The shape of pinned forced polymer loops.

Loop geometry is a frequent encounter in synthetic and biological polymers. Here we provide an analytical theory to characterize the shapes of polymer loops subjected to an external force field. We show how to calculate the polymer density, gyration radius and its distribution. Interestingly, the distribution of the gyration radius shows a non-monotonic behavior as a function of the external force. Furthermore, we analyzed the gyration tensor of the polymer loop characterizing its overall shape. Two parameters called asphericity and the nature of asphericity derived from the gyration tensor, along with the gyration radius, can be used to quantify the shape of polymer loops in theory and experiments.