Monte Carlo Simulations of Locally Melted Supercoiled DNAs in 20 mM Ionic Strength

Abstract

Mesoscopic models of unmelted and locally melted supercoiled DNAs in 20 mM ionic strength are simulated over a range of linking difference from Δ ℓ = 0 to −26 turns, or superhelix density from σ = 0 to −0.062. A domain containing m = 0, 28, or 56 melted basepairs (out of 4349 total) is modeled simply by a region of suitable length with substantially reduced torsion and bending elastic constants. Average structural properties are calculated from the saved configurations, and a reversible work protocol is used to calculate the supercoiling free energy, Δ G sc . The cross-writhe between duplex and melted regions (defined herein) is found to be negligibly small. The total writhe, radius of gyration, and ordered elements of the diagonalized inertial tensor are found to be nearly universal functions of the residual linking difference ( 〈 Δ ℓ r 〉 ) associated with the duplex region, independent of m. However, deformability of the tertiary structure, as manifested by the variance of those same properties, is not a universal function of 〈 Δ ℓ r 〉 , but depends upon m. Δ G sc varies with 〈 Δ ℓ r 〉 more strongly than 〈 Δ ℓ r 〉 2 due to the low ionic strength. The twist energy parameter, E T , obtained from the simulated Δ G sc , 〈 Δ ℓ r 〉 , and net twisting strain of the melted region, 〈 T D 〉 , is found to be independent of m, hence also of the torsion and bending elastic constants of the melted region. However, E T increases linearly with − 〈 Δ ℓ r 〉 , which leads to 1), a small overestimation of E T for any given 〈 Δ ℓ r 〉 , when E T is determined from the observed Δ ℓ and 〈 Δ ℓ r 〉 by the protocol of Bauer and Benham; and 2), a significant enhancement of the apparent slope, ⁡ − ⁡ d E T / d T , obtained via the protocol of Bauer and Benham, relative to the actual slope at fixed 〈 Δ ℓ r 〉 . After taking these two effects into account, the theoretical and experimental E T values and − ⁡ d E T / d T values agree rather well. For the larger Δ ℓ , the melted regions are found preferentially in the linker domains between interwound arms, rather than in the apical regions at the ends of interwound arms.