High-energy deformation of filaments with internal structure and localized torque-induced melting of DNA

Arthur A. Evans and Alex J. Levine

Phys. Rev. E 85, 051915 – Published 22 May 2012

Abstract

We develop a continuum elastic approach to examining the bending mechanics of semiflexible filaments with a local internal degree of freedom that couples to the bending modulus. We apply this model to study the nonlinear mechanics of a double-stranded DNA oligomer (shorter than its thermal persistence length) whose free ends are linked by a single-stranded DNA chain. This construct, studied by H. Qu and G. Zocchi [Europhys. Lett. 94, 18003 (2011)], displays nonlinear strain softening associated with the local melting of the double-stranded DNA under applied torque and serves as a model system with which to study the nonlinear elasticity of DNA under large energy deformations. We show that one can account quantitatively for the observed bending mechanics using an augmented wormlike chain model, the helix-coil wormlike chain. We also predict that the highly bent and partially molten dsDNA should exhibit particularly large end-to-end fluctuations associated with the fluctuation of the length of the molten region, and propose appropriate experimental tests. We suggest that the augmented wormlike chain model discussed here is a useful analytic approach to the nonlinear mechanics of DNA or other biopolymer systems.

Received 14 March 2012

DOI:https://doi.org/10.1103/PhysRevE.85.051915

Authors & Affiliations

Arthur A. Evans¹ and Alex J. Levine^1,2

¹Department of Chemistry & Biochemistry, University of California, Los Angeles, California 90095, USA
²Department of Physics & Astronomy, University of California, Los Angeles, California 90095, USA

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Issue

Vol. 85, Iss. 5 — May 2012

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Images

Figure 1
Internal structure in nanofilaments can lead to nontrivial mechanical behavior. (a) A hybrid loop of dsDNA and ssDNA can be schematically represented as a filament composed of a stiff (red, solid) region and a softer (blue, dashed) melted region, constrained at its ends with a spring. (b) Under external bending, CNTs develop rippling or kinking modes of deformation that can also be described by postulating phase coexistence between two regions (reproduced from [9] with permission). The rippled region has an effectively lower bending rigidity, but there is an energy cost associated with inducing the ripples.Reuse & Permissions
Figure 2
Schematic of the melting elastica.Reuse & Permissions
Figure 3
Melted fraction for the minimum energy configuration as a function of applied force. For small loads the filament does not melt, but at a critical point (dependent on the melting cost $h$ ) the optimal value for the melted fraction increases continuously from zero. At yet higher values of the force there is a discontinuous jump in the stable equilibrium point; these solutions, while interesting, are of limited value for our present study and their presence has been included merely for completeness. Parameter values used are $Δ = 8$ and $j = 0.15$ .Reuse & Permissions
Figure 4
Phase diagram for melted elastica constrained by a spring. For low values of $h$ the entire filament melts under the action of the spring (black region on left of diagram). However, for all other values there is a sharp transition between the unmelted and partially melted phase. Low values of $N_{s}$ indicate a very stiff spring, and thus the filament can remain partially melted for larger $h$ . On the other hand, for larger $N_{s}$ the spring acts only weakly, and we see a very swift transition from completely melted to completely unmelted over a relatively small region of $h$ . The dashed (red) line designates the phase boundary derived from scaling arguments. The parameters used are $Δ = 8$ and $j = 0.15$ .Reuse & Permissions
Figure 5
Total elastic energy of the ssDNA spring and dsDNA system, as a function of the number of ssDNA base pairs $N_{s}$ with the number of base pairs $N_{d} = 18$ shown in the left panel and $N_{d} = 24$ shown in the right. The model prediction is shown as the solid (blue) line. The filled (red) points are data from [26], fitted using the parameters $Δ = 8, j = 0.15, h = 2.1$ for $N_{d} = 18$ and $Δ = 8$ , $h = 0.78$ , $j = 0.12$ for $N_{d} = 24$ . In the low- $N_{s}$ region the spring is relatively stiff, leading to a higher melted fraction in the dsDNA and an effective strain softening of the entire construct.Reuse & Permissions
Figure 6
Energy contours in the space of melted region and projected length. The (yellow) filled point represents the zero-temperature energetic minimum, the (white) dashed lines show the directions of principal curvature, and the (red) elliptical contour corresponds to $k_{B} T$ energy fluctuations away from the minimum, calculated by expanding the energy landscape to quadratic order about the energy minimum. While the melted region remains relatively constant, the applied force undergoes large fluctuations in the presence of Gaussian thermal excitation.Reuse & Permissions

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