Dynamic light‐scattering studies of internal motions in DNA. I. Applicability of the rouse‐zimm model

The intermediate scattering function G ( K , t ) for any polymer model obeying a linear separable Langevin equation can be expressed in terms of the eigenvalues and eigenvectors of its normal coordinate transformation. An algorithm for the extract numerical evaluation of G ( K , t ) for linear Rouse‐Zimm chains in the presence of hydrodynamic interaction has been developed. The computed G ( K , t ) 2 were fit to C( t ) = A exp(− t /τ A ) + B, and apparent diffusion coefficients calculated according to D app ≡ 1/(2τ A K 2 ). G ( K , t ) 2 was surprisingly well‐fit by single‐exponential decays, especially at both small and large values of Kb , where K is the scattering vector and b the root‐mean‐squared subunit extension. Plots of D app vs K 2 in‐variably showed a sigmoidal rise from D 0 at K 2 = O up to a constant plateau value at large K 2 b 2 . Analytical expression for G ( K , t ), exact in the limit of short times, were obtained for circular Rouse‐Zimm chains with and without hydrodynamic interaction, and also for free‐draining linear chains, and in addition for the independent‐segment‐mean‐force (ISMF) model. The predicted behaviors for G ( K , t ) at large Kb (or KR G ) was found in all cases to be single‐exponential with 1/τ ∝ K 2 at large Kb , in agreement with the computational results. A simple procedure for estamating all parameter of the Rouse‐Zimm model from a plot of D app vs K 2 is proposed. Experimental data for both native and pH‐denatured calf‐thymus DNA in 1.0 M Nacl with and without EDTA clearly plateau behavior of D app at large values of K , in harmony with the present Rouse‐Zimm and ISMF theories, and in sharp contrast to previous predictions based on the Rouse‐Zimm model.