Amino acid empirical contact energy definitions for fold recognition in the space of contact maps

Computational Mutagenesis of Antibody Fragments: Disentangling Side Chains from ΔΔG Predictions

The development of highly potent antibodies and antibody fragments as binding agents holds significant implications in fields such as biosensing and biotherapeutics. Their binding strength is intricately linked to the arrangement and composition of residues at the binding interface. Computational techniques offer a robust means to predict the three-dimensional structure of these complexes and to assess the affinity changes resulting from mutations. Given the interdependence of structure and affinity prediction, our objective here is to disentangle their roles. We aim to evaluate independently six side-chain reconstruction methods and ten binding affinity estimation techniques. This evaluation was pivotal in predicting affinity alterations due to single mutations, a key step in computational affinity maturation protocols. Our analysis focuses on a data set comprising 27 distinct antibody/hen egg white lysozyme complexes, each with crystal structures and experimentally determined binding affinities. Using six different side-chain reconstruction methods, we transformed each structure into its corresponding mutant via in silico single-point mutations. Subsequently, these structures undergo minimization and molecular dynamics simulation. We therefore estimate ΔΔG values based on the original crystal structure, its energy-minimized form, and the ensuing molecular dynamics trajectories. Our research underscores the critical importance of selecting reliable side-chain reconstruction methods and conducting thorough molecular dynamics simulations to accurately predict the impact of mutations. In summary, our study demonstrates that the integration of conformational sampling and scoring is a potent approach to precisely characterizing mutation processes in single-point mutagenesis protocols and crucial for computational antibody design.

Connection between MHC class II binding and aggregation propensity: The antigenic peptide 10 of Paracoccidioides brasiliensis as a benchmark study

The aggregation of epitopes that are also able to bind major histocompatibility complex (MHC) alleles raises questions around the potential connection between the formation of epitope aggregates and their affinities to MHC receptors. We first performed a general bioinformatic assessment over a public dataset of MHC class II epitopes, finding that higher experimental binding correlates with higher aggregation-propensity predictors. We then focused on the case of P10, an epitope used as a vaccine candidate against Paracoccidioides brasiliensis that aggregates into amyloid fibrils. We used a computational protocol to design variants of the P10 epitope to study the connection between the binding stabilities towards human MHC class II alleles and their aggregation propensities. The binding of the designed variants was tested experimentally, as well as their aggregation capacity. High-affinity MHC class II binders in vitro were more disposed to aggregate forming amyloid fibrils capable of binding Thioflavin T and congo red, while low affinity MHC class II binders remained soluble or formed rare amorphous aggregates. This study shows a possible connection between the aggregation propensity of an epitope and its affinity for the MHC class II cleft.

Multiple-Allele MHC Class II Epitope Engineering by a Molecular Dynamics-Based Evolution Protocol

Epitopes that bind simultaneously to all human alleles of Major Histocompatibility Complex class II (MHC II) are considered one of the key factors for the development of improved vaccines and cancer immunotherapies. To engineer MHC II multiple-allele binders, we developed a protocol called PanMHC-PARCE, based on the unsupervised optimization of the epitope sequence by single-point mutations, parallel explicit-solvent molecular dynamics simulations and scoring of the MHC II-epitope complexes. The key idea is accepting mutations that not only improve the affinity but also reduce the affinity gap between the alleles. We applied this methodology to enhance a Plasmodium vivax epitope for multiple-allele binding. In vitro rate-binding assays showed that four engineered peptides were able to bind with improved affinity toward multiple human MHC II alleles. Moreover, we demonstrated that mice immunized with the peptides exhibited interferon-gamma cellular immune response. Overall, the method enables the engineering of peptides with improved binding properties that can be used for the generation of new immunotherapies.

Computational Evolution Protocol for Peptide Design

Computational peptide design is useful for therapeutics, diagnostics, and vaccine development. To select the most promising peptide candidates, the key is describing accurately the peptide-target interactions at the molecular level. We here review a computational peptide design protocol whose key feature is the use of all-atom explicit solvent molecular dynamics for describing the different peptide-target complexes explored during the optimization. We describe the milestones behind the development of this protocol, which is now implemented in an open-source code called PARCE. We provide a basic tutorial to run the code for an antibody fragment design example. Finally, we describe three additional applications of the method to design peptides for different targets, illustrating the broad scope of the proposed approach.

Impact of Structural Observables From Simulations to Predict the Effect of Single-Point Mutations in MHC Class II Peptide Binders

The prediction of peptide binders to Major Histocompatibility Complex (MHC) class II receptors is of great interest to study autoimmune diseases and for vaccine development. Most approaches predict the affinities using sequence-based models trained on experimental data and multiple alignments from known peptide substrates. However, detecting activity differences caused by single-point mutations is a challenging task. In this work, we used interactions calculated from simulations to build scoring matrices for quickly estimating binding differences by single-point mutations. We modelled a set of 837 peptides bound to an MHC class II allele, and optimized the sampling of the conformations using the Rosetta backrub method by comparing the results to molecular dynamics simulations. From the dynamic trajectories of each complex, we averaged and compared structural observables for each amino acid at each position of the 9°mer peptide core region. With this information, we generated the scoring-matrices to predict the sign of the binding differences. We then compared the performance of the best scoring-matrix to different computational methodologies that range in computational costs. Overall, the prediction of the activity differences caused by single mutated peptides was lower than 60% for all the methods. However, the developed scoring-matrix in combination with existing methods reports an increase in the performance, up to 86% with a scoring method that uses molecular dynamics.

