Translocation through environments with time dependent mobility

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.

Translocation Dynamics of an Active Filament through a Long-Length Scale Channel

Active filament translocation through a confined space is crucial for diverse biological processes. By using Langevin dynamics simulations, we investigate the translocation dynamics of an axially self-propelled chain through a channel. First, results show a suggestive reciprocal scaling of translocation time versus active force. Second, in the case of a long channel, we demonstrate a very intriguing nonmonotonic change of translocation time with increasing channel width. The driving force shows a similar trend, providing a consistent picture to understand the unexpected channel width effect. In particular, in a moderately broad channel, the disordered chain conformation results in a loss of driving force and thus inhibits translocation dynamics. Chain adsorption might occur in a wide channel, which accounts for a facilitated translocation. Lastly, we connect the translocation process to tension propagation (TP). A modified TP picture is proposed to interpret the waiting time distribution. Our work highlights the new phenomenology owing to the crucial interplay of activity and spacial confinement, which drives the translocation dynamics, going beyond the traditional entropic barrier scenario.

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.

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.

Pore shapes effects on polymer translocation

We translocated polymers through pores of different shapes and interaction patterns in three dimensions by Langevin molecular dynamics. There were four simple cylindrical pores of the same length but with different diameters. The results showed that even though decreasing the pore diameter would always decrease the translocation velocity, it was strongly dependent on the shape of the increased pore diameter. Although increasing the pore diameter made the translocation faster in simple cylindrical pores, it was complicated in different pore shapes, e.g. increasing the diameter in the middle decreased the translocation velocity. Investigating polymer shapes through the translocation process and comparing the shapes by the cumulative waiting time for different pore structures reveals the non-equilibrium properties of translocation. Moreover, polymer shape parameters such as gyration radius, polymer center of mass, and average aspect ratio help us to distinguish different pore shapes and/or different polymers.

Simulation study on the migration of diblock copolymers in periodically patterned slits

The forced migration of diblock copolymers (A_NAB_NB) in periodically patterned slits was investigated by using Langevin dynamics simulation. The lower surface of the slit consists of stripe α and stripe β distributed in alternating sequence, while the upper one is formed only by stripe β. The interaction between block A and stripe α is strongly attractive, while all other interactions are purely repulsive. Simulation results show that the migration of the diblock copolymer is remarkably dependent on the driving force and there is a transition region at moderate driving force. The transition driving force f_t, where the transition region occurs, decreases monotonously with increasing length of block B (N_B) but is independent of the polymer length and the periodic length of the slit, which is interpreted from the free energy landscape of diblock copolymer migration. The results also show that periodic slits could be used to separate diblock polymers with different N_B by tuning the external driving force.

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.

Entropy production and rectification efficiency in colloid transport along a pulsating channel

We study the current rectification of particles moving in a pulsating channel under the influence of an applied force. We have shown the existence of different rectification scenarios in which entropic and energetic effects compete. The effect can be quantified by means of a rectification coefficient that is analyzed in terms of the force, the frequency and the diffusion coefficient. The energetic cost of the motion of the particles expressed in terms of the entropy production depends on the importance of the entropic contribution to the total force. Rectification is more important at low values of the applied force when entropic effects become dominant. In this regime, the entropy production is not invariant under reversal of the applied force. The phenomenon observed could be used to optimize transport in microfluidic devices or in biological channels.

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.

Current fluctuations across a nano-pore

The frequency-dependent spectrum of current fluctuations through nano-scale channels is studied using analytical and computational techniques. Using a stochastic Nernst-Planck description and neglecting the interactions between the ions inside the channel, an expression is derived for the current fluctuations, assuming that the geometry of the channel can be incorporated through the lower limits for various wave-vector modes. Since the resulting expression turns out to be quite complex, a number of further approximations are discussed such that relatively simple expressions can be used for practical purposes. The analytical results are validated using Langevin dynamics 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.

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.

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.

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.