Towards parsimonious generative modeling of RNA families

Generative probabilistic models emerge as a new paradigm in data-driven, evolution-informed design of biomolecular sequences. This paper introduces a novel approach, called Edge Activation Direct Coupling Analysis (eaDCA), tailored to the characteristics of RNA sequences, with a strong emphasis on simplicity, efficiency, and interpretability. eaDCA explicitly constructs sparse coevolutionary models for RNA families, achieving performance levels comparable to more complex methods while utilizing a significantly lower number of parameters. Our approach demonstrates efficiency in generating artificial RNA sequences that closely resemble their natural counterparts in both statistical analyses and SHAPE-MaP experiments, and in predicting the effect of mutations. Notably, eaDCA provides a unique feature: estimating the number of potential functional sequences within a given RNA family. For example, in the case of cyclic di-AMP riboswitches (RF00379), our analysis suggests the existence of approximately 1039 functional nucleotide sequences. While huge compared to the known <4000 natural sequences, this number represents only a tiny fraction of the vast pool of nearly 1082 possible nucleotide sequences of the same length (136 nucleotides). These results underscore the promise of sparse and interpretable generative models, such as eaDCA, in enhancing our understanding of the expansive RNA sequence space.

Generating Interacting Protein Sequences using Domain-to-Domain Translation

MOTIVATION

Being able to artificially design novel proteins of desired function is pivotal in many biological and biomedical applications. Generative statistical modeling has recently emerged as a new paradigm for designing amino acid sequences, including in particular models and embedding methods borrowed from Natural Language Processing (NLP). However, most approaches target single proteins or protein domains, and do not take into account any functional specificity or interaction with the context. To extend beyond current computational strategies, we develop a method for generating protein domain sequences intended to interact with another protein domain. Using data from natural multi-domain proteins, we cast the problem as a translation problem from a given interactor domain to the new domain to be generated, i.e. we generate artificial partner sequences conditional on an input sequence. We also show in an example that the same procedure can be applied to interactions between distinct proteins.

RESULTS

Evaluating our model's quality using diverse metrics, in part related to distinct biological questions, we show that our method outperforms state-of-the-art shallow auto-regressive strategies. We also explore the possibility of fine-tuning pre-trained large language models for the same task and of using Alphafold 2 for assessing the quality of sampled sequences.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics, data and code on https://github.com/barthelemymp/Domain2DomainProteinTranslation.

Combining phylogeny and coevolution improves the inference of interaction partners among paralogous proteins

Predicting protein-protein interactions from sequences is an important goal of computational biology. Various sources of information can be used to this end. Starting from the sequences of two interacting protein families, one can use phylogeny or residue coevolution to infer which paralogs are specific interaction partners within each species. We show that these two signals can be combined to improve the performance of the inference of interaction partners among paralogs. For this, we first align the sequence-similarity graphs of the two families through simulated annealing, yielding a robust partial pairing. We next use this partial pairing to seed a coevolution-based iterative pairing algorithm. This combined method improves performance over either separate method. The improvement obtained is striking in the difficult cases where the average number of paralogs per species is large or where the total number of sequences is modest.

Machine-learning-assisted Monte Carlo fails at sampling computationally hard problems

Several strategies have been recently proposed in order to improve Monte Carlo sampling efficiency using machine learning tools. Here, we challenge these methods by considering a class of problems that are known to be exponentially hard to sample using conventional local Monte Carlo at low enough temperatures. In particular, we study the antiferromagnetic Potts model on a random graph, which reduces to the coloring of random graphs at zero temperature. We test several machine-learning-assisted Monte Carlo approaches, and we find that they all fail. Our work thus provides good benchmarks for future proposals for smart sampling algorithms.

Structure and Function of a Dehydrating Condensation Domain in Nonribosomal Peptide Biosynthesis

Dehydroamino acids are important structural motifs and biosynthetic intermediates for natural products. Many bioactive natural products of nonribosomal origin contain dehydroamino acids; however, the biosynthesis of dehydroamino acids in most nonribosomal peptides is not well understood. Here, we provide biochemical and bioinformatic evidence in support of the role of a unique class of condensation domains in dehydration (C_modAA). We also obtain the crystal structure of a C_modAA domain, which is part of the nonribosomal peptide synthetase AmbE in the biosynthesis of the antibiotic methoxyvinylglycine. Biochemical analysis reveals that AmbE-C_modAA modifies a peptide substrate that is attached to the donor carrier protein. Mutational studies of AmbE-C_modAA identify several key residues for activity, including four residues that are mostly conserved in the C_modAA subfamily. Alanine mutation of these conserved residues either significantly increases or decreases AmbE activity. AmbE exhibits a dimeric conformation, which is uncommon and could enable transfer of an intermediate between different protomers. Our discovery highlights a central dehydrating function for C_modAA domains that unifies dehydroamino acid biosynthesis in diverse nonribosomal peptide pathways. Our work also begins to shed light on the mechanism of C_modAA domains. Understanding C_modAA domain function may facilitate identification of new natural products that contain dehydroamino acids and enable engineering of dehydroamino acids into nonribosomal peptides.

