Persistent draining crossover in DNA and other semi-flexible polymers: Evidence from hydrodynamic models and extensive measurements on DNA solutions.

Although the scaling theory of polymer solutions has had many successes, this type of argument is deficient when applied to hydrodynamic solution properties. Since the foundation of polymer science, it has been appreciated that measurements of polymer size from diffusivity, sedimentation, and solution viscosity reflect a convolution of effects relating to polymer geometry and the strength of the hydrodynamic interactions within the polymer coil, i.e., "draining." Specifically, when polymers are expanded either by self-excluded volume interactions or inherent chain stiffness, the hydrodynamic interactions within the coil become weaker. This means there is no general relationship between static and hydrodynamic size measurements, e.g., the radius of gyration and the hydrodynamic radius. We study this problem by examining the hydrodynamic properties of duplex DNA in solution over a wide range of molecular masses both by hydrodynamic modeling using a numerical path-integration method and by comparing with extensive experimental observations. We also considered how excluded volume interactions influence the solution properties of DNA and confirm that excluded volume interactions are rather weak in duplex DNA in solution so that the simple worm-like chain model without excluded volume gives a good leading-order description of DNA for molar masses up to 10(7) or 10(8) g/mol or contour lengths between 5 μm and 50 μm. Since draining must also depend on the detailed chain monomer structure, future work aiming to characterize polymers in solution through hydrodynamic measurements will have to more carefully consider the relation between chain molecular structure and hydrodynamic solution properties. In particular, scaling theory is inadequate for quantitative polymer characterization.