Identification of direct residue contacts in protein-protein interaction by message passing

Exploring the sequence fitness landscape of a bridge between protein folds

Most foldable protein sequences adopt only a single native fold. Recent protein design studies have, however, created protein sequences which fold into different structures apon changes of environment, or single point mutation, the best characterized example being the switch between the folds of the GA and GB binding domains of streptococcal protein G. To obtain further insight into the design of sequences which can switch folds, we have used a computational model for the fitness landscape of a single fold, built from the observed sequence variation of protein homologues. We have recently shown that such coevolutionary models can be used to design novel foldable sequences. By appropriately combining two of these models to describe the joint fitness landscape of GA and GB, we are able to describe the propensity of a given sequence for each of the two folds. We have successfully tested the combined model against the known series of designed GA/GB hybrids. Using Monte Carlo simulations on this landscape, we are able to identify pathways of mutations connecting the two folds. In the absence of a requirement for domain stability, the most frequent paths go via sequences in which neither domain is stably folded, reminiscent of the propensity for certain intrinsically disordered proteins to fold into different structures according to context. Even if the folded state is required to be stable, we find that there is nonetheless still a wide range of sequences which are close to the transition region and therefore likely fold switches, consistent with recent estimates that fold switching may be more widespread than had been thought.

Analysis of Protein-Protein Interaction Networks through Computational Approaches

The interactions among proteins and genes are extremely important for cellular functions. Molecular interactions at protein or gene levels can be used to construct interaction networks in which the interacting species are categorized based on direct interactions or functional similarities. Compared with the limited experimental techniques, various computational tools make it possible to analyze, filter, and combine the interaction data to get comprehensive information about the biological pathways. By the efficient way of integrating experimental findings in discovering PPIs and computational techniques for prediction, the researchers have been able to gain many valuable data on PPIs, including some advanced databases. Moreover, many useful tools and visualization programs enable the researchers to establish, annotate, and analyze biological networks. We here review and list the computational methods, databases, and tools for protein-protein interaction prediction.

Inferring Neuronal Couplings From Spiking Data Using a Systematic Procedure With a Statistical Criterion

Recent remarkable advances in experimental techniques have provided a background for inferring neuronal couplings from point process data that include a great number of neurons. Here, we propose a systematic procedure for pre- and postprocessing generic point process data in an objective manner to handle data in the framework of a binary simple statistical model, the Ising or generalized McCulloch-Pitts model. The procedure has two steps: (1) determining time bin size for transforming the point process data into discrete-time binary data and (2) screening relevant couplings from the estimated couplings. For the first step, we decide the optimal time bin size by introducing the null hypothesis that all neurons would fire independently, then choosing a time bin size so that the null hypothesis is rejected with the strict criteria. The likelihood associated with the null hypothesis is analytically evaluated and used for the rejection process. For the second postprocessing step, after a certain estimator of coupling is obtained based on the preprocessed data set (any estimator can be used with the proposed procedure), the estimate is compared with many other estimates derived from data sets obtained by randomizing the original data set in the time direction. We accept the original estimate as relevant only if its absolute value is sufficiently larger than those of randomized data sets. These manipulations suppress false positive couplings induced by statistical noise. We apply this inference procedure to spiking data from synthetic and in vitro neuronal networks. The results show that the proposed procedure identifies the presence or absence of synaptic couplings fairly well, including their signs, for the synthetic and experimental data. In particular, the results support that we can infer the physical connections of underlying systems in favorable situations, even when using a simple statistical model.

RNA sectors and allosteric function within the ribosome

The ribosome translates the genetic code into proteins in all domains of life. Its size and complexity demand long-range interactions that regulate ribosome function. These interactions are largely unknown. Here, we apply a global coevolution method, statistical coupling analysis (SCA), to identify coevolving residue networks (sectors) within the 23S ribosomal RNA (rRNA) of the large ribosomal subunit. As in proteins, SCA reveals a hierarchical organization of evolutionary constraints with near-independent groups of nucleotides forming physically contiguous networks within the three-dimensional structure. Using a quantitative, continuous-culture-with-deep-sequencing assay, we confirm that the top two SCA-predicted sectors contribute to ribosome function. These sectors map to distinct ribosome activities, and their origins trace to phylogenetic divergences across all domains of life. These findings provide a foundation to map ribosome allostery, explore ribosome biogenesis, and engineer ribosomes for new functions. Despite differences in chemical structure, protein and RNA enzymes appear to share a common internal logic of interaction and assembly.

Coevolutionary Analysis Reveals a Conserved Dual Binding Interface between Extracytoplasmic Function σ Factors and Class I Anti-σ Factors

Extracytoplasmic function σ factors (ECFs) belong to the most abundant signal transduction mechanisms in bacteria. Among the diverse regulators of ECF activity, class I anti-σ factors are the most important signal transducers in response to internal and external stress conditions. Despite the conserved secondary structure of the class I anti-σ factor domain (ASDI) that binds and inhibits the ECF under noninducing conditions, the binding interface between ECFs and ASDIs is surprisingly variable between the published cocrystal structures. In this work, we provide a comprehensive computational analysis of the ASDI protein family and study the different contact themes between ECFs and ASDIs. To this end, we harness the coevolution of these diverse protein families and predict covarying amino acid residues as likely candidates of an interaction interface. As a result, we find two common binding interfaces linking the first alpha-helix of the ASDI to the DNA-binding region in the σ4 domain of the ECF, and the fourth alpha-helix of the ASDI to the RNA polymerase (RNAP)-binding region of the σ2 domain. The conservation of these two binding interfaces contrasts with the apparent quaternary structure diversity of the ECF/ASDI complexes, partially explaining the high specificity between cognate ECF and ASDI pairs. Furthermore, we suggest that the dual inhibition of RNAP- and DNA-binding interfaces is likely a universal feature of other ECF anti-σ factors, preventing the formation of nonfunctional trimeric complexes between σ/anti-σ factors and RNAP or DNA.IMPORTANCE In the bacterial world, extracytoplasmic function σ factors (ECFs) are the most widespread family of alternative σ factors, mediating many cellular responses to environmental cues, such as stress. This work uses a computational approach to investigate how these σ factors interact with class I anti-σ factors-the most abundant regulators of ECF activity. By comprehensively classifying the anti-σs into phylogenetic groups and by comparing this phylogeny to the one of the cognate ECFs, the study shows how these protein families have coevolved to maintain their interaction over evolutionary time. These results shed light on the common contact residues that link ECFs and anti-σs in different phylogenetic families and set the basis for the rational design of anti-σs to specifically target certain ECFs. This will help to prevent the cross talk between heterologous ECF/anti-σ pairs, allowing their use as orthogonal regulators for the construction of genetic circuits in synthetic biology.

