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The looping of polymers such as DNA is a fundamental process in the molecularbiology of living cells, whose interior is characterised by a high degree ofmolecular crowding. We here investigate in detail the looping dynamics offlexible polymer chains in the presence of different degrees of crowding. Fromthe analysis of the looping-unlooping rates and the looping probabilities ofthe chain ends we show that the presence of small crowders typically slow downthe chain dynamics but larger crowders may in fact facilitate the looping. Werationalise these non-trivial and often counterintuitive effects of the crowdersize onto the looping kinetics in terms of an effective solution viscosity andstandard excluded volume effects. Thus for small crowders the effect of anincreased viscosity dominates, while for big crowders we argue that confinementeffects (caging) prevail. The tradeoff between both trends can thus result inthe impediment or facilitation of polymer looping, depending on the crowdersize. We also examine how the crowding volume fraction, chain length, and theattraction strength of the contact groups of the polymer chain affect thelooping kinetics and hairpin formation dynamics. Our results are relevant forDNA looping in the absence and presence of protein mediation, DNA hairpinformation, RNA folding, and the folding of polypeptide chains underbiologically relevant high-crowding conditions.

Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size