development of ab initio protein structure prediction methods using fragment libraries and fragment assembly techniques. It is also useful in protein secondary structure prediction.

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