Direct observation of the Brownian motion of linear and circular duplex DNA in the chain-length range from about 5 to 300 kilo-basepairs (kbp), as reported by Smith, Perkins, and Chu, [Macromolecules, 1996, 29, 1372–1373] and by Robertson, Laib, and Smith, [Proc. Natl. Acad. Sci. U. S. A., 2006, 103, 7310–7314] has indicated an effective mass-scaling exponent for diffusion, νH, of approximately 0.6, and this correlation was interpreted as implying that duplex DNA in this chain-length range can be described as a flexible polymer swollen by excluded volume interactions. However, we present computational evidence, based on our path-integration technique for computing transport properties, that indicates this inference needs to be reconsidered. Because of variable draining effects, the ratio Rh/Rg for random-coil polymers, including DNA, varies gradually throughout the chain-length range of interest, and does not stabilize to an asymptotic value until the chains are extremely long. This slow exponent crossover is particularly extended in stiff chains such as DNA. In particular, we find that if we take duplex DNA to be a worm-like chain comprised of a number of base pairs in the range between 5 and 300 kbp, then the effective exponent νH happens to be about 0.6, while the effective exponent, ν, for the radius of gyration, Rg, is about 0.52 and 0.51, with and without chain excluded volume, respectively. These results were obtained directly for a stiff lattice-chain model that agrees very well with the predictions of the continuum worm-like chain model. Based on these calculations and consistent experimental observations, we suggest that duplex DNA having a length below about 300 kbp is better described as a worm-like chain than a self-avoiding walk.
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