Pseudodihedrals: simplified protein backbone representation with knowledge-based energy

Classifying protein kinase conformations with machine learning

Protein kinases are key actors of signaling networks and important drug targets. They cycle between active and inactive conformations, distinguished by a few elements within the catalytic domain. One is the activation loop, whose conserved DFG motif can occupy DFG-in, DFG-out, and some rarer conformations. Annotation and classification of the structural kinome are important, as different conformations can be targeted by different inhibitors and activators. Valuable resources exist; however, large-scale applications will benefit from increased automation and interpretability of structural annotation. Interpretable machine learning models are described for this purpose, based on ensembles of decision trees. To train them, a set of catalytic domain sequences and structures was collected, somewhat larger and more diverse than existing resources. The structures were clustered based on the DFG conformation and manually annotated. They were then used as training input. Two main models were constructed, which distinguished active/inactive and in/out/other DFG conformations. They considered initially 1692 structural variables, spanning the whole catalytic domain, then identified ("learned") a small subset that sufficed for accurate classification. The first model correctly labeled all but 3 of 3289 structures as active or inactive, while the second assigned the correct DFG label to all but 17 of 8826 structures. The most potent classifying variables were all related to well-known structural elements in or near the activation loop and their ranking gives insights into the conformational preferences. The models were used to automatically annotate 3850 kinase structures predicted recently with the Alphafold2 tool, showing that Alphafold2 reproduced the active/inactive but not the DFG-in proportions seen in the Protein Data Bank. We expect the models will be useful for understanding and engineering kinases.

Origin of Correlations between Local Conformational States of Consecutive Amino Acid Residues and Their Role in Shaping Protein Structures and in Allostery

By analyzing the Kubo-cluster-cumulant expansion of the potential of mean force of polypeptide chains corresponding to backbone-local interactions averaged over the rotation of the peptide groups about the Cα···Cα virtual bonds, we identified two important kinds of "along-chain" correlations that pertain to extended chain segments bordered by turns (usually the β-strands) and to the folded spring-like segments (usually α-helices), respectively, and are expressed as multitorsional potentials. These terms affect the positioning of structural elements with respect to each other and, consequently, contribute to determining their packing. Additionally, for extended chain segments, the correlation terms contribute to propagating the conformational change at one end to the other end, which is characteristic of allosteric interactions. We confirmed both findings by statistical analysis of the virtual-bond geometry of 77 950 proteins. Augmenting coarse-grained and, possibly, all-atom force fields with these correlation terms could improve their capacity to model protein structure and dynamics.

Local sequence-structure relationships in proteins

We seek to understand the interplay between amino acid sequence and local structure in proteins. Are some amino acids unique in their ability to fit harmoniously into certain local structures? What is the role of sequence in sculpting the putative native state folds from myriad possible conformations? In order to address these questions, we represent the local structure of each Cα atom of a protein by just two angles, θ and μ, and we analyze a set of more than 4,000 protein structures from the PDB. We use a hierarchical clustering scheme to divide the 20 amino acids into six distinct groups based on their similarity to each other in fitting local structural space. We present the results of a detailed analysis of patterns of amino acid specificity in adopting local structural conformations and show that the sequence-structure correlation is not very strong compared with a random assignment of sequence to structure. Yet, our analysis may be useful to determine an effective scoring rubric for quantifying the match of an amino acid to its putative local structure.

Reduced alphabet of prebiotic amino acids optimally encodes the conformational space of diverse extant protein folds

Background

There is wide agreement that only a subset of the twenty standard amino acids existed prebiotically in sufficient concentrations to form functional polypeptides. We ask how this subset, postulated as {A,D,E,G,I,L,P,S,T,V}, could have formed structures stable enough to found metabolic pathways. Inspired by alphabet reduction experiments, we undertook a computational analysis to measure the structural coding behavior of sequences simplified by reduced alphabets. We sought to discern characteristics of the prebiotic set that would endow it with unique properties relevant to structure, stability, and folding.