Modeling sequence-space exploration and emergence of epistatic signals in protein evolution

During their evolution, proteins explore sequence space via an interplay between random mutations and phenotypic selection. Here, we build upon recent progress in reconstructing data-driven fitness landscapes for families of homologous proteins, to propose stochastic models of experimental protein evolution. These models predict quantitatively important features of experimentally evolved sequence libraries, like fitness distributions and position-specific mutational spectra. They also allow us to efficiently simulate sequence libraries for a vast array of combinations of experimental parameters like sequence divergence, selection strength, and library size. We showcase the potential of the approach in reanalyzing two recent experiments to determine protein structure from signals of epistasis emerging in experimental sequence libraries. To be detectable, these signals require sufficiently large and sufficiently diverged libraries. Our modeling framework offers a quantitative explanation for different outcomes of recently published experiments. Furthermore, we can forecast the outcome of time- and resource-intensive evolution experiments, opening thereby a way to computationally optimize experimental protocols.

Efficient generative modeling of protein sequences using simple autoregressive models

Generative models emerge as promising candidates for novel sequence-data driven approaches to protein design, and for the extraction of structural and functional information about proteins deeply hidden in rapidly growing sequence databases. Here we propose simple autoregressive models as highly accurate but computationally efficient generative sequence models. We show that they perform similarly to existing approaches based on Boltzmann machines or deep generative models, but at a substantially lower computational cost (by a factor between 10² and 10³). Furthermore, the simple structure of our models has distinctive mathematical advantages, which translate into an improved applicability in sequence generation and evaluation. Within these models, we can easily estimate both the probability of a given sequence, and, using the model's entropy, the size of the functional sequence space related to a specific protein family. In the example of response regulators, we find a huge number of ca. 10⁶⁸ possible sequences, which nevertheless constitute only the astronomically small fraction 10^-80 of all amino-acid sequences of the same length. These findings illustrate the potential and the difficulty in exploring sequence space via generative sequence models.

Sparse generative modeling via parameter reduction of Boltzmann machines: Application to protein-sequence families

Boltzmann machines (BMs) are widely used as generative models. For example, pairwise Potts models (PMs), which are instances of the BM class, provide accurate statistical models of families of evolutionarily related protein sequences. Their parameters are the local fields, which describe site-specific patterns of amino acid conservation, and the two-site couplings, which mirror the coevolution between pairs of sites. This coevolution reflects structural and functional constraints acting on protein sequences during evolution. The most conservative choice to describe the coevolution signal is to include all possible two-site couplings into the PM. This choice, typical of what is known as Direct Coupling Analysis, has been successful for predicting residue contacts in the three-dimensional structure, mutational effects, and generating new functional sequences. However, the resulting PM suffers from important overfitting effects: many couplings are small, noisy, and hardly interpretable; the PM is close to a critical point, meaning that it is highly sensitive to small parameter perturbations. In this work, we introduce a general parameter-reduction procedure for BMs, via a controlled iterative decimation of the less statistically significant couplings, identified by an information-based criterion that selects either weak or statistically unsupported couplings. For several protein families, our procedure allows one to remove more than 90% of the PM couplings, while preserving the predictive and generative properties of the original dense PM, and the resulting model is far away from criticality, hence more robust to noise.

Aligning biological sequences by exploiting residue conservation and coevolution

Sequences of nucleotides (for DNA and RNA) or amino acids (for proteins) are central objects in biology. Among the most important computational problems is that of sequence alignment, i.e., arranging sequences from different organisms in such a way to identify similar regions, to detect evolutionary relationships between sequences, and to predict biomolecular structure and function. This is typically addressed through profile models, which capture position specificities like conservation in sequences but assume an independent evolution of different positions. Over recent years, it has been well established that coevolution of different amino-acid positions is essential for maintaining three-dimensional structure and function. Modeling approaches based on inverse statistical physics can catch the coevolution signal in sequence ensembles, and they are now widely used in predicting protein structure, protein-protein interactions, and mutational landscapes. Here, we present DCAlign, an efficient alignment algorithm based on an approximate message-passing strategy, which is able to overcome the limitations of profile models, to include coevolution among positions in a general way, and to be therefore universally applicable to protein- and RNA-sequence alignment without the need of using complementary structural information. The potential of DCAlign is carefully explored using well-controlled simulated data, as well as real protein and RNA sequences.

