Locality of contacts determines the subdiffusion exponents in polymeric models of chromatin

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.