Reduced Protein Model Research Articles

Coarse-grained potential for hydrogen bond interactions

Understanding protein structure and dynamics is crucial for investigating numerous biological processes. This however requires proper description of molecular interactions, most notably hydrogen bonds, which are the driving force behind the folding of protein sequences into working molecules. Due to the multi-body character of this interaction, proper mathematical formulation has been a matter of long debate in the literature. This description becomes even more complex in reduced protein models. In this contribution, we propose a novel hydrogen bond energy function definition that is based only on Cα positions and used for coarse-grained simulations. We show that this new method has the capability to recognize hydrogen bonds with over 80% accuracy and can successfully identify β-sheet in β-amyloid peptide simulations.

Evidence of Ternary Complex Formation in Trypanosoma cruzi trans-Sialidase Catalysis

Trypanosoma cruzi trans-sialidase (TcTS) is a key target protein for Chagas disease chemotherapy. In this study, we investigated the implications of active site flexibility on the biochemical mechanism of TcTS. Molecular dynamics studies revealed remarkable plasticity in the TcTS catalytic site, demonstrating, for the first time, how donor substrate engagement with the enzyme induces an acceptor binding site in the catalytic pocket that was not previously captured in crystal structures. Furthermore, NMR data showed cooperative binding between donor and acceptor substrates, supporting theoretical results. In summary, our data put forward a coherent dynamic framework to understand how a glycosidase evolved its highly efficient trans-glycosidase activity.

Mean-Field Interactions between Nucleic-Acid-Base Dipoles can Drive the Formation of a Double Helix

A proposed coarse-grained model of nucleic acids demonstrates that average interactions between base dipoles, together with chain connectivity and excluded-volume interactions, are sufficient to form double-helical structures of DNA and RNA molecules. Additionally, local interactions determine helix handedness and direction of strand packing. This result, and earlier research on reduced protein models, suggests that mean-field multipole-multipole interactions are the principal factors responsible for the formation of regular structure of biomolecules.

Spectral representation of reduced protein models

We consider a spectrum-like two-dimensional graphical representation of proteins based on a reduced protein model in which 20 amino acids are grouped into five classes. This particular grouping of amino acids was suggested by Riddle and co-workers in 1997. The graphical representation is based on depicting sequentially the amino acids on five horizontal lines at equal separations. One-letter codes, B, O, U, X and Y, to which numerical values 1 to 5 have been assigned, are suggested as labels for the fictional amino acids that represent all the amino acids within each group. The approach is illustrated on ND6 proteins of eight species having from 168 to 175 amino acids. While visual inspection of the novel spectral graphical representations of proteins may reveal local similarities and dissimilarities of protein sequences, arithmetic manipulations of spectra offer an elegant route to graphic visualization of the degree of similarity for selected pairs of proteins.

Protein–protein docking in CAPRI using ATTRACT to account for global and local flexibility

A reduced protein model combined with a systematic docking approach has been employed to predict protein-protein complex structures in CAPRI rounds 6-11. The docking approach termed ATTRACT is based on energy minimization in translational and rotational degrees of freedom of one protein with respect to the second protein starting from many thousand initial protein partner placements. It also allows for approximate inclusion of global flexibility of protein partners during systematic docking by conformational relaxation of the partner proteins in precalculated soft collective backbone degrees of freedom. We have submitted models for six targets, achieved acceptable docking solutions for two targets, and predicted >20% correct contacts for five targets. Possible improvements of the docking approach in particular at the scoring and refinement steps are discussed.