An evolution-based model for designing chorismate mutase enzymes

The rational design of enzymes is an important goal for both fundamental and practical reasons. Here, we describe a process to learn the constraints for specifying proteins purely from evolutionary sequence data, design and build libraries of synthetic genes, and test them for activity in vivo using a quantitative complementation assay. For chorismate mutase, a key enzyme in the biosynthesis of aromatic amino acids, we demonstrate the design of natural-like catalytic function with substantial sequence diversity. Further optimization focuses the generative model toward function in a specific genomic context. The data show that sequence-based statistical models suffice to specify proteins and provide access to an enormous space of functional sequences. This result provides a foundation for a general process for evolution-based design of artificial proteins.

Protein–Protein Interaction Methods and Protein Phase Separation

In the last decade, newly developed experimental methods have made it possible to highlight that macromolecules in the cell milieu physically interact to support physiology. This has shifted the problem of protein–protein interaction from a microscopic, electron-density scale to a mesoscopic one. Further, nowadays there is increasing evidence that proteins in the nucleus and in the cytoplasm can aggregate in membraneless organelles for different physiological reasons. In this scenario, it is urgent to face the problem of biomolecule functional annotation with efficient computational methods, suited to extract knowledge from reliable data and transfer information across different domains of investigation. Here, we revise the present state of the art of our knowledge of protein–protein interaction and the computational methods that differently implement it. Furthermore, we explore experimental and computational features of a set of proteins involved in phase separation.

Sparse Epistatic Patterns in the Evolution of Terpene Synthases

We explore sequence determinants of enzyme activity and specificity in a major enzyme family of terpene synthases. Most enzymes in this family catalyze reactions that produce cyclic terpenes-complex hydrocarbons widely used by plants and insects in diverse biological processes such as defense, communication, and symbiosis. To analyze the molecular mechanisms of emergence of terpene cyclization, we have carried out in-depth examination of mutational space around (E)-β-farnesene synthase, an Artemisia annua enzyme which catalyzes production of a linear hydrocarbon chain. Each mutant enzyme in our synthetic libraries was characterized biochemically, and the resulting reaction rate data were used as input to the Michaelis-Menten model of enzyme kinetics, in which free energies were represented as sums of one-amino-acid contributions and two-amino-acid couplings. Our model predicts measured reaction rates with high accuracy and yields free energy landscapes characterized by relatively few coupling terms. As a result, the Michaelis-Menten free energy landscapes have simple, interpretable structure and exhibit little epistasis. We have also developed biophysical fitness models based on the assumption that highly fit enzymes have evolved to maximize the output of correct products, such as cyclic products or a specific product of interest, while minimizing the output of byproducts. This approach results in nonlinear fitness landscapes that are considerably more epistatic. Overall, our experimental and computational framework provides focused characterization of evolutionary emergence of novel enzymatic functions in the context of microevolutionary exploration of sequence space around naturally occurring enzymes.

ResPRE: high-accuracy protein contact prediction by coupling precision matrix with deep residual neural networks

MOTIVATION

Contact-map of a protein sequence dictates the global topology of structural fold. Accurate prediction of the contact-map is thus essential to protein 3D structure prediction, which is particularly useful for the protein sequences that do not have close homology templates in the Protein Data Bank.

RESULTS

We developed a new method, ResPRE, to predict residue-level protein contacts using inverse covariance matrix (or precision matrix) of multiple sequence alignments (MSAs) through deep residual convolutional neural network training. The approach was tested on a set of 158 non-homologous proteins collected from the CASP experiments and achieved an average accuracy of 50.6% in the top-L long-range contact prediction with L being the sequence length, which is 11.7% higher than the best of other state-of-the-art approaches ranging from coevolution coupling analysis to deep neural network training. Detailed data analyses show that the major advantage of ResPRE lies at the utilization of precision matrix that helps rule out transitional noises of contact-maps compared with the previously used covariance matrix. Meanwhile, the residual network with parallel shortcut layer connections increases the learning ability of deep neural network training. It was also found that appropriate collection of MSAs can further improve the accuracy of final contact-map predictions. The standalone package and online server of ResPRE are made freely available, which should bring important impact on protein structure and function modeling studies in particular for the distant- and non-homology protein targets.

AVAILABILITY AND IMPLEMENTATION

https://zhanglab.ccmb.med.umich.edu/ResPRE and https://github.com/leeyang/ResPRE.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

CoRNeA: A Pipeline to Decrypt the Inter-Protein Interfaces from Amino Acid Sequence Information

Decrypting the interface residues of the protein complexes provides insight into the functions of the proteins and, hence, the overall cellular machinery. Computational methods have been devised in the past to predict the interface residues using amino acid sequence information, but all these methods have been majorly applied to predict for prokaryotic protein complexes. Since the composition and rate of evolution of the primary sequence is different between prokaryotes and eukaryotes, it is important to develop a method specifically for eukaryotic complexes. Here, we report a new hybrid pipeline for predicting the protein-protein interaction interfaces in a pairwise manner from the amino acid sequence information of the interacting proteins. It is based on the framework of Co-evolution, machine learning (Random Forest), and Network Analysis named CoRNeA trained specifically on eukaryotic protein complexes. We use Co-evolution, physicochemical properties, and contact potential as major group of features to train the Random Forest classifier. We also incorporate the intra-contact information of the individual proteins to eliminate false positives from the predictions keeping in mind that the amino acid sequence of a protein also holds information for its own folding and not only the interface propensities. Our prediction on example datasets shows that CoRNeA not only enhances the prediction of true interface residues but also reduces false positive rates significantly.

PconsC4: fast, accurate and hassle-free contact predictions

MOTIVATION

Residue contact prediction was revolutionized recently by the introduction of direct coupling analysis (DCA). Further improvements, in particular for small families, have been obtained by the combination of DCA and deep learning methods. However, existing deep learning contact prediction methods often rely on a number of external programs and are therefore computationally expensive.

