  Aiming at the mechanical properties of cross-linked biopolymers, we set up
and analyze a model of two weakly bending wormlike chains subjected to a
tensile force, with regularly spaced inter-chain bonds (cross-links)
represented by harmonic springs. Within this model, we compute the
force-extension curve and the differential stiffness exactly and discuss
several limiting cases. Cross-links effectively stiffen the chain pair by
reducing thermal fluctuations transverse to the force and alignment direction.
The extra alignment due to cross-links increases both with growing number and
with growing strength of the cross-links, and is most prominent for small force
f. For large f, the additional, cross-link-induced extension is subdominant
except for the case of linking the chains rigidly and continuously along their
contour. In this combined limit, we recover asymptotically the elasticity of a
weakly bending wormlike chain without constraints, stiffened by a factor four.
The increase in differential stiffness can be as large as 100% for small f or
large numbers of cross-links.
