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Martin Weigt

Martin Weigt appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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cond-mat.stat-mechQuantitative MethodsBiomoleculescond-mat.dis-nnMolecular NetworksBiological Physicsphysics.data-anPopulations and EvolutionGenomicsMachine LearningMethodology

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Published work

19 published item(s)

preprint2026arXiv

Expanding functional protein sequence space using high entropy generative models

Boltzmann Machines trained on evolutionary sequence data have emerged as a powerful paradigm for the data-driven design of artificial proteins. However, the relationship between model architecture, specifically parameter density, and experimental performance remains poorly understood. Here, we investigate this relationship using the Chorismate Mutase enzyme family as a model system. We compare standard fully connected Boltzmann Machines for Direct Coupling Analysis (bmDCA) with sparse models generated via progressive edge activation (eaDCA) and edge decimation (edDCA). We identify a maximum-entropy model (meDCA) along the decimation trajectory that represents an optimal balance between constraint satisfaction and the flexibility of the probability distribution. We synthesized and tested artificial sequences from all models using an in vivo complementation assay, finding that all architectures, regardless of sparsity, generate functional enzymes with high success rates, even at significant divergence from natural sequences. Despite this functional equivalence, we demonstrate that the meDCA model samples a viable sequence space that is more than fifteen orders of magnitude larger than its low-entropy counterparts. Furthermore, comparative analyses reveal that high-entropy models systematically minimize overfitting and better capture the local neutral spaces surrounding natural proteins. These findings suggest that while various models satisfying coevolutionary statistics can generate functional sequences, high-entropy Boltzmann Machines provide a superior representation of the underlying evolutionary fitness landscape.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

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 re-analyzing 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 the variable success 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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Statistical-physics approaches to RNA molecules, families and networks

This contribution focuses on the fascinating RNA molecule, its sequence-dependent folding driven by base-pairing interactions, the interplay between these interactions and natural evolution, and its multiple regulatory roles. The four of us have dug into these topics using the tools and the spirit of the statistical physics of disordered systems, and in particular the concept of a disordered (energy/fitness) landscape. After an introduction to RNA molecules and the perspectives they open not only in evolutionary and synthetic biology but also in medicine, we will introduce the important notions of energy and fitness landscapes for these molecules. In Section III we will review some models and algorithms for RNA sequence-to-secondary-structure mapping. Section IV discusses how the secondary-structure energy landscape can be derived from unzipping data. Section V deals with the inference of RNA structure from evolutionary sequence data sampled in different organisms. This will shift the focus from the `sequence-to-structure' mapping described in Section III to a `sequence-to-function' landscape that can be inferred from laboratory evolutionary data on DNA aptamers. Finally, in Section VI, we shall discuss the rich theoretical picture linking networks of interacting RNA molecules to the organization of robust, systemic regulatory programs. Along this path, we will therefore explore phenomena across multiple scales in space, number of molecules and time, showing how the biological complexity of the RNA world can be captured by the unifying concepts of statistical physics.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Epistatic models predict mutable sites in SARS-CoV-2 proteins and epitopes

The emergence of new variants of SARS-CoV-2 is a major concern given their potential impact on the transmissibility and pathogenicity of the virus as well as the efficacy of therapeutic interventions. Here, we predict the mutability of all positions in SARS-CoV-2 protein domains to forecast the appearance of unseen variants. Using sequence data from other coronaviruses, pre-existing to SARS-CoV-2, we build statistical models that do not only capture amino-acid conservation but more complex patterns resulting from epistasis. We show that these models are notably superior to conservation profiles in estimating the already observable SARS-CoV-2 variability. In the receptor binding domain of the spike protein, we observe that the predicted mutability correlates well with experimental measures of protein stability and that both are reliable mutability predictors (ROC AUC ~0.8). Most interestingly, we observe an increasing agreement between our model and the observed variability as more data become available over time, proving the anticipatory capacity of our model. When combined with data concerning the immune response, our approach identifies positions where current variants of concern are highly overrepresented. These results could assist studies on viral evolution, future viral outbreaks and, in particular, guide the exploration and anticipation of potentially harmful future SARS-CoV-2 variants.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Global multivariate model learning from hierarchically correlated data