RESULTS

Here, we introduce a novel contact predictor, PconsC4, which performs on par with state of the art methods. PconsC4 is heavily optimized, does not use any external programs and therefore is significantly faster and easier to use than other methods.

AVAILABILITY AND IMPLEMENTATION

PconsC4 is freely available under the GPL license from https://github.com/ElofssonLab/PconsC4. Installation is easy using the pip command and works on any system with Python 3.5 or later and a GCC compiler. It does not require a GPU nor special hardware.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Experimentally-driven protein structure modeling

Revolutions in natural and exact sciences started at the dawn of last century have led to the explosion of theoretical, experimental, and computational approaches to determine structures of molecules, complexes, as well as their rich conformational dynamics. Since different experimental methods produce information that is attributed to specific time and length scales, corresponding computational methods have to be tailored to these scales and experiments. These methods can be then combined and integrated in scales, hence producing a fuller picture of molecular structure and motion from the "puzzle pieces" offered by various experiments. Here, we describe a number of computational approaches to utilize experimental data to glance into structure of proteins and understand their dynamics. We will also discuss the limitations and the resolution of the constraints-based modeling approaches. SIGNIFICANCE: Experimentally-driven computational structure modeling and determination is a rapidly evolving alternative to traditional approaches for molecular structure determination. These new hybrid experimental-computational approaches are proving to be a powerful microscope to glance into the structural features of intrinsically or partially disordered proteins, dynamics of molecules and complexes. In this review, we describe various approaches in the field of experimentally-driven computational structure modeling.

Protein Structure Prediction in CASP13 Using AWSEM-Suite

Recently several techniques have emerged that significantly enhance the quality of predictions of protein tertiary structures. In this study, we describe the performance of AWSEM-Suite, an algorithm that incorporates template-based modeling and coevolutionary restraints with a realistic coarse-grained force field, AWSEM. With its roots in neural networks, AWSEM contains both physical and bioinformatical energies that have been optimized using energy landscape theory. AWSEM-Suite participated in CASP13 as a server predictor and generated reliable predictions for most targets. AWSEM-Suite ranked eighth in both the free-modeling category and the hard-to-model category and in one case provided the best submitted prediction. Here we critically discuss the prediction performance of AWSEM-Suite using several examples from different categories in CASP13. Structure prediction tests on these selected targets, two of them being hard-to-model targets, show that AWSEM-Suite can achieve high-resolution structure prediction after incorporating both template guidances and coevolutionary restraints even when homology is weak. For targets with reliable templates (template-easy category), introducing coevolutionary restraints sometimes damages the overall quality of the predictions. Free energy profile analyses demonstrate, however, that the incorporations of both of these evolutionarily informed terms effectively increase the funneling of the landscape toward native-like structures while still allowing sufficient flexibility to correct for discrepancies between the correct target structure and the provided guidance. In contrast to other predictors that are exclusively oriented toward structure prediction, the connection of AWSEM-Suite to a statistical mechanical basis and affiliated molecular dynamics and importance sampling simulations makes it suitable for functional explorations.

The EVcouplings Python framework for coevolutionary sequence analysis

SUMMARY

Coevolutionary sequence analysis has become a commonly used technique for de novo prediction of the structure and function of proteins, RNA, and protein complexes. We present the EVcouplings framework, a fully integrated open-source application and Python package for coevolutionary analysis. The framework enables generation of sequence alignments, calculation and evaluation of evolutionary couplings (ECs), and de novo prediction of structure and mutation effects. The combination of an easy to use, flexible command line interface and an underlying modular Python package makes the full power of coevolutionary analyses available to entry-level and advanced users.

AVAILABILITY AND IMPLEMENTATION

https://github.com/debbiemarkslab/evcouplings.

Coevolutionary data-based interaction networks approach highlighting key residues across protein families: The case of the G-protein coupled receptors

We present an approach that, by integrating structural data with Direct Coupling Analysis, is able to pinpoint most of the interaction hotspots (i.e. key residues for the biological activity) across very sparse protein families in a single run. An application to the Class A G-protein coupled receptors (GPCRs), both in their active and inactive states, demonstrates the predictive power of our approach. The latter can be easily extended to any other kind of protein family, where it is expected to highlight most key sites involved in their functional activity.

Statistical physics of interacting proteins: Impact of dataset size and quality assessed in synthetic sequences

Identifying protein-protein interactions is crucial for a systems-level understanding of the cell. Recently, algorithms based on inverse statistical physics, e.g., direct coupling analysis (DCA), have allowed to use evolutionarily related sequences to address two conceptually related inference tasks: finding pairs of interacting proteins and identifying pairs of residues which form contacts between interacting proteins. Here we address two underlying questions: How are the performances of both inference tasks related? How does performance depend on dataset size and the quality? To this end, we formalize both tasks using Ising models defined over stochastic block models, with individual blocks representing single proteins and interblock couplings protein-protein interactions; controlled synthetic sequence data are generated by Monte Carlo simulations. We show that DCA is able to address both inference tasks accurately when sufficiently large training sets of known interaction partners are available and that an iterative pairing algorithm allows to make predictions even without a training set. Noise in the training data deteriorates performance. In both tasks we find a quadratic scaling relating dataset quality and size that is consistent with noise adding in square-root fashion and signal adding linearly when increasing the dataset. This implies that it is generally good to incorporate more data even if their quality are imperfect, thereby shedding light on the empirically observed performance of DCA applied to natural protein sequences.

Structures of a dimodular nonribosomal peptide synthetase reveal conformational flexibility

Nonribosomal peptide synthetases (NRPSs) are biosynthetic enzymes that synthesize natural product therapeutics using a modular synthetic logic, whereby each module adds one aminoacyl substrate to the nascent peptide. We have determined five x-ray crystal structures of large constructs of the NRPS linear gramicidin synthetase, including a structure of a full core dimodule in conformations organized for the condensation reaction and intermodular peptidyl substrate delivery. The structures reveal differences in the relative positions of adjacent modules, which are not strictly coupled to the catalytic cycle and are consistent with small-angle x-ray scattering data. The structures and covariation analysis of homologs allowed us to create mutants that improve the yield of a peptide from a module-swapped dimodular NRPS.