Results

Drawing on a large dataset of single-domain proteins, we employed an information-theoretic measure to assess how well the prebiotic amino acid set preserves fold information against all other possible ten-amino acid sets. An extensive virtual mutagenesis procedure revealed that the prebiotic set excellently preserves sequence-dependent information regarding both backbone conformation and tertiary contact matrix of proteins. We observed that information retention is fold-class dependent: the prebiotic set sufficiently encodes the structure space of α/β and α + β folds, and to a lesser extent, of all-α and all-β folds. The prebiotic set appeared insufficient to encode the small proteins. Assessing how well the prebiotic set discriminates native vs. incorrect sequence-structure matches, we found that α/β and α + β folds exhibit more pronounced energy gaps with the prebiotic set than with nearly all alternatives.

Conclusions

The prebiotic set optimally encodes local backbone structures that appear in the folded environment and near-optimally encodes the tertiary contact matrix of extant proteins. The fold-class-specific patterns observed from our structural analysis confirm the postulated timeline of fold appearance in proteogenesis derived from proteomic sequence analyses. Polypeptides arising in a prebiotic environment will likely form α/β and α + β-like folds if any at all. We infer that the progressive expansion of the alphabet allowed the increased conformational stability and functional specificity of later folds, including all-α, all-β, and small proteins. Our results suggest that prebiotic sequences are amenable to mutations that significantly lower native conformational energies and increase discrimination amidst incorrect folds. This property may have assisted the genesis of functional proto-enzymes prior to the expansion of the full amino acid alphabet.

Joint-based description of protein structure: its application to the geometric characterization of membrane proteins

A macroscopic description of a protein structure allows an understanding of the protein conformations in a more simplistic manner. Here, a new macroscopic approach that utilizes the joints of the protein secondary structures as a basic descriptor for the protein structure is proposed and applied to study the arrangement of secondary structures in helical membrane proteins. Two types of dihedral angle, Ω and λ, were defined based on the joint points of the transmembrane (TM) helices and loops, and employed to analyze 103 non-homologous membrane proteins with 3 to 14 TM helices. The Ω-λ plot, which is a distribution plot of the dihedral angles of the joint points, identified the allowed and disallowed regions of helical arrangement. Analyses of consecutive dihedral angle patterns indicated that there are preferred patterns in the helical alignment and extension of TM proteins, and helical extension pattern in TM proteins is varied as the size of TM proteins increases. Finally, we could identify some symmetric protein pairs in TM proteins under the joint-based coordinate and 3-dimensional coordinates. The joint-based approach is expected to help better understand and model the overall conformational features of complicated large-scale proteins, such as membrane proteins.

Minimum action transition paths connecting minima on an energy surface

Dynamics is essential to the biological functions of many bio-molecules, yet our knowledge of dynamics remains fragmented. Experimental techniques for studying bio-molecules either provide high resolution information on static conformations of the molecule or provide low-resolution, ensemble information that does not shed light on single molecule dynamics. In parallel, bio-molecular dynamics occur at time scale that are not yet attainable through detailed simulation methods. These limitations are especially noticeable when studying transition paths. To address this issue, we report in this paper two methods that derive meaningful trajectories for proteins between two of their conformations. The first method, MinActionPath, uses approximations of the potential energy surface for the molecule to derive an analytical solution of the equations of motion related to the concept of minimum action path. The second method, RelaxPath, follows the same principle of minimum action path but implements a more sophisticated potential, including a mixed elastic potential and a collision term to alleviate steric clashes. Using this new potential, the equations of motion cannot be solved analytically. We have introduced a relaxation method for solving those equations. We describe both the theories behind the two methods and their implementations, focusing on the specific techniques we have used that make those implementations amenable to study large molecular systems. We have illustrated the performance of RelaxPath on simple 2D systems. We have also compared MinActionPath and RelaxPath to other methods for generating transition paths on a well suited test set of large proteins, for which the end points of the trajectories as well as an intermediate conformation between those end points are known. We have shown that RelaxPath outperforms those other methods, including MinActionPath, in its ability to generate trajectories that get close to the known intermediates. We have also shown that the structures along the RelaxPath trajectories remain protein-like. Open source versions of the two programs MinActionPath and RelaxPath are available by request.

