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

Crowding induced switching of polymer translocation by the amalgamation of entropy and osmotic pressure

The translocation of polymers is omnipresent in inherently crowded biological systems. We investigate the dynamics of polymer translocation through a pore in free and crowded environments using Langevin dynamics simulation. We observed a location-dependent translocation rate of monomers showcasing counterintuitive behavior in stark contrast to the bead velocity along the polymer backbone. The free energy calculation of asymmetrically placed polymers indicates a critical number of segments to direct receiver-side translocation. For one-sided crowding, we have identified a critical crowding size revealing a nonzero probability of translocation toward the crowded-side. Moreover, we have observed that shifting the polymer toward the crowded-side compensates for one-sided crowding, yielding an equal probability akin to a crowder-free system. In two-sided crowding, a slight variation in crowder size and packing fraction induces a polymer to switch its translocation direction. These conspicuous yet counter-intuitive phenomena are rationalized by minimalistic theoretical arguments based on osmotic pressure and radial entropic forces.

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.

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.

Antiresonant driven systems for particle manipulation

We report on the onset of antiresonant behavior of mass transport systems driven by time-dependent forces. Antiresonances arise from the coupling of a sufficiently high number of space-time modes of the force. The presence of forces having a wide space-time spectrum, a necessary condition for the formation of an antiresonance, is typical of confined systems with uneven and deformable walls that induce entropic forces dependent on space and time. We have analyzed, in particular, the case of polymer chains confined in a flexible channel and shown how they can be sorted and trapped. The presence of resonance-antiresonance pairs found can be exploited to design protocols able to engineer optimal transport processes and to manipulate the dynamics of nano-objects.

Pulling a folded polymer through a nanopore

We investigate the translocation dynamics of a folded linear polymer which is pulled through a nanopore by an external force. To this end, we generalize the iso-flux tension propagation theory for end-pulled polymer translocation to include the case of two segments of the folded polymer traversing simultaneously trough the pore. Our theory is extensively benchmarked with corresponding molecular dynamics (MD) simulations. The translocation process for a folded polymer can be divided into two main stages. In the first stage, both branches are traversing the pore and their dynamics is coupled. If the branches are not of equal length, there is a second stage where translocation of the shorter branch has been completed. Using the assumption of equal monomer flux of both branches confirmed by MD simulations, we analytically derive the equations of motion for both branches and characterize the translocation dynamics in detail from the average waiting time and its scaling form.

Enhanced polymer capture speed and extended translocation time in pressure-solvation traps

The efficiency of nanopore-based biosequencing techniques requires fast anionic polymer capture by like-charged pores followed by a prolonged translocation process. We show that this condition can be achieved by setting a pressure-solvation trap. Polyvalent cation addition to the KCl solution triggers the like-charge polymer-pore attraction. The attraction speeds-up the pressure-driven polymer capture but also traps the molecule at the pore exit, reducing the polymer capture time and extending the polymer escape time by several orders of magnitude. By direct comparison with translocation experiments [D. P. Hoogerheide et al., ACS Nano 8, 7384 (2014)1936-085110.1021/nn5025829], we characterize as well the electrohydrodynamics of polymers transport in pressure-voltage traps. We derive scaling laws that can accurately reproduce the pressure dependence of the experimentally measured polymer translocation velocity and time. We also find that during polymer capture, the electrostatic barrier on the translocating molecule slows down the liquid flow. This prediction identifies the streaming current measurement as a potential way to probe electrostatic polymer-pore interactions.

Theory of pore-driven and end-pulled polymer translocation dynamics through a nanopore: an overview

We review recent progress on the theory of dynamics of polymer translocation through a nanopore based on the iso-flux tension propagation (IFTP) theory. We investigate both pore-driven translocation of flexible and a semi-flexible polymers, and the end-pulled case of flexible chains by means of the IFTP theory and extensive molecular dynamics (MD) simulations. The validity of the IFTP theory can be quantified by the waiting time distributions of the monomers which reveal the details of the dynamics of the translocation process. The IFTP theory allows a parameter-free description of the translocation process and can be used to derive exact analytic scaling forms in the appropriate limits, including the influence due to the pore friction that appears as a finite-size correction to asymptotic scaling. We show that in the case of pore-driven semi-flexible and end-pulled polymer chains the IFTP theory must be augmented with an explicit trans side friction term for a quantitative description of the translocation process.

