  Loop extrusion by motor proteins mediates the attractive interactions in
chromatin on the length scale of megabases, providing the polymer with a
well-defined structure and at the same time determining its dynamics. The mean
square displacement of chromatin loci varies from a Rouse-like scaling to a
more constrained subdiffusion, depending on cell type, genomic region and time
scale. With a simple polymeric model, we show that such a Rouse-like dynamics
occurs when the parameters of the model are chosen so that contacts are local
along the chain, while in presence of non-local contacts, we observe
subdiffusion at short time scales with exponents smaller than 0.5. Such
exponents are independent of the detailed choice of the parameters and build a
master curve that depends only on the mean locality of the resulting contacts.
We compare the loop-extrusion model with a polymeric model with static links,
showing that also in this case only the presence of nonlocal contacts can
produce low-exponent subdiffusion. We interpret these results in terms of a
simple analytical model.