Use of restrained molecular dynamics to predict the conformations of phosphorylated receiver domains in two-component signaling systems

Two‐component signaling (TCS) is the primary means by which bacteria, as well as certain plants and fungi, respond to external stimuli. Signal transduction involves stimulus‐dependent autophosphorylation of a sensor histidine kinase and phosphoryl transfer to the receiver domain of a downstream response regulator. Phosphorylation acts as an allosteric switch, inducing structural and functional changes in the pathway's components. Due to their transient nature, phosphorylated receiver domains are challenging to characterize structurally. In this work, we provide a methodology for simulating receiver domain phosphorylation to predict conformations that are nearly identical to experimental structures. Using restrained molecular dynamics, phosphorylated conformations of receiver domains can be reliably sampled on nanosecond timescales. These simulations also provide data on conformational dynamics that can be used to identify regions of functional significance related to phosphorylation. We first validated this approach on several well‐characterized receiver domains and then used it to compare the upstream and downstream components of the fungal Sln1 phosphorelay. Our results demonstrate that this technique provides structural insight, obtained in the absence of crystallographic or NMR information, regarding phosphorylation‐induced conformational changes in receiver domains that regulate the output of their associated signaling pathway. To our knowledge, this is the first time such a protocol has been described that can be broadly applied to TCS proteins for predictive purposes. Proteins 2016; 85:155–176. © 2016 Wiley Periodicals, Inc.

The flexibility and dynamics of protein disulfide isomerase

We have studied the mobility of the multidomain folding catalyst, protein disulfide isomerase (PDI), by a coarse‐graining approach based on flexibility. We analyze our simulations of yeast PDI (yPDI) using measures of backbone movement, relative positions and orientations of domains, and distances between functional sites. We find that there is interdomain flexibility at every interdomain junction but these show very different characteristics. The extent of interdomain flexibility is such that yPDI's two active sites can approach much more closely than is found in crystal structures—and indeed hinge motion to bring these sites into proximity is the lowest energy normal mode of motion of the protein. The flexibility predicted for yPDI (based on one structure) includes the other known conformation of yPDI and is consistent with (i) the mobility observed experimentally for mammalian PDI and (ii) molecular dynamics. We also observe intradomain flexibility and clear differences between the domains in their propensity for internal motion. Our results suggest that PDI flexibility enables it to interact with many different partner molecules of widely different sizes and shapes, and highlights considerable similarities of yPDI and mammalian PDI. Proteins 2016; 84:1776–1785. © 2016 Wiley Periodicals, Inc.

Differential effect of solution conditions on the conformation of the actinoporins Sticholysin II and Equinatoxin II

Actinoporins are a family of pore-forming proteins with hemolytic activity. The structural basis for such activity appears to depend on their correct folding. Such folding encompasses a phosphocholine binding site, a tryptophan-rich region and the activity-related N-terminus segment. Additionally, different solution conditions are known to be able to influence the pore formation by actinoporins, as for Sticholysin II (StnII) and Equinatoxin II (EqtxII). In this context, the current work intends to characterize the influence of distinct solution conditions in the conformational behavior of these proteins through molecular dynamics (MD) simulations. The obtained data offer structural insights into actinoporins dynamics in solution, characterizing its conformational behavior at the atomic level, in accordance with previous experimental data on StnII and EqtxII hemolytic activities.

