arXiv subjects

Enzo Orlandini

Publications and source records attributed to Enzo Orlandini.

At least 19 recordsLinked to original sources

arXiv2026

Topological localisation and motility of active knots

Nonequilibrium active polymers provide a minimal framework to investigate biopolymers such as DNA and chromatin under the action of molecular motors. Here we study active ring polymers with controlled topology and show that knot type qualitatively determines their nonequilibrium behaviour. We find that activity induces opposite localisation responses in different topological families: torus knots systematically delocalise and inflate, whereas twist knots tighten and remain localised. We trace this divergent behaviour to the distinct symmetry properties of their tangent fields, which control the alignment of active forces along the chain. We show that topology also governs internal and emergent dynamics. Active torus knots behave as soft chiral self-propelled particles exhibiting persistent motion with a well-defined handedness fixed by their topological chirality. In contrast, achiral knots show no net handedness. The knot thus acts as a deformable topological quasiparticle whose morphology and propulsion are selected by topology. These results suggest potential routes toward programmable soft chiral particles with controllable morphology and emergent motility modes.

cond-mat.soft↗

arXiv2026

Nucleoid clustering drives stepwise expansion and segregation of replicating bacterial chromosomes

Bacterial chromosome replication occurs in the absence of a canonical spindle apparatus; yet it reliably produces organised and segregated genomes. While both passive and active mechanisms have been investigated, DNA replication itself is a non-equilibrium process that continuously generates new genetic material and reorganizes the nucleoid. Here, we investigate how replication-driven dynamics, combined with nucleoid-associated protein (NAP) interactions, shape spatiotemporal chromosome organisation using a three-dimensional polymer model that explicitly simulates DNA synthesis. We show that NAP-mediated interactions induce dynamic clustering of DNA, generating density fluctuations in the nucleoid. When coupled to replication, these clusters undergo cycles of stress buildup and release that produce stepwise expansion dynamics consistent with experimental observations. Chromosome segregation occurs naturally in this regime, but only within a finite range of interaction strengths: weak interactions fail to structure the nucleoid, whereas strong interactions hinder replication progression. Within this optimal balance, replication also promotes the spontaneous formation of replication factories. Our results demonstrate that bacterial chromosome organisation can be understood as a non-equilibrium system in which the interplay between replication forces and protein-mediated interactions generates nucleoid mechanics, dynamics, and segregation.

physics.bio-ph↗

arXiv2026

Boundary-Mediated Phases of Self-Propelled Kuramoto Particles

Active agents can transfer energy to their environment through collective motion, generating accumulation patterns near confining obstacles. Here we investigate how the nature of the microscopic drive-self-propulsion or velocity alignment-selects distinct accumulation patterns, leading to either delocalized or compact clustered states. We first characterize the dynamical regimes emerging from the interplay of these two driving mechanisms under perfectly reflective or smooth boundary conditions. We then introduce boundary friction and observe a drastic change in the accumulation patterns, with new dynamical phases that are absent in the previous case. By connecting emergent macroscopic structures to their underlying microscopic interactions, this work provides a practical route to infer the dominant interaction ruling boundary-mediated collective behavior, with applications ranging from single-cell migration to bio-inspired robotics.

cond-mat.soft↗

arXiv2026

Field-induced phase transitions in ferro-antiferromagnetic diblock copolymers

We study the equilibrium properties of a model of magnetic diblock copolymer where each monomer is decorated with an Ising-like spin. Spins interact ferromagnetically within each block and antiferromagnetically across blocks, generating frustration between magnetic ordering and spatial organization. By employing a mean-field approach and Monte Carlo simulations for self-avoiding walks on the cubic lattice, we investigate the system's response to an external magnetic field. We discover a rich phase diagram that includes: a swollen phase with both filaments magnetically disordered and spatially extended; a mixed compact phase characterized by a single globule in which the two filaments are strongly intertwined; a segregated compact phase composed of two globular, magnetically ordered, and spatially separated blocks. Further, if the magnitude of the intra-block ferromagnetic interaction differs between the two blocks, we observe a hybrid segregated (``tadpole'') phase where one extended block coexists with a collapsed one. Mean-field predictions are in quantitative agreement with Monte Carlo results for the location of the phase boundaries. These findings provide a minimal statistical-mechanical framework for field-controlled self-assembly of tunable patterns by magnetically heterogeneous polymers. They may also serve as a simple platform to investigate the coupling between internal epigenetic-like states and chromatin folding.

