Shear Unzipping of DNA

Abstract

We study theoretically the mechanical failure of a simple model of double stranded DNA under an applied shear. Starting from a more microscopic Hamiltonian that describes a sheared DNA, we arrive at a nonlinear generalization of a ladder model of shear unzipping proposed earlier by deGennes [1]. Using this model and a combination of analytical and numerical methods, we study the DNA "unzipping" transition when the shearing force exceeds a critical threshold at zero temperature. We also explore the effects of sequence heterogeneity and finite temperature and discuss possible applications to determine the strength of colloidal nanoparticle assemblies functionalized by DNA.

Shear unzipping of double-stranded DNA

“…This value of f c is close to the value used by Hatch et al [26] to fit their experimental data and the value estimated by Chakrabarti and Nelson [18]. To rupture the end base pairs of a given molecule they must be stretched by the shear force to distanceȳ.…”

“…In the results found in refs [18] and [28]. The other point to be noted from the figure is that the qualitative nature of the distribution of the effect of shear stretching along length of a molecule is same for all values of y −N/2 = y N/2 plotted in the figure.…”

“…The displacements of i th nucleotide from its equilibrium position are denoted by u i for one (the lower one in Fig.1) single stranded DNA (ssDNA) chain and by v i for the other (the upper one) chain. The effective Hamiltonian of the system can be written as [18] …”

“…Since in shear unzipping, a molecule is stretched along its axis we consider the longitudinal displacements of nucleotides and neglect the transverse displacements; the transverse displacements have been found in ref [18] an order of magnitude smaller than those in the direction of shear. We define new variables,…”

“…( II is similar to the nonlinear scaler displacement model of Chakarbarti and Nelson [18]. We calculate the force in both the constant force and constant extension ensembles.…”