Coarse-grained models of the proteins backbone conformational dynamics

Coarse-grained models are more and more frequently used in the studies of the proteins structural and dynamic properties, since the reduced number of degrees of freedom allows to enhance the conformational space exploration. This chapter attempts to provide an overview of the various coarse-grained models that were applied to study the functional conformational changes of the polypeptides main chain around their native state. It will more specifically discuss the methods used to represent the protein backbone flexibility and to account for the physico-chemical interactions that stabilize the secondary structure elements.

Modeling Protein-Protein Recognition in Solution Using the Coarse-Grained Force Field SCORPION

We present here the SCORPION-Solvated COaRse-grained Protein interactION-force field, a physics-based simplified coarse-grained (CG) force field. It combines our previous CG protein model and a novel particle-based water model which makes it suitable for Molecular Dynamics (MD) simulations of protein association processes. The protein model in SCORPION represents each amino acid with one to three beads, for which electrostatic and van der Waals effective interactions are fitted separately to reproduce those of the all-atom AMBER force field. The protein internal flexibility is accounted for by an elastic network model (ENM). We now include in SCORPION a new Polarizable Coarse-Grained Solvent (PCGS) model, which is computationally efficient, consistent with the protein CG representation, and yields accurate electrostatic free energies of proteins. SCORPION is used here for the first time to perform hundreds-of-nanoseconds-long MD simulations of protein/protein recognition in water, here the case of the barnase/barstar complex. These MD simulations showed that, for five of a total of seven simulations starting from several initial conformations, and after a time going from 1 to 500 ns, the proteins bind in a conformation very close to the native bound structure and remain stable in this conformation for the rest of the simulation. An energetic analysis of these MD show that this recognition is driven both by van der Waals and electrostatic interactions between proteins. SCORPION appears therefore as a useful tool to study protein-protein recognition in a solvated environment.

Designing specific protein-protein interactions using computation, experimental library screening, or integrated methods

Given the importance of protein-protein interactions for nearly all biological processes, the design of protein affinity reagents for use in research, diagnosis or therapy is an important endeavor. Engineered proteins would ideally have high specificities for their intended targets, but achieving interaction specificity by design can be challenging. There are two major approaches to protein design or redesign. Most commonly, proteins and peptides are engineered using experimental library screening and/or in vitro evolution. An alternative approach involves using protein structure and computational modeling to rationally choose sequences predicted to have desirable properties. Computational design has successfully produced novel proteins with enhanced stability, desired interactions and enzymatic function. Here we review the strengths and limitations of experimental library screening and computational structure-based design, giving examples where these methods have been applied to designing protein interaction specificity. We highlight recent studies that demonstrate strategies for combining computational modeling with library screening. The computational methods provide focused libraries predicted to be enriched in sequences with the properties of interest. Such integrated approaches represent a promising way to increase the efficiency of protein design and to engineer complex functionality such as interaction specificity.

PAIRWISE PROTEIN STRUCTURE ALIGNMENT BASED ON AN ORIENTATION-INDEPENDENT BACKBONE REPRESENTATION

Determining structural similarities between proteins is an important problem since it can help identify functional and evolutionary relationships. In this paper, an algorithm is proposed to align two protein structures. Given the protein backbones, the algorithm finds a rigid motion of one backbone onto the other such that large substructures are matched. The algorithm uses a representation of the backbones that is independent of their relative orientations in space and applies dynamic programming to this representation to compute an initial alignment, which is then refined iteratively. Experiments indicate that the algorithm is competitive with two well-known algorithms, namely DALI and LOCK.

O-glycosylated cell wall proteins are essential in root hair growth

Root hairs are single cells that develop by tip growth and are specialized in the absorption of nutrients. Their cell walls are composed of polysaccharides and hydroxyproline-rich glycoproteins (HRGPs) that include extensins (EXTs) and arabinogalactan-proteins (AGPs). Proline hydroxylation, an early posttranslational modification of HRGPs that is catalyzed by prolyl 4-hydroxylases (P4Hs), defines the subsequent O-glycosylation sites in EXTs (which are mainly arabinosylated) and AGPs (which are mainly arabinogalactosylated). We explored the biological function of P4Hs, arabinosyltransferases, and EXTs in root hair cell growth. Biochemical inhibition or genetic disruption resulted in the blockage of polarized growth in root hairs and reduced arabinosylation of EXTs. Our results demonstrate that correct O-glycosylation on EXTs is essential for cell-wall self-assembly and, hence, root hair elongation in Arabidopsis thaliana.