Intrinsically Disordered Protein Ensembles Shape Evolutionary Rates Revealing Conformational Patterns

Intrinsically disordered proteins (IDPs) lack stable tertiary structure under physiological conditions. The unique composition and complex dynamical behaviour of IDPs make them a challenge for structural biology and molecular evolution studies. Using NMR ensembles, we found that IDPs evolve under a strong site-specific evolutionary rate heterogeneity, mainly originated by different constraints derived from their inter-residue contacts. Evolutionary rate profiles correlate with the experimentally observed conformational diversity of the protein, allowing the description of different conformational patterns possibly related to their structure-function relationships. The correlation between evolutionary rates and contact information improves when structural information is taken not from any individual conformer or the whole ensemble, but from combining a limited number of conformers. Our results suggest that residue contacts in disordered regions constrain evolutionary rates to conserve the dynamic behaviour of the ensemble and that evolutionary rates can be used as a proxy for the conformational diversity of IDPs.

Alkamides and Piperamides as Potential Antivirals against the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2)

The pandemic caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has quickly spread globally, infecting millions and killing hundreds of thousands of people. Herein, to identify potential antiviral agents, 97 natural amide-like compounds known as alkamides and piperamides were tested against SARS-CoV-2 main protease (Mpro) and RNA-dependent RNA polymerase (RdRp), and the human angiotensin-converting enzyme 2 (ACE2) using molecular docking and molecular dynamics simulations. The docking results showed that alkamides and dimeric piperamides from Piper species have a high binding affinity and potential antiviral activity against SARS-CoV-2. The absorption, distribution, metabolism, and excretion (ADME) profile and Lipinski's rule of five showed that dimeric piperamides have druglikeness potential. The molecular dynamics results showed that pipercyclobutanamide B forms a complex with Mpro at a similar level of stability than N3-I. Our overall results indicate that alkamides and piperamides, and specifically pipercyclobutanamide B, should be further studied as compounds with SARS-CoV-2 antiviral properties.

Predicting the Affinity of Peptides to Major Histocompatibility Complex Class II by Scoring Molecular Dynamics Simulations

Predicting the binding affinity of peptides able to interact with major histocompatibility complex (MHC) molecules is a priority for researchers working in the identification of novel vaccines candidates. Most available approaches are based on the analysis of the sequence of peptides of known experimental affinity. However, for MHC class II receptors, these approaches are not very accurate, due to the intrinsic flexibility of the complex. To overcome these limitations, we propose to estimate the binding affinity of peptides bound to an MHC class II by averaging the score of the configurations from finite-temperature molecular dynamics simulations. The score is estimated for 18 different scoring functions, and we explored the optimal manner for combining them. To test the predictions, we considered eight peptides of known binding affinity. We found that six scoring functions correlate with the experimental ranking of the peptides significantly better than the others. We then assessed a set of techniques for combining the scoring functions by linear regression and logistic regression. We obtained a maximum accuracy of 82% for the predicted sign of the binding affinity using a logistic regression with optimized weights. These results are potentially useful to improve the reliability of in silico protocols to design high-affinity binding peptides for MHC class II receptors.

ANDIS: an atomic angle- and distance-dependent statistical potential for protein structure quality assessment

Background

The knowledge-based statistical potential has been widely used in protein structure modeling and model quality assessment. They are commonly evaluated based on their abilities of native recognition as well as decoy discrimination. However, these two aspects are found to be mutually exclusive in many statistical potentials.

Results

We developed an atomic ANgle- and DIStance-dependent (ANDIS) statistical potential for protein structure quality assessment with distance cutoff being a tunable parameter. When distance cutoff is ≤9.0 Å, “effective atomic interaction” is employed to enhance the ability of native recognition. For a distance cutoff of ≥10 Å, the distance-dependent atom-pair potential with random-walk reference state is combined to strengthen the ability of decoy discrimination. Benchmark tests on 632 structural decoy sets from diverse sources demonstrate that ANDIS outperforms other state-of-the-art potentials in both native recognition and decoy discrimination.

Conclusions

Distance cutoff is a crucial parameter for distance-dependent statistical potentials. A lower distance cutoff is better for native recognition, while a higher one is favorable for decoy discrimination. The ANDIS potential is freely available as a standalone application at http://qbp.hzau.edu.cn/ANDIS/.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2898-y) contains supplementary material, which is available to authorized users.

Molecular dynamics simulations of β2-microglobulin interaction with hydrophobic surfaces

Hydrophobic surfaces are known to adsorb and unfold proteins, a process that has been studied only for a few proteins. Here we address the interaction of β2-microglobulin, a paradigmatic protein for the study of amyloidogenesis, with hydrophobic surfaces. A system with 27 copies of the protein surrounded by a model cubic hydrophobic box is studied by implicit solvent molecular dynamics simulations. Most proteins adsorb on the walls of the box without major distortions in local geometry, whereas free molecules maintain proper structures and fluctuations as observed in explicit solvent molecular dynamics simulations. The major conclusions from the simulations are as follows: (i) the adopted implicit solvent model is adequate to describe protein dynamics and thermodynamics; (ii) adsorption occurs readily and is irreversible on the simulated timescale; (iii) the regions most involved in molecular encounters and stable interactions with the walls are the same as those that are important in protein-protein and protein-nanoparticle interactions; (iv) unfolding following adsorption occurs at regions found to be flexible by both experiments and simulations; (v) thermodynamic analysis suggests a very large contribution from van der Waals interactions, whereas unfavorable electrostatic interactions are not found to contribute much to adsorption energy. Surfaces with different degrees of hydrophobicity may occur in vivo. Our simulations show that adsorption is a fast and irreversible process which is accompanied by partial unfolding. The results and the thermodynamic analysis presented here are consistent with and rationalize previous experimental work.

