  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.
