Biological Physics and Statistical Mechanics: from molecules to cells and beyond

Motivated by a question about the sensitivity of knots’ diffusive motion to the actual sequence of nucleotides placed on a given DNA, here we study a simple model of a sequence-reading diffu- sion on a stretched chain with a frozen sequence of “letters” A and B, having different interaction energies. The chain contains a single distortion - a hernia - which brings the two letters at its bottom together such that they interact. Due to interactions with the solvent, the hernia performs a random hopping motion along the chain with the transition rates dependent on its actual posi- tion. Our two focal questions are a) the dependence of various transport properties on the letters’ interaction energy and b) whether these properties are self-averaging with respect to different re- alizations of sequences. We show that the current through a finite interval, the resistance of this interval and the splitting probabilities on this interval lack self-averaging. On the contrary, the mean first-passage time through a finite interval with N sites and the diffusion coefficient in a pe- riodic chain are self-averaging in the limit N going to infinity. Concurrently, two latter properties exhibit sample-to-sample fluctuations for finite N, as evidenced by numerical simulations.

Morphogenesis, the process through which genes generate form, establishes tissue scale order as a template for constructing the complex shapes of the body plan. The extensive growth required to build these ordered substrates is fueled by cell proliferation, which, naively, should disrupt order. Understanding how active morphogenetic mechanisms couple cellular and mechanical processes to generate order remains an outstanding question in animal development. I will review the sta- tistical mechanics of orientational order and discuss the observation of a fourfold orientationally ordered phase (tetratic) in the model organism Parhyale hawaiensis. I will also discuss theoretical mechanisms for the formation of orientational order that require both motility and cell division, with support from self-propelled vertex models of tissue. The aim is to uncover a robust, active mechanism for generating global orientational order in a non-equilibrium system that then sets the stage for the development of shape and form.

To improve the storage capacity of the Hopfield model, we develop a version of the dreaming al-
gorithm that perpetually reinforces the patterns to be stored (as in the Hebb rule), and erases the
spurious memories (as in dreaming algorithms). For this reason, we called it Daydreaming. Day-
dreaming is not destructive and it converges asymptotically to stationary retrieval maps. When
trained on random uncorrelated examples, the model shows optimal performance in terms of the
size of the basins of attraction of stored examples and the quality of reconstruction. We also train
the Daydreaming algorithm on correlated data obtained via the random-features model and argue
that it spontaneously exploits the correlations, thus increasing even further the storage capacity
and the size of the basins of attraction. Moreover, the Daydreaming algorithm is also able to stabi-
lize the features hidden in the data. Finally, we test Daydreaming on the MNIST dataset and show
that it still works surprisingly well, producing attractors that are close to unseen examples and
class prototypes.

The 3D folding of mammalian DNA (chromatin) is tightly linked to its transcriptional activity, hence its understanding constitutes an important goal in biophysics. In this talk I present a poly- mer physics model to study the 3D folding of a chromatin segment. We find by simulations that, out of the sleuth of a priori possible topologies, only a handful are observed, characterised by an overwhelming predominance of local loops. We rationalise this surprising result by computing analytically the Boltzmann weight of different loop networks. Our results lay down some basic rules to understand the topological alphabet of chromatin folding in mammalian genomes.

Polymer translocation — the process of pulling single filamentous molecules through narrow pores — has long been studied as an example of out-of-equilibrium statistical mechanics and for its rel- evance in DNA sequencing and biological processes. However, the case in which the polymer structure itself is deeply altered by translocation remains largely unexplored. Here, we address this phenomenon in two prototypical cases involving DNA filaments. First, we discuss DNA unzipping, where one of the two strands is pulled through a nanopore while the other remains outside. Next, we examine the consequences on DNA organization of a recently discovered effect, namely that the double-helical segment inside the pore is subject to a solvent-induced rotation. The physical implications of the two settings are discussed for DNA filaments with and without knots.

Chromatin is a complex biopolymer of DNA and proteins that not only packages the genetic material in the nucleus but also controls gene expression. The interactions that stabilise the three-dimensional structure of chromatin are mediated by different proteins, often through out-of- equilibrium mechanisms. We have developed some powerful models to describe such interactions by averaging the degrees of freedom of the proteins. In this way, we can study the dynamics of the polymer and obtain information about its diffusion properties.