Protein Structural Information and Evolutionary Landscape by In Vitro Evolution

Protein structure is tightly intertwined with function according to the laws of evolution. Understanding how structure determines function has been the aim of structural biology for decades. Here, we have wondered instead whether it is possible to exploit the function for which a protein was evolutionary selected to gain information on protein structure and on the landscape explored during the early stages of molecular and natural evolution. To answer to this question, we developed a new methodology, which we named CAMELS (Coupling Analysis by Molecular Evolution Library Sequencing), that is able to obtain the in vitro evolution of a protein from an artificial selection based on function. We were able to observe with CAMELS many features of the TEM-1 beta-lactamase local fold exclusively by generating and sequencing large libraries of mutational variants. We demonstrated that we can, whenever a functional phenotypic selection of a protein is available, sketch the structural and evolutionary landscape of a protein without utilizing purified proteins, collecting physical measurements, or relying on the pool of natural protein variants.

Major antigenic site B of human influenza H3N2 viruses has an evolving local fitness landscape

Antigenic drift of influenza virus hemagglutinin (HA) is enabled by facile evolvability. However, HA antigenic site B, which has become immunodominant in recent human H3N2 influenza viruses, is also evolutionarily constrained by its involvement in receptor binding. Here, we employ deep mutational scanning to probe the local fitness landscape of HA antigenic site B in six different human H3N2 strains spanning from 1968 to 2016. We observe that the fitness landscape of HA antigenic site B can be very different between strains. Sequence variants that exhibit high fitness in one strain can be deleterious in another, indicating that the evolutionary constraints of antigenic site B have changed over time. Structural analysis suggests that the local fitness landscape of antigenic site B can be reshaped by natural mutations via modulation of the receptor-binding mode. Overall, these findings elucidate how influenza virus continues to explore new antigenic space despite strong functional constraints.

Epistatic contributions promote the unification of incompatible models of neutral molecular evolution

Mathematical models of evolution help us understand mechanisms driving protein-sequence change. Previous models recapitulate a disjoint subset of statistical features of natural sequences. We present a neutral evolution model that unifies features including extreme variance of the molecular clock’s tick rate and the observation of an evolutionary Stokes shift, an irreversible effect of mutations in the fitness landscape during sequence evolution. We show that interactions between amino acid sites, which inform our fitness metric, are required to observe these features. These interactions are inferred by using direct coupling analysis, which has been successfully utilized to predict protein structures, dynamics, and complexes from coevolutionary information. We anticipate our model will have applications in phylogenetics, ancestral reconstruction of sequences, and protein design.

We introduce a model of amino acid sequence evolution that accounts for the statistical behavior of real sequences induced by epistatic interactions. We base the model dynamics on parameters derived from multiple sequence alignments analyzed by using direct coupling analysis methodology. Known statistical properties such as overdispersion, heterotachy, and gamma-distributed rate-across-sites are shown to be emergent properties of this model while being consistent with neutral evolution theory, thereby unifying observations from previously disjointed evolutionary models of sequences. The relationship between site restriction and heterotachy is characterized by tracking the effective alphabet dynamics of sites. We also observe an evolutionary Stokes shift in the fitness of sequences that have undergone evolution under our simulation. By analyzing the structural information of some proteins, we corroborate that the strongest Stokes shifts derive from sites that physically interact in networks near biochemically important regions. Perspectives on the implementation of our model in the context of the molecular clock are discussed.

Erasure machine: Inverse Ising inference from reweighting of observation frequencies

Maximum likelihood estimation (MLE) is fundamental to system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system inference, such as Boltzmann machines, MLE requires the arduous computation of partition functions summing over all configurations, both observed and unobserved. We present a conceptually transparent data-driven inference computation based on a reweighting of observed configuration frequencies that allows us to recast the inference problem as a simpler calculation. Modeling our approach on the high-temperature limit of statistical physics, we reweight the frequencies of observed configurations by multiplying with reciprocals of Boltzmann weights and update the Boltzmann weights iteratively to make these products close to the high-temperature limit of the Boltzmann weights. This converts the required partition function computation in the reweighted MLE to a tractable leading-order high-temperature term. We show that this is a convex optimization at each step. Then, for systems with a large number of degrees of freedom where other approaches are intractable, we demonstrate that this data-driven algorithm gives accurate inference with both synthetic data and two real-world examples.

A statistical inference approach to reconstruct intercellular interactions in cell migration experiments

Migration of cells can be characterized by two prototypical types of motion: individual and collective migration. We propose a statistical inference approach designed to detect the presence of cell-cell interactions that give rise to collective behaviors in cell motility experiments. This inference method has been first successfully tested on synthetic motional data and then applied to two experiments. In the first experiment, cells migrate in a wound-healing model: When applied to this experiment, the inference method predicts the existence of cell-cell interactions, correctly mirroring the strong intercellular contacts that are present in the experiment. In the second experiment, dendritic cells migrate in a chemokine gradient. Our inference analysis does not provide evidence for interactions, indicating that cells migrate by sensing independently the chemokine source. According to this prediction, we speculate that mature dendritic cells disregard intercellular signals that could otherwise delay their arrival to lymph vessels.

Maximum Entropy Framework for Predictive Inference of Cell Population Heterogeneity and Responses in Signaling Networks

Predictive models of signaling networks are essential for understanding cell population heterogeneity and designing rational interventions in disease. However, using computational models to predict heterogeneity of signaling dynamics is often challenging because of the extensive variability of biochemical parameters across cell populations. Here, we describe a maximum entropy-based framework for inference of heterogeneity in dynamics of signaling networks (MERIDIAN). MERIDIAN estimates the joint probability distribution over signaling network parameters that is consistent with experimentally measured cell-to-cell variability of biochemical species. We apply the developed approach to investigate the response heterogeneity in the EGFR/Akt signaling network. Our analysis demonstrates that a significant fraction of cells exhibits high phosphorylated Akt (pAkt) levels hours after EGF stimulation. Our findings also suggest that cells with high EGFR levels predominantly contribute to the subpopulation of cells with high pAkt activity. We also discuss how MERIDIAN can be extended to accommodate various experimental measurements.