FilterDCA: Interpretable supervised contact prediction using inter-domain coevolution

Predicting three-dimensional protein structure and assembling protein complexes using sequence information belongs to the most prominent tasks in computational biology. Recently substantial progress has been obtained in the case of single proteins using a combination of unsupervised coevolutionary sequence analysis with structurally supervised deep learning. While reaching impressive accuracies in predicting residue-residue contacts, deep learning has a number of disadvantages. The need for large structural training sets limits the applicability to multi-protein complexes; and their deep architecture makes the interpretability of the convolutional neural networks intrinsically hard. Here we introduce FilterDCA, a simpler supervised predictor for inter-domain and inter-protein contacts. It is based on the fact that contact maps of proteins show typical contact patterns, which results from secondary structure and are reflected by patterns in coevolutionary analysis. We explicitly integrate averaged contacts patterns with coevolutionary scores derived by Direct Coupling Analysis, improving performance over standard coevolutionary analysis, while remaining fully transparent and interpretable. The FilterDCA code is available at http://gitlab.lcqb.upmc.fr/muscat/FilterDCA.

The de novo prediction of tertiary and quaternary protein structures has recently seen important advances, by combining unsupervised, purely sequence-based coevolutionary analyses with structure-based supervision using deep learning for contact-map prediction. While showing impressive performance, deep-learning methods require large training sets and pose severe obstacles for their interpretability. Here we construct a simple, transparent and therefore fully interpretable inter-domain contact predictor, which uses the results of coevolutionary Direct Coupling Analysis in combination with explicitly constructed filters reflecting typical contact patterns in a training set of known protein structures, and which improves the accuracy of predicted contacts significantly. Our approach thereby sheds light on the question how contact information is encoded in coevolutionary signals.

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.

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.

Predicting Interacting Protein Pairs by Coevolutionary Paralog Matching

Even if we know that two families of homologous proteins interact, we do not necessarily know, which specific proteins interact inside each species. The reason is that most families contain paralogs, i.e., more than one homologous sequence per species. We have developed a tool to predict interacting paralogs between the two protein families, which is based on the idea of inter-protein coevolution: our algorithm matches those members of the two protein families, which belong to the same species and collectively maximize the detectable coevolutionary signal. It is applicable even in cases, where simpler methods based, e.g., on genomic co-localization of genes coding for interacting proteins or orthology-based methods fail. In this method paper, we present an efficient implementation of this idea based on freely available software.

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.

A multi-scale coevolutionary approach to predict interactions between protein domains

Interacting proteins and protein domains coevolve on multiple scales, from their correlated presence across species, to correlations in amino-acid usage. Genomic databases provide rapidly growing data for variability in genomic protein content and in protein sequences, calling for computational predictions of unknown interactions. We first introduce the concept of direct phyletic couplings, based on global statistical models of phylogenetic profiles. They strongly increase the accuracy of predicting pairs of related protein domains beyond simpler correlation-based approaches like phylogenetic profiling (80% vs. 30-50% positives out of the 1000 highest-scoring pairs). Combined with the direct coupling analysis of inter-protein residue-residue coevolution, we provide multi-scale evidence for direct but unknown interaction between protein families. An in-depth discussion shows these to be biologically sensible and directly experimentally testable. Negative phyletic couplings highlight alternative solutions for the same functionality, including documented cases of convergent evolution. Thereby our work proves the strong potential of global statistical modeling approaches to genome-wide coevolutionary analysis, far beyond the established use for individual protein complexes and domain-domain interactions.

Selection of sequence motifs and generative Hopfield-Potts models for protein families

Statistical models for families of evolutionary related proteins have recently gained interest: In particular, pairwise Potts models as those inferred by the direct-coupling analysis have been able to extract information about the three-dimensional structure of folded proteins and about the effect of amino acid substitutions in proteins. These models are typically requested to reproduce the one- and two-point statistics of the amino acid usage in a protein family, i.e., to capture the so-called residue conservation and covariation statistics of proteins of common evolutionary origin. Pairwise Potts models are the maximum-entropy models achieving this. Although being successful, these models depend on huge numbers of ad hoc introduced parameters, which have to be estimated from finite amounts of data and whose biophysical interpretation remains unclear. Here, we propose an approach to parameter reduction, which is based on selecting collective sequence motifs. It naturally leads to the formulation of statistical sequence models in terms of Hopfield-Potts models. These models can be accurately inferred using a mapping to restricted Boltzmann machines and persistent contrastive divergence. We show that, when applied to protein data, even 20-40 patterns are sufficient to obtain statistically close-to-generative models. The Hopfield patterns form interpretable sequence motifs and may be used to clusterize amino acid sequences into functional subfamilies. However, the distributed collective nature of these motifs intrinsically limits the ability of Hopfield-Potts models in predicting contact maps, showing the necessity of developing models going beyond the Hopfield-Potts models discussed here.

