Twist neutrality, a zero sum rule for oriented closed space curves with applications to circular DNA

摘要

The interplay between global constraints and local material properties ofchain molecules is a subject of emerging interest. Studies of molecules thatare intrinsically chiral, such as double-stranded DNA, is one example. Theirproperties generally depend on the local geometry, i.e. on curvature andtorsion, yet the paths of closed molecules are globally restricted by topology.Molecules that fulfill a twist neutrality condition, a zero sum rule for theincremental change in the rate of winding along the curve, will behaveneutrally to strain. This has implications for plasmids. For small circularmicroDNAs it follows that there must exist a minimum length for these to bedouble-stranded. It also follows that all microDNAs longer than the minimumlength must be concave. This counterintuitive result is consistent with thekink-like appearance which has been observed for circular DNA. A prediction forthe total negative curvature of a circular microDNA is given as a function ofits length.