  The looping of polymers such as DNA is a fundamental process in the molecular
biology of living cells, whose interior is characterised by a high degree of
molecular crowding. We here investigate in detail the looping dynamics of
flexible polymer chains in the presence of different degrees of crowding. From
the analysis of the looping-unlooping rates and the looping probabilities of
the chain ends we show that the presence of small crowders typically slow down
the chain dynamics but larger crowders may in fact facilitate the looping. We
rationalise these non-trivial and often counterintuitive effects of the crowder
size onto the looping kinetics in terms of an effective solution viscosity and
standard excluded volume effects. Thus for small crowders the effect of an
increased viscosity dominates, while for big crowders we argue that confinement
effects (caging) prevail. The tradeoff between both trends can thus result in
the impediment or facilitation of polymer looping, depending on the crowder
size. We also examine how the crowding volume fraction, chain length, and the
attraction strength of the contact groups of the polymer chain affect the
looping kinetics and hairpin formation dynamics. Our results are relevant for
DNA looping in the absence and presence of protein mediation, DNA hairpin
formation, RNA folding, and the folding of polypeptide chains under
biologically relevant high-crowding conditions.