De novo backbone scaffolds for protein design

In recent years, there have been significant advances in the field of computational protein design including the successful computational design of enzymes based on backbone scaffolds from experimentally solved structures. It is likely that large-scale sampling of protein backbone conformations will become necessary as further progress is made on more complicated systems. Removing the constraint of having to use scaffolds based on known protein backbones is a potential method of solving the problem. With this application in mind, we describe a method to systematically construct a large number of de novo backbone structures from idealized topological forms in a top–down hierarchical approach. The structural properties of these novel backbone scaffolds were analyzed and compared with a set of high-resolution experimental structures from the protein data bank (PDB). It was found that the Ramachandran plot distribution and relative γ- and β-turn frequencies were similar to those found in the PDB. The de novo scaffolds were sequence designed with RosettaDesign, and the energy distributions and amino acid compositions were comparable with the results for redesigned experimentally solved backbones. Proteins 2010. © 2009 Wiley-Liss, Inc.

Four distances between pairs of amino acids provide a precise description of their interaction

The three-dimensional structures of proteins are stabilized by the interactions between amino acid residues. Here we report a method where four distances are calculated between any two side chains to provide an exact spatial definition of their bonds. The data were binned into a four-dimensional grid and compared to a random model, from which the preference for specific four-distances was calculated. A clear relation between the quality of the experimental data and the tightness of the distance distribution was observed, with crystal structure data providing far tighter distance distributions than NMR data. Since the four-distance data have higher information content than classical bond descriptions, we were able to identify many unique inter-residue features not found previously in proteins. For example, we found that the side chains of Arg, Glu, Val and Leu are not symmetrical in respect to the interactions of their head groups. The described method may be developed into a function, which computationally models accurately protein structures.

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.

Dihedral-angle information entropy as a gauge of secondary structure propensity

Protein structural information can be uncovered using an information-theory-based entropy and auxiliary functions by taking advantage of high-quality correlation plots between the dihedral angles around a residue and those between sequential residues. A standard information entropy for a primary sequence has been defined using the values of the probabilities of the most likely dihedral angles along the sequence. The distribution of entropy differences relative to the standard for each protein in a reference set--a sublibrary of the Protein Data Bank at the 90% sequence redundancy level--appears to be nearly Gaussian. It gives rise to an auxiliary checking function whose value signals the extent to which the dihedral angle propensities differ from typical structures. Such deviations can arise either because of incorrect dihedral angle assignments or secondary structural propensities that are atypical of the structures in the reference set. This auxiliary checking function can be readily calculated at the public website, (http://www.d2check.gatech.edu). Its utility is demonstrated here in an analysis displaying differences between experimentally and theoretically derived structures, and in the analysis of structures derived by homology modeling. A comparison of the new measure, D(2)Check, to other checking functions based on backbone conformation-namely, PROCHECK and WHAT_CHECK--is also provided.

Insights into the induced fit mechanism in antithrombin–heparin interaction using molecular dynamics simulations

