A geometrical template for toroidal aggregates of chiral macromolecules

The formation of toroidal aggregates by long chiral molecules of biological origin, as collagen, f-actin and DNA, or by chiral synthetic polypeptides has been observed in specific ionic environments. Such aggregates have received considerable attention in order to identify the various physical factors susceptible to contribute to this original morphogenesis, particularly in the case of those formed by DNA. We consider here the eventual role of a spontaneous uniform twist of micrometric pitch whose possible occurrence is suggested by some observations and by recent studies of DNA dense phases exhibiting cholesteric and "blue" phase structures. Following an approach inspired by the geometry and topology of fiber bundles, we show that the necessity to propagate such a twist in a dense bundle of fibers leads to the formation of aggregates having a toroidal shape and, in the case of the nanometric aggregates of DNA, characteristic sizes similar to those observed.