cond-mat.soft↗

arXiv2025

Fluctuations of driven probes reveal nonequilibrium transitions in complex fluids

Complex fluids subjected to localized microscopic energy inputs, typical of active microrheology setups, exhibit poorly understood nonequilibrium behaviors because of the intricate self-organization of their mesoscopic constituents. In this work we show how to identify changes in the microstructural conformation of the fluid by monitoring the variance of the probe position, based on a general method grounded in the breakdown of the equipartition theorem. To illustrate our method, we perform large-scale Brownian dynamics simulations of an effective model of micellar solution, and we link the different scaling regimes in the variance of the probe's position to the transitions from diffusive to jump dynamics, where the fluid intermittently relaxes the accumulated stress. This suggests stored elastic stress may be the physical mechanism behind the nonlinear friction curves recently measured in micellar solutions, pointing at a mechanism for the observed multi-step rheology. Our approach overcomes the limitations of continuum macroscopic descriptions and introduces an empirical method, applicable in experiments, to detect nonequilibrium transitions in the structure of complex fluids.

cond-mat.stat-mech↗

arXiv2025

Topological weight and structural diversity of polydisperse chromatin loop networks

Current biophysical models for transcriptionally active chromatin view this as a polymer with sticky sites, mimicking transcription units such as promoters and enhancers which interact via the binding of multivalent complexes of chromatin-binding proteins. It has been demonstrated that this model spontaneously leads to microphase separation, resulting in the formation of a network of loops with transcription units serving as anchors. Here, we demonstrate how to compute the topological weights of loop networks with an arbitrary 1D pattern of transcription units along the fibre (or `polydisperse' loop networks), finding an analogy with networks of electric resistors in parallel or in series. We also show how the BEST (de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte) theorem in combinatorics can be used to find the combinatorial multiplicity of any class of loop networks. Our results can be used to compute the structural diversity, or Shannon entropy, of loop networks: we show that this quantity depends on the 1D patterning of transcription units along the chain, possibly providing a pathway to control transcriptional noise in eukaryotic genes.

physics.bio-ph↗

arXiv2025

Variational autoencoders understand knot topology

Supervised machine learning (ML) methods are emerging as valid alternatives to standard mathematical methods for identifying knots in long, collapsed polymers. Here, we introduce a hybrid supervised/unsupervised ML approach for knot classification based on a variational autoencoder enhanced with a knot type classifier (VAEC). The neat organization of knots in its latent representation suggests that the VAEC, only based on an arbitrary labeling of three-dimensional configurations, has grasped complex topological concepts such as chirality, unknotting number, braid index, and the grouping in families such as achiral, torus, and twist knots. The understanding of topological concepts is confirmed by the ability of the VAEC to distinguish the chirality of knots $9_{42}$ and $10_{71}$ not used for its training and with a notoriously undetected chirality to standard tools. The well-organized latent space is also key for generating configurations with the decoder that reliably preserves the topology of the input ones. Our findings demonstrate the ability of a hybrid supervised-generative ML algorithm to capture different topological features of entangled filaments and to exploit this knowledge to faithfully reconstruct or produce new knotted configurations without simulations.

cond-mat.stat-mech↗

arXiv2024

Two-states Brownian particle in a Harmonic Potential

We study the behaviour of a Brownian particle in the overdamped regime in the presence of a harmonic potential, assuming its diffusion coefficient to randomly jump between two distinct values. In particular, we characterize the probability distribution of the particle position and provide detailed expressions for the mean square displacement and the kurtosis. We highlight non-Gaussian behaviour even within the long-term limit carried over with an excess of probability both in the central part and in the distribution's tails. Moreover, when one of the two diffusion coefficients assumes the value zero, we provide evidence that the probability distribution develops a cusp. Most of our results are analytical, and corroborated by numerical simulations.

cond-mat.stat-mech↗

arXiv2024

Upsurge of spontaneous knotting in polar diblock active polymers

Spontaneous formation of knots in long polymers at equilibrium is inevitable but becomes rare in sufficiently short chains. Here, we show that knotting and knot complexity increase by orders of magnitude in diblock polymers with a fraction $p$ of self-propelled monomers. Remarkably, this enhancement is not monotonic in $p$ with an optimal value independent of the monomer's activity. By monitoring the knot's size and position we elucidate the mechanisms of its formation, diffusion, and untying and ascribe the non-monotonic behaviour to the competition between the rate of knot formation and the knot's lifetime. These findings suggest a non-equilibrium mechanism to generate entangled filaments at the nano-scale.

