Probing protein fold space with a simplified model

Quantitative approaches for decoding the specificity of the human T cell repertoire

T cell receptor (TCR)-peptide-major histocompatibility complex (pMHC) interactions play a vital role in initiating immune responses against pathogens, and the specificity of TCRpMHC interactions is crucial for developing optimized therapeutic strategies. The advent of high-throughput immunological and structural evaluation of TCR and pMHC has provided an abundance of data for computational approaches that aim to predict favorable TCR-pMHC interactions. Current models are constructed using information on protein sequence, structures, or a combination of both, and utilize a variety of statistical learning-based approaches for identifying the rules governing specificity. This review examines the current theoretical, computational, and deep learning approaches for identifying TCR-pMHC recognition pairs, placing emphasis on each method's mathematical approach, predictive performance, and limitations.

A review of visualisations of protein fold networks and their relationship with sequence and function

Proteins form arguably the most significant link between genotype and phenotype. Understanding the relationship between protein sequence and structure, and applying this knowledge to predict function, is difficult. One way to investigate these relationships is by considering the space of protein folds and how one might move from fold to fold through similarity, or potential evolutionary relationships. The many individual characterisations of fold space presented in the literature can tell us a lot about how well the current Protein Data Bank represents protein fold space, how convergence and divergence may affect protein evolution, how proteins affect the whole of which they are part, and how proteins themselves function. A synthesis of these different approaches and viewpoints seems the most likely way to further our knowledge of protein structure evolution and thus, facilitate improved protein structure design and prediction.

Evolution of tunnels in α/β-hydrolase fold proteins—What can we learn from studying epoxide hydrolases?

The evolutionary variability of a protein’s residues is highly dependent on protein region and function. Solvent-exposed residues, excluding those at interaction interfaces, are more variable than buried residues whereas active site residues are considered to be conserved. The abovementioned rules apply also to α/β-hydrolase fold proteins—one of the oldest and the biggest superfamily of enzymes with buried active sites equipped with tunnels linking the reaction site with the exterior. We selected soluble epoxide hydrolases as representative of this family to conduct the first systematic study on the evolution of tunnels. We hypothesised that tunnels are lined by mostly conserved residues, and are equipped with a number of specific variable residues that are able to respond to evolutionary pressure. The hypothesis was confirmed, and we suggested a general and detailed way of the tunnels’ evolution analysis based on entropy values calculated for tunnels’ residues. We also found three different cases of entropy distribution among tunnel-lining residues. These observations can be applied for protein reengineering mimicking the natural evolution process. We propose a ‘perforation’ mechanism for new tunnels design via the merging of internal cavities or protein surface perforation. Based on the literature data, such a strategy of new tunnel design could significantly improve the enzyme’s performance and can be applied widely for enzymes with buried active sites.

So far very little is known about proteins tunnels evolution. The goal of this study is to evaluate the evolution of tunnels in the family of soluble epoxide hydrolases—representatives of numerous α/β-hydrolase fold enzymes. As a result two types of tunnels evolution analysis were proposed (a general and a detailed approach), as well as a ‘perforation’ mechanism which can mimic native evolution in proteins and can be used as an additional strategy for enzymes redesign.

HLA-DM Stabilizes the Empty MHCII Binding Groove: A Model Using Customized Natural Move Monte Carlo

MHC class II molecules bind peptides derived from extracellular proteins that have been ingested by antigen-presenting cells and display them to the immune system. Peptide loading occurs within the antigen-presenting cell and is facilitated by HLA-DM. HLA-DM stabilizes the open conformation of the MHCII binding groove when no peptide is bound. While a structure of the MHCII/HLA-DM complex exists, the mechanism of stabilization is still largely unknown. Here, we applied customized Natural Move Monte Carlo to investigate this interaction. We found a possible long-range mechanism that implicates the configuration of the membrane-proximal globular domains in stabilizing the open state of the empty MHCII binding groove.

