Spontaneous curvature-induced dynamical instability of Kirchhoff filaments: Application to DNA kink deformations

The Kirchhoff elastic theory of thin filaments with spontaneous curvature is employed in the understanding of the onset of the kink transitions observed in short DNA rings. Dynamical analysis shows that when its actual curvature is less than some threshold value determined by the spontaneous curvature, a circular DNA will begin to buckle to other shapes. The observable and the dominant deformation modes are also determined by dynamical instability analysis, and the different effects of Zn$^{2+}$ and Mg$^{2+}$ ions on DNA configurational properties are qualitatively discussed.