Collapse and coexistence for a molecular braid with an attractive interaction component subject to mechanical forces

Torque and buckling in stretched intertwined double-helix DNAs

We present a statistical-mechanical model for the behavior of intertwined DNAs, with a focus on their torque and extension as a function of their catenation (linking) number and applied force, as studied in magnetic tweezers experiments. Our model produces results in good agreement with available experimental data and predicts a catenation-dependent effective twist modulus distinct from what is observed for twisted individual double-helix DNAs. We find that buckling occurs near the point where experiments have observed a kink in the extension versus linking number, and that the subsequent "supercoiled braid" state corresponds to a proliferation of multiple small plectoneme structures. We predict a discontinuity in extension at the buckling transition corresponding to nucleation of the first plectoneme domain. We also find that buckling occurs for lower linking number at lower salt; the opposite trend is observed for supercoiled single DNAs.

Statistical mechanical model for a closed loop plectoneme with weak helix specific forces

We develop a statistical mechanical framework, based on a variational approximation, to describe closed loop plectonemes. This framework incorporates weak helix structure dependent forces into the determination of the free energy and average structure of a plectoneme. Notably, due to their chiral nature, helix structure dependent forces break the symmetry between left and right handed supercoiling. The theoretical approach, presented here, also provides a systematic way of enforcing the topological constraint of closed loop supercoiling in the variational approximation. At large plectoneme lengths, by considering correlation functions in an expansion in terms of the spatial mean twist density about its thermally averaged value, it can be argued that topological constraint may be approximated by replacing twist and writhe by their thermal averages. A Lagrange multiplier, containing the sum of average twist and writhe, can be added to the free energy to conveniently inforce this result. The average writhe can be calculated through the thermal average of the Gauss' integral in the variational approximation. Furthermore, this approach allows for a possible way to calculate finite size corrections due to the topological constraint. Using interaction energy terms from the mean-field Kornyshev-Leikin theory, for parameter values that correspond to weak helix dependent forces, we calculate the free energy, fluctuation magnitudes and mean geometric parameters for the plectoneme. We see a slight asymmetry, where interestingly, left handed supercoils have a looser structure than right handed ones, although with a lower free energy, unlike what the previous ground state calculations would suggest.