Ratchet rectification effect on the translocation of a flexible polyelectrolyte chain

Optimizing Work Extraction in the Presence of an Entropic Potential: An Entropic Stochastic Resonance

We study the nontrivial thermodynamic responses of an overdamped Brownian system driven by an unbiased driving force when the particle is confined inside a bilobal irregular structure. The spatial irregularity of the confinement results in an effective entropic bistable potential along the direction of transport. We calculate the thermodynamic response functions in terms of the averaged work done and the absorbed heat over a cycle of driving. We find that the thermodynamic responses are influenced by the nonlinearity of the effective entropic potential, the frequency of the external periodic driving force, and the random thermal fluctuations in a nontrivial way. In the presence of an optimal amount of thermal noise and a favoring driving frequency, the process exhibits a resonance-like precedent in terms of both output work and absorbed heat. We explore the conditions to get best synchronized work extraction (or absorbed heat), which can be utilized as a potential quantifier of an entropic stochastic resonance phenomenon. Finally, we identify a hallmark of entropy dominance over an analogous energy-driven scenario in terms of output work.

Nonmonotonous Translocation Time of Polymers across Pores

Polymers confined in corrugated channels, i.e., channels of varying amplitude, display multiple local maxima and minima of the diffusion coefficient upon increasing their degree of polymerization N. We propose a theoretical effective free energy for linear polymers based on a Fick-Jacobs approach. We validate the predictions against numerical data, obtaining quantitative agreement for the effective free energy, the diffusion coefficient, and the mean first passage time. Finally, we employ the effective free energy to compute the polymer lengths N_{min} at which the diffusion coefficient presents a minimum: we find a scaling expression that we rationalize with a blob model. Our results could be useful to design porous adsorbers, that separate polymers of different sizes without the action of an external flow.

Geometric Brownian information engine: Essentials for the best performance

We investigate a geometric Brownian information engine (GBIE) in the presence of an error-free feedback controller that transforms the information gathered on the state of Brownian particles entrapped in monolobal geometric confinement into extractable work. Outcomes of the information engine depend on the reference measurement distance x_{m}, the feedback site x_{f}, and the transverse force G. We determine the benchmarks for utilizing the available information in an output work and the optimum operating requisites for best achievable work. Transverse bias force (G) tunes the entropic contribution in the effective potential and hence the standard deviation (σ) of the equilibrium marginal probability distribution. We recognize that the amount of extractable work reaches a global maximum when x_{f}=2x_{m} with x_{m}∼0.6σ, irrespective of the extent of the entropic limitation. Because of the higher loss of information during the relaxation process, the best achievable work of a GBIE is lower in an entropic system. The feedback regulation also bears the unidirectional passage of particles. The average displacement increases with growing entropic control and is maximum when x_{m}∼0.81σ. Finally, we explore the efficacy of the information engine, a quantity that regulates the efficiency in utilizing the information acquired. With x_{f}=2x_{m}, the maximum efficacy reduces with increasing entropic control and shows a crossover from 2 to 11/9. We discover that the condition for the best efficacy depends only on the confinement lengthscale along the feedback direction. The broader marginal probability distribution accredits the increased average displacement in a cycle and the lower efficacy in an entropy-dominated system.

Ratcheting Charged Polymers through Symmetric Nanopores Using Pulsed Fields: Designing a Low Pass Filter for Concentrating Polyelectrolytes

We present a new concept for the separation of DNA molecules by contour length that combines a nanofluidic ratchet, nanopore translocation, and pulsed fields. Using Langevin dynamics simulations, we show that it is possible to design pulsed field sequences to ratchet captured semiflexible molecules in such a way that only short chains successfully translocate, effectively transforming the nanopore process into a low pass molecular filter. We also show that asymmetric pulses can significantly enhance the device efficiency. The process itself can be performed with many pores in parallel, and it should be possible to integrate it directly into nanopore sequencing devices, increasing its potential utility.

Experimental study of a nanoscale translocation ratchet

Despite an extensive theoretical and numerical background, the translocation ratchet mechanism, which is fundamental for the transmembrane transport of biomolecules, has never been experimentally reproduced at the nanoscale. Only the Sec61 and bacterial type IV pilus pores were experimentally shown to exhibit a translocation ratchet mechanism. Here we designed a synthetic translocation ratchet and quantified its efficiency as a nanopump. We measured the translocation frequency of DNA molecules through nanoporous membranes and showed that polycations at the trans side accelerated the translocation in a ratchet-like fashion. We investigated the ratchet efficiency according to geometrical and kinetic parameters and observed the ratchet to be only dependent on the size of the DNA molecule with a power law [Formula: see text]. A threshold length of 3 kbp was observed, below which the ratchet did not operate. We interpreted this threshold in a DNA looping model, which quantitatively explained our results.

First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry

We investigate the first passage properties of a Brownian particle diffusing freely inside a d-dimensional sphere with absorbing spherical surface subject to stochastic resetting. We derive the mean time to absorption (MTA) as functions of resetting rate γ and initial distance r of the particle to the center of the sphere. We find that when r>r_{c} there exists a nonzero optimal resetting rate γ_{opt} at which the MTA is a minimum, where r_{c}=sqrt[d/(d+4)]R and R is the radius of the sphere. As r increases, γ_{opt} exhibits a continuous transition from zero to nonzero at r=r_{c}. Furthermore, we consider that the particle lies between two two-dimensional or three-dimensional concentric spheres with absorbing boundaries, and obtain the domain in which resetting expedites the MTA, which is (R_{1},r_{c_{1}})∪(r_{c_{2}},R_{2}), with R_{1} and R_{2} being the radii of inner and outer spheres, respectively. Interestingly, when R_{1}/R_{2} is less than a critical value, γ_{opt} exhibits a discontinuous transition at r=r_{c_{1}}; otherwise, such a transition is continuous. However, at r=r_{c_{2}} the transition is always continuous.