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.

Frequency-control of protein translocation across an oscillating nanopore

The translocation of a lipid binding protein (LBP) is studied using a phenomenological coarse-grained computational model that simplifies both chain and pore geometry.

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.

Polymer translocation through nano-pores in vibrating thin membranes

Polymer translocation is a promising strategy for the next-generation DNA sequencing technologies. The use of biological and synthetic nano-pores, however, still suffers from serious drawbacks. In particular, the width of the membrane layer can accommodate several bases at the same time, making difficult accurate sequencing applications. More recently, the use of graphene membranes has paved the way to new sequencing capabilities, with the possibility to measure transverse currents, among other advances. The reduced thickness of these new membranes poses new questions on the effect of deformability and vibrations of the membrane on the translocation process, two features which are not taken into account in the well established theoretical frameworks. Here, we make a first step forward in this direction. We report numerical simulation work on a model system simple enough to allow gathering significant insight on the effect of these features on the average translocation time, with appropriate statistical significance. We have found that the interplay between thermal fluctuations and the deformability properties of the nano-pore play a crucial role in determining the process. We conclude by discussing new directions for further work.

Self-Assembly of a [2]Pseudorotaxane by an Inchworm-Motion Mechanism

The threading of biomolecules through pores or channels in membranes is important to validate the physiological activities of cells. To aid understanding of the controlling factors required for the translocation in space with confined size and distorted conformation, it is desirable to identify experimental systems with minimized complexity. We demonstrate the mechanism of a linear guest L1 threading into a tris(crown ether) host TC with a combinational distorted cavity to form a triply interlocked [2]pseudorotaxane 3in-[L1⊂TC]. An inchworm-motion mechanism is proposed for the process. For the forward-threading steps that lead to the formation of higher-order interlocked species, guest L1 must adopt a bent conformation to find the next crown ether cavity. Two simplified models are applied to investigate the self-assembly dynamic of 3in-[L1⊂TC]. Kinetic NMR spectroscopic and molecular dynamics (MD) studies show that formation of the singly penetrated species is fast, whereas formation of the doubly and triply threaded species is several orders of magnitude slower. During threading the freedom of both the guest L1 and host TC gradually decrease due to their interactions. This results in a significant entropy effect for the threading dynamic, which is also observed for the threading of a biomolecular chain through a channel.

Surface-adsorption-induced polymer translocation through a nanopore: Effects of the adsorption strength and the surface corrugation

The surface corrugation plays an important role in single polymer diffusion on attractive surfaces. However, its effect on dynamics of surface adsorption-induced polymer translocation through a nanopore is not clear. Using three-dimensional Langevin dynamics simulations, we investigate the dynamics of a flexible polymer chain translocation through a nanopore induced by the selective adsorption of translocated segments onto the trans side of the membrane. The translocation probability Ptrans increases monotonically, while the mean translocation time τ has a minimum as a function of the adsorption strength ɛ, which are explained from the perspective of the effective driving force for the translocation. With the surface being smoother, τ as well as the scaling exponent α of τ with the chain length N decreases. Finally, we show that the distributions of the translocation time are non-Gaussian even for strong adsorption at a moderate surface corrugation. A nearly Gaussian distribution of the translocation time is observed only for the smoothest surface we studied.

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.

Ionic current inversion in pressure-driven polymer translocation through nanopores

We predict streaming current inversion with multivalent counterions in hydrodynamically driven polymer translocation events from a correlation-corrected charge transport theory including charge fluctuations around mean-field electrostatics. In the presence of multivalent counterions, electrostatic many-body effects result in the reversal of the DNA charge. The attraction of anions to the charge-inverted DNA molecule reverses the sign of the ionic current through the pore. Our theory allows for a comprehensive understanding of the complex features of the resulting streaming currents. The underlying mechanism is an efficient way to detect DNA charge reversal in pressure-driven translocation experiments with multivalent cations.

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.

Polymer translocation: the first two decades and the recent diversification

Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.