Computer-based techniques for lead identification and optimization I: Basics

This chapter focuses on computational techniques for identifying and optimizing lead molecules, with a special emphasis on natural compounds. A number of case studies have been specifically discussed, such as the case of the naphthyridine scaffold, discovered through a structure-based virtual screening (SBVS) and proposed as the starting point for further lead optimization process, to enhance its telomeric RNA selectivity. Another example is the case of Liphagal, a tetracyclic meroterpenoid extracted fromAka coralliphaga, known as PI3Kα inhibitor, provide an evidence for the design of new active congeners against PI3Kα using molecular dynamics (MD) simulations. These are only two of the numerous examples of the computational techniques’ powerful in drug design and drug discovery fields. Finally, the design of drugs that can simultaneously interact with multiple targets as a promising approach for treating complicated diseases has been reported. An example of polypharmacological agents are the compounds extracted from mushrooms identified by means of molecular docking experiments. This chapter may be a useful manual of molecular modeling techniques used in the lead-optimization and lead identification processes.

Avoiding False Positive Conclusions in Molecular Simulation: The Importance of Replicas

Molecular simulations are a computational technique used to investigate the dynamics of proteins and other molecules. The free energy landscape of these simulations is often rugged, and minor differences in the initial velocities, floating-point precision, or underlying hardware can cause identical simulations (replicas) to take different paths in the landscape. In this study we investigated the magnitude of these effects based on 310 000 ns of simulation time. We performed 100 identically parametrized replicas of 3000 ns each for a small 10 amino acid system as well as 100 identically parametrized replicas of 100 ns each for an 827 residue T-cell receptor/MHC system. Comparing randomly chosen subgroups within these replica sets, we estimated the reproducibility and reliability that can be achieved by a given number of replicas at a given simulation time. These results demonstrate that conclusions drawn from single simulations are often not reproducible and that conclusions drawn from multiple shorter replicas are more reliable than those from a single longer simulation. The actual number of replicas needed will always depend on the question asked and the level of reliability sought. On the basis of our data, it appears that a good rule of thumb is to perform a minimum of five to 10 replicas.

Variable Regions of Antibodies and T-Cell Receptors May Not Be Sufficient in Molecular Simulations Investigating Binding

Antibodies and T-cell receptors are important proteins of the immune system that share similar structures. Both contain variable and constant regions. Insight into the dynamics of their binding can be provided by computational simulations. For these simulations the constant regions are often removed to save runtime as binding occurs in the variable regions. Here we present the first study to investigate the effect of removing the constant regions from antibodies and T-cell receptors on such simulations. We performed simulations of an antibody/antigen and T-cell receptor/MHC system with and without constant regions using 10 replicas of 100 ns of each of the four setups. We found that simulations without constant regions show significantly different behavior compared to simulations with constant regions. If the constant regions are not included in the simulations alterations in the binding interface hydrogen bonds and even partial unbinding can occur. These results indicate that constant regions should be included in antibody and T-cell receptor simulations for reliable conclusions to be drawn.

Modeling Functional Motions of Biological Systems by Customized Natural Moves

Simulating the functional motions of biomolecular systems requires large computational resources. We introduce a computationally inexpensive protocol for the systematic testing of hypotheses regarding the dynamic behavior of proteins and nucleic acids. The protocol is based on natural move Monte Carlo, a highly efficient conformational sampling method with built-in customization capabilities that allows researchers to design and perform a large number of simulations to investigate functional motions in biological systems. We demonstrate the use of this protocol on both a protein and a DNA case study. Firstly, we investigate the plasticity of a class II major histocompatibility complex in the absence of a bound peptide. Secondly, we study the effects of the epigenetic mark 5-hydroxymethyl on cytosine on the structure of the Dickerson-Drew dodecamer. We show how our customized natural moves protocol can be used to investigate causal relationships of functional motions in biological systems.

Melody discrimination and protein fold classification

One of the greatest challenges in theoretical biophysics and bioinformatics is the identification of protein folds from sequence data. This can be regarded as a pattern recognition problem. In this paper we report the use of a melody generation software where the inputs are derived from calculations of evolutionary information, secondary structure, flexibility, hydropathy and solvent accessibility from multiple sequence alignment data. The melodies so generated are derived from the sequence, and by inference, of the fold, in ways that give each fold a sound representation that may facilitate analysis, recognition, or comparison with other sequences.