How Pairwise Coevolutionary Models Capture the Collective Residue Variability in Proteins?

Global coevolutionary models of homologous protein families, as constructed by direct coupling analysis (DCA), have recently gained popularity in particular due to their capacity to accurately predict residue-residue contacts from sequence information alone, and thereby to facilitate tertiary and quaternary protein structure prediction. More recently, they have also been used to predict fitness effects of amino-acid substitutions in proteins, and to predict evolutionary conserved protein-protein interactions. These models are based on two currently unjustified hypotheses: 1) correlations in the amino-acid usage of different positions are resulting collectively from networks of direct couplings; and 2) pairwise couplings are sufficient to capture the amino-acid variability. Here, we propose a highly precise inference scheme based on Boltzmann-machine learning, which allows us to systematically address these hypotheses. We show how correlations are built up in a highly collective way by a large number of coupling paths, which are based on the proteins three-dimensional structure. We further find that pairwise coevolutionary models capture the collective residue variability across homologous proteins even for quantities which are not imposed by the inference procedure, like three-residue correlations, the clustered structure of protein families in sequence space or the sequence distances between homologs. These findings strongly suggest that pairwise coevolutionary models are actually sufficient to accurately capture the residue variability in homologous protein families.

Inter-residue, inter-protein and inter-family coevolution: bridging the scales

Interacting proteins coevolve at multiple but interconnected scales, from the residue-residue over the protein-protein up to the family-family level. The recent accumulation of enormous amounts of sequence data allows for the development of novel, data-driven computational approaches. Notably, these approaches can bridge scales within a single statistical framework. Although being currently applied mostly to isolated problems on single scales, their immense potential for an evolutionary informed, structural systems biology is steadily emerging.

Meet-U: Educating through research immersion

We present a new educational initiative called Meet-U that aims to train students for collaborative work in computational biology and to bridge the gap between education and research. Meet-U mimics the setup of collaborative research projects and takes advantage of the most popular tools for collaborative work and of cloud computing. Students are grouped in teams of 4–5 people and have to realize a project from A to Z that answers a challenging question in biology. Meet-U promotes "coopetition," as the students collaborate within and across the teams and are also in competition with each other to develop the best final product. Meet-U fosters interactions between different actors of education and research through the organization of a meeting day, open to everyone, where the students present their work to a jury of researchers and jury members give research seminars. This very unique combination of education and research is strongly motivating for the students and provides a formidable opportunity for a scientific community to unite and increase its visibility. We report on our experience with Meet-U in two French universities with master’s students in bioinformatics and modeling, with protein–protein docking as the subject of the course. Meet-U is easy to implement and can be straightforwardly transferred to other fields and/or universities. All the information and data are available at www.meet-u.org.

Inverse statistical physics of protein sequences: a key issues review

In the course of evolution, proteins undergo important changes in their amino acid sequences, while their three-dimensional folded structure and their biological function remain remarkably conserved. Thanks to modern sequencing techniques, sequence data accumulate at unprecedented pace. This provides large sets of so-called homologous, i.e. evolutionarily related protein sequences, to which methods of inverse statistical physics can be applied. Using sequence data as the basis for the inference of Boltzmann distributions from samples of microscopic configurations or observables, it is possible to extract information about evolutionary constraints and thus protein function and structure. Here we give an overview over some biologically important questions, and how statistical-mechanics inspired modeling approaches can help to answer them. Finally, we discuss some open questions, which we expect to be addressed over the next years.

[From sequence variability to structural and functional prediction: modeling of homologous protein families]

Thanks to next-generation sequencing, the number of sequenced genomes grows rapidly, providing in particular ample examples for the sequence variability between homologous proteins. This article discusses data-driven probabilistic sequence models, which are able to extract a multitude of information from sequence data alone, including (i) structural features like residue-residue contacts, which are formed in the folded protein, (ii) protein-protein interaction interfaces and (iii) phenotypic effects of amino-acid substitutions in proteins.

