Abstract

In the first part of my talk, I discuss general features of helix specific interactions, particularly those of DNA . I review the form of the potential for a mean field theory of the electrostatics of helical molecules in electrolyte solution- the Kornyshev-Leikin theory. However, real DNA is not an ideal helix, nor straight, due to structural and thermal distortions. I consider how one can quantify helix disorder due to a random base pair text and thermal fluctuations, and how these affect the form of the interaction energy.

In the second part, I start by considering a free ended braid formed from two molecules. It is possible to show that where there is attraction, for long molecules, a left handed, braided state may have lower energy than two parallel molecules. This effect is most pronounced when the two molecules have the same base pair text, as opposed to uncorrelated texts. Next, I review the topological law/constraint for closed loop DNA . Lastly, I present a simple model for a closed loop plasmid, based around the free braided state, but with the topological constraint as well as end-loops. The simple model suggests that when helix specific interactions are large, positive supercoiling is actually more energetically favourable than negative supercoiling, and that the state of lowest energy could be one of positive writhe (a braided configuration) instead of zero writhe (open circle or a flat loop). This might be realized under certain experimental conditions, discussed here. Finally, I point to future work.