Identification of Protein Functional Regions

Protein sequence stores the information relative to both functionality and stability, thus making it difficult to disentangle the two contributions. However, the identification of critical residues for function and stability has important implications for the mapping of the proteome interactions, as well as for many pharmaceutical applications, e. g. the identification of ligand binding regions for targeted pharmaceutical protein design. In this work, we propose a computational method to identify critical residues for protein functionality and stability and to further categorise them in strictly functional, structural and intermediate. We evaluate single site conservation and use Direct Coupling Analysis (DCA) to identify co-evolved residues both in natural and artificial evolution processes. We reproduce artificial evolution using protein design and base our approach on the hypothesis that artificial evolution in the absence of any functional constraint would exclusively lead to site conservation and co-evolution events of the structural type. Conversely, natural evolution intrinsically embeds both functional and structural information. By comparing the lists of conserved and co-evolved residues, outcomes of the analysis on natural and artificial evolution, we identify the functional residues without the need of any a priori knowledge of the biological role of the analysed protein.

Deep Analysis of Residue Constraints (DARC): identifying determinants of protein functional specificity

Protein functional constraints are manifest as superfamily and functional-subgroup conserved residues, and as pairwise correlations. Deep Analysis of Residue Constraints (DARC) aids the visualization of these constraints, characterizes how they correlate with each other and with structure, and estimates statistical significance. This can identify determinants of protein functional specificity, as we illustrate for bacterial DNA clamp loader ATPases. These load ring-shaped sliding clamps onto DNA to keep polymerase attached during replication and contain one δ, three γ, and one δ’ AAA+ subunits semi-circularly arranged in the order δ-γ₁-γ₂-γ₃-δ’. Only γ is active, though both γ and δ’ functionally influence an adjacent γ subunit. DARC identifies, as functionally-congruent features linking allosterically the ATP, DNA, and clamp binding sites: residues distinctive of γ and of γ/δ’ that mutually interact in trans, centered on the catalytic base; several γ/δ’-residues and six γ/δ’-covariant residue pairs within the DNA binding N-termini of helices α2 and α3; and γ/δ’-residues associated with the α2 C-terminus and the clamp-binding loop. Most notable is a trans-acting γ/δ’ hydroxyl group that 99% of other AAA+ proteins lack. Mutation of this hydroxyl to a methyl group impedes clamp binding and opening, DNA binding, and ATP hydrolysis—implying a remarkably clamp-loader-specific function.

Coevolutionary Analysis of Protein Subfamilies by Sequence Reweighting

Extracting structural information from sequence co-variation has become a common computational biology practice in the recent years, mainly due to the availability of large sequence alignments of protein families. However, identifying features that are specific to sub-classes and not shared by all members of the family using sequence-based approaches has remained an elusive problem. We here present a coevolutionary-based method to differentially analyze subfamily specific structural features by a continuous sequence reweighting (SR) approach. We introduce the underlying principles and test its predictive capabilities on the Response Regulator family, whose subfamilies have been previously shown to display distinct, specific homo-dimerization patterns. Our results show that this reweighting scheme is effective in assigning structural features known a priori to subfamilies, even when sequence data is relatively scarce. Furthermore, sequence reweighting allows assessing if individual structural contacts pertain to specific subfamilies and it thus paves the way for the identification specificity-determining contacts from sequence variation data.

Braiding topology and the energy landscape of chromosome organization proteins

Assemblies of structural maintenance of chromosomes (SMC) proteins and kleisin subunits are essential to chromosome organization and segregation across all kingdoms of life. While structural data exist for parts of the SMC-kleisin complexes, complete structures of the entire complexes have yet to be determined, making mechanistic studies difficult. Using an integrative approach that combines crystallographic structural information about the globular subdomains, along with coevolutionary information and an energy landscape optimized force field (AWSEM), we predict atomic-scale structures for several tripartite SMC-kleisin complexes, including prokaryotic condensin, eukaryotic cohesin, and eukaryotic condensin. The molecular dynamics simulations of the SMC-kleisin protein complexes suggest that these complexes exist as a broad conformational ensemble that is made up of different topological isomers. The simulations suggest a critical role for the SMC coiled-coil regions, where the coils intertwine with various linking numbers. The twist and writhe of these braided coils are coupled with the motion of the SMC head domains, suggesting that the complexes may function as topological motors. Opening, closing, and translation along the DNA of the SMC-kleisin protein complexes would allow these motors to couple to the topology of DNA when DNA is entwined with the braided coils.

Pervasive within-host recombination and epistasis as major determinants of the molecular evolution of the foot-and-mouth disease virus capsid

Although recombination is known to occur in foot-and-mouth disease virus (FMDV), it is considered only a minor determinant of virus sequence diversity. Analysis at phylogenetic scales shows inter-serotypic recombination events are rare, whereby recombination occurs almost exclusively in non-structural proteins. In this study we have estimated recombination rates within a natural host in an experimental setting. African buffaloes were inoculated with a SAT-1 FMDV strain containing two major viral sub-populations differing in their capsid sequence. This population structure enabled the detection of extensive within-host recombination in the genomic region coding for structural proteins and allowed recombination rates between the two sub-populations to be estimated. Quite surprisingly, the effective recombination rate in VP1 during the acute infection phase turns out to be about 0.1 per base per year, i.e. comparable to the mutation/substitution rate. Using a high-resolution map of effective within-host recombination in the capsid-coding region, we identified a linkage disequilibrium pattern in VP1 that is consistent with a mosaic structure with two main genetic blocks. Positive epistatic interactions between co-evolved variants appear to be present both within and between blocks. These interactions are due to intra-host selection both at the RNA and protein level. Overall our findings show that during FMDV co-infections by closely related strains, capsid-coding genes recombine within the host at a much higher rate than expected, despite the presence of strong constraints dictated by the capsid structure. Although these intra-host results are not immediately translatable to a phylogenetic setting, recombination and epistasis must play a major and so far underappreciated role in the molecular evolution of the virus at all scales.

There are 7 serotypes of Foot-and-Mouth Disease Virus and multiple strains of each serotype. The emergence of new strains can result in widespread outbreaks of disease and requires new vaccines to be developed. The major mechanisms driving variation are thought to be substitutions in the viral genome. Recombination in the capsid-coding region of the virus genome has been described at phylogenetic scales but not thought to play a major role in generating variants. In the current experiment, a co-infection of African buffaloes with closely related sub-populations of viruses allowed us to detect recombination events. For structural protein-coding sequences, the genetic composition of the population is driven by extensive within-host recombination. During the acute infection phase the intra-host recombination rates of 0.1 per base per year are comparable to the typical mutation rates of the virus. The recombination map reveals two strongly linked regions within the VP1 protein-coding sequence. Epistatic interactions between co-evolved mutations in VP1 are caused by intra-host selection at the RNA and protein level and are present both within and between the two regions. Our findings in this experimental setting support a major role for recombination and epistasis in the intra-host evolution of FMDV.