Large-scale identification of coevolution signals across homo-oligomeric protein interfaces by direct coupling analysis

Proteins have evolved to perform diverse cellular functions, from serving as reaction catalysts to coordinating cellular propagation and development. Frequently, proteins do not exert their full potential as monomers but rather undergo concerted interactions as either homo-oligomers or with other proteins as hetero-oligomers. The experimental study of such protein complexes and interactions has been arduous. Theoretical structure prediction methods are an attractive alternative. Here, we investigate homo-oligomeric interfaces by tracing residue coevolution via the global statistical direct coupling analysis (DCA). DCA can accurately infer spatial adjacencies between residues. These adjacencies can be included as constraints in structure prediction techniques to predict high-resolution models. By taking advantage of the ongoing exponential growth of sequence databases, we go significantly beyond anecdotal cases of a few protein families and apply DCA to a systematic large-scale study of nearly 2,000 Pfam protein families with sufficient sequence information and structurally resolved homo-oligomeric interfaces. We find that large interfaces are commonly identified by DCA. We further demonstrate that DCA can differentiate between subfamilies with different binding modes within one large Pfam family. Sequence-derived contact information for the subfamilies proves sufficient to assemble accurate structural models of the diverse protein-oligomers. Thus, we provide an approach to investigate oligomerization for arbitrary protein families leading to structural models complementary to often-difficult experimental methods. Combined with ever more abundant sequential data, we anticipate that this study will be instrumental to allow the structural description of many heteroprotein complexes in the future.

Improving landscape inference by integrating heterogeneous data in the inverse Ising problem

The inverse Ising problem and its generalizations to Potts and continuous spin models have recently attracted much attention thanks to their successful applications in the statistical modeling of biological data. In the standard setting, the parameters of an Ising model (couplings and fields) are inferred using a sample of equilibrium configurations drawn from the Boltzmann distribution. However, in the context of biological applications, quantitative information for a limited number of microscopic spins configurations has recently become available. In this paper, we extend the usual setting of the inverse Ising model by developing an integrative approach combining the equilibrium sample with (possibly noisy) measurements of the energy performed for a number of arbitrary configurations. Using simulated data, we show that our integrative approach outperforms standard inference based only on the equilibrium sample or the energy measurements, including error correction of noisy energy measurements. As a biological proof-of-concept application, we show that mutational fitness landscapes in proteins can be better described when combining evolutionary sequence data with complementary structural information about mutant sequences.

Inter-Protein Sequence Co-Evolution Predicts Known Physical Interactions in Bacterial Ribosomes and the Trp Operon

Interaction between proteins is a fundamental mechanism that underlies virtually all biological processes. Many important interactions are conserved across a large variety of species. The need to maintain interaction leads to a high degree of co-evolution between residues in the interface between partner proteins. The inference of protein-protein interaction networks from the rapidly growing sequence databases is one of the most formidable tasks in systems biology today. We propose here a novel approach based on the Direct-Coupling Analysis of the co-evolution between inter-protein residue pairs. We use ribosomal and trp operon proteins as test cases: For the small resp. large ribosomal subunit our approach predicts protein-interaction partners at a true-positive rate of 70% resp. 90% within the first 10 predictions, with areas of 0.69 resp. 0.81 under the ROC curves for all predictions. In the trp operon, it assigns the two largest interaction scores to the only two interactions experimentally known. On the level of residue interactions we show that for both the small and the large ribosomal subunit our approach predicts interacting residues in the system with a true positive rate of 60% and 85% in the first 20 predictions. We use artificial data to show that the performance of our approach depends crucially on the size of the joint multiple sequence alignments and analyze how many sequences would be necessary for a perfect prediction if the sequences were sampled from the same model that we use for prediction. Given the performance of our approach on the test data we speculate that it can be used to detect new interactions, especially in the light of the rapid growth of available sequence data.

Coevolutionary Landscape Inference and the Context-Dependence of Mutations in Beta-Lactamase TEM-1

The quantitative characterization of mutational landscapes is a task of outstanding importance in evolutionary and medical biology: It is, for example, of central importance for our understanding of the phenotypic effect of mutations related to disease and antibiotic drug resistance. Here we develop a novel inference scheme for mutational landscapes, which is based on the statistical analysis of large alignments of homologs of the protein of interest. Our method is able to capture epistatic couplings between residues, and therefore to assess the dependence of mutational effects on the sequence context where they appear. Compared with recent large-scale mutagenesis data of the beta-lactamase TEM-1, a protein providing resistance against beta-lactam antibiotics, our method leads to an increase of about 40% in explicative power as compared with approaches neglecting epistasis. We find that the informative sequence context extends to residues at native distances of about 20 Å from the mutated site, reaching thus far beyond residues in direct physical contact.

Direct-Coupling Analysis of nucleotide coevolution facilitates RNA secondary and tertiary structure prediction

Despite the biological importance of non-coding RNA, their structural characterization remains challenging. Making use of the rapidly growing sequence databases, we analyze nucleotide coevolution across homologous sequences via Direct-Coupling Analysis to detect nucleotide-nucleotide contacts. For a representative set of riboswitches, we show that the results of Direct-Coupling Analysis in combination with a generalized Nussinov algorithm systematically improve the results of RNA secondary structure prediction beyond traditional covariance approaches based on mutual information. Even more importantly, we show that the results of Direct-Coupling Analysis are enriched in tertiary structure contacts. By integrating these predictions into molecular modeling tools, systematically improved tertiary structure predictions can be obtained, as compared to using secondary structure information alone.