We investigate a large set of electronic health records (EHRs) collected by wellbeing services county of Soutwest Finland (Varha) [1]. Different diseases have different prevalence in a given population. For this reason, the observation of a specific comorbidity in a given patient could be just the result of a random co-occurrence of two unrelated diseases. Therefore a comorbidity net- work of diseases obtained from EHR data can in principle mix comorbidity occurrences originating either from random or from biological/medical origin. To extract from EHR data information on biologically or medically induced comorbidity we perform the detection of so-called statistically validated networks [2,3]. In this approach, all links of a projected network (PROJ) obtained start- ing from a bipartite network (patient-disease) are subjet to a statistical test. Each link in the PROJ network of diseases is subjected to a statistical test able to discriminate whether the presence of a link is an indication of comorbidity of unknown origin (i.e. in technical terms compatible with a so-called “null hypothesis”) or as an indication of potential comorbidity of biological/medical origin. By performing the same statistical test for all diseases’ pairs present in the PROJ network we extract what we address as a SVN. The SVN is providing a selection of those comorbidities that cannot be statistically explained only by random co-occurrence of diseases of different prevalence.

[1] P. Crisafulli, T. Galla, A. Karlsson, R.N. Mantegna, S. Miccichè, and J. Piilo, Statistically Validated Comorbidity Networks, manuscript in preparation (2025). [2] M. Tumminello et al. Statistically validated networks in bipartite complex systems. PLoS ONE, 6(3):e17994, Mar. 2011. [3] M.-X. Li et al . Statistically validated mobile communication networks: the evolution of motifs in european and chinese data. New Journal of Physics, 16(8):083038, 2014.

I will recap our effort to represent populations of cells using Maximum-Entropy models defined on the space of single-cell metabolic states. At odds with more conventional optimization-based theories, these models place the emphasis on (a) cell-to-cell variability, (b) its relationship with fitness, and (c) inter-cellular interactions. Advantages, limitations and challenges will hopefully emerge. I will also discuss the problem of the physical meaning of the ‘metabolic temperature’ of a population, along with some new directions, mainly concerning the large-scale metabolic structuring of populations.

Stochastic resonance (SR) phenomena provide insight into the behavior of complex biological sys- tems. Furthermore, a method for characterizing SR-type behavior in excitable systems with ape- riodic and arbitrary inputs, such as broadband signals, has been developed and termed aperiodic stochastic resonance (ASR). It was discovered that noise can enhance the response of a sensory neu- ron to a subthreshold aperiodic input signal, suggesting a functional role for input noise in sensory systems. The simple addition of noise enhances a system’s sensitivity, improving its ability to dis- criminate weak signals. The southern green stink bug, Nezara viridula (L.), is a cosmopolitan and highly polyphagous insect prevalent in many tropical and subtropical regions, representing one of the most significant pentatomid pests worldwide. Acoustic communication during mating is fundamental to this species’ reproductive behavior and offers a promising avenue for population control through traps that emit acoustic signals. In this study, we demonstrate how environmental noise can enhance intersexual communication by analyzing behavior using the source-direction movement (SDM) ratio. Our findings reveal that the SDM exhibits a nonmonotonic trend with two distinct maxima, suggesting the presence of a “double” behavioral stochastic resonance. Fur- thermore, the external noise intensity values employed in laboratory experiments closely match those observed in open-field measurements. These results confirm that environmental noise plays a crucial role in the acoustic communication of N. viridula during the mating period.

Healthy brains exhibit a rich dynamic repertoire with flexible and diverse spatiotemporal pattern replays across microscopic and macroscopic scales.We hypothesize that the system must operate near a critical regime for the functional repertoire to be fully explored, and flexible dynamics to emerge.To test this hypothesis, we employ a modular Spiking Neuronal Network model, where each group of Leaky Integrate-and-Fire neurons represents a cortical region.A learning rule based on Spike-Timing-Dependent Plasticity (STDP) is used to encode patterns of activations that prop- agate between modules.The patterns exploit empirical information on the number of white-matter fibers between regions. The model [1] displays two distinct dynamical regimes: an uncorrelated low-rate state and a strongly correlated state, marked by a high Order Parameter value (indicating the similarity of spontaneous activity with one of stored patterns).These regimes are separated by either a first-order or second-order phase transition, depending on the strength of global inhi- bition and structured connections. When the hysteresis loop shrinks, a continuous phase transi- tion occurs, and it opens up an extended region with high order parameter fluctuations (close a Widom line with maxima of fluctuations).The model predictions are compared with empirical data from magnetoencephalographic (MEG) recordings in healthy adults. We show that the structural- function correlation is maximized when the model is the extended critical regime.Then, the Lev- enshtein distance is used to quantify the similarity between the sequences of region activations in neural avalanches from both the empirical data and the model simulations.Notably a similar reper- toire of sequence is observed in synthetic data and MEG, only when the model operates within the critical extended regime.