A Novel Framework for Ab Initio Coarse Protein Structure Prediction

Hydrophobic-Polar model is a simplified representation of Protein Structure Prediction (PSP) problem. However, even with the HP model, the PSP problem remains NP-complete. This work proposes a systematic and problem specific design for operators of the evolutionary program which hybrids with local search hill climbing, to efficiently explore the search space of PSP and thereby obtain an optimum conformation. The proposed algorithm achieves this by incorporating the following novel features: (i) new initialization method which generates only valid individuals with (rather than random) better fitness values; (ii) use of probability-based selection operators that limit the local convergence; (iii) use of secondary structure based mutation operator that makes the structure more closely to the laboratory determined structure; and (iv) incorporating all the above-mentioned features developed a complete two-tier framework. The developed framework builds the protein conformation on the square and triangular lattice. The test has been performed using benchmark sequences, and a comparative evaluation is done with various state-of-the-art algorithms. Moreover, in addition to hypothetical test sequences, we have tested protein sequences deposited in protein database repository. It has been observed that the proposed framework has shown superior performance regarding accuracy (fitness value) and speed (number of generations needed to attain the final conformation). The concepts used to enhance the performance are generic and can be used with any other population-based search algorithm such as genetic algorithm, ant colony optimization, and immune algorithm.

Dynamics and Thermodynamics of Transthyretin Association from Molecular Dynamics Simulations

Molecular dynamics simulations are used in this work to probe the structural stability and the dynamics of engineered mutants of transthyretin (TTR), i.e., the double mutant F87M/L110M (MT-TTR) and the triple mutant F87M/L110M/S117E (3M-TTR), in relation to wild-type. Free energy analysis from end-point simulations and statistical effective energy functions are used to analyze trajectories, revealing that mutations do not have major impact on protein structure but rather on protein association, shifting the equilibria towards dissociated species. The result is confirmed by the analysis of 3M-TTR which shows dissociation within the first 10 ns of the simulation, indicating that contacts are lost at the dimer-dimer interface, whereas dimers (formed by monomers which pair to form two extended β-sheets) appear fairly stable. Overall the simulations provide a detailed view of the dynamics and thermodynamics of wild-type and mutant transthyretins and a rationale of the observed effects.

Prediction of HIV Drug Resistance by Combining Sequence and Structural Properties

Drug resistance is a major obstacle faced by therapist in treating HIV infected patients. The reason behind these phenomena is either protein mutation or the changes in gene expression level that induces resistance to drug treatments. These mutations affect the drug binding activity, hence resulting in failure of treatment. Therefore, it is necessary to conduct resistance testing in order to carry out HIV effective therapy. This study combines both sequence and structural features for predicting HIV resistance by applying SVM and Random Forests classifiers. The model was tested on the mutants of HIV-1 protease and reverse transcriptase. Taken together the features we have used in our method, total contact energies among multiple mutations have a strong impact in predicting resistance as they are crucial in understanding the interactions of HIV mutants. The combination of sequence-structure features offers high accuracy with support vector machines as compared to Random Forests classifier. Both single and acquisition of multiple mutations are important in predicting HIV resistance to certain drug treatments. We have discovered the practicality of these features; hence, these can be used in the future to predict resistance for other complex diseases.

Pockets as structural descriptors of EGFR kinase conformations

Epidermal Growth Factor Receptor (EGFR), a tyrosine kinase receptor, is one of the main tumor markers in different types of cancers. The kinase native state is mainly composed of two populations of conformers: active and inactive. Several sequence variations in EGFR kinase region promote the differential enrichment of conformers with higher activity. Some structural characteristics have been proposed to differentiate kinase conformations, but these considerations could lead to ambiguous classifications. We present a structural characterisation of EGFR kinase conformers, focused on active site pocket comparisons, and the mapping of known pathological sequence variations. A structural based clustering of this pocket accurately discriminates active from inactive, well-characterised conformations. Furthermore, this main pocket contains, or is in close contact with, ≈65% of cancer-related variation positions. Although the relevance of protein dynamics to explain biological function has been extensively recognised, the usage of the ensemble of conformations in dynamic equilibrium to represent the functional state of proteins and the importance of pockets, cavities and/or tunnels was often neglected in previous studies. These functional structures and the equilibrium between them could be structurally analysed in wild type as well as in sequence variants. Our results indicate that biologically important pockets, as well as their shape and dynamics, are central to understanding protein function in wild-type, polymorphic or disease-related variations.

Guided macro-mutation in a graded energy based genetic algorithm for protein structure prediction

Protein structure prediction is considered as one of the most challenging and computationally intractable combinatorial problem. Thus, the efficient modeling of convoluted search space, the clever use of energy functions, and more importantly, the use of effective sampling algorithms become crucial to address this problem. For protein structure modeling, an off-lattice model provides limited scopes to exercise and evaluate the algorithmic developments due to its astronomically large set of data-points. In contrast, an on-lattice model widens the scopes and permits studying the relatively larger proteins because of its finite set of data-points. In this work, we took the full advantage of an on-lattice model by using a face-centered-cube lattice that has the highest packing density with the maximum degree of freedom. We proposed a graded energy-strategically mixes the Miyazawa-Jernigan (MJ) energy with the hydrophobic-polar (HP) energy-based genetic algorithm (GA) for conformational search. In our application, we introduced a 2 × 2 HP energy guided macro-mutation operator within the GA to explore the best possible local changes exhaustively. Conversely, the 20 × 20 MJ energy model-the ultimate objective function of our GA that needs to be minimized-considers the impacts amongst the 20 different amino acids and allow searching the globally acceptable conformations. On a set of benchmark proteins, our proposed approach outperformed state-of-the-art approaches in terms of the free energy levels and the root-mean-square deviations.

