Extend the reversible-curvature polymer model beyond two-dimensional equilibrium weak bending

Develop a more complete theoretical treatment of semiflexible polymers with reversible spontaneous curvature that incorporates three-dimensional curvature and twist, the kinetics of binding and unbinding under mechanical loading, and arc-length-dependent occupation-number distributions for longer polymers rather than all-or-none transitions.

Background

The paper develops an analytically tractable two-state model for semiflexible polymers that reversibly switch between an uncurved state and a state with spontaneous curvature. The analysis is restricted to two dimensions, the weak-bending regime, and equilibrium elasticity, with state changes treated as all-or-none transitions between global conformational states.

The authors explicitly identify several limitations requiring further development. A more complete model should include three-dimensional curvature and twist as well as binding and unbinding kinetics under mechanical loading. In addition, the all-or-none description is considered inadequate for longer polymers, for which occupation should vary along the contour through an arc-length-dependent distribution.

References

Several extensions remain open. The present theoretical work is based on a simplified two-dimensional weak-bending description. A more complete treatment could include three-dimensional curvature and twist, and the kinetics of binding and unbinding under mechanical loading. Our investigation focuses on all-or-none transitions. This may be a reasonable approach for hybridization at the oligonucleotide level, but it fails in the case of longer polymers. An arc-length-dependent distribution of occupation numbers would be more appropriate in that case.

— The elasticity of semiflexible polymers with reversible spontaneous curvature in two dimensions  (2609.04856 - Kim et al., 4 Sep 2026) in Section 4, Discussion-Conclusions