Stretching weakly bending filaments with spontaneous curvature in two dimensions

Some important biomolecules (for instance, bacterial FtsZ and eukaryotic DNA) are known to posses spontaneous (intrinsic) curvature. Using a simple extension of the wormlike chain model, we study the response of a weakly bending filament in two dimensions to a pulling force applied at its ends (a configuration common in classical in-vitro experiments and relevant to several in-vivo cell cases). The spontaneous curvature of such a chain or filament can in general be arc-length dependent and we study a case of sinusoidal variation, from which an arbitrary case can be reconstructed via Fourier transformation. We obtain analytic results for the force-extension relationship and the width of transverse fluctuations. We show that spontaneous-curvature undulations can affect the force-extension behavior even in relatively flexible filaments with a persistence length smaller than the contour length.