arXiv subjects

Angelo Rosa

Publications and source records attributed to Angelo Rosa.

At least 19 recordsLinked to original sources

arXiv2026

Theory of associating polymers with annealed and quenched sticker disorder: Mean-field solution and phase behavior

We develop a density-functional theory for solutions of associating polymers where attractions among charged monomers (stickers) are represented by local binary degrees of freedom, which are randomly placed along the chains. Extending the original Garel and Orland's field-theoretic scheme for single-chain systems to an ensemble of interacting chains, we give the exact formulations of the model in both cases of annealed and quenched distributions of charges which we solve at the mean-field level. The solution produces qualitatively different free energy functionals. In the annealed case, the theory naturally yields a nontrivial scalar order parameter for the fraction of bonded sticker monomers and a self-consistent mass-action law at the saddle point. By contrast, in the quenched case no independent bonding order parameter emerges and the main effect is a renormalization of the effective two-body and three-body interaction parameters. The formulation is microscopic at the Hamiltonian level and, within the same field-theoretic framework, provides a systematic starting point for fluctuation corrections beyond the mean-field approximation.

cond-mat.soft↗

arXiv2026

Mesoscopic simulations of linear and ring polymer solutions with explicit hydrodynamics under good and poor solvent conditions

We employ large-scale Dissipative Particle Dynamics simulations to investigate dilute solutions of linear polymers and unknotted, non-concatenated ring polymers in explicit solvent. By systematically varying solvent quality, we examine the interplay between hydrodynamic interactions, chain architecture, and intermolecular association. Under good solvent conditions, both linear and ring polymers remain expanded and well dispersed, displaying center-of-mass dynamics consistent with normal diffusion. In poor solvents, attractive polymer-polymer interactions drive the formation of irregular aggregates characterized by partial chain collapse, substantial interpenetration, and slower dynamics. Despite their different topologies, the two polymer architectures exhibit remarkably similar structural and dynamical responses across the solvent conditions considered. These results indicate that solvent quality largely determines the organization and transport properties of dilute polymer solutions, whereas topological effects remain comparatively weak in the investigated regime.

cond-mat.soft↗

arXiv2026

Coherent modeling of double-folded ring polymers and their underlying random tree structure

Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have recently obtained expressions for the configurational entropy in ensembles with controlled branching activity. Here we demonstrate that they are equivalent up to a contribution originating from the number of distinct wrappings of a single tree. This allows us to develop a coherent framework for freely switching between the two representations. Importantly, the equivalence extends to interacting systems provided the interactions are treated consistently on the tree and on the ring level. To demonstrate the utility of the scheme, we introduce a generalization of the Amoeba Monte Carlo algorithm capable of generating the required ensembles of trees with fluctuating sizes. While the tree algorithm reproduces results obtained by dynamic simulations of the corresponding ring model, it is $O(N)$ faster for the purpose of sampling static properties and leverages the utility of the ring model for the study of dynamical properties, when used for the preparation of equilibrated starting states.

cond-mat.soft↗

arXiv2025

Configurational entropy of randomly double-folding ring polymers

Topologically constrained genome-like polymers often double-fold into tree-like configurations. Here we calculate the exact number of tightly double-folded configurations available to a ring polymer in ideal conditions. For this purpose, we introduce a scheme which allows us to define a ``code'' specifying how a ring wraps a randomly branching tree and calculate the number of admissible wrapping codes via a variant of Bertrand's ballot theorem. As a validation, we demonstrate that data from Monte Carlo simulations of an elastic lattice model of non-interacting tightly double-folded rings with controlled branching activity are in excellent agreement with exact expressions for branch-node and tree size statistics that can be derived from our expression for the ring entropy.

cond-mat.soft↗

arXiv2025

Ring polymers in two-dimensional melts double-fold around randomly branching "primitive shapes"

Drawing inspiration from the concept of the "primitive path" of a linear chain in melt conditions, we introduce here a numerical protocol which allows us to detect, in an unambiguous manner, the "primitive shapes" of ring polymers in two-dimensional melts. Then, by analysing the conformational properties of these primitive shapes, we demonstrate that they conform to the statistics of two-dimensional branched polymers (or, trees) in the same melt conditions, in agreement with seminal theoretical work by Khokhlov, Nechaev and Rubinstein. Results for polymer dynamics in light of the branched nature of the rings are also presented and discussed.