cond-mat.soft↗

arXiv2024

Being heterogeneous is disadvantageous: Brownian non-Gaussian searches

Diffusing diffusivity models, polymers in the grand canonical ensemble and polydisperse, and continuous-time random walks all exhibit stages of non-Gaussian diffusion. Is non-Gaussian targeting more efficient than Gaussian? We address this question, central to, e.g., diffusion-limited reactions and some biological processes, through a general approach that makes use of Jensen's inequality and that encompasses all these systems. In terms of customary mean first-passage time, we show that Gaussian searches are more effective than non-Gaussian ones. A companion paper argues that non-Gaussianity becomes instead highly more efficient in applications where only a small fraction of tracers is required to reach the target.

cond-mat.stat-mech↗

arXiv2024

Being Heterogeneous Is Advantageous: Extreme Brownian Non-Gaussian Searches

Redundancy in biology may be explained by the need to optimize extreme searching processes, where one or few among many particles are requested to reach the target like in human fertilization. We show that non-Gaussian rare fluctuations in Brownian diffusion dominates such searches, introducing drastic corrections to the known Gaussian behavior. Our demonstration entails different physical systems and pinpoints the relevance of diversity within redundancy to boost fast targeting. We sketch an experimental context to test our results: polydisperse systems.

cond-mat.stat-mech↗

arXiv2024

3D active nematic disclinations behave as Majorana quasiparticles

Quasiparticles are low-energy excitations with important roles in condensed matter physics. An intriguing example is provided by Majorana fermions, quasiparticles which are identical to their antiparticles. Despite being implicated in neutrino oscillations and topological superconductivity, their experimental realisations remain scarce. Here we propose a purely classical realisation of Majorana fermions, in terms of 3-dimensional disclination lines in active nematics. Activity is required to overcome the elastic cost associated with these excitations, so they can appear in steady state. We combine topology and simulations to show that active nematics under confinement spontaneously create in their interior topologically charged disclination lines and loops, akin to Majorana quasiparticles with finite momentum. Within an elongated channel, we find a phenomenology similar to that of the Kitaev chain, as local Majorana-like excitations appear near surfaces, while a non-local system-spanning helical disclination line can arise along the centre. In unconfined active turbulence, Majorana-like charged loops are instead exceedingly rare, suggesting that boundaries are crucial to generate these quasiparticles, as in quantum condensed matter. We suggest that 3-dimensional active disclinations can be used to probe the physics of Majorana spinors at a much larger scale than traditionally considered, potentially facilitating the experimental observation of their dynamics.

cond-mat.soft↗

arXiv2023

Combinatorics and topological weights of chromatin loop networks

Polymer physics models suggest that chromatin spontaneously folds into loop networks with transcription units (TUs), such as enhancers and promoters, as anchors. Here we use combinatoric arguments to enumerate the emergent chromatin loop networks, both in the case where TUs are labelled and where they are unlabelled. We then combine these mathematical results with those of computer simulations aimed at finding the inter-TU energy required to form a target loop network. We show that different topologies are vastly different in terms of both their combinatorial weight and energy of formation. We explain the latter result qualitatively by computing the topological weight of a given network -- i.e., its partition function in statistical mechanics language -- in the approximation where excluded volume interactions are neglected. Our results show that networks featuring local loops are statistically more likely with respect to networks including more non-local contacts. We suggest our classification of loop networks, together with our estimate of the combinatorial and topological weight of each network, will be relevant to catalogue 3D structures of chromatin fibres around eukaryotic genes, and to estimate their relative frequency in both simulations and experiments.

