Normal-mode analysis of circular DNA at the base-pair level. 1. Comparison of computed motions with the predicted behavior of an ideal elastic rod

We have extended a newly developed approach to study the low-frequency normal modes of mesoscopic fragments of linear DNA in order to investigate the dynamics of closed circular molecules of comparable size, i.e., a few hundred base pairs. We have added restraint energy terms and a global minimization step to treat the more complicated, spatially constrained duplex in terms of the intrinsic conformation and flexibility of the constituent base-pair "step" parameters. Initial application of the methodology to the normal modes of an ideal closed circular DNA molecule-which is naturally straight in its relaxed open linear state, inextensible, and capable of isotropic bending and independent twisting at the base-pair level-matches theoretical predictions of elastic rod dynamics. The energy-optimized closed circular states and the types of low frequency motions follow expected behavior, with (1) uniform twist density and uniform energy density in the minimum energy state; (2) a near-zero frequency torsional mode with "free" rotation about the global helical axis; (3) higher-order torsional modes accompanied by global rocking motions and pure in-plane and out-of-plane bending motions in the torsionally relaxed circle; and (4) mixed modes of bending when the chain is supercoiled (over- or undertwisted). Furthermore, the computed changes in normal-mode frequencies with imposed supercoiling or with variation of chain length are virtually identical to theoretically predicted values.