Entropic Elasticity, Cooperative Extensibility and Supercoiling Property of DNA: A Unified Viewpoint

A unified model is constructed to study the recently observed DNA entropic elasticity, cooperative extensibility, and supercoiling property. With the introduction of a new structural parameter (the folding angle ϕ), bending deformations of sugar-phosphate backbones, steric effects of nucleotide basepairs, and short-range basestacking interactions are considered. The comprehensive agreement of theoretical results with experimental observations on both torsionally relaxed and negatively su-percoiled DNAs strongly indicates that, basestacking interactions, although short-ranged in nature, dominate the elasticity of DNA and hence are of vital biological significance. Recent in vitro experiments done on single double-stranded DNA (dsDNA) molecules or DNA-protein complexes reveal that DNA double-helix has nontrivial elas-tical properties [1–7]. At low external forces, it can be viewed as a simple wormlike chain [8]; at moderate forces, it becomes a rod with a large stretch modulus. But if pulled with a large force of about 70 pN the molecule as a whole can suddenly be driven to an almost fully stretched state with a contour length 1.7 times its native value [3,4]. More strikingly, if a dsDNA at the same time has a slight deficit in linking number, i.e., negatively su-percoiled, a pulling force as small as 0.3 pN can distort the native structure of DNA considerablely [5,6,9]. On the theoretical side, to understand these novel properties of DNA is of current interest and many models are suggested and some valuable insights attained [8,10–20]. For example, to interpret the extensibility of DNA, some authors suggest one-dimensional two-state models with [3,12,13,19] or without [14] nearest-neighbor interactions; and to explain the supercoiling property of DNA, wormlike rod chain models, with [12,16] or without [10,11,15] bend-twist and/or stretch-twist coupling, are investigated. Nevertheless, a unified description still seems to be lacking and the underlying mechanism which should account for DNA cooperative extensibility and novel supercoiling properties still elusive. Here, we show that it is possible to understand all these experimental observations from a unified viewpoint. A simple elastical model is proposed by taking into account the structural properties of realistic dsDNA. Bending energy of the sugar-phosphate backbones, basestack-ing interaction between adjacent nucleotide basepairs as well as their steric effects on DNA axial bending rigidity are considered. We have introduced a new structural parameter , the folding angle ϕ. Model calculations on the elastical properties of torsionally relaxed and negatively supercoiled DNAs are in quantitative agreement with all the known experimental observations [1,3–6]. The model indicates that basestacking …