Rajeev Kapri

Complete phase diagram of DNA unzipping: eye, Y fork, and triple point

We study the unzipping of double stranded DNA by applying a pulling force at a fraction s (0< or =s < or =1) from the anchored end. From exact analytical and numerical results, the complete phase diagram is presented. The phase diagram shows a strong ensemble dependence for various values of s. In addition, we show the existence of an eye phase and a triple point.

Randomly forced DNA.

We study the effect of random forces on a double-stranded DNA in unzipping the two strands, analogous to the problem of an adsorbed polymer under a random force. The ground state develops bubbles of various lengths as the random force fluctuation is increased. The unzipping phase diagram is shown to be drastically different from the pure case.

Asymptotic shape of the region visited by an Eulerian walker.

We study an Eulerian walker on a square lattice, starting from an initial randomly oriented background using Monte Carlo simulations. We present evidence that, for a large number of steps N , the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as N1/3, for large N , and the width of the boundary region grows as Nalpha/3, with alpha=0.40+/-0.06 . If we introduce stochasticity in the evolution rules, the mean-square displacement of the walker, approximately approximately N2nu, shows a crossover from the Eulerian (nu=1/3) to a simple random-walk (nu=1/2) behavior.

Manipulating a single adsorbed DNA for a critical endpoint

We show the existence of a critical endpoint in the phase diagram of unzipping of an adsorbed double-stranded (ds) polymer like DNA. The competition of base pairing, adsorption and stretching by an external force leads to the critical end point. From exact results, the location of the critical end point is determined and its classical nature established.

Unzipping DNA by force: thermodynamics and finite size behaviour

We discuss the thermodynamic behaviour near the force induced unzipping transition of double-stranded DNA in two different ensembles. The Y-fork is identified as the coexisting phases in the fixed distance ensemble. From finite size scaling of thermodynamic quantities like the extensibility and the length of the unzipped segment of a Y-fork, the phase diagram can be recovered. We suggest that such procedures could be used to obtain the thermodynamic phase diagram from experiments on finite length DNA.

Hysteresis and nonequilibrium work theorem for DNA unzipping

We study by using Monte Carlo simulations the hysteresis in unzipping and rezipping of a double stranded DNA (dsDNA) by pulling its strands in opposite directions in the fixed force ensemble. The force is increased at a constant rate from an initial value g(0) to some maximum value g(m) that lies above the phase boundary and then decreased back again to g(0). We observed hysteresis during a complete cycle of unzipping and rezipping. We obtained probability distributions of work performed over a cycle of unzipping and rezipping for various pulling rates. The mean of the distribution is found to be close (the difference being within 10%, except for very fast pulling) to the area of the hysteresis loop. We extract the equilibrium force versus separation isotherm by using the work theorem on repeated nonequilibrium force measurements. Our method is capable of reproducing the equilibrium and the nonequilibrium force-separation isotherms for the spontaneous rezipping of dsDNA.

Can a double stranded DNA be unzipped by pulling a single strand?: Phases of adsorbed DNA

We study the unzipping of a double stranded DNA (dsDNA) by applying an external force on a single strand while leaving the other strand free. We find that the dsDNA can be unzipped to two single strands if the external force exceeds a critical value. We obtain the phase diagram, which is found to be different from the phase diagram of unzipping by pulling both the strands in opposite directions. In the presence of an attractive surface near DNA, the phase diagram gets modified drastically and shows richer surprises including a critical end point and a triple point.

Unzipping an adsorbed polymer in a dirty or random environment

The phase diagram of unzipping of an adsorbed directed polymer in two dimensions in a random medium has been determined. Both the hard-wall and the soft-wall cases are considered. Exact solutions for the pure problem with different affinities on the two sides are given. The results obtained by the numerical procedure adopted here are shown to agree with the exact results for the pure case. The characteristic exponents for unzipping for the random problem are different from the pure case. The distribution functions for the unzipped length, first bubble, and the spacer are determined.

Order-parameter scaling in fluctuation-dominated phase ordering.

In systems exhibiting fluctuation-dominated phase ordering, a single order parameter does not suffice to characterize the order, and it is necessary to monitor a larger set. For hard-core sliding particles on a fluctuating surface and the related coarse-grained depth (CD) models, this set comprises the long-wavelength Fourier components of the density profile, which capture the breakup and remerging of particle-rich regions. We study both static and dynamic scaling laws obeyed by the Fourier modes Q_{mL} and find that the mean value obeys the static scaling law 〈Q_{mL}〉∼L^{-ϕ}f(m/L) with ϕ≃2/3 and ϕ≃3/5 for Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) surface evolution, respectively, and ϕ≃3/4 for the CD model. The full probability distribution P(Q_{mL}) exhibits scaling as well. Further, time-dependent correlation functions such as the steady-state autocorrelation and cross-correlations of order-parameter components are scaling functions of t/L^{z}, where L is the system size and z is the dynamic exponent, with z=2 for EW and z=3/2 for KPZ surface evolution. In addition we find that the CD model shows temporal intermittency, manifested in the dynamical structure functions of the density and the weak divergence of the flatness as the scaled time approaches 0.

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

Using Monte Carlo simulations, we study the hysteresis in the unzipping of double-stranded DNA whose ends are subjected to a time-dependent periodic force with frequency (ω) and amplitude (G). For the static force, i.e., ω→0, the DNA is in equilibrium with no hysteresis. On increasing ω, the area of the hysteresis loop initially increases and becomes maximum at frequency ω*(G), which depends on the force amplitude G. If the frequency is increased further, 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 decreases, 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 occur in the loop area. We find that the area of the hysteresis loop scales as 1/ω in the high-frequency regime, whereas it scales as G(α)ω(β) with exponents α=1 and β=5/4 at low frequencies. The values of the exponents α and β are different from the exponents reported earlier based on the hysteresis of small hairpins.