Active disordered elastic networks: Collapse, swimming, and subdiffusion with application to chromatin dynamics

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 ∼ tν , with an exponent identical to that of the thermal system, ν=1-ds/2 , where ds  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 “swimming”/“crawling” rotational motion 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 ν≃ 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], with excluded-volume interaction included. The thermal and force-monopoles subdiffusion exponents are altered, yet the absence of subdiffusion for force dipoles is maintained. Moreover, force-dipoles produce translational center-of-mass diffusion (i.e. random swimming), in addition to the rotational swimming motion.   We also discuss results from disordered fractals, both critical percolation clusters and clusters that are away from criticality, showing the effect of the isostatic point (known also as “rigidity percolation”) [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, to be published.

[3] D. Majumdar, S. Singh, and R. Granek, J. Chem. Phys. 163, 114902 (2025); DOI: 10.1063/5.0278300.

[4] Y. Ben Yaish, S. Singh, and R. Granek, to be published.