Unzipping DNA by a periodic force: Hysteresis loop area and its scaling

Abstract

Using Monte Carlo simulations, we study the hysteresis in unzipping of a double stranded DNA whose ends are subjected to a time dependent periodic force with frequency ($\omega$) and amplitude ($G$). For the static force, i.e., $\omega \to 0$, the DNA is in equilibrium with no hysteresis. On increasing $\omega$, the area of the hysteresis loop initially increases and becomes maximum at frequency $\omega^{*}(G)$, which depends on the force amplitude $G$. If the frequency is further increased, we find that for lower amplitudes the loop area decreases monotonically to zero, but for higher amplitudes it has an oscillatory component. The height of subsequent peaks decrease and finally the loop area becomes zero at very high frequencies. The number of peaks depends on the length of the DNA. We give a simple analysis to estimate the frequencies at which maxima and minima occurs in the loop area. We find that the area of the hysteresis loop scales as $1/\omega$ in high-frequency regime whereas, it scales as $G^{\alpha} \omega^{\beta}$ with exponents $\alpha =1$ and $\beta = 5/4$ at low-frequencies. The values of the exponents $\alpha$ and $\beta$ are different from the exponents reported earlier based on the hysteresis of small hairpins.Comment: 9 pages, 6 figures, Published Versio

Periodically driven DNA: Theory and simulation

“…When a DNA chain is driven by an oscillatory force, a finite relaxation time produces a lag between force and response, and hence produces hysteresis [14][15][16][17][18][19]. The area of hysteresis loop, A loop , under a periodic force with amplitude F and frequency ν was found numerically in a rather detailed model to scale as F α ν β [16].…”

“…In the highfrequency limit, A loop remains independent of the chain length with α = 2 and β = −1. Employing Monte Carlo simulations on two interacting directed random walks, Kapri [19] observed that in the high-frequency limit, the scaling exponents remain the same, whereas at low frequency, he reported α = 1 and β = 5/4. At this stage, there is no unanimity, thus these discrepancies must be resolved either by longer simulations based on the realistic model of DNA or through a minimal model for which an analytic solution can be derived.…”

Unzipping DNA by a periodic force: Hysteresis loops, dynamical order parameter, correlations, and equilibrium curves

“…The model used in this paper has been used previously to study the unzipping of DNA by periodic forcing. 31,32 In this model, the two strands of a homopolymer DNA are represented by two directed self-avoiding walks on a (d = 1 + 1)-dimensional square lattice. The walks starting from the origin are restricted to go towards the positive direction of the diagonal axis (z-direction) without crossing each other, i.e., in every step, the z coordinate is incremented by 1 and the x coordinate changes by ±1.…”

“…33 In Ref. 32 , we have reported the behavior of A loop at high and low frequencies at various force amplitudes G using Monte Carlo simulations. In this paper, we focus mainly on the results related to the dynamical order parameter Q.…”

Rigidity of melting DNA

“…To isolate the entropic and the intrinsic elastic behavior, two types of models are considered, viz., a flexible model, the standard model used for melting and unzipping [39,40,[52][53][54], and a rigid model, built from the flexible model. See Fig.…”