cond-mat.soft↗

arXiv2025

Entropy of self-avoiding branching polymers: mean field theory and Monte Carlo simulations

We study the statistics of branching polymers with excluded-volume interactions, by modeling them as single self-avoiding trees on a generic regular periodic lattice with coordination number $q$. Each lattice site can be occupied at most by one tree node, and the fraction of occupied sites can vary from dilute to dense conditions. By adopting the statistics of rooted-directed trees as a proxy for that of undirected trees without internal loops and by an exact mapping of the model into a field theory, we compute the entropy and the mean number of branch-nodes within a mean field approximation and in the thermodynamic limit. In particular, we find that the mean number of branch-nodes is independent of both the lattice details and the lattice occupation, depending only on the associated chemical potential. Monte Carlo simulations in $d=2,3,4$ provide evidence of the remarkable accuracy of the mean field theory, more accurate for higher dimensions.

cond-mat.stat-mech↗

arXiv2025

The configurational entropy of random trees

We present a graph theoretical approach to the configurational statistics of random tree-like objects, such as randomly branching polymers. In particular, for ideal trees we show that Pr\"ufer labelling provides: (i) direct access to the exact configurational entropy as a function of the tree composition, (ii) computable exact expressions for partition functions and important experimental observables for tree ensembles with controlled branching activity and (iii) an efficient sampling scheme for corresponding tree configurations and arbitrary static properties.

cond-mat.stat-mech↗

arXiv2024

bioSBM: a random graph model to integrate epigenomic data in chromatin structure prediction

The spatial organization of chromatin within the nucleus plays a crucial role in gene expression and genome function. However, the quantitative relationship between this organization and nuclear biochemical processes remains under debate. In this study, we present a graph-based generative model, bioSBM, designed to capture long-range chromatin interaction patterns from Hi-C data and, importantly, simultaneously link these patterns to biochemical features. Applying bioSBM to Hi-C maps of the GM12878 lymphoblastoid cell line, we identified a latent structure of chromatin interactions, revealing 7 distinct communities that strongly align with known biological annotations. Additionally, we infer a linear transformation that maps biochemical observables, such as histone marks, to the parameters of the generative graph model, enabling accurate genome-wide predictions of chromatin contact maps on out-of-sample data, both within the same cell line, and on the completely unseen HCT116 cell line under RAD21 depletion. These findings highlight bioSBM's potential as a powerful tool for elucidating the relationship between biochemistry and chromatin architecture and predicting long-range genome organization from independent biochemical data.

q-bio.QM↗

arXiv2024

Amoeba Monte Carlo algorithms for random trees with controlled branching activity: efficient trial move generation and universal dynamics

The reptation Monte Carlo algorithm is a simple, physically motivated and efficient method for equilibrating semi-dilute solutions of linear polymers. Here we propose two simple generalizations for the analogue {\it Amoeba} algorithm for randomly branching chains, which allow to efficiently deal with random trees with controlled branching activity. We analyse the rich relaxation dynamics of Amoeba algorithms and demonstrate the existence of an unexpected scaling regime for the tree relaxation. In particular, our results suggests that the equilibration time for Amoeba algorithms scales in general like $N^2 \langle n_{\rm lin}\rangle^\Delta$, where $N$ denotes the number of tree nodes, $\langle n_{\rm lin}\rangle$ the mean number of linear segments the trees are composed of and $\Delta \simeq 0.4$.

cond-mat.soft↗

arXiv2024

Theory of polymers in binary solvent solutions: mean-field free energy and phase behavior

We present a lattice model for polymer solutions, explicitly incorporating interactions with a bath of solvent and cosolvent molecules. By exploiting the well-known analogy between polymer systems and the $O(n)$-vector spin model in the limit $n \to 0$, we derive an exact field-theoretic expression for the partition function of the system. The latter is then evaluated at the saddle point, providing a mean-field estimate of the free energy. The resulting expression, which conforms to the Flory-Huggins type, is then used to analyze the system's stability with respect to phase separation, complemented by a numerical approach based on convex hull evaluation. We demonstrate that this simple lattice model can effectively explain the behavior of a variety of seemingly unrelated polymer systems, which have been predominantly investigated in the past only through numerical simulations. This includes both, single-chain and multi-chain, solutions. Our findings emphasize the fundamental, mutually competing, roles of solvent and cosolvent in polymer systems.