Fast and accurate multivariate Gaussian modeling of protein families: predicting residue contacts and protein-interaction partners

In the course of evolution, proteins show a remarkable conservation of their three-dimensional structure and their biological function, leading to strong evolutionary constraints on the sequence variability between homologous proteins. Our method aims at extracting such constraints from rapidly accumulating sequence data, and thereby at inferring protein structure and function from sequence information alone. Recently, global statistical inference methods (e.g. direct-coupling analysis, sparse inverse covariance estimation) have achieved a breakthrough towards this aim, and their predictions have been successfully implemented into tertiary and quaternary protein structure prediction methods. However, due to the discrete nature of the underlying variable (amino-acids), exact inference requires exponential time in the protein length, and efficient approximations are needed for practical applicability. Here we propose a very efficient multivariate Gaussian modeling approach as a variant of direct-coupling analysis: the discrete amino-acid variables are replaced by continuous Gaussian random variables. The resulting statistical inference problem is efficiently and exactly solvable. We show that the quality of inference is comparable or superior to the one achieved by mean-field approximations to inference with discrete variables, as done by direct-coupling analysis. This is true for (i) the prediction of residue-residue contacts in proteins, and (ii) the identification of protein-protein interaction partner in bacterial signal transduction. An implementation of our multivariate Gaussian approach is available at the website http://areeweb.polito.it/ricerca/cmp/code.

Direct coupling analysis for protein contact prediction

During evolution, structure, and function of proteins are remarkably conserved, whereas amino-acid sequences vary strongly between homologous proteins. Structural conservation constrains sequence variability and forces different residues to coevolve, i.e., to show correlated patterns of amino-acid occurrences. However, residue correlation may result from direct coupling, e.g., by a contact in the folded protein, or be induced indirectly via intermediate residues. To use empirically observed correlations for predicting residue-residue contacts, direct and indirect effects have to be disentangled. Here we present mechanistic details on how to achieve this using a methodology called Direct Coupling Analysis (DCA). DCA has been shown to produce highly accurate estimates of amino-acid pairs that have direct reciprocal constraints in evolution. Specifically, we provide instructions and protocols on how to use the algorithmic implementations of DCA starting from data extraction to predicted-contact visualization in contact maps or representative protein structures.

Perturbation biology: inferring signaling networks in cellular systems

We present a powerful experimental-computational technology for inferring network models that predict the response of cells to perturbations, and that may be useful in the design of combinatorial therapy against cancer. The experiments are systematic series of perturbations of cancer cell lines by targeted drugs, singly or in combination. The response to perturbation is quantified in terms of relative changes in the measured levels of proteins, phospho-proteins and cellular phenotypes such as viability. Computational network models are derived de novo, i.e., without prior knowledge of signaling pathways, and are based on simple non-linear differential equations. The prohibitively large solution space of all possible network models is explored efficiently using a probabilistic algorithm, Belief Propagation (BP), which is three orders of magnitude faster than standard Monte Carlo methods. Explicit executable models are derived for a set of perturbation experiments in SKMEL-133 melanoma cell lines, which are resistant to the therapeutically important inhibitor of RAF kinase. The resulting network models reproduce and extend known pathway biology. They empower potential discoveries of new molecular interactions and predict efficacious novel drug perturbations, such as the inhibition of PLK1, which is verified experimentally. This technology is suitable for application to larger systems in diverse areas of molecular biology.

Drugs that target specific effects of signaling proteins are promising agents for treating cancer. One of the many obstacles facing optimal drug design is inadequate quantitative understanding of the coordinated interactions between signaling proteins. De novo model inference of network or pathway models refers to the algorithmic construction of mathematical predictive models from experimental data without dependence on prior knowledge. De novo inference is difficult because of the prohibitively large number of possible sets of interactions that may or may not be consistent with observations. Our new method overcomes this difficulty by adapting a method from statistical physics, called Belief Propagation, which first calculates probabilistically the most likely interactions in the vast space of all possible solutions, then derives a set of individual, highly probable solutions in the form of executable models. In this paper, we test this method on artificial data and then apply it to model signaling pathways in a BRAF-mutant melanoma cancer cell line based on a large set of rich output measurements from a systematic set of perturbation experiments using drug combinations. Our results are in agreement with established biological knowledge, predict novel interactions, and predict efficacious drug targets that are specific to the experimental cell line and potentially to related tumors. The method has the potential, with sufficient systematic perturbation data, to model, de novo and quantitatively, the effects of hundreds of proteins on cellular responses, on a scale that is currently unreachable in diverse areas of cell biology. In a disease context, the method is applicable to the computational design of novel combination drug treatments.