A Web-Based Protocol for Interprotein Contact Prediction by Deep Learning

Identifying residue-residue contacts in protein-protein interactions or complex is crucial for understanding protein and cell functions. DCA (direct-coupling analysis) methods shed some light on this, but they need many sequence homologs to yield accurate prediction. Inspired by the success of our deep-learning method for intraprotein contact prediction, we have developed RaptorX-ComplexContact, a web server for interprotein residue-residue contact prediction. Given a pair of interacting protein sequences, RaptorX-ComplexContact first searches for their sequence homologs and builds two paired multiple sequence alignments (MSA) based on genomic distance and phylogeny information, respectively. Then, RaptorX-ComplexContact uses two deep convolutional residual neural networks (ResNet) to predict interprotein contacts from sequential features and coevolution information of paired MSAs. RaptorX-ComplexContact shall be useful for protein docking, protein-protein interaction prediction, and protein interaction network construction.

Inference of compressed Potts graphical models

We consider the problem of inferring a graphical Potts model on a population of variables. This inverse Potts problem generally involves the inference of a large number of parameters, often larger than the number of available data, and, hence, requires the introduction of regularization. We study here a double regularization scheme, in which the number of Potts states (colors) available to each variable is reduced and interaction networks are made sparse. To achieve the color compression, only Potts states with large empirical frequency (exceeding some threshold) are explicitly modeled on each site, while the others are grouped into a single state. We benchmark the performances of this mixed regularization approach, with two inference algorithms, adaptive cluster expansion (ACE) and pseudolikelihood maximization (PLM), on synthetic data obtained by sampling disordered Potts models on Erdős-Rényi random graphs. We show in particular that color compression does not affect the quality of reconstruction of the parameters corresponding to high-frequency symbols, while drastically reducing the number of the other parameters and thus the computational time. Our procedure is also applied to multisequence alignments of protein families, with similar results.

The Distance Precision Matrix: computing networks from non-linear relationships

Motivation

Full-order partial correlation, a fundamental approach for network reconstruction, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the covariance matrix) as an indicator of which variables are directly associated. The precision matrix assumes Gaussian linear data and its entries are zero for pairs of variables that are independent given all other variables. However, there is still very little theory on network reconstruction under the assumption of non-linear interactions among variables.

Results

We propose Distance Precision Matrix, a network reconstruction method aimed at both linear and non-linear data. Like partial distance correlation, it builds on distance covariance, a measure of possibly non-linear association, and on the idea of full-order partial correlation, which allows to discard indirect associations. We provide evidence that the Distance Precision Matrix method can successfully compute networks from linear and non-linear data, and consistently so across different datasets, even if sample size is low. The method is fast enough to compute networks on hundreds of nodes.

Availability and implementation

An R package DPM is available at https://github.molgen.mpg.de/ghanbari/DPM.

Supplementary information

Supplementary data are available at Bioinformatics online.

A protocol to automatically calculate homo-oligomeric protein structures through the integration of evolutionary constraints and NMR ambiguous contacts

Protein assemblies are involved in many important biological processes. Solid-state NMR (SSNMR) spectroscopy is a technique suitable for the structural characterization of samples with high molecular weight and thus can be applied to such assemblies. A significant bottleneck in terms of both effort and time required is the manual identification of unambiguous intermolecular contacts. This is particularly challenging for homo-oligomeric complexes, where simple uniform labeling may not be effective. We tackled this challenge by exploiting coevolution analysis to extract information on homo-oligomeric interfaces from NMR-derived ambiguous contacts. After removing the evolutionary couplings (ECs) that are already satisfied by the 3D structure of the monomer, the predicted ECs are matched with the automatically generated list of experimental contacts. This approach provides a selection of potential interface residues that is used directly in monomer-monomer docking calculations. We validated the protocol on tetrameric L-asparaginase II and dimeric Sod1.

Evolutionary coupling analysis identifies the impact of disease-associated variants at less-conserved sites

Genome-wide association studies have discovered a large number of genetic variants in human patients with the disease. Thus, predicting the impact of these variants is important for sorting disease-associated variants (DVs) from neutral variants. Current methods to predict the mutational impacts depend on evolutionary conservation at the mutation site, which is determined using homologous sequences and based on the assumption that variants at well-conserved sites have high impacts. However, many DVs at less-conserved but functionally important sites cannot be predicted by the current methods. Here, we present a method to find DVs at less-conserved sites by predicting the mutational impacts using evolutionary coupling analysis. Functionally important and evolutionarily coupled sites often have compensatory variants on cooperative sites to avoid loss of function. We found that our method identified known intolerant variants in a diverse group of proteins. Furthermore, at less-conserved sites, we identified DVs that were not identified using conservation-based methods. These newly identified DVs were frequently found at protein interaction interfaces, where species-specific mutations often alter interaction specificity. This work presents a means to identify less-conserved DVs and provides insight into the relationship between evolutionarily coupled sites and human DVs.

Deciphering protein evolution and fitness landscapes with latent space models

Protein sequences contain rich information about protein evolution, fitness landscapes, and stability. Here we investigate how latent space models trained using variational auto-encoders can infer these properties from sequences. Using both simulated and real sequences, we show that the low dimensional latent space representation of sequences, calculated using the encoder model, captures both evolutionary and ancestral relationships between sequences. Together with experimental fitness data and Gaussian process regression, the latent space representation also enables learning the protein fitness landscape in a continuous low dimensional space. Moreover, the model is also useful in predicting protein mutational stability landscapes and quantifying the importance of stability in shaping protein evolution. Overall, we illustrate that the latent space models learned using variational auto-encoders provide a mechanism for exploration of the rich data contained in protein sequences regarding evolution, fitness and stability and hence are well-suited to help guide protein engineering efforts.