Efficient conformational space exploration in ab initio protein folding simulation

Ab initio protein folding simulation largely depends on knowledge-based energy functions that are derived from known protein structures using statistical methods. These knowledge-based energy functions provide us with a good approximation of real protein energetics. However, these energy functions are not very informative for search algorithms and fail to distinguish the types of amino acid interactions that contribute largely to the energy function from those that do not. As a result, search algorithms frequently get trapped into the local minima. On the other hand, the hydrophobic-polar (HP) model considers hydrophobic interactions only. The simplified nature of HP energy function makes it limited only to a low-resolution model. In this paper, we present a strategy to derive a non-uniform scaled version of the real 20×20 pairwise energy function. The non-uniform scaling helps tackle the difficulty faced by a real energy function, whereas the integration of 20×20 pairwise information overcomes the limitations faced by the HP energy function. Here, we have applied a derived energy function with a genetic algorithm on discrete lattices. On a standard set of benchmark protein sequences, our approach significantly outperforms the state-of-the-art methods for similar models. Our approach has been able to explore regions of the conformational space which all the previous methods have failed to explore. Effectiveness of the derived energy function is presented by showing qualitative differences and similarities of the sampled structures to the native structures. Number of objective function evaluation in a single run of the algorithm is used as a comparison metric to demonstrate efficiency.

Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations

Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes. In particular: reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements;the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state;backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy);the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic.

A Multi-Objective Approach for Protein Structure Prediction Based on an Energy Model and Backbone Angle Preferences

Protein structure prediction (PSP) is concerned with the prediction of protein tertiary structure from primary structure and is a challenging calculation problem. After decades of research effort, numerous solutions have been proposed for optimisation methods based on energy models. However, further investigation and improvement is still needed to increase the accuracy and similarity of structures. This study presents a novel backbone angle preference factor, which is one of the factors inducing protein folding. The proposed multiobjective optimisation approach simultaneously considers energy models and backbone angle preferences to solve the ab initio PSP. To prove the effectiveness of the multiobjective optimisation approach based on the energy models and backbone angle preferences, 75 amino acid sequences with lengths ranging from 22 to 88 amino acids were selected from the CB513 data set to be the benchmarks. The data sets were highly dissimilar, therefore indicating that they are meaningful. The experimental results showed that the root-mean-square deviation (RMSD) of the multiobjective optimization approach based on energy model and backbone angle preferences was superior to those of typical energy models, indicating that the proposed approach can facilitate the ab initio PSP.

Mechanistic overview of ADP-ribosylation reactions

ADP-ribosylation reactions consist of mono-ADP-ribosylation, poly-ADP-ribosylation and cyclic ADP-ribosylation. These reactions play essential roles in many important physiological and pathophysiological events. The types of chemical linkages, the evolutionarily conserved motif within the enzymes to determine the target specificity, stereochemistry of the ADP-ribosylated products, and the chemical reactions taking place among the enzymes and substrates are discussed.

How good are simplified models for protein structure prediction?

Protein structure prediction (PSP) has been one of the most challenging problems in computational biology for several decades. The challenge is largely due to the complexity of the all-atomic details and the unknown nature of the energy function. Researchers have therefore used simplified energy models that consider interaction potentials only between the amino acid monomers in contact on discrete lattices. The restricted nature of the lattices and the energy models poses a twofold concern regarding the assessment of the models. Can a native or a very close structure be obtained when structures are mapped to lattices? Can the contact based energy models on discrete lattices guide the search towards the native structures? In this paper, we use the protein chain lattice fitting (PCLF) problem to address the first concern; we developed a constraint-based local search algorithm for the PCLF problem for cubic and face-centered cubic lattices and found very close lattice fits for the native structures. For the second concern, we use a number of techniques to sample the conformation space and find correlations between energy functions and root mean square deviation (RMSD) distance of the lattice-based structures with the native structures. Our analysis reveals weakness of several contact based energy models used that are popular in PSP.

A Parallel Framework for Multipoint Spiral Search in ab Initio Protein Structure Prediction

Protein structure prediction is computationally a very challenging problem. A large number of existing search algorithms attempt to solve the problem by exploring possible structures and finding the one with the minimum free energy. However, these algorithms perform poorly on large sized proteins due to an astronomically wide search space. In this paper, we present a multipoint spiral search framework that uses parallel processing techniques to expedite exploration by starting from different points. In our approach, a set of random initial solutions are generated and distributed to different threads. We allow each thread to run for a predefined period of time. The improved solutions are stored threadwise. When the threads finish, the solutions are merged together and the duplicates are removed. A selected distinct set of solutions are then split to different threads again. In our ab initio protein structure prediction method, we use the three-dimensional face-centred-cubic lattice for structure-backbone mapping. We use both the low resolution hydrophobic-polar energy model and the high-resolution 20 × 20 energy model for search guiding. The experimental results show that our new parallel framework significantly improves the results obtained by the state-of-the-art single-point search approaches for both energy models on three-dimensional face-centred-cubic lattice. We also experimentally show the effectiveness of mixing energy models within parallel threads.