[1]The role of criticality in the structure-function relationship in the human brain. M.Angiolelli S.Scarpetta et al. Physical Review Research 2025

Leveraging the large body of work devoted in recent years to describe redundancy and synergy in higher order interactions among random variables, we propose an adaptive version of a well- known metric of feature importance, named Leave One Covariate Out (LOCO), to disentangle high- order effects involving a given input feature in regression problems. Applications to biological data sets will be described.

Heterogeneous and complex networks represent the intertwined interactions between real-world elements or agents. Determining the multi-scale mesoscopic organization of clusters and inter- twined structures is still a fundamental and open problem of complex network theory. By taking advantage of the recent Laplacian Renormalization Group [1-4] approach , we scrutinize informa- tion diffusion pathways throughout networks to shed further light on this issue. Based on inter- node communicability, our definition provides a clear-cut framework for resolving the multi-scale mesh of structures in complex networks, disentangling their intrinsic arboreal architecture. As it does not consider any topological null-model assumption, the LRG naturally permits the intro- duction of scale-dependent optimal partitions and determines the existence of a particular class of nodes, called “metastable” nodes, that switching regions to which they belong at different scales, are expected to play a central role in the communication between them and, therefore, in managing macroscopic effects of the whole network [5].

[1] P Villegas, T Gili, G Caldarelli, A Gabrielli, Laplacian renormalization group for heterogeneous networks, Nature Physics 19 (3), 445-450 (2023) [2] P Villegas, A Gabrielli, F Santucci, G Caldarelli, T Gili, Laplacian paths in complex networks: Information core emerges from entropic transitions, Physical Review Research 4, 033196 (2022) [3] A. Gabrielli, D. Garlaschelli, S. Patil, M. A. Serrano, Network Renormalization, https://arxiv.org/abs/2412.12988, to appear on Nature Review Physics (2025). [4] A. Poggialini, P. Villegas, M.A. Munoz, A. Gabrielli, Networks with Many Structural Scales: A Renormalization Group Perspective, Phys. Rev. Lett. 134, 057401 (2025) [5] P. Villegas, A. Gabrielli, A. Poggialini, T. Gili, Multi-scale Laplacian community detection in heterogeneous networks, Phys. Rev. Res. 7, 013065 (2025)

Protein fitness landscapes frequently exhibit epistasis, where the effect of a mutation depends on the genetic context, i.e., the rest of the protein sequence. Epistasis increases landscape complexity, often resulting in multiple fitness peaks. In its simplest form, known as global epistasis, fitness is modeled as a non-linear function of an underlying additive trait. In contrast, more complex epistasis arises from a network of (pairwise or many-body) interactions between residues, which cannot be removed by a single non-linear transformation. Recent studies have explored how global and network epistasis contribute to the emergence of functional bottlenecks - fitness landscape topologies where two broad high-fitness basins, representing distinct phenotypes, are separated by a bottleneck that can only be crossed via one or a few mutational paths. I will introduce and analyze a simple model of global epistasis with an additive underlying trait, and demonstrate that functional bottlenecks arise with high probability if the model is properly calibrated. These results underscore the necessity of sufficient heterogeneity in mutational effects for the emergence of functional bottlenecks. Moreover, the model agrees with experimental findings, at least in small enough combinatorial mutational spaces.

The advent of deep learning algorithms for protein folding opened a new era in the ability of pre- dicting and optimizing the function of proteins once the sequence is known. The task is more intricate when cofactors like metal ions or small ligands are essential to functioning. In this case, the combined use of traditional simulation methods based on interatomic force fields and deep learning predictions is mandatory. We use the example of [FeFe] hydrogenases, enzymes of uni- cellular algae promising for biotechnology applications to illustrate this situation. [FeFe] hydroge- nase is an iron–sulfur protein that catalyses the chemical reduction of protons dissolved in liquid water into molecular hydrogen as a gas. Hydrogen production efficiency and cell sensitivity to dioxygen are important parameters to optimize the industrial applications of biological hydro- gen production. Both parameters are related to the organization of iron–sulfur clusters within protein domains. In this work, we propose possible three- dimensional structures of Chlorella vulgaris 211/11P [FeFe] hydrogenase, the sequence of which was extracted from the recently pub- lished genome of the given strain. Initial structural models are built using: (i) the deep learning algorithm AlphaFold; (ii) the homology modeling server SwissModel; (iii) a manual construction based on the best known bacterial crystal structure. Missing iron–sulfur clusters are included and microsecond-long molecular dynamics of initial structures embedded into the water solution envi- ronment were performed. Multiple- walkers metadynamics was also used to enhance the sampling of structures encompassing both functional and non-functional organizations of iron–sulfur clus- ters. The resulting structural model provided by deep learning is consistent with functional [FeFe] hydrogenase characterized by peculiar interactions between cofactors and the protein matrix.