Computing the Pathogenicity of Wilson's Disease ATP7B Mutations: Implications for Disease Prevalence

Genetic variations in the gene encoding the copper-transport protein ATP7B are the primary cause of Wilson's disease. Controversially, clinical prevalence seems much smaller than the prevalence estimated by genetic screening tools, causing fear that many people are undiagnosed, although early diagnosis and treatment is essential. To address this issue, we benchmarked 16 state-of-the-art computational disease-prediction methods against established data of missense ATP7B mutations. Our results show that the quality of the methods varies widely. We show the importance of optimizing the threshold of the methods used to distinguish pathogenic from nonpathogenic mutations against data of clinically confirmed pathogenic and nonpathogenic mutations. We find that most methods use thresholds that predict too many ATP7B mutations to be pathogenic. Thus, our findings explain the current controversy on Wilson's disease prevalence because meta-analysis and text search methods include many computational estimates that lead to higher disease prevalence than clinically observed. As proteins and diseases differ widely, a one-size-fits-all threshold cannot distinguish pathogenic and nonpathogenic mutations efficiently, as shown here. We also show that amino acid changes with small evolutionary substitution probability, mainly due to amino acid volume, are more associated with the disease, implying a pathological effect on the conformational state of the protein, which could affect copper transport or adenosine triphosphate recognition and hydrolysis. These findings may be a first step toward a more quantitative genotype-phenotype relationship of Wilson's disease.

Statistical characteristics of amino acid covariance as possible descriptors of viral genomic complexity

At the sequence level it is hard to describe the complexity of viruses which allows them to challenge host immune system, some for a few weeks and others up to a complete compromise. Paradoxically, viral genomes are both complex and simple. Complex because amino acid mutation rates are very high, and yet viruses remain functional. Simple because they have barely around 10 types of proteins, so viral protein-protein interaction networks are not insightful. In this work we use fine-grained amino acid level information and their evolutionary characteristics obtained from large-scale genomic data to develop a statistical panel, towards the goal of developing quantitative descriptors for the biological complexity of viruses. Networks were constructed from pairwise covariation of amino acids and were statistically analyzed. Three differentiating factors arise: predominantly intra- vs inter-protein covariance relations, the nature of the node degree distribution and network density. Interestingly, the covariance relations were primarily intra-protein in avian influenza and inter-protein in HIV. The degree distributions showed two universality classes: a power-law with exponent −1 in HIV and avian-influenza, random behavior in human flu and dengue. The calculated covariance network density correlates well with the mortality strengths of viruses on the viral-Richter scale. These observations suggest the potential utility of the statistical metrics for describing the covariance patterns in viruses. Our host-virus interaction analysis point to the possibility that host proteins which can interact with multiple viral proteins may be responsible for shaping the inter-protein covariance relations. With the available data, it appears that network density might be a surrogate for the virus Richter scale, however the hypothesis needs a re-examination when large scale complete genome data for more viruses becomes available.

Genome-wide epistasis and co-selection study using mutual information

Covariance-based discovery of polymorphisms under co-selective pressure or epistasis has received considerable recent attention in population genomics. Both statistical modeling of the population level covariation of alleles across the chromosome and model-free testing of dependencies between pairs of polymorphisms have been shown to successfully uncover patterns of selection in bacterial populations. Here we introduce a model-free method, SpydrPick, whose computational efficiency enables analysis at the scale of pan-genomes of many bacteria. SpydrPick incorporates an efficient correction for population structure, which adjusts for the phylogenetic signal in the data without requiring an explicit phylogenetic tree. We also introduce a new type of visualization of the results similar to the Manhattan plots used in genome-wide association studies, which enables rapid exploration of the identified signals of co-evolution. Simulations demonstrate the usefulness of our method and give some insight to when this type of analysis is most likely to be successful. Application of the method to large population genomic datasets of two major human pathogens, Streptococcus pneumoniae and Neisseria meningitidis, revealed both previously identified and novel putative targets of co-selection related to virulence and antibiotic resistance, highlighting the potential of this approach to drive molecular discoveries, even in the absence of phenotypic data.

A common root for coevolution and substitution rate variability in protein sequence evolution

We introduce a simple model that describes the average occurrence of point variations in a generic protein sequence. This model is based on the idea that mutations are more likely to be fixed at sites in contact with others that have mutated in the recent past. Therefore, we extend the usual assumptions made in protein coevolution by introducing a time dumping on the effect of a substitution on its surrounding and makes correlated substitutions happen in avalanches localized in space and time. The model correctly predicts the average correlation of substitutions as a function of their distance along the sequence. At the same time, it predicts an among-site distribution of the number of substitutions per site highly compatible with a negative binomial, consistently with experimental data. The promising outcomes achieved with this model encourage the application of the same ideas in the field of pairwise and multiple sequence alignment.

Assessing the accuracy of contact predictions in CASP13

The accuracy of sequence-based tertiary contact predictions was assessed in a blind prediction experiment at the CASP13 meeting. After 4 years of significant improvements in prediction accuracy, another dramatic advance has taken place since CASP12 was held 2 years ago. The precision of predicting the top L/5 contacts in the free modeling category, where L is the corresponding length of the protein in residues, has exceeded 70%. As a comparison, the best-performing group at CASP12 with a 47% precision would have finished below the top 1/3 of the CASP13 groups. Extensively trained deep neural network approaches dominate the top performing algorithms, which appear to efficiently integrate information on coevolving residues and interacting fragments or possibly utilize memories of sequence similarities and sometimes can deliver accurate results even in the absence of virtually any target specific evolutionary information. If the current performance is evaluated by F-score on L contacts, it stands around 24% right now, which, despite the tremendous impact and advance in improving its utility for structure modeling, also suggests that there is much room left for further improvement.

Identifying genuine protein-protein interactions within communities of gene co-expression networks using a deconvolution method

Direct relationships between biological molecules connected in a gene co-expression network tend to reflect real biological activities such as gene regulation, protein-protein interactions (PPIs), and metabolisation. As correlation-based networks contain numerous indirect connections, those direct relationships are always 'hidden' in them. Compared with the global network, network communities imply more biological significance on predicting protein function, detecting protein complexes and studying network evolution. Therefore, identifying direct relationships in communities is a pervasive and important topic in the biological sciences. Unfortunately, this field has not been well studied. A major thrust of this study is to apply a deconvolution algorithm on communities stemming from different gene co-expression networks, which are constructed by fixing different thresholds for robustness analysis. Using the fifth Dialogue on Reverse Engineering Assessment and Methods challenge (DREAM5) framework, the authors demonstrate that nearly all new communities extracted from a 'deconvolution filter' contain more genuine PPIs than before deconvolution.

pydca v1.0: a comprehensive software for direct coupling analysis of RNA and protein sequences

Motivation

The ongoing advances in sequencing technologies have provided a massive increase in the availability of sequence data. This made it possible to study the patterns of correlated substitution between residues in families of homologous proteins or RNAs and to retrieve structural and stability information. Direct coupling analysis (DCA) infers coevolutionary couplings between pairs of residues indicating their spatial proximity, making such information a valuable input for subsequent structure prediction.