A firefly-inspired method for protein structure prediction in lattice models

We introduce a Firefly-inspired algorithmic approach for protein structure prediction over two different lattice models in three-dimensional space. In particular, we consider three-dimensional cubic and three-dimensional face-centred-cubic (FCC) lattices. The underlying energy models are the Hydrophobic-Polar (H-P) model, the Miyazawa–Jernigan (M-J) model and a related matrix model. The implementation of our approach is tested on ten H-P benchmark problems of a length of 48 and ten M-J benchmark problems of a length ranging from 48 until 61. The key complexity parameter we investigate is the total number of objective function evaluations required to achieve the optimum energy values for the H-P model or competitive results in comparison to published values for the M-J model. For H-P instances and cubic lattices, where data for comparison are available, we obtain an average speed-up over eight instances of 2.1, leaving out two extreme values (otherwise, 8.8). For six M-J instances, data for comparison are available for cubic lattices and runs with a population size of 100, where, a priori, the minimum free energy is a termination criterion. The average speed-up over four instances is 1.2 (leaving out two extreme values, otherwise 1.1), which is achieved for a population size of only eight instances. The present study is a test case with initial results for ad hoc parameter settings, with the aim of justifying future research on larger instances within lattice model settings, eventually leading to the ultimate goal of implementations for off-lattice models.

Mixing energy models in genetic algorithms for on-lattice protein structure prediction

Protein structure prediction (PSP) is computationally a very challenging problem. The challenge largely comes from the fact that the energy function that needs to be minimised in order to obtain the native structure of a given protein is not clearly known. A high resolution 20 × 20 energy model could better capture the behaviour of the actual energy function than a low resolution energy model such as hydrophobic polar. However, the fine grained details of the high resolution interaction energy matrix are often not very informative for guiding the search. In contrast, a low resolution energy model could effectively bias the search towards certain promising directions. In this paper, we develop a genetic algorithm that mainly uses a high resolution energy model for protein structure evaluation but uses a low resolution HP energy model in focussing the search towards exploring structures that have hydrophobic cores. We experimentally show that this mixing of energy models leads to significant lower energy structures compared to the state-of-the-art results.

SP-dock: protein-protein docking using shape and physicochemical complementarity

In this paper, a framework for protein-protein docking is proposed, which exploits both shape and physicochemical complementarity to generate improved docking predictions. Shape complementarity is achieved by matching local surface patches. However, unlike existing approaches, which are based on single-patch or two-patch matching, we developed a new algorithm that compares simultaneously, groups of neighboring patches from the receptor with groups of neighboring patches from the ligand. Taking into account the fact that shape complementarity in protein surfaces is mostly approximate rather than exact, the proposed group-based matching algorithm fits perfectly to the nature of protein surfaces. This is demonstrated by the high performance that our method achieves especially in the case where the unbound structures of the proteins are considered. Additionally, several physicochemical factors, such as desolvation energy, electrostatic complementarity (EC), hydrophobicity (HP), Coulomb potential (CP), and Lennard-Jones potential are integrated using an optimized scoring function, improving geometric ranking in more than 60 percent of the complexes of Docking Benchmark 2.4.

Studying interactions by molecular dynamics simulations at high concentration

Molecular dynamics simulations have been used to study molecular encounters and recognition. In recent works, simulations using high concentration of interacting molecules have been performed. In this paper, we consider the practical problems for setting up the simulation and to analyse the results of the simulation. The simulation of beta 2-microglobulin association and the simulation of the binding of hydrogen peroxide by glutathione peroxidase are provided as examples.

Molecular dynamics simulation of β₂-microglobulin in denaturing and stabilizing conditions

β₂-Microglobulin has been a model system for the study of fibril formation for 20 years. The experimental study of β₂-microglobulin structure, dynamics, and thermodynamics in solution, at atomic detail, along the pathway leading to fibril formation is difficult because the onset of disorder and aggregation prevents signal resolution in Nuclear Magnetic Resonance experiments. Moreover, it is difficult to characterize conformers in exchange equilibrium. To gain insight (at atomic level) on processes for which experimental information is available at molecular or supramolecular level, molecular dynamics simulations have been widely used in the last decade. Here, we use molecular dynamics to address three key aspects of β₂-microglobulin, which are known to be relevant to amyloid formation: (1) 60 ns molecular dynamics simulations of β₂-microglobulin in trifluoroethanol and in conditions mimicking low pH are used to study the behavior of the protein in environmental conditions that are able to trigger amyloid formation; (2) adaptive biasing force molecular dynamics simulation is used to force cis-trans isomerization at Proline 32 and to calculate the relative free energy in the folded and unfolded state. The native-like trans-conformer (known as intermediate 2 and determining the slow phase of refolding), is simulated for 10 ns, detailing the possible link between cis-trans isomerization and conformational disorder; (3) molecular dynamics simulation of highly concentrated doxycycline (a molecule able to suppress fibril formation) in the presence of β₂-microglobulin provides details of the binding modes of the drug and a rationale for its effect.

Protein-protein docking by shape-complementarity and property matching

We present a computational approach to protein-protein docking based on surface shape complementarity ("ProBinder"). Within this docking approach, we implemented a new surface decomposition method that considers local shape features on the protein surface. This new surface shape decomposition results in a deterministic representation of curvature features on the protein surface, such as "knobs," "holes," and "flats" together with their point normals. For the actual docking procedure, we used geometric hashing, which allows for the rapid, translation-, and rotation-free comparison of point coordinates. Candidate solutions were scored based on knowledge-based potentials and steric criteria. The potentials included electrostatic complementarity, desolvation energy, amino acid contact preferences, and a van-der-Waals potential. We applied ProBinder to a diverse test set of 68 bound and 30 unbound test cases compiled from the Dockground database. Sixty-four percent of the protein-protein test complexes were ranked with an root mean square deviation (RMSD) < 5 A to the target solution among the top 10 predictions for the bound data set. In 82% of the unbound samples, docking poses were ranked within the top ten solutions with an RMSD < 10 A to the target solution.