Improved contact prediction in proteins: using pseudolikelihoods to infer Potts models

Spatially proximate amino acids in a protein tend to coevolve. A protein's three-dimensional (3D) structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D structures from such correlations is an open problem in structural biology, pursued with increasing vigor as more and more protein sequences continue to fill the data banks. Within this task lies a statistical inference problem, rooted in the following: correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network-propagated via intermediate sites; observed correlation is not enough to guarantee proximity. To separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics, where the task is to learn model parameters (fields, couplings) from observables (magnetizations, correlations, samples) in large systems. In the context of protein sequences, the approach has been referred to as direct-coupling analysis. Here we show that the pseudolikelihood method, applied to 21-state Potts models describing the statistical properties of families of evolutionarily related proteins, significantly outperforms existing approaches to the direct-coupling analysis, the latter being based on standard mean-field techniques. This improved performance also relies on a modified score for the coupling strength. The results are verified using known crystal structures of specific sequence instances of various protein families. Code implementing the new method can be found at http://plmdca.csc.kth.se/.

Dissecting the specificity of protein-protein interaction in bacterial two-component signaling: orphans and crosstalks

Predictive understanding of the myriads of signal transduction pathways in a cell is an outstanding challenge of systems biology. Such pathways are primarily mediated by specific but transient protein-protein interactions, which are difficult to study experimentally. In this study, we dissect the specificity of protein-protein interactions governing two-component signaling (TCS) systems ubiquitously used in bacteria. Exploiting the large number of sequenced bacterial genomes and an operon structure which packages many pairs of interacting TCS proteins together, we developed a computational approach to extract a molecular interaction code capturing the preferences of a small but critical number of directly interacting residue pairs. This code is found to reflect physical interaction mechanisms, with the strongest signal coming from charged amino acids. It is used to predict the specificity of TCS interaction: Our results compare favorably to most available experimental results, including the prediction of 7 (out of 8 known) interaction partners of orphan signaling proteins in Caulobacter crescentus. Surveying among the available bacterial genomes, our results suggest 15∼25% of the TCS proteins could participate in out-of-operon “crosstalks”. Additionally, we predict clusters of crosstalking candidates, expanding from the anecdotally known examples in model organisms. The tools and results presented here can be used to guide experimental studies towards a system-level understanding of two-component signaling.

Inference of sparse combinatorial-control networks from gene-expression data: a message passing approach

Background

Transcriptional gene regulation is one of the most important mechanisms in controlling many essential cellular processes, including cell development, cell-cycle control, and the cellular response to variations in environmental conditions. Genes are regulated by transcription factors and other genes/proteins via a complex interconnection network. Such regulatory links may be predicted using microarray expression data, but most regulation models suppose transcription factor independence, which leads to spurious links when many genes have highly correlated expression levels.

Results

We propose a new algorithm to infer combinatorial control networks from gene-expression data. Based on a simple model of combinatorial gene regulation, it includes a message-passing approach which avoids explicit sampling over putative gene-regulatory networks. This algorithm is shown to recover the structure of a simple artificial cell-cycle network model for baker's yeast. It is then applied to a large-scale yeast gene expression dataset in order to identify combinatorial regulations, and to a data set of direct medical interest, namely the Pleiotropic Drug Resistance (PDR) network.

Conclusions

The algorithm we designed is able to recover biologically meaningful interactions, as shown by recent experimental results [1]. Moreover, new cases of combinatorial control are predicted, showing how simple models taking this phenomenon into account can lead to informative predictions and allow to extract more putative regulatory interactions from microarray databases.

Computational modeling of phosphotransfer complexes in two-component signaling

Two-component signal transduction systems enable cells in bacteria, fungi, and plants to react to extracellular stimuli. A sensor histidine kinase (SK) detects such stimuli with its sensor domains and transduces the input signals to a response regulator (RR) by trans-phosphorylation. This trans-phosphorylation reaction requires the formation of a complex formed by the two interacting proteins. The complex is stabilized by transient interactions. The nature of the transient interactions makes it challenging for experimental techniques to gain structural information. X-ray crystallography requires stable crystals, which are difficult to grow and stabilize. Similarly, the mere size of these systems proves problematic for NMR. Theoretical methods can, however, complement existing data. The statistical direct coupling analysis presented in the previous chapter reveals the interacting residues at the contact interface of the SK/RR pair. This information can be combined with the structures of the individual proteins in molecular dynamical simulation to generate structural models of the complex. The general approach, referred to as MAGMA, was tested on the sporulation phosphorelay phosphotransfer complex, the Spo0B/Spo0F pair, delivering crystal resolution accuracy. The MAGMA method is described here in a step-by-step explanation. The developed parameters are transferrable to other SK/RR systems.

