Resonant helical deformations in nonhomogeneous Kirchhoff filaments

Abstract

We study the three-dimensional static configurations of nonhomogeneous Kirchhoff filaments with periodically varying Young's modulus. This type of variation may occur in long tandemly repeated sequences of DNA. We analyse the effects of the Young's modulus frequence and amplitude of oscillation in the stroboscopic maps, and in the regular (non chaotic) spatial configurations of the filaments. Our analysis shows that the tridimensional conformations of long filaments may depend critically on the Young's modulus frequence in case of resonance with other natural frequencies of the filament. As expected, far from resonance the shape of the solutions remain very close to that of the homogeneous case. In the case of biomolecules, it is well known that various other elements, besides sequence-dependent effects, combine to determine their conformation, like self-contact, salt concentration, thermal fluctuations, anisotropy and interaction with proteins. Our results show that sequence-dependent effects alone may have a significant influence on the shape of these molecules, including DNA. This could, therefore, be a possible mechanical function of the ``junk'' sequences.