  We analyze the stretching elasticity of a wormlike chain with a tension
discontinuity resulting from a Hookean spring connecting its backbone to a
fixed point. The elasticity of isolated semiflexible filaments has been the
subject in a significant body of literature, primarily because of its relevance
to the mechanics of biological matter. In real systems, however, these
filaments are usually part of supramolecular structures involving cross-linkers
or molecular motors which cause tension discontinuities. Our model is intended
as a minimal structural element incorporating such a discontinuity. We obtain
analytical results in the weakly bending limit of the filament, concerning its
force-extension relation and the response of the two parts in which the
filament is divided by the spring. For a small tension discontinuity, the
linear response of the filament extension to this discontinuity strongly
depends on the external tension. For large external tension $f$, the spring
force contributes a subdominant correction $\sim 1/f^{3/2}$ to the well known
$\sim 1/\sqrt{f}$ dependence of the end-to-end extension.

Biological Physics;Soft Condensed Matter;Statistical Mechanics