Homopolymer and heteropolymer translocation through patterned pores under fluctuating forces.

We investigate the translocation of a semiflexible polymer through extended patterned pores using Langevin dynamics simulations, specifically focusing on the influence of a time-dependent driving force. Our findings reveal that, akin to its flexible counterpart, a rigid chain-like molecule translocates faster when subjected to an oscillating force than a constant force of equivalent average magnitude. The enhanced translocation is strongly correlated with the stiffness of the polymer and the stickiness of the pores. The arrangement of the pores plays a pivotal role in translocation dynamics, deeply influenced by the interplay between polymer stiffness and pore-polymer interactions. For heterogeneous polymers with periodically varying stiffness, the oscillating force introduces significant variations in the translocation time distributions based on segment sizes and orientations. On the basis of these insights, we propose a sequencing approach that harnesses distinct pore surface properties that are capable of accurately predicting sequences in heteropolymers with diverse bending rigidities.

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

The unzipping of a double stranded DNA whose ends are subjected to a time dependent periodic force with frequency ω and amplitude G is studied using Monte Carlo simulations. We obtain the dynamical order parameter, Q, defined as the time average extension between the end monomers of two strands of the DNA over a period, and its probability distributions P(Q) at various force amplitudes and frequencies. We also study the time autocorrelations of extension and the dynamical order parameter for various chain lengths. The equilibrium force-distance isotherms were also obtained at various frequencies by using nonequilibrium work measurements.

Sequencing of semiflexible polymers of varying bending rigidity using patterned pores.

We study the translocation of a semiflexible polymer through extended pores with patterned stickiness, using Langevin dynamics simulations. We find that the consequence of pore patterning on the translocation time dynamics is dramatic and depends strongly on the interplay of polymer stiffness and pore-polymer interactions. For heterogeneous polymers with periodically varying stiffness along their lengths, we find that variation of the block size of the sequences and the orientation results in large variations in the translocation time distributions. We show how this fact may be utilized to develop an effective sequencing strategy. This strategy involving multiple pores with patterned surface energetics can predict heteropolymer sequences having different bending rigidity to a high degree of accuracy.

Gain reversal in the translocation dynamics of a semiflexible polymer through a flickering pore.

We study the driven translocation of a semiflexible polymer through an attractive extended pore with a periodically oscillating width. Similar to its flexible counterpart, a stiff polymer translocates through an oscillating pore more quickly than a static pore whose width is equal to the oscillating pore's mean width. This efficiency quantified as a gain in the translocation time, highlights a considerable dependence of the translocation dynamics on the stiffness of the polymer and the attractive nature of the pore. The gain characteristics for various polymer stiffness exhibit a trend reversal when the stickiness of the pore is changed. The gain reduces with increasing stiffness for a lower attractive strength of the pore, whereas it increases with increasing stiffness for higher attractive strengths. Such a dependence leads to the possibility of a high degree of robust selectivity in the translocation process.

Stochastic resonance in a model of a periodically driven DNA: Multiple transitions, scaling, and sequence dependence.

We numerically study stochastic resonance in the unzipping of a model double-stranded DNA by a periodic force. We observe multiple peaks in stochastic resonance in the output signal as the driving force frequency is varied for different force amplitudes, temperature, chain length, and chain heterogeneity. Multiple peaks point to the existence of multiple stable and metastable states, which correspond to dynamical states of partially zipped and unzipped conformations and transitions between them. We quantify such transitions by looking at the time evolution of the fraction of bound base pairs. We obtain phase diagrams in the force amplitude-temperature plane both in the resonance frequency of the primary peak and the output signal at the peak value. We further obtain an excellent scaling behavior of the output signal for changing lengths of the DNA. Resonance behavior is also affected by chain heterogeneity as it depends strongly on which base pair the periodic forcing is applied.

Driven translocation of a semiflexible polymer through a conical channel in the presence of attractive surface interactions.

We study the translocation of a semiflexible polymer through a conical channel with attractive surface interactions and a driving force which varies spatially inside the channel. Using the results of the translocation dynamics of a flexible polymer through an extended channel as control, we first show that the asymmetric shape of the channel gives rise to non-monotonic features in the total translocation time as a function of the apex angle of the channel. The waiting time distributions of individual monomer beads inside the channel show unique features strongly dependent on the driving force and the surface interactions. Polymer stiffness results in longer translocation times for all angles of the channel. Further, non-monotonic features in the translocation time as a function of the channel angle changes substantially as the polymer becomes stiffer, which is reflected in the changing features of the waiting time distributions. We construct a free energy description of the system incorporating entropic and energetic contributions in the low force regime to explain the simulation results.

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

Using Langevin dynamics simulations, we study the hysteresis in unzipping of longer double-stranded DNA chains whose ends are subjected to a time-dependent periodic force with frequency ω and amplitude G keeping the other end fixed. We find that the area of the hysteresis loop, A_{loop}, scales as 1/ω at higher frequencies, whereas it scales as (G-G_{c})^{α}ω^{ß} with exponents α=1 and ß=1.25 in the low-frequency regime. These values are same as the exponents obtained in Monte Carlo simulation studies of a directed self-avoiding walk model of a homopolymer DNA [R. Kapri, Phys. Rev. E 90, 062719 (2014)10.1103/PhysRevE.90.062719], and the block copolymer DNA [R. K. Yadav and R. Kapri, Phys. Rev. E 103, 012413 (2021)2470-004510.1103/PhysRevE.103.012413] on a square lattice, and differs from the values reported earlier using Langevin dynamics simulation studies on a much shorter DNA hairpins.

Unzipping of a double-stranded block copolymer DNA by a periodic force.

Using Monte Carlo simulations, we study the hysteresis in unzipping of a double-stranded block copolymer DNA with -A_{n}B_{n}- repeat units. Here A and B represent two different types of base pairs having two and three bonds, respectively, and 2n represents the number of such base pairs in a unit. The end of the DNA are subjected to a time-dependent periodic force with frequency (ω) and amplitude (g_{0}) keeping the other end fixed. We find that the equilibrium force-temperature phase diagram for the static force is independent of the DNA sequence. For a periodic force case, the results are found to be dependent on the block copolymer DNA sequence and on the base pair type on which the periodic force is acting. We observe hysteresis loops of various shapes and sizes and obtain the scaling of loop area both at low- and high-frequency regimes.

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.

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 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.

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(ß) with exponents α=1 and ß=5/4 at low frequencies. The values of the exponents α and ß are different from the exponents reported earlier based on the hysteresis of small hairpins.

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.

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.

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.

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.