Cyclization of short DNA molecules (150-160 bp) is an excellent testing ground for continuum elastic models, in that entropic and solvent effects are minimized, so one can focus on the mechanics of DNA bending and twisting. We have computed cyclization equilibria using a combination of (1) a continuum model which includes DNA intrinsic curvature derived from experimental studies of base-pair stacking, (2) parameter continuation computations using the collocation package AUTO, (3) stability computations to determine which equilibria are local minima, and (4) visualization software tailored to the continuation computations. This combination gives a qualitative understanding of the set of equilibria as physical parameters (e.g. bend phasing, DNA length, twist and bend stiffnesses) are varied. Continuum cyclization energies match the equilibrium energies of the base-pair-level wedge-angle model, and also agree with experimental cyclization rates.
This project represents joint work with John Maddocks, Jason
Kahn, and Kathleen Rogers.