Exploring peptide/MHC detachment processes using hierarchical natural move Monte Carlo

MOTIVATION

The binding between a peptide and a major histocompatibility complex (MHC) is one of the most important processes for the induction of an adaptive immune response. Many algorithms have been developed to predict peptide/MHC (pMHC) binding. However, no approach has yet been able to give structural insight into how peptides detach from the MHC.

RESULTS

In this study, we used a combination of coarse graining, hierarchical natural move Monte Carlo and stochastic conformational optimization to explore the detachment processes of 32 different peptides from HLA-A*02:01. We performed 100 independent repeats of each stochastic simulation and found that the presence of experimentally known anchor amino acids affects the detachment trajectories of our peptides. Comparison with experimental binding affinity data indicates the reliability of our approach (area under the receiver operating characteristic curve 0.85). We also compared to a 1000 ns molecular dynamics simulation of a non-binding peptide (AAAKTPVIV) and HLA-A*02:01. Even in this simulation, the longest published for pMHC, the peptide does not fully detach. Our approach is orders of magnitude faster and as such allows us to explore pMHC detachment processes in a way not possible with all-atom molecular dynamics simulations.

AVAILABILITY AND IMPLEMENTATION

The source code is freely available for download at http://www.cs.ox.ac.uk/mosaics/.

CONTACT

bernhard.knapp@stats.ox.ac.uk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Machine Learnable Fold Space Representation based on Residue Cluster Classes

MOTIVATION

Protein fold space is a conceptual framework where all possible protein folds exist and ideas about protein structure, function and evolution may be analyzed. Classification of protein folds in this space is commonly achieved by using similarity indexes and/or machine learning approaches, each with different limitations.

RESULTS

We propose a method for constructing a compact vector space model of protein fold space by representing each protein structure by its residues local contacts. We developed an efficient method to statistically test for the separability of points in a space and showed that our protein fold space representation is learnable by any machine-learning algorithm.

AVAILABILITY

An API is freely available at https://code.google.com/p/pyrcc/.

Nonlinearities in protein space limit the utility of informatics in protein biophysics

We examine the utility of informatic-based methods in computational protein biophysics. To do so, we use newly developed metric functions to define completely independent sequence and structure spaces for a large database of proteins. By investigating the relationship between these spaces, we demonstrate quantitatively the limits of knowledge-based correlation between the sequences and structures of proteins. It is shown that there are well-defined, nonlinear regions of protein space in which dissimilar structures map onto similar sequences (the conformational switch), and dissimilar sequences map onto similar structures (remote homology). These nonlinearities are shown to be quite common-almost half the proteins in our database fall into one or the other of these two regions. They are not anomalies, but rather intrinsic properties of structural encoding in amino acid sequences. It follows that extreme care must be exercised in using bioinformatic data as a basis for computational structure prediction. The implications of these results for protein evolution are examined.

Biophysics of protein evolution and evolutionary protein biophysics

The study of molecular evolution at the level of protein-coding genes often entails comparing large datasets of sequences to infer their evolutionary relationships. Despite the importance of a protein's structure and conformational dynamics to its function and thus its fitness, common phylogenetic methods embody minimal biophysical knowledge of proteins. To underscore the biophysical constraints on natural selection, we survey effects of protein mutations, highlighting the physical basis for marginal stability of natural globular proteins and how requirement for kinetic stability and avoidance of misfolding and misinteractions might have affected protein evolution. The biophysical underpinnings of these effects have been addressed by models with an explicit coarse-grained spatial representation of the polypeptide chain. Sequence-structure mappings based on such models are powerful conceptual tools that rationalize mutational robustness, evolvability, epistasis, promiscuous function performed by 'hidden' conformational states, resolution of adaptive conflicts and conformational switches in the evolution from one protein fold to another. Recently, protein biophysics has been applied to derive more accurate evolutionary accounts of sequence data. Methods have also been developed to exploit sequence-based evolutionary information to predict biophysical behaviours of proteins. The success of these approaches demonstrates a deep synergy between the fields of protein biophysics and protein evolution.