Results

Here, we present pydca, a standalone Python-based software package for the DCA of protein- and RNA-homologous families. It is based on two popular inverse statistical approaches, namely, the mean-field and the pseudo-likelihood maximization and is equipped with a series of functionalities that range from multiple sequence alignment trimming to contact map visualization. Thanks to its efficient implementation, features and user-friendly command line interface, pydca is a modular and easy-to-use tool that can be used by researchers with a wide range of backgrounds.

Availability and implementation

pydca can be obtained from https://github.com/KIT-MBS/pydca or from the Python Package Index under the MIT License.

Supplementary information

Supplementary data are available at Bioinformatics online.

Searching for collective behavior in a small brain

In large neuronal networks, it is believed that functions emerge through the collective behavior of many interconnected neurons. Recently, the development of experimental techniques that allow simultaneous recording of calcium concentration from a large fraction of all neurons in Caenorhabditis elegans-a nematode with 302 neurons-creates the opportunity to ask whether such emergence is universal, reaching down to even the smallest brains. Here, we measure the activity of 50+ neurons in C. elegans, and analyze the data by building the maximum entropy model that matches the mean activity and pairwise correlations among these neurons. To capture the graded nature of the cells' responses, we assign each cell multiple states. These models, which are equivalent to a family of Potts glasses, successfully predict higher statistical structure in the network. In addition, these models exhibit signatures of collective behavior: the state of single cells can be predicted from the state of the rest of the network; the network, despite being sparse in a way similar to the structural connectome, distributes its response globally when locally perturbed; the distribution over network states has multiple local maxima, as in models of memory; and the parameters that describe the real network are close to a critical surface in this family of models.

Structural complementarity of distance constraints obtained from chemical cross-linking and amino acid coevolution

The analysis of amino acid coevolution has emerged as a practical method for protein structural modeling by providing structural contact information from alignments of amino acid sequences. In parallel, chemical cross-linking/mass spectrometry (XLMS) has gained attention as a universally applicable method for obtaining low-resolution distance constraints to model the quaternary arrangements of proteins, and more recently even protein tertiary structures. Here, we show that the structural information obtained by XLMS and coevolutionary analysis are effectively complementary: the distance constraints obtained by each method are almost exclusively associated with non-coincident pairs of residues, and modeling results obtained by the combination of both sets are improved relative to considering the same total number of constraints of a single type. The structural rationale behind the complementarity of the distance constraints is discussed and illustrated for a representative set of proteins with different sizes and folds.

Toward Inferring Potts Models for Phylogenetically Correlated Sequence Data

Global coevolutionary models of protein families have become increasingly popular due to their capacity to predict residue–residue contacts from sequence information, but also to predict fitness effects of amino acid substitutions or to infer protein–protein interactions. The central idea in these models is to construct a probability distribution, a Potts model, that reproduces single and pairwise frequencies of amino acids found in natural sequences of the protein family. This approach treats sequences from the family as independent samples, completely ignoring phylogenetic relations between them. This simplification is known to lead to potentially biased estimates of the parameters of the model, decreasing their biological relevance. Current workarounds for this problem, such as reweighting sequences, are poorly understood and not principled. Here, we propose an inference scheme that takes the phylogeny of a protein family into account in order to correct biases in estimating the frequencies of amino acids. Using artificial data, we show that a Potts model inferred using these corrected frequencies performs better in predicting contacts and fitness effect of mutations. First, only partially successful tests on real protein data are presented, too.

Advances in protein structure prediction and design

The prediction of protein three-dimensional structure from amino acid sequence has been a grand challenge problem in computational biophysics for decades, owing to its intrinsic scientific interest and also to the many potential applications for robust protein structure prediction algorithms, from genome interpretation to protein function prediction. More recently, the inverse problem - designing an amino acid sequence that will fold into a specified three-dimensional structure - has attracted growing attention as a potential route to the rational engineering of proteins with functions useful in biotechnology and medicine. Methods for the prediction and design of protein structures have advanced dramatically in the past decade. Increases in computing power and the rapid growth in protein sequence and structure databases have fuelled the development of new data-intensive and computationally demanding approaches for structure prediction. New algorithms for designing protein folds and protein-protein interfaces have been used to engineer novel high-order assemblies and to design from scratch fluorescent proteins with novel or enhanced properties, as well as signalling proteins with therapeutic potential. In this Review, we describe current approaches for protein structure prediction and design and highlight a selection of the successful applications they have enabled.

AlphaFold at CASP13

SUMMARY

Computational prediction of protein structure from sequence is broadly viewed as a foundational problem of biochemistry and one of the most difficult challenges in bioinformatics. Once every two years the Critical Assessment of protein Structure Prediction (CASP) experiments are held to assess the state of the art in the field in a blind fashion, by presenting predictor groups with protein sequences whose structures have been solved but have not yet been made publicly available. The first CASP was organized in 1994, and the latest, CASP13, took place last December, when for the first time the industrial laboratory DeepMind entered the competition. DeepMind's entry, AlphaFold, placed first in the Free Modeling (FM) category, which assesses methods on their ability to predict novel protein folds (the Zhang group placed first in the Template-Based Modeling (TBM) category, which assess methods on predicting proteins whose folds are related to ones already in the Protein Data Bank.) DeepMind's success generated significant public interest. Their approach builds on two ideas developed in the academic community during the preceding decade: (i) the use of co-evolutionary analysis to map residue co-variation in protein sequence to physical contact in protein structure, and (ii) the application of deep neural networks to robustly identify patterns in protein sequence and co-evolutionary couplings and convert them into contact maps. In this Letter, we contextualize the significance of DeepMind's entry within the broader history of CASP, relate AlphaFold's methodological advances to prior work, and speculate on the future of this important problem.