Terminal twist induced continuous writhe of a circular rod with intrinsic curvature

It is well known that a large linking number induces an abrupt writhing of a circular rod with zero intrinsic curvature, i.e., the stress-free state of the rod is straight. We show here that for any rod with a uniform natural curvature, no matter how small the intrinsic curvature is, a twist will induce a continuous writhing from the circular configuration and the abrupt writhing is only the limiting case when the intrinsic curvature is absolutely zero. The implication of this result on elastic models of circular DNA is discussed.