Why Do Proteins Divide into Domains? Insights from Lattice Model Simulations

It is known that larger globular proteins are built from domains, relatively independent structural units. A domain size seems to be limited, and a single domain consists of from few tens to a couple of hundred amino acids. Based on Monte Carlo simulations of a reduced protein model restricted to the face centered simple cubic lattice, with a minimal set of short-range and long-range interactions, we have shown that some model sequences upon the folding transition spontaneously divide into separate domains. The observed domain sizes closely correspond to the sizes of real protein domains. Short chains with a proper sequence pattern of the hydrophobic and polar residues undergo a two-state folding transition to the structurally ordered globular state, while similar longer sequences follow a multistate transition. Homopolymeric (uniformly hydrophobic) chains and random heteropolymers undergo a continuous collapse transition into a single globule, and the globular state is much less ordered. Thus, the factors responsible for the multidomain structure of proteins are sufficiently long polypeptide chain and characteristic, protein-like, sequence patterns. These findings provide some hints for the analysis of real sequences aimed at prediction of the domain structure of large proteins.

A Coarse-Grained Protein−Protein Potential Derived from an All-Atom Force Field

In order to study protein-protein nonbonded interactions, we present the development of a new reduced protein model that represents each amino acid residue with one to three coarse grains, whose physical properties are derived in a consistent bottom-up procedure from the higher-resolution all-atom AMBER force field. The resulting potential energy function is pairwise additive and includes distinct van-der-Waals and Coulombic terms. The van-der-Waals effective interactions are deduced from preliminary molecular dynamics simulations of all possible amino acid homodimers. They are best represented by a soft 1/r6 repulsion and a Gaussian attraction, with parameters obeying Lorentz-Berthelot mixing rules. For the Coulombic interaction, coarse grain charges are optimized for each separate protein in order to best represent the all-atom electrostatic potential outside the protein core. This approach leaves the possibility of using any implicit solvent model to describe solvation effects and electrostatic screening. The coarse-grained force field is tested carefully for a small homodimeric complex, the magainin. It is shown to reproduce satisfactorily the specificity of the all-atom underlying potential, in particular within a PB/SA solvation model. The coarse-grained potential is applied to the redocking prediction of three different protein-protein complexes: the magainin dimer, the barnase-barstar, and the trypsin-BPTI complexes. It is shown to provide per se an efficient and discriminating scoring energy function for the protein-protein docking problem that remains pertinent at both the global and refinement stage.

Protein-Folding Dynamics: Overview of Molecular Simulation Techniques

Molecular dynamics (MD) is an invaluable tool with which to study protein folding in silico. Although just a few years ago the dynamic behavior of a protein molecule could be simulated only in the neighborhood of the experimental conformation (or protein unfolding could be simulated at high temperature), the advent of distributed computing, new techniques such as replica-exchange MD, new approaches (based on, e.g., the stochastic difference equation), and physics-based reduced models of proteins now make it possible to study protein-folding pathways from completely unfolded structures. In this review, we present algorithms for MD and their extensions and applications to protein-folding studies, using all-atom models with explicit and implicit solvent as well as reduced models of polypeptide chains.

Scoring predictive models using a reduced representation of proteins: model and energy definition

BackgroundReduced representations of proteins have been playing a keyrole in the study of protein folding. Many such models are available, with different representation detail. Although the usefulness of many such models for structural bioinformatics applications has been demonstrated in recent years, there are few intermediate resolution models endowed with an energy model capable, for instance, of detecting native or native-like structures among decoy sets. The aim of the present work is to provide a discrete empirical potential for a reduced protein model termed here PC2CA, because it employs a PseudoCovalent structure with only 2 Centers of interactions per Amino acid, suitable for protein model quality assessment.ResultsAll protein structures in the set top500H have been converted in reduced form. The distribution of pseudobonds, pseudoangle, pseudodihedrals and distances between centers of interactions have been converted into potentials of mean force. A suitable reference distribution has been defined for non-bonded interactions which takes into account excluded volume effects and protein finite size. The correlation between adjacent main chain pseudodihedrals has been converted in an additional energetic term which is able to account for cooperative effects in secondary structure elements. Local energy surface exploration is performed in order to increase the robustness of the energy function.ConclusionThe model and the energy definition proposed have been tested on all the multiple decoys' sets in the Decoys'R'us database. The energetic model is able to recognize, for almost all sets, native-like structures (RMSD less than 2.0 Å). These results and those obtained in the blind CASP7 quality assessment experiment suggest that the model compares well with scoring potentials with finer granularity and could be useful for fast exploration of conformational space. Parameters are available at the url: .

