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Boundaries of the universal K 3 region and plateau region of the dynamic structure factor for DNA
Author(s) -
Schurr J. Michael
Publication year - 1983
Publication title -
biopolymers
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.556
H-Index - 125
eISSN - 1097-0282
pISSN - 0006-3525
DOI - 10.1002/bip.360221007
Subject(s) - plateau (mathematics) , chemistry , function (biology) , physics , diffusion , boundary (topology) , crystallography , condensed matter physics , quantum mechanics , mathematical analysis , mathematics , evolutionary biology , biology
A sufficiently long semiflexible filamentous macromolecule is theroretically expected to exhibit three different domains of behavior of its apparent diffusion coefficient D app ( K ) as a function of scattering vector K : (1) the small wave vector limit, where D app ( K ) = D 0 is the translational diffusion coefficient of the center‐of‐mass; (2) the universal K 3 region, where D app ( K ) = ( k B T /6πη) K is a universal function of K independent of any property of the molecule itself; ( c ) the plateau region at large K 2 , where D app ( 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 K 3 region and the plateau region are determined theoretically here using precise quantitative criteria for universal or plateau behavior of D app ( 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 K 3 region is given by K 2 R 2 G = K 2 Nb 2 /6 ≥ 7 and K 2 b 2 ⩽ 0.54. Allowing as much as 10% nonplateau behavior, the boundary for onset of plateau behavior is K 2 b 2 = 18.3. D app ( K ) is at least 50% nonuniversal when K 2 b 2 /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 K 3 region exists for DNA with M r ⩽ 10 7 and persistence length a ≥ 450 Å, although marginally (⩽17% nonuniversal) universal behavior, is exhibited in a very narrow domain 0.64 × 10 10 ⩽ K 2 ⩽ 0.84 × 10 10 cm −2 for ϕ29 DNA ( M r = 11.5 × 10 6 ). More than 50% of D app ( K ) is governed by local (elastic) rigid‐body motions when K 2 = 5.23 × 10 10 cm −2 . The existence of a very wide region of nonuniversal apparent K 3 behavior extending up to very large K 2 , far into the plateau region, is demonstrated in a plot of D app ( K )/ K vs K 2 for the Rouse‐Zimm model. This is shown to stem in part from visual artifacts of plotting D app ( K )/ K vs K 2 , even for rigid species.