The nonlinear elasticity of an $\alpha$-helical polypeptide

TL;DR

This paper introduces a nonlinear elastic model for alpha-helical polypeptides, revealing sharp lengthening and buckling transitions due to secondary structure coupling, with implications for protein conformational changes.

Contribution

It extends the worm-like chain model to include secondary structure effects, providing new insights into the nonlinear mechanical response of alpha-helical polypeptides.

Findings

Demonstrates a sharp lengthening transition under tensile stress.

Shows a buckling transition under applied torque.

Reveals highly nonlinear response due to secondary structure coupling.

Abstract

We study a minimal extension of the worm-like chain to describe polypeptides having alpha-helical secondary structure. In this model presence/absence of secondary structure enters as a scalar variable that controls the local chain bending modulus. Using this model we compute the extensional compliance of an alpha-helix under tensile stress, the bending compliance of the molecule under externally imposed torques, and the nonlinear interaction of such torques and forces on the molecule. We find that, due to coupling of the ``internal'' secondary structure variables to the conformational degrees of freedom of the polymer, the molecule has a highly nonlinear response to applied stress and force couples. In particular we demonstrate a sharp lengthening transition under applied force and a buckling transition under applied torque. Finally, we speculate that the inherent bistability of the molecule may underlie protein conformational change \emph{in vivo}.