Accounting for loop flexibility during protein–protein docking

Although reliable docking can now be achieved for systems that do not undergo important induced conformational change upon association, the presence of flexible surface loops, which must adapt to the steric and electrostatic properties of a partner, generally presents a major obstacle. We report here the first docking method that allows large loop movements during a systematic exploration of the possible arrangements of the two partners in terms of position and rotation. Our strategy consists in taking into account an ensemble of possible loop conformations by a multi-copy representation within a reduced protein model. The docking process starts from regularly distributed positions and orientations of the ligand around the whole receptor. Each starting configuration is submitted to energy minimization during which the best-fitting loop conformation is selected based on the mean-field theory. Trials were carried out on proteins with significant differences in the main-chain conformation of the binding loop between isolated form and complexed form, which were docked to their partner considered in their bound form. The method is able to predict complexes very close to the crystal complex both in terms of relative position of the two partners and of the geometry of the flexible loop. We also show that introducing loop flexibility on the isolated protein form during systematic docking largely improves the predictions of relative position of the partners in comparison with rigid-body docking.

ATTRACT: Protein–protein docking in CAPRI using a reduced protein model

Protein-protein complex structures have been predicted for CAPRI Rounds 3 and 5 using a reduced protein model. Proteins are represented by up to 3 pseudoatoms per amino acid. The docking approach termed ATTRACT is based on energy minimization in translational and rotational degrees of freedom of one protein with respect to another protein. The reduced protein model allows one to perform systematic docking minimization of many thousand start structures in reasonable computer time. Flexibility of critical surface side-chains can be accounted for by a multiple conformational copy approach. The multicopy approach allows simultaneous adjustment of side-chain conformations and optimization of translational and rotational degrees of freedom of one protein with respect to the partner during docking. For 3 (Targets 8, 14, and 19) out of 5 CAPRI targets, the approach resulted in predictions in close agreement with experiment [root-mean-square deviation (RMSD) of backbone atoms within 10 A of the protein-protein interface < 1.8 A]. The comparison of predicted and experimental structures of the CAPRI targets indicates that besides local conformational changes (e.g., changes in side-chain conformations), global conformational changes of the protein backbone can be critical for complex formation. These conformational changes not accounted for during docking are a likely reason for the unrealistic predictions in 2 cases (Targets 9 and 18).

A Quadratic Programming Formulation for the Design of Reduced Protein Models in Continuous Sequence Space

The notion of optimization is inherent in the design of a sequence of amino acid monomer types in a long heteropolymer chain of a protein that should fold to a desired conformation. Building upon our previous work wherein continuous parametrization and deterministic optimization approach were introduced for protein sequence design, in this paper we present an alternative formulation that leads to a quadratic programming problem in the first stage of a two-stage design procedure. The new quadratic formulation, which uses the linear interpolation of the states of the monomers in Stage I could be solved to identify the globally optimal sequence(s). Furthermore, the global minimum solution of the quadratic programming problem gives a lower bound on the energy for a given conformation in the sequence space. In practice, even a local optimization algorithm often gives sequences with global minimum, as demonstrated in the examples considered in this paper. The solutions of the first stage are then used to provide an appropriate initial guess for the second stage, where a rescaled Gaussian probability distribution function-based interpolation is used to refine the states to their original discrete states. The performance of this method is demonstrated with HP (hydrophobic and polar) lattice models of proteins. The results of this method are compared with the results of exhaustive enumeration as well as our earlier method that uses a graph-spectral method in Stage I. The computational efficiency of the new method is also demonstrated by designing HP models of real proteins. The method outlined in this paper is applicable to very large chains and can be extended to the case of multiple monomer types.

A reduced protein model with accurate native-structure identification ability.