cond-mat.soft↗

arXiv2024

Phase behaviour and self-assembly of semiflexible polymers in poor-solvent solutions

Using Langevin dynamics complemented by Wang-Landau Monte Carlo simulations, we study the phase behavior of single and multiple semiflexible polymer chains in solution under poor-solvent conditions. In the case of a single chain, we obtain the full phase diagram in the temperature-bending rigidity (stiffness) plane and we provide connections with a classical mean field result on a lattice as well as with past results on the same model. At low bending rigidity and upon cooling, we find a second order coil-globule transition, followed by a subsequent first order globule-crystal transition at lower temperatures. The obtained crystals have the shape of a twisted rod whose length increases with the increase of the stiffness of the chain. Above a critical value of the stiffness, we also find a direct first order globule-crystal transition, with the crystal having the form of a twisted toroid. Close to the triple point, we find a region with isoenergetic structures with frequent switching from rods to toroids, with the toroid eventually becoming the only observed stable phase at higher stiffness. The model is then extended to many thermally equilibrated chains in a box and the analogous phase diagram is deduced where the chains are observed to first fold into a globule bundle at low stiffness upon cooling, and then rearrange into a nematic bundle via a nucleation process involving an isotropic-nematic transition. As in the single chain counterpart, above a critical stiffness the chains are observed to undergo a direct transition from a gas of isotropically distributed chains to a nematic bundle as the temperature decreases in agreement with recent suggestions from mean field theory. The consequences of these findings for self-assembly of biopolymers in solutions are discussed.

cond-mat.soft↗

arXiv2024

Universal time and length scales of polar active polymer melts

We present an in-depth multi-scale analysis of the conformations and dynamics of polar active polymers, comparing very dilute and very dense conditions. We unveil characteristic length and time scales, common to both dilute and dense systems, that recapitulate the conformational and dynamical properties of these active polymers upon varying both the polymer size and the strength of the activity. Specifically, we find that a correlation (or looping) length characterises the polymer conformations and the monomer dynamics. Instead, the dynamics of the center of mass can be fully characterised by the end-to-end mean-square distance and by the associated relaxation time. As such, we show that the dynamics in melts of polar active polymers are not controlled by entanglements but only by the strength of the self-propulsion.

cond-mat.soft↗

arXiv2023

Phase behaviour of semiflexible lattice polymers in poor-solvent solution: mean-field theory and Monte Carlo simulations

We study a solution of interacting semiflexible polymers with curvature energy in poor-solvent conditions on the d-dimensional cubic lattice using mean-field theory and Monte Carlo computer simulations. Building upon past studies on a single chain, we construct a field-theory representation of the system and solve it within a mean-field approximation supported by Monte Carlo simulations in d=3. A gas-liquid transition is found in the temperature-density plane that is then interpreted in terms of real systems. Interestingly, we find this transition to be independent of the bending rigidity. Past classical Flory-Huggins and Flory mean-field results are shown to be particular cases of this more general framework. Perspectives in terms of guiding experimental results towards optimal conditions are also proposed.

cond-mat.soft↗

arXiv2023

Spatial organization of slit-confined melts of ring polymers with non-conserved topology: A lattice Monte Carlo study

We present Monte Carlo computer simulations for melts of semiflexible randomly knotted and randomly concatenated ring polymers on the fcc lattice and in slit confinement. Through systematic variation of the slit width at fixed melt density, we first explore the influence of confinement on single-chain conformations and inter-chain interactions. We demonstrate that confinement makes chains globally larger and more elongated, while enhancing both contacts and knottedness propensities. As for multi-chain properties, we show that ring-ring contacts decrease with the confinement, yet neighbouring rings are more overlapped as confinement grows. These aspects are reflected on the decrease of the links formation between pairs of rings. The results suggest that confinement can be used to fine-tune the mechanical properties of the polymer network. In particular, confinement biases the synthesis of networks that are softer to mechanical stress. Finally, in connection with a previous study of us and recent simulations on two-dimensional polymer melts, our findings suggest that entanglements in polymer melts arise from pairwise ring-ring links alone.

