Francesco Zamponi’s research while affiliated with Paris Diderot University and other places

Protein evolution involves mutations occurring across a wide range of time scales [Di Bari et al., PNAS 121, e2406807121 (2024)]. In analogy with other disordered systems, 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 epistatic landscape. By applying spatio-temporal correlation functions inspired by statistical physics, we disentangle fluctuations originating from the ancestral protein sequence 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.

Protein evolution involves mutations occurring across a wide range of time scales [Di Bari et al., PNAS 121, e2406807121 (2024)]. In analogy with other disordered systems, 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 epistatic landscape. By applying spatio-temporal correlation functions inspired by statistical physics, we disentangle fluctuations originating from the ancestral protein sequence 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.

We analyze the problem of storing random pattern-label associations using two classes of continuous non-convex weights models, namely the perceptron with negative margin and an infinite width two layer neural network with non-overlapping receptive fields and generic activation function. Using a full-RSB ansatz we compute the exact value of the SAT/UNSAT transition. Furthermore, in the case of the negative perceptron model we show that, depending on the value of the margin and the constrained density, there is a line separating a phase in which the distribution of overlaps of typical states does not possess a gap from one in which it does. Our results show that the hypothesis underlying some recently developed theorems claiming that Approximate Message Passing (AMP) based algorithms are able to reach capacity, does not hold in general. Finally, we show that Gradient Descent is not able to reach the maximal capacity both in cases where there is and there is not a non-overlap gap phase for the typical states. This, similarly to what occurs in binary weight models, suggests that gradient-based algorithms are biased towards highly atypical states, whose inaccessibility determines the algorithmic threshold.

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. Thus, we conduct a family wide analysis of the B1 metallo-β-lactamases, combining experiments (deep mutational scanning, DMS) on two distant homologs (NDM-1 and VIM-2) and computational analyses (in silico DMS based on Direct Coupling Analysis, DCA) of 100 homologs. The methods jointly reveal and quantify prevalent epistasis, as ~1/3rd of equivalent mutations are epistatic in DMS. From DCA, half of the positions have a >6.5 fold difference in effective number of tolerated mutations across the entire family. Notably, both methods locate residues with the strongest epistasis in regions of intermediate residue burial, suggesting a balance of residue packing and mutational freedom in forming epistatic networks. We identify entrenched WT residues between NDM-1 and VIM-2 in DMS, which display statistically distinct behaviors in DCA from non-entrenched residues. Entrenched residues are not easily compensated by changes in single nearby interactions, reinforcing existing findings where a complex epistatic network compounds smaller effects from many interacting residues.

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 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.

Estimating the plausibility of RNA self-reproduction is central to origin-of-life scenarios but self-reproduction has been shown in only a handful of systems. Here, we populated a vast sequence space of ribozymes using statistical covariation models and secondary structure prediction. Experimentally assayed sequences were found active as far as 65 mutations from a reference natural sequence. The number of potentially generated sequences together with the experimental success rate indicate that at least 10 ³⁹ such ribozymes may exist. Randomly sampled artificial ribozymes exhibited autocatalytic self-reproduction akin to the reference sequence. The combination of high-throughput screening and probabilistic modeling considerably improves our estimation of the number of self-reproducing systems, paving the way for a statistical approach to the origin of life.

The task of sampling efficiently the Gibbs-Boltzmann distribution of disordered systems is important both for the theoretical understanding of these models and for the solution of practical optimization problems. Unfortunately, this task is known to be hard, especially for spin glasses at low temperatures. Recently, many attempts have been made to tackle the problem by mixing classical Monte Carlo schemes with newly devised Neural Networks that learn to propose smart moves. In this article we introduce the Nearest-Neighbours Neural Network (4N) architecture, a physically-interpretable deep architecture whose number of parameters scales linearly with the size of the system and that can be applied to a large variety of topologies. We show that the 4N architecture can accurately learn the Gibbs-Boltzmann distribution for the two-dimensional Edwards-Anderson model, and specifically for some of its most difficult instances. In particular, it captures properties such as the energy, the correlation function and the overlap probability distribution. Finally, we show that the 4N performance increases with the number of layers, in a way that clearly connects to the correlation length of the system, thus providing a simple and interpretable criterion to choose the optimal depth.

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation,...

Boltzmann machines (BMs) are graphical models with interconnected binary units, employed for the unsupervised modeling of data distributions. When trained on real data, BMs show the tendency to behave like critical systems, displaying a high susceptibility of the model under a small rescaling of the inferred parameters. This behavior is not convenient for the purpose of generating data, because it slows down the sampling process, and induces the model to overfit the training-data. In this study, we introduce a regularization method for BMs to improve the robustness of the model under rescaling of the parameters. The new technique shares formal similarities with the unlearning algorithm, an iterative procedure used to improve memory associativity in Hopfield-like neural networks. We test our unlearning regularization on synthetic data generated by two simple models, the Curie–Weiss ferromagnetic model and the Sherrington–Kirkpatrick spin glass model. We show that it outperforms Lp -norm schemes and discuss the role of parameter initialization. Eventually, the method is applied to learn the activity of real neuronal cells, confirming its efficacy at shifting the inferred model away from criticality and coming out as a powerful candidate for actual scientific implementations.