Information-theoretic analysis of the reference state in contact potentials used for protein structure prediction

Using information-theoretic concepts, we examine the role of the reference state, a crucial component of empirical potential functions, in protein fold recognition. We derive an information-based connection between the probability distribution functions of the reference state and those that characterize the decoy set used in threading. In examining commonly used contact reference states, we find that the quasi-chemical approximation is informatically superior to other variant models designed to include characteristics of real protein chains, such as finite length and variable amino acid composition from protein to protein. We observe that in these variant models, the total divergence, the operative function that quantifies discrimination, decreases along with threading performance. We find that any amount of nativeness encoded in the reference state model does not significantly improve threading performance. A promising avenue for the development of better potentials is suggested by our information-theoretic analysis of the action of contact potentials on individual protein sequences. Our results show that contact potentials perform better when the compositional properties of the data set used to derive the score function probabilities are similar to the properties of the sequence of interest. Results also suggest to use only sequences of similar composition in deriving contact potentials, to tailor the contact potential specifically for a test sequence.

A hybrid approach to protein folding problem integrating constraint programming with local search

Background

The protein folding problem remains one of the most challenging open problems in computational biology. Simplified models in terms of lattice structure and energy function have been proposed to ease the computational hardness of this optimization problem. Heuristic search algorithms and constraint programming are two common techniques to approach this problem. The present study introduces a novel hybrid approach to simulate the protein folding problem using constraint programming technique integrated within local search.

Results

Using the face-centered-cubic lattice model and 20 amino acid pairwise interactions energy function for the protein folding problem, a constraint programming technique has been applied to generate the neighbourhood conformations that are to be used in generic local search procedure. Experiments have been conducted for a few small and medium sized proteins. Results have been compared with both pure constraint programming approach and local search using well-established local move set. Substantial improvements have been observed in terms of final energy values within acceptable runtime using the hybrid approach.

Conclusion

Constraint programming approaches usually provide optimal results but become slow as the problem size grows. Local search approaches are usually faster but do not guarantee optimal solutions and tend to stuck in local minima. The encouraging results obtained on the small proteins show that these two approaches can be combined efficiently to obtain better quality solutions within acceptable time. It also encourages future researchers on adopting hybrid techniques to solve other hard optimization problems.

Another look at the conditions for the extraction of protein knowledge-based potentials

Protein knowledge-based potentials are effective free energies obtained from databases of known protein structures. They are used to parameterize coarse-grained protein models in many folding simulation and structure prediction methods. Two common approaches are used in the derivation of knowledge-based potentials. One assumes that the energy parameters optimize the native structure stability. The other assumes that interaction events are related to their energies according to the Boltzmann distribution, and that they are distributed independently of other events, that is, the quasi-chemical approximation. Here, these assumptions are systematically tested by extracting contact energies from artificial databases of lattice proteins with predefined pairwise contact energies. Databases of protein sequences are designed to either satisfy the Boltzmann distribution at high or low temperatures, or to simultaneously optimize the native stability and folding kinetics. It is found that the quasi-chemical approximation, with the ideal reference state, accurately reproduce the true energies for high temperature Boltzmann distributed sequences (weakly interacting residues), but less accurately at low temperatures, where the sequences correspond to energy minima and the residues are strongly interacting. To overcome this problem, an iterative procedure for Boltzmann distributed sequences is introduced, which accounts for interacting residue correlations and eliminates the need for the quasi-chemical approximation. In this case, the energies are accurately reproduced at any ensemble temperature. However, when the database of sequences designed for optimal stability and kinetics is used, the energy correlation is less than optimal using either method, exhibiting random and systematic deviations from linearity. Therefore, the assumption that native structures are maximally stable or that sequences are determined according to the Boltzmann distribution seems to be inadequate for obtaining accurate energies. The limited number of sequences in the database and the inhomogeneous concentration of amino acids from one structure to another do not seem to be major obstacles for improving the quality of the extracted pairwise energies, with the exception of repulsive interactions.

ProCKSI: a decision support system for Protein (structure) Comparison, Knowledge, Similarity and Information

Background

We introduce the decision support system for Protein (Structure) Comparison, Knowledge, Similarity and Information (ProCKSI). ProCKSI integrates various protein similarity measures through an easy to use interface that allows the comparison of multiple proteins simultaneously. It employs the Universal Similarity Metric (USM), the Maximum Contact Map Overlap (MaxCMO) of protein structures and other external methods such as the DaliLite and the TM-align methods, the Combinatorial Extension (CE) of the optimal path, and the FAST Align and Search Tool (FAST). Additionally, ProCKSI allows the user to upload a user-defined similarity matrix supplementing the methods mentioned, and computes a similarity consensus in order to provide a rich, integrated, multicriteria view of large datasets of protein structures.