cond-mat.soft↗

arXiv2023

Scaling properties of RNA as a randomly branching polymer

Formation of base pairs between the nucleotides of an RNA sequence gives rise to a complex and often highly branched RNA structure. While numerous studies have demonstrated the functional importance of the high degree of RNA branching -- for instance, for its spatial compactness or interaction with other biological macromolecules -- RNA branching topology remains largely unexplored. Here, we use the theory of randomly branching polymers to explore the scaling properties of RNAs by mapping their secondary structures onto planar tree graphs. Focusing on random RNA sequences of varying lengths, we determine the two scaling exponents related to their topology of branching. Our results indicate that ensembles of RNA secondary structures are characterized by annealed random branching and scale similarly to self-avoiding trees in three dimensions. We further show that the obtained scaling exponents are robust upon changes in nucleotide composition, tree topology, and folding energy parameters. Finally, in order to apply the theory of branching polymers to biological RNAs, whose length cannot be arbitrarily varied, we demonstrate how both scaling exponents can be obtained from the distributions of the related topological quantities of individual RNA molecules with fixed length. In this way, we establish a framework to study the branching properties of RNA and compare them to other known classes of branched polymers. By understanding the scaling properties of RNA related to its branching structure we aim to improve our understanding of the underlying principles and open up the possibility to design RNA sequences with desired topological properties.

physics.bio-ph↗

arXiv2023

Topological analysis and the recovery of entanglements in polymer melts

The viscous flow of polymer chains in dense melts is dominated by topological constraints whenever the single chain contour length, N, becomes larger than the characteristic scale Ne, defining comprehensively the macroscopic rheological properties of the highly entangled polymer systems. Even though the latter are naturally connected to the presence of hard constraints like knots and links within the polymer chains, the difficulty of integrating the rigorous language of mathematical topology with the physics of polymer melts has limited somehow a genuine topological approach to the problem of classifying these constraints and to how they are related to the rheological entanglements. In this work, we tackle this problem by studying the occurrence of knots and links in lattice melts of randomly knotted and randomly concatenated ring polymers of various bending stiffness. Specifically, by introducing an algorithm which shrinks the chains to their minimal shapes which do not violate topological constraints and by analyzing those in terms of suitable topological invariants, we provide a detailed characterization of the topological properties at the intra-chain level (knots) and of links between pairs and triplets of distinct chains. Then, by employing the Z1-algorithm on the minimal conformations in order to extract the entanglement length $N_e$, we show that the ratio $N/N_e$, the number of entanglements per chain, can be remarkably well reconstructed in terms of 2-chain links solely.

cond-mat.soft↗

arXiv2022

Viral RNA as a branched polymer

Myriad viruses use positive-strand RNA molecules as their genomes. Far from being only a repository of genetic material, viral RNA performs numerous other functions mediated by its physical structure and chemical properties. In this chapter, we focus on its structure and discuss how long RNA molecules can be treated as branched polymers through planar graphs. We describe the major results that can be obtained by this approach, in particular the observation that viral RNA genomes have a characteristic compactness that sets them aside from similar random RNAs. We also discuss how different parameters used in the current RNA folding software influence the resulting structures and how they can be related to experimentally observable quantities. Finally, we show how the connection to branched polymers can be extended to take advantage of known results from polymer physics and can be further moulded to include additional interactions, such as excluded volume or electrostatics.

physics.bio-ph↗

arXiv2022

Bottom-up data integration in polymer models of chromatin organisation

Cellular functions crucially depend on the precise execution of complex biochemical reactions taking place on the chromatin fiber in the tightly packed environment of the cell nucleus. Despite the availability of large data sets probing this process from multiple angles, we still lack a bottom-up framework which can incorporate the sequence-specific nature of biochemistry in a unified model of 3D chromatin dynamics. Here we propose SEMPER (Sequence Enhanced Magnetic PolymER), a novel stochastic polymer model which naturally incorporates observational data about sequence-driven biochemical processes, such as binding of transcription factor proteins, in a 3D model of chromatin structure. By introducing a new algorithm for approximate Bayesian inference, we discuss how to estimate in a robust manner the relative importance of biochemical vs. polymer signals in the determination of the chromatin epigenetic states which is leading to a significant revision of the interpretation of previous models. Furthermore we show that, without additional input from the genome 3D structure, our model can predict with reasonable accuracy some notable and non trivial conformational features of chromatin folding within the nucleus. Our work highlights the importance of introducing physically realistic statistical models for predicting chromatin states from epigenetic data, and opens the way to a new class of more systematic approaches to interpret epigenomic data.

q-bio.QM↗