Active fractal networks with stochastic force monopoles and force dipoles: Application to subdiffusion of chromosomal loci

by Prof. Rony Granek

Dept of Biotechnology Engineering, BGU

at Biological and soft-matter physics

Thu, 08 May 2025, 12:10
Sacta-Rashi Building for Physics (54), room 207

Abstract

Motivated by the well-known fractal packing of chromatin, we study the Rouse-type dynamics of elastic fractal networks with embedded, stochastically driven, active force monopoles and force dipoles that are temporally correlated [1]. We compute, analytically -- using a general theoretical framework -- and via Langevin dynamics simulations, the mean square displacement (MSD) of a network bead. Following a short-time superdiffusive behavior, force monopoles yield anomalous subdiffusion, MSD$\sim t^{\nu}$, with an exponent identical to that of the thermal system, $\nu=1-d_s/2$, where $d_s$ is the spectral dimension. In contrast, force dipoles do not induce subdiffusion, and the early superdiffusive MSD crosses over to a relatively small, system-size-independent saturation value. In addition, we find that force dipoles may lead to “crawling" rotational motion – or “rotational swimming” – of the whole network and to network collapse beyond a critical force strength. We apply our results to the motion of chromosomal loci in bacteria and yeast cells' chromatin, where anomalous sub-diffusion with $\nu\simeq 0.4$ was found in both normal and ATP-depleted cells. We show that the combination of thermal, monopolar, and dipolar forces in chromatin is typically dominated by the active monopolar and thermal forces, explaining this observation.

We extend our studies to Zimm-type dynamics [2], where hydrodynamic interaction is included. We also discuss results from active critical percolation clusters forming disordered fractals, and percolation clusters above the rigidity percolation threshold [3]. We conclude by structure and dynamic studies of a collapsed chain model with added crosslinks as a specific model for chromatin and show that various broken exponents found for chromatin are theoretically recovered [4].

References:

[1] S. Singh and R. Granek, Chaos 34, 113107 (2024); DOI: 10.1063/5.0227341.

[2] S. Singh and R. Granek, manuscript in preparation.

[3] D. Majumdar, S. Singh, and R. Granek, preprint https://arxiv.org/abs/2504.16510, to be submitted for publication.

[4] Y. Ben Yaish, S. Singh, and R. Granek, work in progress.

Created on 01-05-2025 by Feingold, Mario (mario)
Updaded on 01-05-2025 by Feingold, Mario (mario)