Results

We present ProCKSI's architecture and workflow describing its intuitive user interface, and show its potential on three distinct test-cases. In the first case, ProCKSI is used to evaluate the results of a previous CASP competition, assessing the similarity of proposed models for given targets where the structures could have a large deviation from one another. To perform this type of comparison reliably, we introduce a new consensus method. The second study deals with the verification of a classification scheme for protein kinases, originally derived by sequence comparison by Hanks and Hunter, but here we use a consensus similarity measure based on structures. In the third experiment using the Rost and Sander dataset (RS126), we investigate how a combination of different sets of similarity measures influences the quality and performance of ProCKSI's new consensus measure. ProCKSI performs well with all three datasets, showing its potential for complex, simultaneous multi-method assessment of structural similarity in large protein datasets. Furthermore, combining different similarity measures is usually more robust than relying on one single, unique measure.

Conclusion

Based on a diverse set of similarity measures, ProCKSI computes a consensus similarity profile for the entire protein set. All results can be clustered, visualised, analysed and easily compared with each other through a simple and intuitive interface.

ProCKSI is publicly available at for academic and non-commercial use.

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

Background

Reduced 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.

Results

All 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.

Conclusion

The 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: .

Molecular dynamics simulation suggests possible interaction patterns at early steps of beta2-microglobulin aggregation

Early events in aggregation of proteins are not easily accessible by experiments. In this work, we perform a 5-ns molecular dynamics simulation of an ensemble of 27 copies of beta(2)-microglobulin in explicit solvent. During the simulation, the formation of intermolecular contacts is observed. The simulation highlights the importance of apical residues and, in particular, of those at the N-terminus end of the molecule. The most frequently found pattern of interaction involves a head-to-head contact arrangement of molecules. Hydrophobic contacts appear to be important for the establishment of long-lived (on the simulation timescale) contacts. Although early events on the pathway to aggregation and fibril formation are not directly related to the end-state of the process, which is reached on a much longer timescale, simulation results are consistent with experimental data and in general with a parallel arrangement of intermolecular beta-strand pairs.

Mutation-biased adaptation in a protein NK model

Evolutionary trends responsible for systematic differences in genome and proteome composition have been attributed to GC:AT mutation bias in the context of neutral evolution or to selection acting on genome composition. A possibility that has been ignored, presumably because it is part of neither the Modern Synthesis nor the Neutral Theory, is that mutation may impose a directional bias on adaptation. This possibility is explored here with simulations of the effect of a GC:AT bias on amino acid composition during adaptive walks on an abstract protein fitness landscape called an "NK" model. The results indicate that adaptation does not preclude mutation-biased evolution. In the complete absence of neutral evolution, a modest GC:AT bias of realistic magnitude can displace the trajectory of adaptation in a mutationally favored direction, to such a degree that amino acid composition is biased substantially and persistently. Thus, mutational explanations for evolved patterns need not presuppose neutral evolution.

Novel knowledge-based mean force potential at the profile level

Background

The development and testing of functions for the modeling of protein energetics is an important part of current research aimed at understanding protein structure and function. Knowledge-based mean force potentials are derived from statistical analyses of interacting groups in experimentally determined protein structures. Current knowledge-based mean force potentials are developed at the atom or amino acid level. The evolutionary information contained in the profiles is not investigated. Based on these observations, a class of novel knowledge-based mean force potentials at the profile level has been presented, which uses the evolutionary information of profiles for developing more powerful statistical potentials.

Results

The frequency profiles are directly calculated from the multiple sequence alignments outputted by PSI-BLAST and converted into binary profiles with a probability threshold. As a result, the protein sequences are represented as sequences of binary profiles rather than sequences of amino acids. Similar to the knowledge-based potentials at the residue level, a class of novel potentials at the profile level is introduced. We develop four types of profile-level statistical potentials including distance-dependent, contact, Φ/Ψ dihedral angle and accessible surface statistical potentials. These potentials are first evaluated by the fold assessment between the correct and incorrect models generated by comparative modeling from our own and other groups. They are then used to recognize the native structures from well-constructed decoy sets. Experimental results show that all the knowledge-base mean force potentials at the profile level outperform those at the residue level. Significant improvements are obtained for the distance-dependent and accessible surface potentials (5–6%). The contact and Φ/Ψ dihedral angle potential only get a slight improvement (1–2%). Decoy set evaluation results show that the distance-dependent profile-level potentials even outperform other atom-level potentials. We also demonstrate that profile-level statistical potentials can improve the performance of threading.

Conclusion

The knowledge-base mean force potentials at the profile level can provide better discriminatory ability than those at the residue level, so they will be useful for protein structure prediction and model refinement.

The victor/FRST function for model quality estimation

Scoring functions are widely used in the final step of model selection in protein structure prediction. This is of interest both for comparative modeling targets, where it is important to select the best model among a set of many good, "correct" ones, as well as for other (fold recognition or novel fold) targets, where the set may contain many incorrect models. A novel combination of four knowledge-based potentials recognizing different features of native protein structures is introduced and tested. The pairwise, solvation, hydrogen bond, and torsion angle potentials contain largely orthogonal information. Of these, the torsion angle potential is found to show the strongest correlation with model quality. Combining these features with a linear weighting function, it was possible to construct a robust energy function capable of discriminating native-like structures on several benchmarking sets. In a recent blind test (CAFASP-4 MQAP), the scoring function ranked consistently well and was able to reliably distinguish the correct template from an ensemble of high quality decoys in 52 of 70 cases (33 of 34 for comparative modeling). An executable version of the Victor/FRST function for Linux PCs is available for download from the URL http://protein.cribi.unipd.it/frst/.

A decoy set for the thermostable subdomain from chicken villin headpiece, comparison of different free energy estimators

BACKGROUND

Estimators of free energies are routinely used to judge the quality of protein structural models. As these estimators still present inaccuracies, they are frequently evaluated by discriminating native or native-like conformations from large ensembles of so-called decoy structures.

