The possibility of intrinsic local curvature in DNA toroids

A variety of solution conditions are known to induce collapse of linear DNA into a compact configuration without dramatic change of local structure. When visualized, these compact forms frequently have a toroidal appearance. We ask whether the molecular basis of the toroidal shape can be a stable curvature of isolated rodlike DNA segments. Application of the classical Euler-Lagrange theory for the buckling of elastic rods provides us with an affirmative answer. Specifically, we see that, in principle, sufficient addition of inert polymer to DNA solutions can induce buckling of DNA segments. However, no attempt is made to quantitate the Euler-Lagrange condition for sufficiency in terms of added polymer concentration. We find also that complete neutralization of the phosphate charge is more than sufficient to induce buckling of DNA segments of length comparable to a Kuhn segment. The quantitative argument involves comparison of buckling forces provided by polyelectrolyte theory with the Euler-Lagrange criterion. Knowledge of the ionic-strength dependence of DNA bending stiffness (persistence length) is not required.