Heparin was isolated in the beginning of the 20th century and until today remains as one of the most important drugs able to interfere with the haemostatic process. Due to the side effects produced by heparin therapy, new promising drugs have been developed, as the synthetic pentasaccharide (synthetically derived from the sequence GlcN-GlcA-GlcN-IdoA-GlcN). The anticoagulant activity of this compound is based on potentiation of antithrombin (AT) inhibitory activity upon serine proteinases of clotting cascade, a mechanism based on the conformational modification of AT. In this context, we present here a molecular dynamics (MD) study of the interaction between the synthetic pentasaccharide and AT. The obtained data correctly predicted an induced fit mechanism in AT-pentasaccharide interaction, showing a solvent-exposed P1 residue instead of a hided conformation. Also, the specific contribution of important amino acid residues to the overall process was also characterized, both in (2)S(0) and (1)C(4) conformations of IdoA residue, suggesting that there is no conformational requirement to the interaction of this residue with AT. Altogether, the results show that MD simulations could be used to characterize and quantify the interaction of synthetic compounds with AT, predicting its specific capacity to induce conformational changes in AT structure. Thus, MD simulations of heparin (and heparin-derived)-AT interactions are proposed here as a powerful tool to assist and support drug design of new antithrombotic agents.

Effect of chain connectivity on the structure of Lennard-Jones liquid and its implicationon statistical potentials for protein folding

Statistical contact potentials and bead-spring models have been widely used for computational studies of protein folding. However, there has been speculation that systematic error may arise in the contact energy calculations when the statistical potentials are deduced under the assumption that the chain connectivity in proteins can be ignored. To address this issue, we have performed molecular-dynamics simulations to study the structure and dynamics of a simple liquid system in which the beads are either connected or unconnected with springs. Results from the present study provide useful information for assessing the accuracy of the statistical potentials for protein structure simulations.

Application of a novel graph-theoretic folding degree index to the study of steroid-DB3 antibody binding affinity

A novel folding degree index, together with other macromolecular descriptors, is used to study steroid-DB3 antibody interactions. This index is based on graph spectral moments of a matrix representing the dihedral angles of a protein backbone. The causes influencing the different order of binding affinity of steroids to DB3 antibody are identified. It is shown that the changes in the chain compactness of the DB3 antibody with respect to its center of mass (radius of gyration) is compensated by a change in the folding degree index in the contrary sense. In fact, the increment in compactness of chain L and the lower increment in the folding degree index of chain H are able to explain the variations in affinity for DB3 of the steroids studied. Consequently, the highest binding affinities are reached by increasing the compactness of chain L in DB3 at the same time that producing the smallest increment in the folding degree of chain H. This study shows the possibilities of application for the graph-theoretic folding degree index in studying drug-protein interactions.

Natural coordinate representation for the protein backbone structure

A new model for describing the geometry of the C(alpha) backbone atoms in protein molecules is derived. This model uses one continuous variable per amino acid. This is half the number of degrees-of-freedom used in traditional backbone models. The new model was tested on 721 PDB structures and its average accuracy was determined to be 1.14 A cRMSD. This model can be used as a description of local structure that provides higher resolution than the traditional secondary structure categories. Also, because this structure description is one-dimensional, it can be used to align structures with the same efficiency and convergence properties available in the popular sequence alignment tools. Furthermore, the 1:1 correspondence with the amino acid sequence has implications for combined sequence/structure alignment. Conventional secondary structure prediction was used to further reduce the number of degrees-of-freedom in 16 test proteins. In those cases, the average cRMSD degraded from 0.96 to 2.33 A while the number of degrees-of-freedom improved (reduced) by more than 30%.

Analysis of knowledge-based protein-ligand potentials using a self-consistent method

We propose a self-consistent approach to analyze knowledge-based atom-atom potentials used to calculate protein-ligand binding energies. Ligands complexed to actual protein structures were first built using the SMoG growth procedure (DeWitte & Shakhnovich, 1996) with a chosen input potential. These model protein-ligand complexes were used to construct databases from which knowledge-based protein-ligand potentials were derived. We then tested several different modifications to such potentials and evaluated their performance on their ability to reconstruct the input potential using the statistical information available from a database composed of model complexes. Our data indicate that the most significant improvement resulted from properly accounting for the following key issues when estimating the reference state: (1) the presence of significant nonenergetic effects that influence the contact frequencies and (2) the presence of correlations in contact patterns due to chemical structure. The most successful procedure was applied to derive an atom-atom potential for real protein-ligand complexes. Despite the simplicity of the model (pairwise contact potential with a single interaction distance), the derived binding free energies showed a statistically significant correlation (approximately 0.65) with experimental binding scores for a diverse set of complexes.

