arXiv subjects

Elham Ghobadpour

Publications and source records attributed to Elham Ghobadpour.

4 recordsLinked to original sources

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

The emergent dynamics of double-folded randomly branching ring polymers

The statistics of randomly branching double-folded ring polymers are relevant to the secondary structure of RNA, the large-scale branching of plectonemic DNA (and thus bacterial chromosomes), the conformations of single-ring polymers migrating through an array of obstacles, as well as to the conformational statistics of eukaryotic chromosomes and melts of crumpled, non-concatenated ring polymers. Double-folded rings fall into different dynamical universality classes depending on whether the random tree-like graphs underlying the double-folding are quenched or annealed, and whether the trees can undergo unhindered Brownian motion in their spatial embedding. Locally, one can distinguish (i) repton-like mass transport around a fixed tree, (ii) the spontaneous creation and deletion of side branches, and (iii) displacements of tree node, where complementary ring segments diffuse together in space. Here we employ dynamic Monte Carlo simulations of a suitable elastic lattice polymer model of double-folded, randomly branching ring polymers to explore the mesoscopic dynamics that emerge from different combinations of the above local modes in three different systems: ideal non-interacting rings, self-avoiding rings, and rings in the melt state. We observe the expected scaling regimes for ring reptation, the dynamics of double-folded rings in an array of obstacles, and Rouse-like tree dynamics as limiting cases. Of particular interest, the monomer mean-square displacements of $g_1\sim t^{0.4}$ observed for crumpled rings with $\nu=1/3$ are similar to the subdiffusive regime observed in bacterial chromosomes. In our analysis, we focus on the question to which extent contributions of different local dynamical modes to the emergent dynamics are simply additive. Notably, we reveal a non-trivial acceleration of the dynamics of interacting rings, when all three types of local motion are present.

cond-mat.soft↗

arXiv2023

DNA supercoiling in bacteria: state of play and challenges from a viewpoint of physics based modeling

DNA supercoiling is central to many fundamental processes of living organisms. Its average level along the chromosome and over time reflects the dynamic equilibrium of opposite activities of topoisomerases, which are required to relax mechanical stresses that are inevitably produced during DNA replication and gene transcription. Supercoiling affects all scales of the spatio-temporal organization of bacterial DNA, from the base pair to the large scale chromosome conformation. Highlighted in vitro and in vivo in the 1960s and 1970s, respectively, the first physical models were proposed concomitantly in order to predict the deformation properties of the double helix. About fifteen years later, polymer physics models demonstrated on larger scales the plectonemic nature and the tree-like organization of supercoiled DNA. Since then, many works have tried to establish a better understanding of the multiple structuring and physiological properties of bacterial DNA in thermodynamic equilibrium and far from equilibrium. The purpose of this essay is to address upcoming challenges by thoroughly exploring the relevance, predictive capacity, and limitations of current physical models, with a specific focus on structural properties beyond the scale of the double helix. We discuss more particularly the problem of DNA conformations, the interplay between DNA supercoiling with gene transcription and DNA replication, its role on nucleoid formation and, finally, the problem of scaling up models. Our primary objective is to foster increased collaboration between physicists and biologists. To achieve this, we have reduced the respective jargon to a minimum and we provide some explanatory background material for the two communities.

q-bio.BM↗