arXiv subjects

Martin Weigt

Publications and source records attributed to Martin Weigt.

At least 19 recordsLinked to original sources

arXiv2026

Modeling Protein Evolution with Generative Models: from Extant Sequence Data to Evolutionary Dynamics

Protein sequences carry a record of evolutionary history shaped by mutation, selection, drift, and epistasis. Recent generative models trained on homologous sequence families offer a new way to read this record: they define probabilistic landscapes that score sequences, generate viable variants, and capture constraints that are difficult to measure experimentally. In this review, we discuss how such landscapes can be used not only for protein design or mutation-effect prediction, but also for modeling evolutionary dynamics. We focus particularly on Direct Coupling Analysis as an interpretable and experimentally validated framework, while placing it in the broader context of generative sequence modeling. We first describe how generative sequence landscapes are inferred and assessed, then review how they can be coupled to population-genetic or substitution-model dynamics to simulate protein evolution across experimental and phylogenetic timescales. Applications include viral evolution, laboratory drift experiments, historical contingency, entrenchment, epistatic drift over time, and long-term sequence-space exploration. We conclude by discussing open challenges, including score-fitness calibration, phylogenetic structure, codon-level mutation biases, indels, and the integration of experimental data.

q-bio.PE↗

arXiv2026

Towards coevolution-aware ancestral sequence reconstruction

Ancestral sequence reconstruction (ASR) is a powerful approach for studying molecular evolution and the emergence of protein function. Yet most ASR methods assume that sites evolve independently, neglecting the epistatic constraints that shape protein structure, stability, and function. This simplification affects both ancestral inference and its evaluation: maximum-a-posteriori reconstructions may over-concentrate probability into a single over-idealized sequence, whereas independent posterior sampling can generate implausible or poorly functional ancestors. Here, we introduce a coevolution-aware ASR framework that combines standard phylogenetic inference with Direct Coupling Analysis (DCA), thereby preserving site-wise ancestral uncertainty while enforcing residue-residue constraints learned from extant protein families. To benchmark the method, we develop a controlled forward-evolution framework based on a DCA evolutionary sampler, allowing reconstructed ancestors to be compared with known ground-truth sequences generated under realistic epistatic constraints. Applied to beta-lactamases and DNA-binding domains, the approach improves reconstruction when ancestral states are epistatically constrained, and yields ensembles of candidate ancestors that are both phylogenetically consistent and statistically compatible with natural protein families. This framework bridges the gap between single-sequence MAP reconstruction and unconstrained posterior sampling, providing a practical route toward ancestral reconstructions that better reflect the coupled nature of protein evolution.

q-bio.BM↗

arXiv2026

Reconstructability of evolutionary intermediates in generative epistatic landscapes

Evolutionary intermediates connect observed proteins, but the sequence of steps that produced them is rarely recoverable from extant data alone. Here we ask what can, and cannot, be inferred about such intermediates from the endpoints. Using generative sequence landscapes as controlled models of protein-family evolution, we benchmark data-driven reconstruction against ground-truth simulated trajectories. We find that the best point prediction is not necessarily the most faithful evolutionary reconstruction: maximum-likelihood intermediates can be residue-wise accurate yet statistically atypical, whereas conditional sampling better captures the ensemble of plausible histories. Predictability is limited by the topology of the landscape. Constrained, low-mutability regions preserve information about the path, while permissive high-mutability regions open many alternative routes and erase path-specific memory. We also show that sequence divergence alone is an insufficient measure of elapsed evolutionary time; incorporating endpoint mutability provides a more reliable way to place intermediates in the landscape. These results recast intermediate reconstruction as a calibrated probabilistic problem. Rather than seeking a single "true" sequence, data-driven models should identify when endpoints contain evolutionary information, and return realistic ensembles.

q-bio.PE↗

arXiv2026

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.

q-bio.QM↗

arXiv2025

From Scarce Functional Labels to Label-Aware Generation in Homologous Protein Families

Accurately annotating and controlling protein function from sequence data remains a major challenge in protein engineering, especially when functional labels are scarce within large homologous families. Here, we study a two-stage light-supervision strategy for fine-grained functional annotation and label-aware sequence generation. First, we compare several sequence representations, including one-hot encodings, Restricted Boltzmann Machines (RBMs), and ESM2-based protein language model embeddings, for predicting intra-family specificity labels from limited supervision. By using train/test splits that explicitly reduce phylogenetic leakage, we show that ESM2-based representations do not systematically outperform family-specific RBM embeddings or even simple one-hot baselines in this regime. Second, we use the inferred annotations to train an annotation-aware RBM capable of generating artificial homologs conditioned on prescribed labels. Across several protein families, we quantify how the number and quality of available labels determine the reliability of conditional generation. Our results show that scarce annotations can support label-aware protein design when they are accurately propagated, while also highlighting the importance of phylogeny-aware evaluation for assessing functional annotation methods within homologous families.

q-bio.QM↗

arXiv2025

Integrating experimental feedback improves generative models for biological sequences

Generative probabilistic models have shown promise in designing artificial RNA and protein sequences but often suffer from high rates of false positives, where sequences predicted as functional fail experimental validation. To address this critical limitation, we explore the impact of reintegrating experimental feedback into the model design process. We propose a likelihood-based reintegration scheme, which we test through extensive computational experiments on both RNA and protein datasets, as well as through wet-lab experiments on the self-splicing ribozyme from the group I intron RNA family where our approach demonstrates particular efficacy. We show that integrating recent experimental data enhances the model's capacity of generating functional sequences (e.g. from 6.7\% to 63.7\% of active designs at 45 mutations). This feedback-driven approach thus provides a significant improvement in the design of biomolecular sequences by directly tackling the false-positive challenge.