Over the last decade, the combined development of accurate time- resolved experimental tech- niques and advanced algorithms for computer simulations has opened the possibility of investigat- ing biological mechanisms at atomic resolution with physics-based models. In particular, combi- nation of experimental information and enhanced sampling techniques now allow the reconstruc- tion of the co- translational folding pathways of biologically relevant proteins, at an atomic level of resolution. These innovative computational technologies reveals the existence of non-native metastable states transiently appearing along the co-transcriptional folding process of such pro- teins. The lifetime of these intermediates is set by the amino- acid synthesis rate, hence is in the several second time scale. In this talk, we review the evidence indicating that these protein fold- ing intermediates play roles in post-translational regulation. We also discuss how the information encoded into protein folding pathways is being exploited in an entirely new generation of drugs capable of promoting the selective degradation of protein targets.

[1] G. Spagnolli et al., “Pharmacological inactivation of the prion protein by targeting a folding intermediate”, Communications Biology 4 (1), 6223–124 (2021). DOI:10.1038/s42003-020-01585-x. [2] E. Biasini and P. Faccioli “Functional, pathogenic, and pharmacological role of protein folding pathways”. Proteins. 2023; 1-9.

Gene regulation is a complex web across biological levels, and its intricacy often complicates pre- cise interventions, with off-target effects being a major hurdle. To transform this, we here propose a photoactivatable microRNA-based circuit that enables unmatched accuracy in gene targeting, po- tentially reducing off-target effects. Our approach leverages the concept of microRNAs (miRNAs) as frequency decoders, interpreting signal frequencies—such as oscillatory pulses—to regulate vi- tal cellular processes. We’ve recently shown that periodically expressed miRNAs can selectively repress targets within specific frequency ranges, creating bell-shaped response curves typical of true frequency decoders. Our model highlights the importance of miRNA-target interaction dy- namics in frequency-dependent repression, adding an orthogonal layer of specificity beyond mere sequence pairing. After introducing our theoretical results, we present a simple yet powerful cir- cuit in which a photoactivatable miRNA, whose expression can be periodically controlled by light, enables dynamic gene expression modulation in single cells.

I will review some concepts and applications of Reinforcement Learning to modeling of animal behavior

Unlike gas molecules at equilibrium, the spatial organization of self-propelled particles can be very sensitive to what happens at the boundaries of their container. Understanding the link between boundary phenomena and bulk stationary distributions could enable the design of optimized con- tainer shapes for the geometric control of confined active particles. Here we propose a boundary method based on the flux transfer formalism typical of radiometry problems, where surface ele- ments transmit and receive “rays” of active particles with infinite persistence length. We demon- strate the power of this boundary method in the case of the swimming microalgae Euglena gracilis trapped in light-defined billiard geometries. Leveraging our boundary method, we were able to design a stacked multi-stage billiard geometry, with a connection scheme between subunits that breaks spatial symmetry and achieves an exponential amplification of cell concentration between its two ends. Surprisingly, the sensitive dependence on boundary geometry observed in closed microbial billiards stands in marked contrast to the robust invariance of mean path lengths traced by E.coli bacteria swimming in microfabricated open billiards with frozen internal disorder.

Marker genes are genes that have expression profiles able to distinguish the sub-populations of cells present in the data. They are used to annotate cell types and “understand” their biology. In cancerous tissues they are used to identify cancer subtypes and thus to fine-tune therapies. Complex pathologies (in particular cancer) are characterized by strong variability at the molecular level. Each patient has a different way of developing cancer. A precise tailoring of therapies requires rapid identification of the particular cancer subtype and of the altered pathways of the patient. This is typically done using marker genes which are often themselves the targets of the therapy. However marker genes are typically selected using clustering algorithms and their choice is strongly influenced by the choice of the algorithm, with large uncertainties and, in some cases, contradictory results. A physicist’s point of view in this game can greatly improve the quality of the results and enhance their robustness. In this talk I will discuss a few results obtained in this context in our group in the past few years. In particular I will discuss the use of probabilistic models and of algorithms based on a hierarchical version of stochastic block modelling to identify marker genes.

