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Elasticity of Short DNA Molecules: Theory and Experiment for Contour Lengths of 0.6–7 µm

Yeonee Seol ^*, Jinyu Li , Philip C. Nelson ^¶, Thomas T. Perkins ^*  and M. D. Betterton 

^* JILA, National Institute of Standards and Technology and University of Colorado, Department of Applied Mathematics, Department of Molecular, Cellular and Developmental Biology, Department of Physics, University of Colorado, Boulder, Colorado; and ^¶ Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania

Correspondence: Address reprint requests to Thomas T. Perkins, Tel.: 303-492-5291; E-mail: tperkins{at}jila.colorado.edu; or M. D. Betterton, Tel.: 303-735-6235; E-mail: mdb{at}colorado.edu.

The wormlike chain (WLC) model currently provides the best description of double-stranded DNA elasticity for micron-sized molecules. This theory requires two intrinsic material parameters—the contour length L and the persistence length p. We measured and then analyzed the elasticity of double-stranded DNA as a function of L (632 nm–7.03 µm) using the classic solution to the WLC model. When the elasticity data were analyzed using this solution, the resulting fitted value for the persistence length p_wlc depended on L; even for moderately long DNA molecules (L = 1300 nm), this apparent persistence length was 10% smaller than its limiting value for long DNA. Because p is a material parameter, and cannot depend on length, we sought a new solution to the WLC model, which we call the "finite wormlike chain (FWLC)," to account for effects not considered in the classic solution. Specifically we accounted for the finite chain length, the chain-end boundary conditions, and the bead rotational fluctuations inherent in optical trapping assays where beads are used to apply the force. After incorporating these corrections, we used our FWLC solution to generate force-extension curves, and then fit those curves with the classic WLC solution, as done in the standard experimental analysis. These results qualitatively reproduced the apparent dependence of p_wlc on L seen in experimental data when analyzed with the classic WLC solution. Directly fitting experimental data to the FWLC solution reduces the apparent dependence of p_fwlc on L by a factor of 3. Thus, the FWLC solution provides a significantly improved theoretical framework in which to analyze single-molecule experiments over a broad range of experimentally accessible DNA lengths, including both short (a few hundred nanometers in contour length) and very long (microns in contour length) molecules.

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