Tuning cytokine receptor signaling by re-orienting dimer geometry with surrogate ligands

Most cell-surface receptors for cytokines and growth factors signal as dimers, but it is unclear whether remodeling receptor dimer topology is a viable strategy to "tune" signaling output. We utilized diabodies (DA) as surrogate ligands in a prototypical dimeric receptor-ligand system, the cytokine Erythropoietin (EPO) and its receptor (EpoR), to dimerize EpoR ectodomains in non-native architectures. Diabody-induced signaling amplitudes varied from full to minimal agonism, and structures of these DA/EpoR complexes differed in EpoR dimer orientation and proximity. Diabodies also elicited biased or differential activation of signaling pathways and gene expression profiles compared to EPO. Non-signaling diabodies inhibited proliferation of erythroid precursors from patients with a myeloproliferative neoplasm due to a constitutively active JAK2V617F mutation. Thus, intracellular oncogenic mutations causing ligand-independent receptor activation can be counteracted by extracellular ligands that re-orient receptors into inactive dimer topologies. This approach has broad applications for tuning signaling output for many dimeric receptor systems.

Global view of the protein universe

To explore protein space from a global perspective, we consider 9,710 SCOP (Structural Classification of Proteins) domains with up to 70% sequence identity and present all similarities among them as networks: In the "domain network," nodes represent domains, and edges connect domains that share "motifs," i.e., significantly sized segments of similar sequence and structure. We explore the dependence of the network on the thresholds that define the evolutionary relatedness of the domains. At excessively strict thresholds the network falls apart completely; for very lax thresholds, there are network paths between virtually all domains. Interestingly, at intermediate thresholds the network constitutes two regions that can be described as "continuous" versus "discrete." The continuous region comprises a large connected component, dominated by domains with alternating alpha and beta elements, and the discrete region includes the rest of the domains in isolated islands, each generally corresponding to a fold. We also construct the "motif network," in which nodes represent recurring motifs, and edges connect motifs that appear in the same domain. This network also features a large and highly connected component of motifs that originate from domains with alternating alpha/beta elements (and some all-alpha domains), and smaller isolated islands. Indeed, the motif network suggests that nature reuses such motifs extensively. The networks suggest evolutionary paths between domains and give hints about protein evolution and the underlying biophysics. They provide natural means of organizing protein space, and could be useful for the development of strategies for protein search and design.

Effective moment feature vectors for protein domain structures

Imaging processing techniques have been shown to be useful in studying protein domain structures. The idea is to represent the pairwise distances of any two residues of the structure in a 2D distance matrix (DM). Features and/or submatrices are extracted from this DM to represent a domain. Existing approaches, however, may involve a large number of features (100-400) or complicated mathematical operations. Finding fewer but more effective features is always desirable. In this paper, based on some key observations on DMs, we are able to decompose a DM image into four basic binary images, each representing the structural characteristics of a fundamental secondary structure element (SSE) or a motif in the domain. Using the concept of moments in image processing, we further derive 45 structural features based on the four binary images. Together with 4 features extracted from the basic images, we represent the structure of a domain using 49 features. We show that our feature vectors can represent domain structures effectively in terms of the following. (1) We show a higher accuracy for domain classification. (2) We show a clear and consistent distribution of domains using our proposed structural vector space. (3) We are able to cluster the domains according to our moment features and demonstrate a relationship between structural variation and functional diversity.

Reducing the dimensionality of the protein-folding search problem

How does a folding protein negotiate a vast, featureless conformational landscape and adopt its native structure in biological real time? Motivated by this search problem, we developed a novel algorithm to compare protein structures. Procedures to identify structural analogs are typically conducted in three-dimensional space: the tertiary structure of a target protein is matched against each candidate in a database of structures, and goodness of fit is evaluated by a distance-based measure, such as the root-mean-square distance between target and candidate. This is an expensive approach because three-dimensional space is complex. Here, we transform the problem into a simpler one-dimensional procedure. Specifically, we identify and label the 11 most populated residue basins in a database of high-resolution protein structures. Using this 11-letter alphabet, any protein's three-dimensional structure can be transformed into a one-dimensional string by mapping each residue onto its corresponding basin. Similarity between the resultant basin strings can then be evaluated by conventional sequence-based comparison. The disorder → order folding transition is abridged on both sides. At the onset, folding conditions necessitate formation of hydrogen-bonded scaffold elements on which proteins are assembled, severely restricting the magnitude of accessible conformational space. Near the end, chain topology is established prior to emergence of the close-packed native state. At this latter stage of folding, the chain remains molten, and residues populate natural basins that are approximated by the 11 basins derived here. In essence, our algorithm reduces the protein-folding search problem to mapping the amino acid sequence onto a restricted basin string.