Inverse statistical physics aims at inferring models compatible with a set of empirical averages estimated from a high-dimensional dataset of independently distributed equilibrium configurations of a given system. However, in several applications such as biology, data result from stochastic evolutionary processes, and configurations are related through a hierarchical structure, typically represented by a tree, and therefore not independent. In turn, empirical averages of observables superpose intrinsic signal related to the equilibrium distribution of the studied system and spurious historical (or phylogenetic) signal resulting from the structure underlying the data-generating process. The naive application of inverse statistical physics techniques therefore leads to systematic biases and an effective reduction of the sample size. To advance on the currently open task of extracting intrinsic signals from correlated data, we study a system described by a multivariate Ornstein-Uhlenbeck process defined on a finite tree. Using a Bayesian framework, we can disentangle covariances in the data corresponding to their multivariate Gaussian equilibrium distribution from those resulting from the historical correlations. Our approach leads to a clear gain in accuracy in the inferred equilibrium distribution, which corresponds to an effective two- to fourfold increase in sample size.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

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 inter-block 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 are available, and that an iterative pairing algorithm (IPA) 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 its quality is imperfect, thereby shedding light on the empirically observed performance of DCA applied to natural protein sequences.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Phylogenetic correlations can suffice to infer protein partners from sequences

Determining which proteins interact together is crucial to a systems-level understanding of the cell. Recently, algorithms based on Direct Coupling Analysis (DCA) pairwise maximum-entropy models have allowed to identify interaction partners among paralogous proteins from sequence data. This success of DCA at predicting protein-protein interactions could be mainly based on its known ability to identify pairs of residues that are in contact in the three-dimensional structure of protein complexes and that coevolve to remain physicochemically complementary. However, interacting proteins possess similar evolutionary histories. What is the role of purely phylogenetic correlations in the performance of DCA-based methods to infer interaction partners? To address this question, we employ controlled synthetic data that only involve phylogeny and no interactions or contacts. We find that DCA accurately identifies the pairs of synthetic sequences that share evolutionary history. While phylogenetic correlations confound the identification of contacting residues by DCA, they are thus useful to predict interacting partners among paralogs. We find that DCA performs as well as phylogenetic methods to this end, and slightly better than them with large and accurate training sets. Employing DCA or phylogenetic methods within an Iterative Pairing Algorithm (IPA) allows to predict pairs of evolutionary partners without a training set. We demonstrate the ability of these various methods to correctly predict pairings among real paralogous proteins with genome proximity but no known physical interaction, illustrating the importance of phylogenetic correlations in natural data. However, for physically interacting and strongly coevolving proteins, DCA and mutual information outperform phylogenetic methods. We discuss how to distinguish physically interacting proteins from those only sharing evolutionary history.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Simultaneous identification of specifically interacting paralogs and inter-protein contacts by Direct-Coupling Analysis

Understanding protein-protein interactions is central to our understanding of almost all complex biological processes. Computational tools exploiting rapidly growing genomic databases to characterize protein-protein interactions are urgently needed. Such methods should connect multiple scales from evolutionary conserved interactions between families of homologous proteins, over the identification of specifically interacting proteins in the case of multiple paralogs inside a species, down to the prediction of residues being in physical contact across interaction interfaces. Statistical inference methods detecting residue-residue coevolution have recently triggered considerable progress in using sequence data for quaternary protein structure prediction; they require, however, large joint alignments of homologous protein pairs known to interact. The generation of such alignments is a complex computational task on its own; application of coevolutionary modeling has in turn been restricted to proteins without paralogs, or to bacterial systems with the corresponding coding genes being co-localized in operons. Here we show that the Direct-Coupling Analysis of residue coevolution can be extended to connect the different scales, and simultaneously to match interacting paralogs, to identify inter-protein residue-residue contacts and to discriminate interacting from noninteracting families in a multiprotein system. Our results extend the potential applications of coevolutionary analysis far beyond cases treatable so far.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

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, e.g., 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 to 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 to approaches neglecting epistasis. We find that the informative sequence context extends to residues at native distances of about 20Å from the mutated site, reaching thus far beyond residues in direct physical contact.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

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

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

From principal component to direct coupling analysis of coevolution in proteins: Low-eigenvalue modes are needed for structure prediction