physics.bio-ph↗

arXiv2023

Topological spectra and entropy of chromatin loop networks

The 3D folding of a mammalian gene can be studied by a polymer model, where the chromatin fibre is represented by a semiflexible polymer which interacts with multivalent proteins, representing complexes of DNA-binding transcription factors and RNA polymerases. This physical model leads to the natural emergence of clusters of proteins and binding sites, accompanied by the folding of chromatin into a set of topologies, each associated with a different network of loops. Here we combine numerics and analytics to first classify these networks and then find their relative importance or statistical weight, when the properties of the underlying polymer are those relevant to chromatin. Unlike polymer networks previously studied, our chromatin networks have finite average distances between successive binding sites, and this leads to giant differences between the weights of topologies with the same number of edges and nodes but different wiring. These weights strongly favour rosette-like structures with a local cloud of loops with respect to more complicated non-local topologies. Our results suggest that genes should overwhelmingly fold into a small fraction of all possible 3D topologies, which can be robustly characterised by the framework we propose here.

physics.bio-ph↗

arXiv2023

Interpretable machine learning of amino acid patterns in proteins: a statistical ensemble approach

Explainable and interpretable unsupervised machine learning helps understand the underlying structure of data. We introduce an ensemble analysis of machine learning models to consolidate their interpretation. Its application shows that restricted Boltzmann machines compress consistently into a few bits the information stored in a sequence of five amino acids at the start or end of $α$-helices or $β$-sheets. The weights learned by the machines reveal unexpected properties of the amino acids and the secondary structure of proteins: (i) His and Thr have a negligible contribution to the amphiphilic pattern of $α$-helices; (ii) there is a class of $α$-helices particularly rich in Ala at their end; (iii) Pro occupies most often slots otherwise occupied by polar or charged amino acids, and its presence at the start of helices is relevant; (iv) Glu and especially Asp on one side, and Val, Leu, Iso, and Phe on the other, display the strongest tendency to mark amphiphilic patterns, i.e., extreme values of an "effective hydrophobicity", though they are not the most powerful (non) hydrophobic amino acids.

q-bio.BM↗

arXiv2023

Topological Phases and Curvature-Driven Pattern Formation in Cholesteric Shells

We study the phase behaviour of cholesteric liquid crystal shells with different geometries. We compare the cases of tangential and no anchoring at the surface, focussing on the former case, which leads to a competition between the intrinsic tendency of the cholesteric to twist and the anchoring free energy which suppresses it. We then characterise the topological phases arising close to the isotropic-cholesteric transition. These typically consist of quasi-crystalline or amorphous tessellations of the surface by half-skyrmions, which are stable at lower and larger shell size respectively. For ellipsoidal shells, defects in the tessellation couple to local curvature, and according to the shell size they either migrate to the poles or distribute uniformly on the surface. For toroidal shells, the variations in the local curvature of the surface stabilises heterogeneous phases where cholesteric or isotropic patterns coexist with hexagonal lattices of half-skyrmions.

cond-mat.soft↗

arXiv2022

Machine learning understands knotted polymers

Simulated configurations of flexible knotted rings confined inside a spherical cavity are fed into long-short term memory neural networks (LSTM NNs) designed to distinguish knot types. The results show that they perform well in knot recognition even if tested against flexible, strongly confined and therefore highly geometrically entangled rings. In agreement with the expectation that knots are delocalized in dense polymers, a suitable coarse-graining procedure on configurations boosts the performance of the LSTMs when knot identification is applied to rings much longer than those used for training. Notably, when the NNs fail, usually the wrong prediction still belongs to the same topological family of the correct one. The fact that the LSTMs are able to grasp some basic properties of the ring's topology is corroborated by a test on knot types not used for training. We also show that the choice of the NN architecture is important: simpler convolutional NNs do not perform so well. Finally, all results depend on the features used for input: surprisingly, coordinates or bond directions of the configurations provide the best accuracy to the NNs, even if they are not invariant under rotations (while the knot type is invariant). Other rotational invariant features we tested are based on distances, angles, and dihedral angles.

cond-mat.soft↗

arXiv2022

Brownian non-Gaussian diffusion of self-avoiding walks

Three-dimensional Monte Carlo simulations provide a striking confirmation to a recent theoretical prediction: the Brownian non-Gaussian diffusion of critical self-avoiding walks. Although the mean square displacement of the polymer center of mass grows linearly with time (Brownian behavior), the initial probability density function is strongly non-Gaussian and crosses over to Gaussianity only at large time. Full agreement between theory and simulations is achieved without the employment of fitting parameters. We discuss simulation techniques potentially capable of addressing the study of anomalous diffusion under complex conditions like adsorption- or Theta-transition.

cond-mat.stat-mech↗