Periodically driven DNA: Theory and simulation

Abstract

We propose a generic model of driven DNA under the influence of an oscillatory force of amplitude F and frequency ν and show the existence of a dynamical transition for a chain of finite length. We find that the area of the hysteresis loop, A_{loop}, scales with the same exponents as observed in a recent study based on a much more detailed model. However, towards the true thermodynamic limit, the high-frequency scaling regime extends to lower frequencies for larger chain length L and the system has only one scaling (A_{loop}≈ν^{-1}F^{2}). Expansion of an analytical expression for A_{loop} obtained for the model system in the low-force regime revealed that there is a new scaling exponent associated with force (A_{loop}≈ν^{-1}F^{2.5}), which has been validated by high-precision numerical calculation. By a combination of analytical and numerical arguments, we also deduce that for large but finite L, the exponents are robust and independent of temperature and friction coefficient.

Hysteresis loop area scaling exponents in DNA unzipping by a periodic force: A Langevin dynamics simulation study

“…In recent years, the behavior of a dsDNA under a periodic force with frequency ω and amplitude G has been studied by using Brownian dynamics (BD) or Langevin dynamics (LD) simulation of an off-lattice coarse-grained model for short chains which are limited to a maximum number of N = 16 base pairs and 32 monomers [20][21][22][23][24], and by using Monte Carlo (MC) simulations of DNA chains having 1024 monomers with N = 512 base pairs on a (d = 1 + 1)-dimensional square lattice [1,2,25,26]. Both LD and MC simulation studies show the existence of a dynamical phase transition, where the DNA can be taken from the zipped state to an unzipped state via a new dynamical state.…”

“…The values of the exponents α and β obtained in BD/LD and MC simulations are however different. In BD/LD simulation studies on shorter DNA hairpins [20][21][22][23][24], a chain having 2N monomers, whose first N monomers are complementary to the rest half. The monomers of the chain are chosen in such a manner that the ith monomer from the anchored end can bind only with the (N − i)th monomer of the chain, thus mimicking a base pair of the DNA.…”

“…Initial BD/LD simulation studies reported exponent values α = β = 1/2 [20][21][22]. These were later modified to α = 0.33 and β = 1/2 [23]. However, a different set of exponents, α = 1 and β = 1.25, were obtained for longer homopolymer DNA chains in MC simulation studies [1].…”

Polymer translocation across an oscillating nanopore: study of several distribution functions of relevant Brownian functionals

“…The first passage time statistics for a Wiener process with an exponential time dependent drift term are analyzed in the context of neuron dynamics in references [24][25][26]. Also, recent studies of DNA unzipping under periodic forcing need to be mentioned [27][28][29][30]. Molini et al [31] make a study on first passage statistics of BM with purely time dependent drift and diffusion terms using method of images.…”

Nonlinear Brownian Machines

“…In the previous chapters we have studied extensively the properties of a machine composed of a single particle under the influence of a nonlinear quartic potential as k 4 x 4 /4, which in nature could represent a FPUT-α potential [62]. In a more realistic situation we may be faced with more exotic types of potentials [52,63]. Motivated by this, we dedicate Chapter 4 to study a more general class of nonlinear potential.…”