Multiscale natural moves refine macromolecules using single-particle electron microscopy projection images

The method presented here refines molecular conformations directly against projections of single particles measured by electron microscopy. By optimizing the orientation of the projection at the same time as the conformation, the method is well-suited to two-dimensional class averages from cryoelectron microscopy. Such direct use of two-dimensional images circumvents the need for a three-dimensional density map, which may be difficult to reconstruct from projections due to structural heterogeneity or preferred orientations of the sample on the grid. Our refinement protocol exploits Natural Move Monte Carlo to model a macromolecule as a small number of segments connected by flexible loops, on multiple scales. After tests on artificial data from lysozyme, we applied the method to the Methonococcus maripaludis chaperonin. We successfully refined its conformation from a closed-state initial model to an open-state final model using just one class-averaged projection. We also used Natural Moves to iteratively refine against heterogeneous projection images of Methonococcus maripaludis chaperonin in a mix of open and closed states. Our results suggest a general method for electron microscopy refinement specially suited to macromolecules with significant conformational flexibility. The algorithm is available in the program Methodologies for Optimization and Sampling In Computational Studies.

Modeling and design by hierarchical natural moves

We develop a unique algorithm implemented in the program MOSAICS (Methodologies for Optimization and Sampling in Computational Studies) that is capable of nanoscale modeling without compromising the resolution of interest. This is achieved by modeling with customizable hierarchical degrees of freedom, thereby circumventing major limitations of conventional molecular modeling. With the emergence of RNA-based nanotechnology, large RNAs in all-atom representation are used here to benchmark our algorithm. Our method locates all favorable structural states of a model RNA of significant complexity while improving sampling accuracy and increasing speed many fold over existing all-atom RNA modeling methods. We also modeled the effects of sequence mutations on the structural building blocks of tRNA-based nanotechnology. With its flexibility in choosing arbitrary degrees of freedom as well as in allowing different all-atom energy functions, MOSAICS is an ideal tool to model and design biomolecules of the nanoscale.

Conformational optimization with natural degrees of freedom: a novel stochastic chain closure algorithm

The present article introduces a set of novel methods that facilitate the use of "natural moves" or arbitrary degrees of freedom that can give rise to collective rearrangements in the structure of biological macromolecules. While such "natural moves" may spoil the stereochemistry and even break the bonded chain at multiple locations, our new method restores the correct chain geometry by adjusting bond and torsion angles in an arbitrary defined molten zone. This is done by successive stages of partial closure that propagate the location of the chain break backwards along the chain. At the end of these stages, the size of the chain break is generally reduced so much that it can be repaired by adjusting the position of a single atom. Our chain closure method is efficient with a computational complexity of O(N(d)), where N(d) is the number of degrees of freedom used to repair the chain break. The new method facilitates the use of arbitrary degrees of freedom including the "natural" degrees of freedom inferred from analyzing experimental (X-ray crystallography and nuclear magnetic resonance [NMR]) structures of nucleic acids and proteins. In terms of its ability to generate large conformational moves and its effectiveness in locating low energy states, the new method is robust and computationally efficient.

Splitting statistical potentials into meaningful scoring functions: testing the prediction of near-native structures from decoy conformations

Background

Recent advances on high-throughput technologies have produced a vast amount of protein sequences, while the number of high-resolution structures has seen a limited increase. This has impelled the production of many strategies to built protein structures from its sequence, generating a considerable amount of alternative models. The selection of the closest model to the native conformation has thus become crucial for structure prediction. Several methods have been developed to score protein models by energies, knowledge-based potentials and combination of both.

Results

Here, we present and demonstrate a theory to split the knowledge-based potentials in scoring terms biologically meaningful and to combine them in new scores to predict near-native structures. Our strategy allows circumventing the problem of defining the reference state. In this approach we give the proof for a simple and linear application that can be further improved by optimizing the combination of Zscores. Using the simplest composite score () we obtained predictions similar to state-of-the-art methods. Besides, our approach has the advantage of identifying the most relevant terms involved in the stability of the protein structure. Finally, we also use the composite Zscores to assess the conformation of models and to detect local errors.