Controlling polymer translocation and ion transport via charge correlations

We develop a correlation-corrected transport theory in order to predict ionic and polymer transport properties of membrane nanopores under physical conditions where mean-field electrostatics breaks down. The experimentally observed low KCl conductivity of open α-hemolysin pores is quantitatively explained by the presence of surface polarization effects. Upon the penetration of a DNA molecule into the pore, these polarization forces combined with the electroneutrality of DNA sets a lower boundary for the ionic current, explaining the weak salt dependence of blocked pore conductivities at dilute ion concentrations. The addition of multivalent counterions to the solution results in the reversal of the polymer charge and the direction of the electroosmotic flow. With trivalent spermidine or quadrivalent spermine molecules, the charge inversion is strong enough to stop the translocation of the polymer and to reverse its motion. This mechanism can be used efficiently in translocation experiments in order to improve the accuracy of DNA sequencing by minimizing the translocation velocity of the polymer.

Polymer translocation through a nanopore driven by binding particles: influence of chain rigidity

We investigate the influence of chain rigidity on the dynamics of polymer translocation in the presence of binding particles (BPs) through a nanopore using two-dimensional Langevin dynamics simulations. With increasing chain rigidity κ, the mean translocation time 〈τ〉 increases monotonically due to an increase in the radius of gyration and a decrease in the center of mass velocity. Particularly for weak binding, we further find that 〈τ〉 shows a power-law behavior with the persistence length lp. Analysis indicates a scaling relation between the average velocity of the center of mass of a chain 〈vc.m.〉 and lp. As the chain becomes stiffer, the distribution of the translocation time τ approximates the Gaussian distribution and gets broader with the peak position being shifted towards longer translocation time. The corresponding translocation coordinate smax of the maximum waiting time gets smaller with increasing chain rigidity. Finally, under an extremely low BP concentration, 〈τ〉 shows a minimum for small κ, while it decreases monotonically for large κ with increasing binding energy. Our results suggest a nontrivial effect of the intrinsic property of chains on the dynamics of polymer translocation driven by BPs.

Driven polymer transport through a periodically patterned channel

We study the driven transport of polymers in a periodically patterned channel using Langevin dynamics simulations in two dimensions. The channel walls are patterned with periodically alternating patches of attractive and non-attractive particles that act as trapping sites for the polymer. We find that the system shows rich dynamical behavior, observing giant diffusion, negative differential mobility, and several different transition mechanisms between the attractive patches. We also show that the channel can act as an efficient high-pass filter for polymers longer than a threshold length Nthr, which can be tuned by adjusting the length of the attractive patches and the driving force. Our findings suggest the possibility of fabricating polymer filtration devices based on patterned nanochannels.

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.

Translocation of a polymer through a nanopore modulated by a sticky site

Using a one-dimensional model for the translocation of a polymer through a nanopore, the effect of a "sticky site" at which the polymer binds to the pore is explored via exact numerical techniques. Results for the mean translocation time and the probability of translocation on the insertion of the first monomer in the pore are generated across a wide range of driving forces and binding potential strengths (well depths). The balance between the driving force, diffusion, and well depth yields a rich set of dynamics that depend strongly on where the sticky site is located along the polymer. For example, when the sticky site is located near the head of the polymer, the translocation time is found to be a maximum at an intermediate driving force with events at lower driving forces taking less time. Additionally, the critical well depth at which the sticky site dominates the dynamics, is found to be a non-monotonic function of the driving force when the sticky site is located at the head or tail of the polymer, but not in the middle. Modeling of the process yields good agreement with simulation results.

Influence of non-universal effects on dynamical scaling in driven polymer translocation

We study the dynamics of driven polymer translocation using both molecular dynamics (MD) simulations and a theoretical model based on the non-equilibrium tension propagation on the cis side subchain. We present theoretical and numerical evidence that the non-universal behavior observed in experiments and simulations are due to finite chain length effects that persist well beyond the relevant experimental and simulation regimes. In particular, we consider the influence of the pore-polymer interactions and show that they give a major contribution to the non-universal effects. In addition, we present comparisons between the theory and MD simulations for several quantities, showing extremely good agreement in the relevant parameter regimes. Finally, we discuss the potential limitations of the present theories.