Cellular signaling pathways operate as nonequilibrium biochemical networks that transduce di- rected chemical or mechanical signals across the cell. These cascades, initiated for example by ligand binding to membrane receptors, involve multiple biochemical reactions and complex for- mations. Because signaling pathways rely on branched, multiplicative processes, errors can propagate rapidly, threatening fidelity. For instance, incorrect molecular incorporation at any stage can disrupt signal integrity. To counteract this, cells have evolved proofreading mechanisms that ensure remarkable accuracy in processes such as DNA replication and enzymatic reactions. Since the pioneering work of Hopfield and Ninio in the 1970s, it has been understood that ki- netic proofreading (KP) increases fidelity by introducing intermediate chemical steps, powered by nonequilibrium energy sources, at the cost of slower propagation. Later advances showed that catalytic proofreading (CP) can accelerate these error-checking steps, reducing the delay inherent in KP. An alternative approach involves spatial proofreading, where errors are tested over a finite distance via directed diffusive fluxes, instead of delaying in chemical space, thus achieving high fidelity “at a distance.” This lecture will explore the general physics of proofreading in signal transduction and introduce a thermodynamically consistent model that integrates spatial and chemical proofreading. I will also discuss how these principles apply to real biochemical systems, highlighting potential proof- reading mechanisms in G-protein coupled receptor signaling and multi-protein self-assembly.

Proliferating cells organize their resources in order to harness nutrients from the environment and grow. Work in bacteria has highlighted how this behavior leads to striking emergent “growth laws” linking growth to cellular composition. However, beyond bacteria, we still have limited insight on the generality of such laws and even in bacteria some of the key mechanistic aspects underlying them are unclear. I will present our efforts towards a flexible and predictive modeling framework integrating different aspects of biosynthesis and its regulation, with applications in bacteria, budding yeast and mammalian cells.

Eukaryotic cells maintain their internal order through a hectic process of sorting and distillation of molecular factors taking place on their lipid membranes. A similar sorting process is implied in the assembly and budding of enveloped viruses. We have proposed a theoretical model of the process, in which molecular sorting emerges from the coupling of phase separation and membrane bending. Localized sorting domains form by phase separation on lipid membranes and grow by ab- sorbing laterally diffusing molecules. The domains induce membrane bending and the nucleation of a lipid vesicle. Since the newly generated vesicle is enriched in the biochemical factors of the engulfed domain, this results in a natural distillation process. We found that sorting efficiency is optimal at intermediate values of the aggregation strength, where the number of sorting domains is minimized and simple scaling laws hold. Experimental data suggest that living systems may have evolved to exploit these optimal conditions. In this context, a natural parameter controlling the efficiency of molecular distillation is the critical size of sorting domains. In the experiments, sorting domains are classified into unproductive—characterized by short lifetimes and low proba- bility of extraction—and productive—those that evolve into vesicles that are ultimately extracted. This observation is in agreement with the predictions of classical nucleation theory for subcritical and supercritical phase separated domains. Simple estimates suggest that a large pool of distinct molecular species can be sorted in parallel without significantly interfering with each other, par- ticularly when their homotypic affinities are comparable. However, the mean time spent by sorted molecules on the membrane increases with the heterogeneity of the pool. Overall, these findings provide a unifying perspective on molecular sorting in biological membranes and offer broader insights into cellular organization and viral assembly.

Molecular sorting is a vital process in eukaryotic cells, where proteins and other biomolecules are sorted and encapsulated into lipid vesicles for targeted transport to specific organelles and sub- cellular locations. Recent studies suggest this process is driven by a physical mechanism based on phase separation, in which the formation and growth of sorting domains depends primarily on direct intermolecular interactions. On fluctuating biological membranes, entropic Casimir-like forces also play a significant role in promoting this molecular distillation process, particularly in regimes where direct interactions are weak. Our findings, based on a combination of theoretical analysis and numerical simulations, reveal that Casimir-like forces enhance sorting by reducing the critical radius for the formation of new sorting domains and facilitating the capture of molecules in these domains. The relative rigidity of the membrane and domains are identified as key param- eters governing sorting efficiency. These insights provide a deeper understanding of the physical principles shaping molecular organization in biological membranes.