Elasticity of a semiflexible filament with a discontinuous tension due to a cross-link or a molecular motor.
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 ∼1/f^{3/2} to the well-known ∼1/sqrt[f]-dependence of the end-to-end extension.
Institute for Theoretical Physics, Georg August University, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
Mohammadhosein
M
Razbin
Department of Physics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 702-701, Republic of Korea.
Panayotis
P
Benetatos
Institute for Theoretical Physics, Georg August University, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
Annette
A
Zippelius
D001696:Biomechanical Phenomena; D004548:Elasticity; D020409:Molecular Motor Proteins / Q000378:metabolism*
D020409:Molecular Motor Proteins