RESULTS

A decoy set is obtained from snapshots taken from 5 long (100 ns) molecular dynamics (MD) simulations of the thermostable subdomain from chicken villin headpiece. An evaluation of the energy of the decoys is given using: i) a residue based contact potential supplemented by a term for the quality of dihedral angles; ii) a recently introduced combination of four statistical scoring functions for model quality estimation (FRST); iii) molecular mechanics with solvation energy estimated either according to the generalized Born surface area (GBSA) or iv) the Poisson-Boltzmann surface area (PBSA) method.

CONCLUSION

The decoy set presented here has the following features which make it attractive for testing energy scoring functions:1) it covers a broad range of RMSD values (from less than 2.0 A to more than 12 A);2) it has been obtained from molecular dynamics trajectories, starting from different non-native-like conformations which have diverse behaviour, with secondary structure elements correctly or incorrectly formed, and in one case folding to a native-like structure. This allows not only for scoring of static structures, but also for studying, using free energy estimators, the kinetics of folding;3) all structures have been obtained from accurate MD simulations in explicit solvent and after molecular mechanics (MM) energy minimization using an implicit solvent method. The quality of the covalent structure therefore does not suffer from steric or covalent problems. The statistical and physical effective energy functions tested on the set behave differently when native simulation snapshots are included or not in the set and when averaging over the trajectory is performed.

QUASAR--scoring and ranking of sequence-structure alignments

SUMMARY

Sequence-structure alignments are a common means for protein structure prediction in the fields of fold recognition and homology modeling, and there is a broad variety of programs that provide such alignments based on sequence similarity, secondary structure or contact potentials. Nevertheless, finding the best sequence-structure alignment in a pool of alignments remains a difficult problem. QUASAR (quality of sequence-structure alignments ranking) provides a unifying framework for scoring sequence-structure alignments that aids finding well-performing combinations of well-known and custom-made scoring schemes. Those scoring functions can be benchmarked against widely accepted quality scores like MaxSub, TMScore, Touch and APDB, thus enabling users to test their own alignment scores against 'standard-of-truth' structure-based scores. Furthermore, individual score combinations can be optimized with respect to benchmark sets based on known structural relationships using QUASAR's in-built optimization routines.

Application of MM/PBSA colony free energy to loop decoy discrimination: toward correlation between energy and root mean square deviation

Accurate free energy estimation is needed in many predictive tasks. The molecular mechanics/Poisson-Boltzmann solvent accessible surface area (MM/PBSA) approach has proven to be accurate. However, the correlation between the estimated free energy and the distance (e.g., root mean square deviation [RMSD]) from the most stable conformation is hindered by the strong free energy dependence on minor conformational variations. In this paper, a protocol for MM/PBSA free energy estimation is designed and tested on several loop decoy sets. We show that further integration of MM/PBSA free energy estimator with the colony energy approach makes the correlation between the free energy and RMSD from the native structure apparent, for the test sets on which it could be applied. Our results suggest that (1) the MM/PBSA free energy estimator is able to detect native-like structures for most decoy sets, and (2) application of the colony energy approach greatly hampers the MM/energy strong dependence on minor conformational changes.

Generality of the Structurally Constrained Protein Evolution model: assessment on representatives of the four main fold classes

The Structurally Constrained Protein Evolution (SCPE) model simulates protein evolution by introducing random mutations into the evolving sequences and selecting them against too much structural perturbation. Given a single protein structure, the SCPE model can be used to obtain a whole set of site-dependent amino acid substitution matrices. The set of SCPE substitution matrices for a given protein family can be seen as an independent-sites model of evolution for that family. Thus, these matrices can be compared with other substitution-matrix-based models of evolution. So far, SCPE has been tested only on left-handed parallel beta helix (LbetaH) proteins. Here, we address the question of generality by assessing the SCPE model on representatives of the four main classes of folds: alpha, beta, alpha+beta, and alpha/beta. We compare with other models using the likelihood ratio test with parametric bootstrapping. We show that SCPE performs better than the popular JTT model for all cases considered. Furthermore, by considering the relative contributions of mutation and selection, we found that the key to the success of the SCPE model is the selection step.

Constraint Logic Programming approach to protein structure prediction

Background

The protein structure prediction problem is one of the most challenging problems in biological sciences. Many approaches have been proposed using database information and/or simplified protein models. The protein structure prediction problem can be cast in the form of an optimization problem. Notwithstanding its importance, the problem has very seldom been tackled by Constraint Logic Programming, a declarative programming paradigm suitable for solving combinatorial optimization problems.

Results

Constraint Logic Programming techniques have been applied to the protein structure prediction problem on the face-centered cube lattice model. Molecular dynamics techniques, endowed with the notion of constraint, have been also exploited. Even using a very simplified model, Constraint Logic Programming on the face-centered cube lattice model allowed us to obtain acceptable results for a few small proteins. As a test implementation their (known) secondary structure and the presence of disulfide bridges are used as constraints. Simplified structures obtained in this way have been converted to all atom models with plausible structure. Results have been compared with a similar approach using a well-established technique as molecular dynamics.

Conclusions

The results obtained on small proteins show that Constraint Logic Programming techniques can be employed for studying protein simplified models, which can be converted into realistic all atom models. The advantage of Constraint Logic Programming over other, much more explored, methodologies, resides in the rapid software prototyping, in the easy way of encoding heuristics, and in exploiting all the advances made in this research area, e.g. in constraint propagation and its use for pruning the huge search space.