Various approaches have explored the covariation of residues in multiple-sequence alignments of homologous proteins to extract functional and structural information. Among those are principal component analysis (PCA), which identifies the most correlated groups of residues, and direct coupling analysis (DCA), a global inference method based on the maximum entropy principle, which aims at predicting residue-residue contacts. In this paper, inspired by the statistical physics of disordered systems, we introduce the Hopfield-Potts model to naturally interpolate between these two approaches. The Hopfield-Potts model allows us to identify relevant 'patterns' of residues from the knowledge of the eigenmodes and eigenvalues of the residue-residue correlation matrix. We show how the computation of such statistical patterns makes it possible to accurately predict residue-residue contacts with a much smaller number of parameters than DCA. This dimensional reduction allows us to avoid overfitting and to extract contact information from multiple-sequence alignments of reduced size. In addition, we show that low-eigenvalue correlation modes, discarded by PCA, are important to recover structural information: the corresponding patterns are highly localized, that is, they are concentrated in few sites, which we find to be in close contact in the three-dimensional protein fold.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

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/.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Perturbation Biology: inferring signaling networks in cellular systems

We present a new experimental-computational technology of 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 measured in terms of levels of proteins and phospho-proteins and of cellular phenotype 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, which is three orders of magnitude more efficient than 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 inhibition of Raf kinase. The resulting network models reproduce and extend known pathway biology. They can be applied to discover new molecular interactions and to predict the effect of novel drug perturbations, one of which is verified experimentally. The technology is suitable for application to larger systems in diverse areas of molecular biology.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Direct-coupling analysis of residue co-evolution captures native contacts across many protein families

The similarity in the three-dimensional structures of homologous proteins imposes strong constraints on their sequence variability. It has long been suggested that the resulting correlations among amino acid compositions at different sequence positions can be exploited to infer spatial contacts within the tertiary protein structure. Crucial to this inference is the ability to disentangle direct and indirect correlations, as accomplished by the recently introduced Direct Coupling Analysis (DCA) (Weigt et al. (2009) Proc Natl Acad Sci 106:67). Here we develop a computationally efficient implementation of DCA, which allows us to evaluate the accuracy of contact prediction by DCA for a large number of protein domains, based purely on sequence information. DCA is shown to yield a large number of correctly predicted contacts, recapitulating the global structure of the contact map for the majority of the protein domains examined. Furthermore, our analysis captures clear signals beyond intra- domain residue contacts, arising, e.g., from alternative protein conformations, ligand- mediated residue couplings, and inter-domain interactions in protein oligomers. Our findings suggest that contacts predicted by DCA can be used as a reliable guide to facilitate computational predictions of alternative protein conformations, protein complex formation, and even the de novo prediction of protein domain structures, provided the existence of a large number of homologous sequences which are being rapidly made available due to advances in genome sequencing.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2009arXiv

Statistical mechanics of sparse generalization and model selection

One of the crucial tasks in many inference problems is the extraction of sparse information out of a given number of high-dimensional measurements. In machine learning, this is frequently achieved using, as a penality term, the $L_p$ norm of the model parameters, with $p\leq 1$ for efficient dilution. Here we propose a statistical-mechanics analysis of the problem in the setting of perceptron memorization and generalization. Using a replica approach, we are able to evaluate the relative performance of naive dilution (obtained by learning without dilution, following by applying a threshold to the model parameters), $L_1$ dilution (which is frequently used in convex optimization) and $L_0$ dilution (which is optimal but computationally hard to implement). Whereas both $L_p$ diluted approaches clearly outperform the naive approach, we find a small region where $L_0$ works almost perfectly and strongly outperforms the simpler to implement $L_1$ dilution.

0 citations0 reviewsNo code linkedOpen access
preprint2002arXiv

Dynamics of heuristic optimization algorithms on random graphs

In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex degree. This vertex, and some environment of it, is covered and removed from the graph. This graph reduction process can be described as a Markovian dynamics in the space of random graphs of arbitrary degree distribution. We discuss some solvable cases, including algorithms already analysed using different techniques, and develop approximation schemes for more complicated cases. The approximations are corroborated by numerical simulations.

0 citations0 reviewsNo code linkedOpen access