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Motivated by the well-known fractal packing of chromatin, we study theRouse-type dynamics of elastic fractal networks with embedded, stochasticallydriven, active force monopoles and force dipoles that are temporallycorrelated. We compute, analytically -- using a general theoretical framework-- and {\it via} Langevin dynamics simulations, the mean square displacement(MSD) of a network bead. Following a short-time superdiffusive behavior, forcemonopoles yield anomalous subdiffusion with an exponent identical to that ofthe thermal system. In contrast, force dipoles do not induce subdiffusion, andthe early superdiffusive MSD crosses over to a relatively small,system-size-independent saturation value. In addition, we find that forcedipoles may lead to "crawling" rotational motion of the whole network,reminiscent of that found for triangular micro-swimmers and consistent withgeneral theories of the rotation of deformable bodies. Moreover, force dipoleslead to network collapse beyond a critical force strength, which persists withincreasing system size, signifying a true first-order dynamical phasetransition. We apply our results to the motion of chromosomal loci in bacteriaand yeast cells' chromatin, where anomalous sub-diffusion, MSD$\sim t^{\nu}$with $\nu\simeq 0.4$, was found in both normal and ATP-depleted cells, albeitwith different apparent diffusion coefficients. We show that the combination ofthermal, monopolar, and dipolar forces in chromatin is typically dominated bythe active monopolar and thermal forces, explaining the observed normal cellsvs the ATP-depleted cells behavior.

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