Intramolecular interference effects in dynamic light scattering: rigid double spirals and superhelical DNAs

A model for the binding of E. coli single-strand binding protein to supercoiled DNA

A model is proposed for the binding of E. coli single strand binding protein (SSB) to supercoiled DNA. The basic tetrameric binding units of SSB are assumed to bind in pairs to the complementary single strands of a locally melted region. The cooperativity of the binding includes contributions from both protein-protein and base-pair stacking interactions. Each bound SSB tetramer is assumed to unwind l = 34 bp, which implies an unwinding angle of 3.27 turns. The resulting loss of superhelical strain is the essential driving force for binding SSB to supercoiled DNAs. All molecular parameters entering into the theory are estimated from available data, except for the composite binding constant (Ka), which is adjusted to best-fit the theory to the fluorescence quenching (FQ) and diffusion coefficient (D0) data of Langowski et al. Very good fits are obtained with optimum values of Ka that are consistent with estimates from other data. This binding model predicts several noteworthy features. (1) SSB binds essentially always in a single contiguous stack on a supercoiled plasmid, and relative fluctuations in stack length are quite small, in agreement with results of electron microscopy studies. (2) The progressive loss of superhelical strain with increasing bound ligand decreases the affinity of the DNA for SSB. This anti-cooperativity offsets the cooperativity of the binding and causes apparent saturation of the binding at rather low binding ratios. Consequently, over the limited span of the measurements, the FQ data can also be satisfactorily fitted by a non-cooperative model comprising a small number of independent sites. (3) When SSB binds to a population of different topoisomers, the distribution of linking differences of the resulting complexes is extremely narrow. Thus, SSB acts to level any differences in superhelical strain in a population of topoisomers. Finally, the effects of restricting binding to a region comprising only part of the plasmid are assessed.

Dynamic light scattering from weakly bending rods: estimation of the dynamic bending rigidity of the M13 virus

A theory is presented for the dynamic structure factor [S(K,t]) of weakly bending rods. This treatment is based on a discrete bead model for the Brownian dynamics in which all bead motions associated with bending are constrained to occur in a plane perpendicular to the end-to-end vector, thus prohibiting extension or contraction along that axis. Preset hydrodynamic interactions are incorporated in a numerically exact manner. The predicted normalized dynamic structure factor S(K,t)/S(K,0) should be valid for short times t such that the rms rotation of the end-to-end vector around any transverse axis is much less than 1.0 radian. With geometrical parameters appropriate for the M13 virus, the intensity autocorrelation function G(2) (K,t) = 1 + magnitude of S(K,t)/S(K,0)2 is calculated over a range of times and scattering vectors K for selected values of the persistence length P. The calculated G(2) (K,t) are fitted to a single exponential with unit baseline over the same range of times as the experimental photon correlation functions, and the apparent diffusion coefficients Dapp (K) are obtained from the best-fit relaxation times. For the sake of completeness, an exact expression is derived for the apparent diffusion coefficient obtained from the initial slope of the dynamic structure factor. However, this does not reduce to the known correct result in the rigid rod limit. To obtain the correct result, the limit of infinite bending rigidity must be taken before the limit of zero time. For this and other reasons, the initial slope value of Dapp (K) is not useful for weakly bending rods. Photon correlation functions are measured for the M13 virus, which is virtually identical to the often-studied fd virus. The experimental photon correlation functions are fitted over 8 relaxation times to a single-exponential plus baseline, and the Dapp (K) are calculated from the best-fit relaxation times. Theoretical curves of Dapp (K) vs K2 for selected values of P are compared with the experimental data, which are satisfactorily reproduced when P = 22000 +/- 2000 A. This dynamic value is close to the static value, P = 20000 +/- 2000 A, reported for the very similar fd virus. The most recent theories of Maeda and Fujime and their dynamic light scattering studies of fd virus are compared with the present results in some detail. Their optimum value of P is in surprisingly good agreement with the present value.