q-bio.BM↗

arXiv2025

adabmDCA 2.0 -- a flexible but easy-to-use package for Direct Coupling Analysis

In this methods article, we provide a flexible but easy-to-use implementation of Direct Coupling Analysis (DCA) based on Boltzmann machine learning, together with a tutorial on how to use it. The package \texttt{adabmDCA 2.0} is available in different programming languages (C++, Julia, Python) usable on different architectures (single-core and multi-core CPU, GPU) using a common front-end interface. In addition to several learning protocols for dense and sparse generative DCA models, it allows to directly address common downstream tasks like residue-residue contact prediction, mutational-effect prediction, scoring of sequence libraries and generation of artificial sequences for sequence design. It is readily applicable to protein and RNA sequence data.

q-bio.QM↗

arXiv2024

Fluctuations and the limit of predictability in protein evolution

Protein evolution involves mutations occurring across a wide range of time scales. In analogy with disordered systems in statistical physics, this dynamical heterogeneity suggests strong correlations between mutations happening at distinct sites and times. To quantify these correlations, we examine the role of various fluctuation sources in protein evolution, simulated using a data-driven energy landscape as a proxy for protein fitness. By applying spatio-temporal correlation functions developed in the context of disordered physical systems, we disentangle fluctuations originating from the initial condition, i.e. the ancestral sequence from which the evolutionary process originated, from those driven by stochastic mutations along independent evolutionary paths. Our analysis shows that, in diverse protein families, fluctuations from the ancestral sequence predominate at shorter time scales. This allows us to identify a time scale over which ancestral sequence information persists, enabling its reconstruction. We link this persistence to the strength of epistatic interactions: ancestral sequences with stronger epistatic signatures impact evolutionary trajectories over extended periods. At longer time scales, however, ancestral influence fades as epistatically constrained sites evolve collectively. To confirm this idea, we apply a standard ancestral sequence reconstruction algorithm and verify that the time-dependent recovery error is influenced by the properties of the ancestor itself. Overall, our results reveal that the properties of ancestral sequences - particularly their epistatic constraints - influence the initial evolutionary dynamics and the performance of standard ancestral sequence reconstruction algorithms.

q-bio.BM↗

arXiv2024

Emergent time scales of epistasis in protein evolution

We introduce a data-driven epistatic model of protein evolution, capable of generating evolutionary trajectories spanning very different time scales reaching from individual mutations to diverged homologs. Our in silico evolution encompasses random nucleotide mutations, insertions and deletions, and models selection using a fitness landscape, which is inferred via a generative probabilistic model for protein families. We show that the proposed framework accurately reproduces the sequence statistics of both short-time (experimental) and long-time (natural) protein evolution, suggesting applicability also to relatively data-poor intermediate evolutionary time scales, which are currently inaccessible to evolution experiments. Our model uncovers a highly collective nature of epistasis, gradually changing the fitness effect of mutations in a diverging sequence context, rather than acting via strong interactions between individual mutations. This collective nature triggers the emergence of a long evolutionary time scale, separating fast mutational processes inside a given sequence context, from the slow evolution of the context itself. The model quantitatively reproduces epistatic phenomena such as contingency and entrenchment, as well as the loss of predictability in protein evolution observed in deep mutational scanning experiments of distant homologs. It thereby deepens our understanding of the interplay between mutation and selection in shaping protein diversity and novel functions, allows one to statistically forecast evolution, and challenges the prevailing independent-site models of protein evolution, which are unable to capture the fundamental importance of epistasis.

q-bio.BM↗

arXiv2023

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 $\mathbf{10^{39}}$ functional nucleotide sequences. While huge compared to the known $< \mathbf{4,000}$ natural sequences, this number represents only a tiny fraction of the vast pool of nearly $\mathbf{10^{82}}$ 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.

q-bio.BM↗

arXiv2023

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.

cond-mat.dis-nn↗

arXiv2022

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.

q-bio.BM↗

arXiv2022

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.

cond-mat.stat-mech↗

arXiv2022

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.

q-bio.BM↗

arXiv2021

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.

q-bio.GN↗

arXiv2021

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 $10^2$ and $10^3$). 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. $10^{68}$ 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.

q-bio.BM↗

arXiv2021

adabmDCA: Adaptive Boltzmann machine learning for biological sequences

Boltzmann machines are energy-based models that have been shown to provide an accurate statistical description of domains of evolutionary-related protein and RNA families. They are parametrized in terms of local biases accounting for residue conservation, and pairwise terms to model epistatic coevolution between residues. From the model parameters, it is possible to extract an accurate prediction of the three-dimensional contact map of the target domain. More recently, the accuracy of these models has been also assessed in terms of their ability in predicting mutational effects and generating in silico functional sequences. Our adaptive implementation of Boltzmann machine learning, adabmDCA, can be generally applied to both protein and RNA families and accomplishes several learning set-ups, depending on the complexity of the input data and on the user requirements. The code is fully available at https://github.com/anna-pa-m/adabmDCA. As an example, we have performed the learning of three Boltzmann machines modeling the Kunitz and Beta-lactamase2 protein domains and TPP-riboswitch RNA domain. The models learned by adabmDCA are comparable to those obtained by state-of-the-art techniques for this task, in terms of the quality of the inferred contact map as well as of the synthetically generated sequences. In addition, the code implements both equilibrium and out-of-equilibrium learning, which allows for an accurate and lossless training when the equilibrium one is prohibitive in terms of computational time, and allows for pruning irrelevant parameters using an information-based criterion.

q-bio.QM↗

arXiv2021

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

Boltzmann machines (BM) are widely used as generative models. For example, pairwise Potts models (PM), 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 in generating new functional sequences. However, the resulting PM suffers from important over-fitting 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.

q-bio.BM↗