Translocation time of periodically forced polymer chains

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.

Polymer translocation: effects of periodically driven confinement

We study the influence of confinement on the dynamics of translocation of a linear polymer chain in a good solvent through a cone-shaped pore. Using the Langevin dynamics simulations, we calculate both the first attempt time and translocation time as a function of the position of the back wall and apex angle α. As the in vivo confining environment is inherently dynamic, we extended the present study to explore the consequences of a periodically driven back wall and apex angles on the translocation dynamics. Our findings reveal that the translocation time initially decreases as the driving frequency increases, but increases after a certain frequency. The frequency at which the translocation time is found to be minimum is referred to as the resonance activation. Analyzing the distribution of translocation times around this frequency renders interesting information about the translocation process. We further explore the translocation dynamics by calculating the residence time of individual monomers, shedding light on the microscopic aspects of the process.

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.

Polymer translocation driven by longitudinal and transversal time-dependent end-pulling forces

In this article, we simulate the translocation of a semiflexible homopolymer through an extended pore, driven by both a constant and a time-dependent end-pulled force, employing a model introduced in previous studies. The time dependence is simplistically modeled as a cosine function, and we distinguish between two scenarios for the driving--longitudinal force and transversal force-depending on the relative orientation of the force, parallel or perpendicular, respectively, with respect to the pore axis. Besides some key differences between the two drivings, the mean translocation times present a large minimum region as a function of the frequency of the force that is typical of the resonant activation effect. The presence of the minimum is independent on the elastic characteristics of the polymeric chains and reveals a linear relation between the optimum mean translocation time and the corresponding period of the driving. The mean translocation times show different scaling exponents with the polymer length for different flexibilities. Lastly, we derive an analytical expression of the mean translocation time for low driving frequency, which clearly agrees with the simulations.

Active translocation of a semiflexible polymer assisted by an ATP-based molecular motor

In this work we study the assisted translocation of a polymer across a membrane nanopore, inside which a molecular motor exerts a force fuelled by the hydrolysis of ATP molecules. In our model the motor switches to its active state for a fixed amount of time, while it waits for an ATP molecule which triggers the motor, during an exponentially distributed time lapse. The polymer is modelled as a beads-springs chain with both excluded volume and bending contributions, and moves in a stochastic three dimensional environment modelled with a Langevin dynamics at a fixed temperature. The resulting dynamics shows a Michaelis-Menten translocation velocity that depends on the chain flexibility. The scaling behavior of the mean translocation time with the polymer length for different bending values is also investigated.

Stochastic resonance during a polymer translocation process

We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

Thermal and inertial resonances in DNA unzipping

Single-molecule experiments combined with alternate forces are able to provide useful information not present in standard constant-force and -velocity pulling protocols. Here, we study the effects of such forces in the DNA mechanical unzipping by using an extension of the Peyrard-Bishop-Dauxois model. By changing the damping regime in the dynamical equations, we obtained two resonant mechanisms in both the mean time and the mean force of unzipping. One is thermally assisted and it is characterized by a matching between the period of the external force and the mean unzipping time of the DNA chain, while the other depends on the inertial properties of the system. Both mechanisms are studied systematically under different opening protocols and different parameters of the system. The main results here presented contribute in characterizing and finding optimized conditions in DNA unzipping experiments.

Active polymer translocation in the three-dimensional domain

In this work we study the translocation process of a polymer through a nanochannel where a time dependent force is acting. Two conceptually different types of driving are used: a deterministic sinusoidal one and a random telegraph noise force. The mean translocation time presents interesting resonant minima as a function of the frequency of the external driving. For the computed sizes, the translocation time scales with the polymer length according to a power law with the same exponent for almost all the frequencies of the two driving forces. The dependence of the translocation time with the polymer rigidity, which accounts for the persistence length of the molecule, shows a different low frequency dependence for the two drivings.

Translocation dynamics of a short polymer driven by an oscillating force

We study the translocation dynamics of a short polymer moving in a noisy environment and driven by an oscillating force. The dynamics is numerically investigated by solving a Langevin equation in a two-dimensional domain. We consider a phenomenological cubic potential with a metastable state to model the polymer-pore interaction and the entropic free energy barrier characterizing the translocation process. The mean first translocation time of the center of inertia of polymers shows a nonmonotonic behavior, with a minimum, as a function of the number of the monomers. The dependence of the mean translocation time on the polymer chain length shows a monotonically increasing behavior for high values of the number of monomers. Moreover, the translocation time shows a minimum as a function of the frequency of the oscillating forcing field for all the polymer lengths investigated. This finding represents the evidence of the resonant activation phenomenon in the dynamics of polymer translocation, whose occurrence is maintained for different values of the noise intensity.

Translocation through environments with time dependent mobility

We consider single particle and polymer translocation where the frictional properties experienced from the environment are changing in time. This work is motivated by the interesting frequency responsive behaviour observed when a polymer is passing through a pore with an oscillating width. In order to explain this better we construct general diffusive and non-diffusive frequency response of the gain in translocation time for a single particle in changing environments and look at some specific variations. For two state confinement, where the particle either has constant drift velocity or is stationary, we find exact expressions for both the diffusive and non-diffusive gain. We then apply this approach to polymer translocation under constant forcing through a pore with a sinusoidally varying width. We find good agreement for small polymers at low frequency oscillation with deviations occurring at longer lengths and higher frequencies. Unlike periodic forcing of a single particle at constant mobility, constant forcing with time dependent mobility is amenable to exact solution through manipulation of the Fokker-Planck equation.

Polymer translocation under time-dependent driving forces: resonant activation induced by attractive polymer-pore interactions

We study the driven translocation of polymers under time-dependent driving forces using N-particle Langevin dynamics simulations. We consider the force to be either sinusoidally oscillating in time or dichotomic noise with exponential correlation time, to mimic both plausible experimental setups and naturally occurring biological conditions. In addition, we consider both the case of purely repulsive polymer-pore interactions and the case with additional attractive polymer-pore interactions, typically occurring inside biological pores. We find that the nature of the interaction fundamentally affects the translocation dynamics. For the non-attractive pore, the translocation time crosses over to a fast translocation regime as the frequency of the driving force decreases. In the attractive pore case, because of a free energy well induced inside the pore, the translocation time can be a minimum at the optimal frequency of the force, the so-called resonant activation. In the latter case, we examine the effect of various physical parameters on the resonant activation, and explain our observations using simple theoretical arguments.

Single-polymer dynamics under constraints: scaling theory and computer experiment

The relaxation, diffusion and translocation dynamics of single linear polymer chains in confinement is briefly reviewed with emphasis on the comparison between theoretical scaling predictions and observations from experiment or, most frequently, from computer simulations. Besides cylindrical, spherical and slit-like constraints, related problems such as the chain dynamics in a random medium and the translocation dynamics through a nanopore are also considered. Another particular kind of confinement is imposed by polymer adsorption on attractive surfaces or selective interfaces--a short overview of single-chain dynamics is also contained in this survey. While both theory and numerical experiments consider predominantly coarse-grained models of self-avoiding linear chain molecules with typically Rouse dynamics, we also note some recent studies which examine the impact of hydrodynamic interactions on polymer dynamics in confinement. In all of the aforementioned cases we focus mainly on the consequences of imposed geometric restrictions on single-chain dynamics and try to check our degree of understanding by assessing the agreement between theoretical predictions and observations.