Conclusion

We have introduced a method to split knowledge-based potentials and to solve the problem of defining a reference state. The new scores have detected near-native structures as accurately as state-of-art methods and have been successful to identify wrongly modeled regions of many near-native conformations.

A coarse-grained potential for fold recognition and molecular dynamics simulations of proteins

A coarse-grained potential for protein simulations and fold ranking is presented. The potential is based on a two-point model of individual amino acids and a specific implementation of hydrogen bonding. Parameters are determined for distance dependent pair interactions, pseudo bonds, angles, and torsions. A scaling factor for a hydrogen bonding term is also determined. Iterative sampling for 4867 proteins reproduces distributions of internal coordinates and distances observed in the Protein Data Bank. The adjustment of the potential and resampling are in the spirit of the generalized ensemble approach. No native structure information (e.g., secondary structure) is used in the calculation of the potential or in the simulation of a particular protein. The potential is subject to two tests as follows: (i) simulations of 956 globular proteins in the neighborhood of their native folds (these proteins were not used in the training set) and (ii) discrimination between native and decoy structures for 2470 proteins with 305,000 decoys and the "Decoys 'R' Us" dataset. In the first test, 58% of tested proteins stay within 5 A from the native fold in Molecular Dynamics simulations of more than 20 nanoseconds using the new potential. The potential is also useful in differentiating between correct and approximate folds providing significant signal for structure prediction algorithms. Sampling with the potential consistently regenerates the distribution of distances and internal coordinates it learned. Nevertheless, during Molecular Dynamics simulations structures are found that reproduce the learned distributions but are far from the native fold.

Evolutionary constraints on structural similarity in orthologs and paralogs

Although a quantitative relationship between sequence similarity and structural similarity has long been established, little is known about the impact of orthology on the relationship between protein sequence and structure. Among homologs, orthologs (derived by speciation) more frequently have similar functions than paralogs (derived by duplication). Here, we hypothesize that an orthologous pair will tend to exhibit greater structural similarity than a paralogous pair at the same level of sequence similarity. To test this hypothesis, we used 284,459 pairwise structure-based alignments of 12,634 unique domains from SCOP as well as orthology and paralogy assignments from OrthoMCL DB. We divided the comparisons by sequence identity and determined whether the sequence-structure relationship differed between the orthologs and paralogs. We found that at levels of sequence identity between 30 and 70%, orthologous domain pairs indeed tend to be significantly more structurally similar than paralogous pairs at the same level of sequence identity. An even larger difference is found when comparing ligand binding residues instead of whole domains. These differences between orthologs and paralogs are expected to be useful for selecting template structures in comparative modeling and target proteins in structural genomics.

Optimizing energy potential for protein fold recognition with parametric evaluation function

In this paper, a new optimization method is proposed to determine a simplified energy potential for protein fold recognition, which consists of the residue-residue contact, hydrophobicity, and pseudodihedral potentials. With a parametric evaluation function method, the Z-scores of all the proteins in a training set are optimized simultaneously to obtain the best parameter set of the potential. For this multi-objective and multi-constraint problem, the new optimization scheme is very effective. The derived potential is then tested on two high-quality decoy sets and compared with other classical fold recognition potentials. With the simplified energy potential, we achieve a high level of discrimination capability between correct and incorrect folds.

A simple Calpha-SC potential with higher accuracy for protein fold recognition

In this paper, an improved C(alpha)-SC energy potential designed for protein fold recognition was reported. It consists of three extremely simple interaction terms which are supposed to be the dominant interactions in protein folding: residue-residue contact, hydrophobicity and pseudodihedral potentials. The potential function only contains 210 contacts, one hydrophobic and one torsion parameters, which have been optimized using an interior point algorithm of linear programming. Tests of the derived potential function on commonly used decoy sets illustrate that it outperforms most of the existing coarse-grained potentials in terms of its capabilities in recognizing native structures and consistency in achieving high Z-scores across decoy sets, and it has almost equivalent performance to the potentials which considered complex intra-molecular interactions. The results show that our scoring function is a generally prospective potential for protein structure prediction and modeling with regard to its recognition and computation efficacy.