Single polymers collapse from a random coil conformation to a dense state once the solvent gets sufficiently poor. For a flexible chain the condition of minimal surface energy yields an approximately spherical globule, but for semiflexible polymers the situation is more complex: The local structure of the dense phase then consists of essentially straight chains with a basically parallel alignment, in order to minimize bending energy and maximize density, respectively. Such a state can be characterized by a smooth field of tangent vectors, but in the spherical case this field must have at least two energetically unfavorable defects on the surface. However, for a torus many defect-free fields are possible. Indeed, DNA, the probably best studied semiflexible polymer, readily forms beautiful nanotori after adding any one of a variety of possible condensing agents (like polyethylenglycol (PEG), multivalent counterions, or bundling proteins) to a dilute solution of DNA chains. These tori are surprisingly monodisperse, having a radius comparable to the persistence length of DNA (~50 nm) basically independent of the condensation method.

We propose that semiflexible polymers in poor solvent collapse in two stages. The first stage is the well known formation of a dense toroidal aggregate. However, if the solvent is sufficiently poor, the condensate will undergo a second structural transition to a twisted entangled state, in which individual filaments lower their bending energy by additionally orbiting around the mean path along which they wind. This ``topological ripening'' is consistent with known simulations and experimental results. It connects and rationalizes various experimental observations ranging from strong DNA entanglement in viral capsids to the unusually short pitch of the cholesteric phase of DNA in sperm-heads. We propose that topological ripening of DNA toroids could improve the efficiency and stability of gene delivery.

Publications

I. M. Kulic, D. Andrienko, M. Deserno, Twist-bend instability for toroidal DNA condensates, Europhys. Lett., 67, pp. 418-424, 2004, [cond-mat/0312198].