A protein model that is simple enough to be used in protein-folding simulations but accurate enough to identify a protein native fold is described. Its geometry consists of describing the residues by one, two, or three pseudoatoms, depending on the residue size. Its energy is given by a pairwise, knowledge-based potential obtained for all the pseudoatoms as a function of their relative distance. The pseudoatomic potential is also a function of the primary chain separation and residue order. The model is tested by gapless threading on a large, representative set of known protein and decoy structures obtained from the "Decoys 'R' Us" database. It is also tested by threading on gapped decoys generated for proteins with many homologs. The gapless threading tests show near 98% native-structure recognition as the lowest energy structure and almost 100% as one of the three lowest energy structures for over 2200 test proteins. In decoy threading tests, the model recognized the majority of the native structures. It is also able to recognize native structures among gapped decoys, in spite of close structural similarities. The results indicate that the pseudoatomic model has native recognition ability similar to comparable atomic-based models but much better than equivalent residue-based models.

New energy terms for reduced protein models implemented in an off‐lattice force field

AbstractParameterization and test calculations of a reduced protein model with new energy terms are presented. The new energy terms retain the steric properties and the most significant degrees of freedom of protein side chains in an efficient way using only one to three virtual atoms per amino acid residue. The energy terms are implemented in a force field containing predefined secondary structure elements as constraints, electrostatic interaction terms, and a solvent‐accessible surface area term to include the effect of solvation. In the force field the main‐chain peptide units are modeled as electric dipoles, which have constant directions in α‐helices and β‐sheets and variable conformation‐dependent directions in loops. Protein secondary structures can be readily modeled using these dipole terms. Parameters of the force field were derived using a large set of experimental protein structures and refined by minimizing RMS errors between the experimental structures and structures generated using molecular dynamics simulations. The final average RMS error was 3.7 Å for the main‐chain virtual atoms (Cα atoms) and 4.2 Å for all virtual atoms for a test set of 10 proteins with 58–294 amino acid residues. The force field was further tested with a substantially larger test set of 608 proteins yielding somewhat lower accuracy. The fold recognition capabilities of the force field were also evaluated using a set of 27,814 misfolded decoy structures. © 2001 John Wiley &amp; Sons, Inc. J Comput Chem 22: 1229–1242, 2001

Computer simulations of the properties of the ?2, ?2C, and ?2D de novo designed helical proteins

Reduced lattice models of the three de novo designed helical proteins alpha2, alpha2C, and alpha2D were studied. Low temperature stable folds were obtained for all three proteins. In all cases, the lowest energy folds were four-helix bundles. The folding pathway is qualitatively the same for all proteins studied. The energies of various topologies are similar, especially for the alpha2 polypeptide. The simulated crossover from molten globule to native-like behavior is very similar to that seen in experimental studies. Simulations on a reduced protein model reproduce most of the experimental properties of the alpha2, alpha2C, and alpha2D proteins. Stable four-helix bundle structures were obtained, with increasing native-like behavior on-going from alpha2 to alpha2D that mimics experiment.

Computer simulations of the properties of the α2, α2C, and α2D de novo designed helical proteins

Reduced lattice models of the three de novo designed helical proteins α2, α2C, and α2D were studied. Low temperature stable folds were obtained for all three proteins. In all cases, the lowest energy folds were four-helix bundles. The folding pathway is qualitatively the same for all proteins studied. The energies of various topologies are similar, especially for the α2 polypeptide. The simulated crossover from molten globule to native-like behavior is very similar to that seen in experimental studies. Simulations on a reduced protein model reproduce most of the experimental properties of the α2, α2C, and α2D proteins. Stable four-helix bundle structures were obtained, with increasing native-like behavior on-going from α2 to α2D that mimics experiment. Proteins 2000;38:17–28. ©2000 Wiley-Liss, Inc.

