  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.
