Understanding epistatic networks in the B1 β-lactamases through coevolutionary statistical modeling and deep mutational scanning.

Throughout evolution, protein families undergo substantial sequence divergence while preserving structure and function. Although most mutations are deleterious, evolution can explore sequence space via epistatic networks of intramolecular interactions that alleviate the harmful mutations. However, comprehensive analysis of such epistatic networks across protein families remains limited.

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.

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.

The nature of non-phononic excitations in disordered systems.

The frequency scaling exponent of low-frequency excitations in microscopically small glasses, which do not allow for the existence of waves (phonons), has been in the focus of the recent literature. The density of states g(ω) of these modes obeys an ω scaling, where the exponent s, ranging between 2 and 5, depends on the quenching protocol. The orgin of these findings remains controversal.

Scaling regimes and fluctuations of observables in computer glasses approaching the unjamming transition.

Under decompression, disordered solids undergo an unjamming transition where they become under-coordinated and lose their structural rigidity. The mechanical and vibrational properties of these materials have been an object of theoretical, numerical, and experimental research for decades. In the study of low-coordination solids, understanding the behavior and physical interpretation of observables that diverge near the transition is of particular importance.

Finding defects in glasses through machine learning.

Structural defects control the kinetic, thermodynamic and mechanical properties of glasses. For instance, rare quantum tunneling two-level systems (TLS) govern the physics of glasses at very low temperature. Due to their extremely low density, it is very hard to directly identify them in computer simulations.

Creating bulk ultrastable glasses by random particle bonding.

A recent breakthrough in glass science has been the synthesis of ultrastable glasses via physical vapor deposition techniques. These samples display enhanced thermodynamic, kinetic and mechanical stability, with important implications for fundamental science and technological applications. However, the vapor deposition technique is limited to atomic, polymer and organic glass-formers and is only able to produce thin film samples.

Microscopic observation of two-level systems in a metallic glass model.

The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm.

Finite-Disorder Critical Point in the Yielding Transition of Elastoplastic Models.

Upon loading, amorphous solids can exhibit brittle yielding, with the abrupt formation of macroscopic shear bands leading to fracture, or ductile yielding, with a multitude of plastic events leading to homogeneous flow. It has been recently proposed, and subsequently questioned, that the two regimes are separated by a sharp critical point, as a function of some control parameter characterizing the intrinsic disorder strength and the degree of stability of the solid. In order to resolve this issue, we have performed extensive numerical simulations of athermally driven elastoplastic models with long-range and anisotropic realistic interaction kernels in two and three dimensions.

Equilibrium fluctuations in mean-field disordered models.

Mean-field models of glasses that present a random first order transition exhibit highly nontrivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for all equilibrium conditions. By means of the replica method we evaluate Gaussian fluctuations of the overlaps around the thermodynamic limit, decomposing them in thermal fluctuations inside each state and heterogeneous fluctuations between different states.

Local Dynamical Heterogeneity in Simple Glass Formers.

We study the local dynamical fluctuations in glass-forming models of particles embedded in d-dimensional space, in the mean-field limit of d→∞. Our analytical calculation reveals that single-particle observables, such as squared particle displacements, display divergent fluctuations around the dynamical (or mode-coupling) transition, due to the emergence of nontrivial correlations between displacements along different directions. This effect notably gives rise to a divergent non-Gaussian parameter, α_{2}.

Supervised perceptron learning vs unsupervised Hebbian unlearning: Approaching optimal memory retrieval in Hopfield-like networks.

The Hebbian unlearning algorithm, i.e., an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron.

Three simple scenarios for high-dimensional sphere packings.

Based on results from the physics and mathematics literature which suggest a series of clearly defined conjectures, we formulate three simple scenarios for the fate of hard sphere crystallization in high dimension: in scenario A, crystallization is impeded and the glass phase constitutes the densest packing; in scenario B, crystallization from the liquid is possible, but takes place much beyond the dynamical glass transition and is thus dynamically implausible; and in scenario C, crystallization is possible and takes place before (or just after) dynamical arrest, thus making it plausibly accessible from the liquid state. In order to assess the underlying conjectures and thus obtain insight into which scenario is most likely to be realized, we investigate the densest sphere packings for dimension d=3-10 using cell-cluster expansions as well as numerical simulations. These resulting estimates of the crystal entropy near close packing tend to support scenario C.

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.

Active matter in infinite dimensions: Fokker-Planck equation and dynamical mean-field theory at low density.

We investigate the behavior of self-propelled particles in infinite space dimensions by comparing two powerful approaches in many-body dynamics: the Fokker-Planck equation and dynamical mean-field theory. The dynamics of the particles at low densities and infinite persistence time is solved in the steady state with both methods, thereby proving the consistency of the two approaches in a paradigmatic out-of-equilibrium system. We obtain the analytic expression for the pair distribution function and the effective self-propulsion to first-order in the density, confirming the results obtained in a previous paper [T.

adabmDCA: adaptive Boltzmann machine learning for biological sequences.

Background: 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.

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 and 10).

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.

Mean-Field Caging in a Random Lorentz Gas.

The random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional, → ∞ limit: the localization transition is then expected to be for the former and for the latter. As a putative resolution, we have recently suggested that, as increases, the behavior of the RLG converges to the glassy description and that percolation physics is recovered thanks to finite- perturbative and nonperturbative (instantonic) corrections [Biroli et al. 2021, 103, L030104].

Interplay between percolation and glassiness in the random Lorentz gas.

The random Lorentz gas (RLG) is a minimal model of transport in heterogeneous media that exhibits a continuous localization transition controlled by void space percolation. The RLG also provides a toy model of particle caging, which is known to be relevant for describing the discontinuous dynamical transition of glasses. In order to clarify the interplay between the seemingly incompatible percolation and caging descriptions of the RLG, we consider its exact mean-field solution in the infinite-dimensional d→∞ limit and perform numerics in d=2.

V-, U-, L- or W-shaped economic recovery after Covid-19: Insights from an Agent Based Model.

We discuss the impact of a Covid-19-like shock on a simple model economy, described by the previously developed Mark-0 Agent-Based Model. We consider a mixed supply and demand shock, and show that depending on the shock parameters (amplitude and duration), our model economy can display V-shaped, U-shaped or W-shaped recoveries, and even an L-shaped output curve with permanent output loss. This is due to the economy getting trapped in a self-sustained "bad" state.

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.