De novo predictions of the quaternary structure of leucine zippers and other coiled coils

Coiled coils possess a quaternary structure comprised of the side-by-side arrangement of α-helices. Due their inherent structural simplicity, they are ideal model systems for both theoretical and experimental studies. Among the coiled coils are the leucine zippers, which play an important role in the activation of DNA transcription. In contrast to the large amount of available experimental data, an overview of which is presented, there are very few theoretical studies. To address this need, the status of existing theoretical approaches to predict coiled coil quaternary structure is described. Furthermore, to treat the conformational equilibria inherent in these systems, an extension of entropy sampling Monte Carlo simulations is developed that can treat multimers. Here, the approach is applied to GCN4 leucine zippers in the context of a reduced protein model. Not only is the native conformation successfully predicted, but the model also reproduces the experimentally observed helix content in the denatured state and the observed two-state thermodynamic behavior. Such two-state behavior arises from the dissociation of highly helical dimeric chains to form monomers of low, isolated chain helix content. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 165–176, 1999

Reduced Protein Models and their Application to the Protein Folding Problem

One of the most important unsolved problems of computational biology is prediction of the three-dimensional structure of a protein from its amino acid sequence. In practice, the solution to the protein folding problem demands that two interrelated problems be simultaneously addressed. Potentials that recognize the native state from the myriad of misfolded conformations are required, and the multiple minima conformational search problem must be solved. A means of partly surmounting both problems is to use reduced protein models and knowledge-based potentials. Such models have been employed to elucidate a number of general features of protein folding, including the nature of the energy landscape, the factors responsible for the uniqueness of the native state and the origin of the two-state thermodynamic behavior of globular proteins. Reduced models have also been used to predict protein tertiary and quaternary structure. When combined with a limited amount of experimental information about secondary and tertiary structure, molecules of substantial complexity can be assembled. If predicted secondary structure and tertiary restraints are employed, low resolution models of single domain proteins can be successfully predicted. Thus, simplified protein models have played an important role in furthering the understanding of the physical properties of proteins.

Computer Simulations of De Novo Designed Helical Proteins

In the context of reduced protein models, Monte Carlo simulations of three de novo designed helical proteins (four-member helical bundle) were performed. At low temperatures, for all proteins under consideration, protein-like folds having different topologies were obtained from random starting conformations. These simulations are consistent with experimental evidence indicating that these de novo designed proteins have the features of a molten globule state. The results of Monte Carlo simulations suggest that these molecules adopt four-helix bundle topologies. They also give insight into the possible mechanism of folding and association, which occurs in these simulations by on-site assembly of the helices. The low-temperature conformations of all three sequences have the features of a molten globule state.

Fold assembly of small proteins using Monte Carlo simulations driven by restraints derived from multiple sequence alignments

The feasibility of predicting the global fold of small proteins by incorporating predicted secondary and tertiary restraints into ab initio folding simulations has been demonstrated on a test set comprised of 20 non-homologous proteins, of which one was a blind prediction of target 42 in the recent CASP2 contest. These proteins contain from 37 to 100 residues and represent all secondary structural classes and a representative variety of global topologies. Secondary structure restraints are provided by the PHD secondary structure prediction algorithm that incorporates multiple sequence information. Predicted tertiary restraints are derived from multiple sequence alignments via a two-step process. First, seed side-chain contacts are identified from correlated mutation analysis, and then a threading-based algorithm is used to expand the number of these seed contacts. A lattice-based reduced protein model and a folding algorithm designed to incorporate these predicted restraints is described. Depending upon fold complexity, it is possible to assemble native-like topologies whose coordinate root-mean-square deviation from native is between 3.0 Å and 6.5 Å. The requisite level of accuracy in side-chain contact map prediction can be roughly 25% on average, provided that about 60% of the contact predictions are correct within ±1 residue and 95% of the predictions are correct within ±4 residues. Precision in tertiary contact prediction is more critical than absolute accuracy. Furthermore, only a subset of the tertiary contacts, on the order of 25% of the total, is sufficient for successful topology assembly. Overall, this study suggests that the use of restraints derived from multiple sequence alignments combined with a fold assembly algorithm holds considerable promise for the prediction of the global topology of small proteins.