SOFT MATTER AND BIOMATERIALS 110 PLECTONEMIC STRUCTURE OF TOPOLOGICALLY CONSTRAINED, SUPERCOILED DNA

Closed circular DNA usually exists in a supercoiled configuration, in which the duplex is wound around another part of the same molecule to form a higher order helix. Supercoiling is utilized in many cellular mechanisms. Here, we explore the extent to which supercoiling controls the compaction of pUC18 bacterial plasmid (2686 base pairs) in a liquid crystal [1,2]. For this purpose, the configuration of the superhelix is monitored with SANS through the phase transition. Figure 1. Plectonemic helix with length L, radius r, pitch p and opening angle a. The topological constraint is characterized by the linking number deficit LkD, which is the number of turns the duplex is turned before closure to form a ring. LkD is conserved and is distributed among writhe Wr and excess twist TwD exerted on the duplex according to Lk Wr TwD = + D. For a right-handed, regular supercoil without end loops, Wr is proportional to the number of crossings n when viewed perpendicular to the superhelical axis sinWr n a =-, with the pitch angle a as in figure 1. It is convenient to define the normalized length 2 /L l, with l being the length of the DNA molecule. From integration along the contour follows ()1 22 22L l p p r = +, (1) if the end loops are neglected. The pitch angle a is given by ( ) () ()1 22tan / 2 / 1 2 /p r L l L la = =- (2) and the writhe reads () ()2 22Wr lp p rp =- +. (3) The local structure of the superhelix is fully characterized by p and r. These parameters determine a, Wr and 2 /L l. In our experiments, the range of momentum transfer q exceeds L-1 by at least an order of magnitude. In this high q-range, the scattering is sensitive to interference over an extent on the order of r and p and effects of overall flexibility and/or branching of the supercoil are beyond observation. We can accordingly use the high-q approximate form of the form factor of a regular superheli