Clustering by soft-constraint affinity propagation: applications to gene-expression data

MOTIVATION

Similarity-measure-based clustering is a crucial problem appearing throughout scientific data analysis. Recently, a powerful new algorithm called Affinity Propagation (AP) based on message-passing techniques was proposed by Frey and Dueck (2007a). In AP, each cluster is identified by a common exemplar all other data points of the same cluster refer to, and exemplars have to refer to themselves. Albeit its proved power, AP in its present form suffers from a number of drawbacks. The hard constraint of having exactly one exemplar per cluster restricts AP to classes of regularly shaped clusters, and leads to suboptimal performance, e.g. in analyzing gene expression data.

RESULTS

This limitation can be overcome by relaxing the AP hard constraints. A new parameter controls the importance of the constraints compared to the aim of maximizing the overall similarity, and allows to interpolate between the simple case where each data point selects its closest neighbor as an exemplar and the original AP. The resulting soft-constraint affinity propagation (SCAP) becomes more informative, accurate and leads to more stable clustering. Even though a new a priori free parameter is introduced, the overall dependence of the algorithm on external tuning is reduced, as robustness is increased and an optimal strategy for parameter selection emerges more naturally. SCAP is tested on biological benchmark data, including in particular microarray data related to various cancer types. We show that the algorithm efficiently unveils the hierarchical cluster structure present in the data sets. Further on, it allows to extract sparse gene expression signatures for each cluster.

Propagation of external regulation and asynchronous dynamics in random Boolean networks

Boolean networks and their dynamics are of great interest as abstract modeling schemes in various disciplines, ranging from biology to computer science. Whereas parallel update schemes have been studied extensively in past years, the level of understanding of asynchronous updates schemes is still very poor. In this paper we study the propagation of external information given by regulatory input variables into a random Boolean network. We compute both analytically and numerically the time evolution and the asymptotic behavior of this propagation of external regulation (PER). In particular, this allows us to identify variables that are completely determined by this external information. All those variables in the network that are not directly fixed by PER form a core which contains, in particular, all nontrivial feedback loops. We design a message-passing approach allowing to characterize the statistical properties of these cores in dependence of the Boolean network and the external condition. At the end we establish a link between PER dynamics and the full random asynchronous dynamics of a Boolean network.

Message passing for vertex covers

Constructing a minimal vertex cover of a graph can be seen as a prototype for a combinatorial optimization problem under hard constraints. In this paper, we develop and analyze message-passing techniques, namely, warning and survey propagation, which serve as efficient heuristic algorithms for solving these computational hard problems. We show also, how previously obtained results on the typical-case behavior of vertex covers of random graphs can be recovered starting from the message-passing equations, and how they can be extended.

Statistical mechanics of combinatorial auctions

Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solutions. We introduce an iterative algorithm to solve intermediate and large instances, and discuss competing states of optimal revenue and maximal number of satisfied bidders. The algorithm can be generalized to the hard phase and to more sophisticated auction protocols.

Core percolation and onset of complexity in boolean networks

The determination and classification of fixed points of large Boolean networks is addressed in terms of a constraint-satisfaction problem. We develop a general simplification scheme that, removing all those variables and functions belonging to trivial logical cascades, returns the computational core of the network. The transition line from an easy to a complex regulatory phase is described as a function of the parameters of the model, identifying thereby both theoretically and algorithmically the relevant regulatory variables.

Cavity approach to the random solid state

The cavity approach is used to address the physical properties of random solids in equilibrium. Particular attention is paid to the fraction of localized particles and the distribution of localization lengths characterizing their thermal motion. This approach is of relevance to a wide class of random solids, including rubbery media (formed via the vulcanization of polymer fluids) and chemical gels (formed by the random covalent bonding of fluids of atoms or small molecules). The cavity approach confirms results that have been obtained previously via replica mean-field theory, doing so in a way that sheds new light on their physical origin.

Threshold values, stability analysis, and high-q asymptotics for the coloring problem on random graphs

We consider the problem of coloring Erdös-Rényi and regular random graphs of finite connectivity using q colors. It has been studied so far using the cavity approach within the so-called one-step replica symmetry breaking (1RSB) ansatz. We derive a general criterion for the validity of this ansatz and, applying it to the ground state, we provide evidence that the 1RSB solution gives exact threshold values c(q) for the transition from the colorable to the uncolorable phase with q colors. We also study the asymptotic thresholds for q>>1 finding c(q) =2q ln q-ln q-1+o (1) in perfect agreement with rigorous mathematical bounds, as well as the nature of excited states, and give a global phase diagram of the problem.