Exact results on the ground-state of a model for an intrinsically curved semiflexible biopolymer

This work explores the ground-state of an elastic model for an intrinsically curved semiflexible biopolymer. We find that the two- and three-dimensional systems have exactly the same mechanical property and show that the signed curvature of the model is nowhere continuous so that the standard variational technique fails in continuous model. Moreover, we show that the ground-state configuration of the model is a sawtooth line, and find that the relative extension of the corresponding discrete model is zr=cos[2c0/(4+f)] when c0 < π/6, where c0 is the reduced intrinsic signed curvature and f is the reduced stretching force. Finite size effect on zr is negligible in this system. Since zr is a single-valued function of f, there is not discontinuous change in zr which is consistent with the finite temperature result.