Conformational dynamics of chymotrypsin inhibitor 2 by coarse-grained simulations

A coarse-grained dynamic Monte Carlo (MC) simulation method is used to investigate the conformational dynamics of chymotrypsin inhibitor 2 (CI2). Each residue is represented therein by two interaction sites, one at the alpha-carbon and the other on the amino acid side-chain. The energy and geometry parameters extracted from databank structures are used. The calculated rms fluctuations of alpha-carbon atoms are in good agreement with crystallographic temperature factors. The two regions of the protein that pack against each other to form the main hydrophobic core exhibit negatively correlated fluctuations. The conformational dynamics could efficiently be probed by the time-delayed orientational and conformational correlation functions of the virtual bonds: the active site loop, excluding the active site bond, the turn region, and the N-terminal of the alpha-helix are relatively more mobile regions of the structure. A correlation is observed between the hydrogen/deuterium (H/D) exchange behavior and the long-time orientational and conformational autocorrelation function values for CI2. A cooperativity in the rotations of the bonds near in sequence is observed at all time windows, whereas the cooperative rotations of the bonds far along the sequence appear at long time windows; these correlations contribute to the stability of the secondary structures and the tertiary structure, respectively.

Protein threading by recursive dynamic programming

We present the recursive dynamic programming (RDP) method for the threading approach to three-dimensional protein structure prediction. RDP is based on the divide-and-conquer paradigm and maps the protein sequence whose backbone structure is to be found (the protein target) onto the known backbone structure of a model protein (the protein template) in a stepwise fashion, a technique that is similar to computing local alignments but utilising different cost functions. We begin by mapping parts of the target onto the template that show statistically significant similarity with the template sequence. After mapping, the template structure is modified in order to account for the mapped target residues. Then significant similarities between the yet unmapped parts of the target and the modified template are searched, and the resulting segments of the target are mapped onto the template. This recursive process of identifying segments in the target to be mapped onto the template and modifying the template is continued until no significant similarities between the remaining parts of target and template are found. Those parts which are left unmapped by the procedure are interpreted as gaps. The RDP method is robust in the sense that different local alignment methods can be used, several alternatives of mapping parts of the target onto the template can be handled and compared in the process, and the cost functions can be dynamically adapted to biological needs. Our computer experiments show that the RDP procedure is efficient and effective. We can thread a typical protein sequence against a database of 887 template domains in about 12 hours even on a low-cost workstation (SUN Ultra 5). In statistical evaluations on databases of known protein structures, RDP significantly outperforms competing methods. RDP has been especially valuable in providing accurate alignments for modeling active sites of proteins.RDP is part of the ToPLign system (GMD Toolbox for protein alignment) and can be accessed via the WWW independently or in concert with other ToPLign tools at http://cartan.gmd.de/ToPLign.html.

Packing of sidechains in low-resolution models for proteins

BACKGROUND

Atomic level rotamer libraries for sidechains in proteins have been proposed by several groups. Conformations of side groups in coarse-grained models, on the other hand, have not yet been analyzed, although low resolution approaches are the only efficient way to explore global structural features.

RESULTS

A residue-specific backbone-dependent library for sidechain isomers, compatible with a coarse-grained model, is proposed. The isomeric states are utilized in packing sidechains of known backbone structures. Sidechain positions are predicted with a root-mean-square deviation (r.m.s.d.) of 2.40 A with respect to crystal structure for 50 test proteins. The rmsd for core residues is 1.60 A and decreases to 1.35 A when conformational correlations and directional effects in inter-residue couplings are considered.

CONCLUSIONS

An automated method for assigning sidechain positions in coarse-grained model proteins is proposed and made available on the internet; the method accounts satisfactorily for sidechain packing, particularly in the core.

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.