Boundaries of the universal K3 region and plateau region of the dynamic structure factor for DNA.

Abstract

AbstractA sufficiently long semiflexible filamentous macromolecule is theroretically expected to exhibit three different domains of behavior of its apparent diffusion coefficient Dapp(K) as a function of scattering vector K: (1) the small wave vector limit, where Dapp(K) = D0 is the translational diffusion coefficient of the center‐of‐mass; (2) the universal K3 region, where Dapp(K) = (kBT/6πη)K is a universal function of K independent of any property of the molecule itself; (c) the plateau region at large K2, where Dapp(K) approaches either a plateau, or gradually sloping quasiplateau, characteristic of local (elastic) rigid‐body motions of the filament. The existence of each of these different domains has now been established experimentally for at least some polymers. The boundaries of the universal K3 region and the plateau region are determined theoretically here using precise quantitative criteria for universal or plateau behavior of Dapp(K) for a Rouse‐Zimm model containing N + 1 subchains with rms subchain extension b. Allowing a maximum of 13% nonuniversal behavior, the domain of the universal K3 region is given by K2R2G = K2Nb2/6 ≥ 7 and K2b2 ⩽ 0.54. Allowing as much as 10% nonplateau behavior, the boundary for onset of plateau behavior is K2b2 = 18.3. Dapp(K) is at least 50% nonuniversal when K2b2/6 = 6 ln 3. Extension of these results to DNA is examined theoretically, and good agreement of the pertinent predictions with published experimental data is demonstrated.It is concluded that no truly universal K3 region exists for DNA with Mr ⩽ 107 and persistence length a ≥ 450 Å, although marginally (⩽17% nonuniversal) universal behavior, is exhibited in a very narrow domain 0.64 × 1010 ⩽ K2 ⩽ 0.84 × 1010 cm−2 for ϕ29 DNA (Mr = 11.5 × 106). More than 50% of Dapp(K) is governed by local (elastic) rigid‐body motions when K2 = 5.23 × 1010 cm−2. The existence of a very wide region of nonuniversal apparent K3 behavior extending up to very large K2, far into the plateau region, is demonstrated in a plot of Dapp(K)/K vs K2 for the Rouse‐Zimm model. This is shown to stem in part from visual artifacts of plotting Dapp(K)/K vs K2, even for rigid species.