Elasticity of short DNA molecules: theory and
experiment for contour lengths of 0.6-7 µm
Yeonee Seol 1, Jinyu Li 2, Philip Nelson 3, Thomas T. Perkins 4 and M. D. Betterton 2*
1 JILA
2 University of Colorado at Boulder
3 University of Pennsylvania
4 University of Colorado, Boulder
* To whom correspondence should be addressed. E-mail: mdb{at}colorado.edu.
Submitted on May 21, 2007
Revised on July 15, 2007
Accepted on 8 August 2007
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Abstract |
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The worm-like 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 pwlc depended on L; even for moderately long DNA molecules (L = 1300 nm), the 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 worm-like 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 pwlc 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 pfwlc 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.
Key Words:
DNA elasticity, force-extension behavior, optical trapping, single-molecule, stretching DNA, worm-like chain