Absolute negative mobility of active polymer chains in steady laminar flows

We investigate the transport of active polymer chains in steady laminar flows in the presence of thermal noise and an external constant force. In the model, the polymer chain is worm-like and is propelled by active forces along its tangent vectors. Compared with inertial Brownian particles, active polymer chains in steady laminar flows exhibit richer movement patterns due to their specific spatial structures. The simulation results show that the velocity-force relation is strongly dependent on the system parameters such as the chain length, bending rigidity, active force and so on. The polymer chain may move in some preferential movement directions and exhibits absolute negative mobility within appropriate parameter regimes, i.e., the polymer chain can move in a direction opposite to the external constant force. In particular, we can observe giant negative mobility in a broad range of parameter regimes.

Geometric Brownian information engine: Upper bound of the achievable work under feedback control

We design a geometric Brownian information engine by considering overdamped Brownian particles inside a two-dimensional monolobal confinement with irregular width along the transport direction. Under such detention, particles experience an effective entropic potential which has a logarithmic form. We employ a feedback control protocol as an outcome of error-free position measurement. The protocol comprises three stages: measurement, feedback, and relaxation. We reposition the center of the confinement to the measurement distance (x_p) instantaneously when the position of the trapped particle crosses x_p for the first time. Then, the particle is allowed for thermal relaxation. We calculate the extractable work, total information, and unavailable information associated with the feedback control using this equilibrium probability distribution function. We find the exact analytical value of the upper bound of extractable work as (53-2ln2)k_BT. We introduce a constant force G downward to the transverse coordinate (y). A change in G alters the effective potential of the system and tunes the relative dominance of entropic and energetic contributions in it. The upper bound of the achievable work shows a crossover from (53-2ln2)k_BT to 12k_BT when the system changes from an entropy-dominated regime to an energy-dominated one. Compared to an energetic analog, the loss of information during the relaxation process is higher in the entropy-dominated region, which accredits the less value in achievable work. Theoretical predictions are in good agreement with the Langevin dynamics simulation studies.

Effect of particle size oscillations on drift and diffusion along a periodically corrugated channel

We study diffusive transport of a particle in a channel with periodically varying cross-section, occurring when the size of the particle periodically switches between two values. In such a situation, the entropy potential, which accounts for the area accessible for diffusion particle, varies both spatially (along the channel axis) and temporally. This underlies the complex interplay between different timescales of the system and leads to novel dynamic regimes. The most notable observations are: emergence of directed motion (in case of asymmetric channel) and resonant diffusion, both controlled by the switching frequency. Resonantlike behaviors of the drift velocity and the effective diffusion coefficient are shown and discussed. Based on heuristic arguments, an approximate analytical treatment of the transport process is proposed. As a comparison with the results obtained from Brownian dynamics simulations indicates, this approach provides a satisfactory way to handle the problem analytically.

Force-dependent diffusion coefficient of molecular Brownian ratchets

We study the mean velocity and diffusion constant in three related models of molecular Brownian ratchets. Brownian ratchets can be used to describe translocation of biopolymers like DNA through nanopores in cells in the presence of chaperones on the trans side of the pore. Chaperones can bind to the polymer and prevent it from sliding back through the pore. First, we study a simple model that describes the translocation in terms of an asymmetric random walk. It serves as an introductory example but already captures the main features of a Brownian ratchet. We then provide an analytical expression for the diffusion constant in the classical model of a translocation ratchet that was first proposed by Peskin et al. [C. S. Peskin, G. M. Odell, and G. F. Oster, Cellular motions and thermal fluctuations: The Brownian ratchet, Biophys. J. 65, 316 (1993)BIOJAU0006-349510.1016/S0006-3495(93)81035-X]. This model is based on the assumption that the binding and unbinding of the chaperones are much faster than the diffusion of the DNA strand. To remedy this shortcoming, we propose a modified model that is also applicable if the (un)binding rates are finite. We calculate the force-dependent mean velocity and diffusivity for this model and compare the results to the original one. Our analysis shows that for large pulling forces the predictions of both models can differ strongly even if the (un)binding rates are large in comparison to the diffusion timescale but still finite. Furthermore, implications of the thermodynamic uncertainty relation on the efficiency of Brownian ratchets are discussed.

Temperature dependence of the translocation time of polymer through repulsive nanopores

The forced translocation of a polymer chain through repulsive nanopores was studied by using Langevin dynamics simulations. The polymer is in the compact globule state at low temperature and in the random coil state at high temperature. Simulation results show that the mean translocation time 〈τ〉 is highly dependent on the temperature T and the minimal 〈τ〉 is located near the coil-globule transition temperature. Moreover, the scaling behaviors 〈τ〉 ∼ N^α and 〈τ〉 ∼ F^-δ are studied, with N the polymer length and F the driving force inside the nanopore. Universal values α = 1.4 and δ = 0.85 are observed for the polymer in the random coil state. While for the polymer in the compact globule state, α decreases from α = 2 at weak driving to 1.2 at strong driving for short N and δ increases with decreasing T in the low F region, but we find universal exponents α = 1.6 for long N and δ = 0.85 in the large F region. Results show that polymer's conformation plays a much more important role than the diffusion coefficient in controlling the translocation time of the polymer chain.

The concept of entropic rectifier facing experiments

The transport of molecules in confined media is subject to entropic barriers. So theoretically, asymmetry of the confinement length may lead to molecular ratchets with entropy as the only driving force for the biased transport. We address experimentally this question by performing alternative ionic current measurements on electrolytes confined in neutral conical nanopores. In case anions and cations widely differ in size, we show that rectification of ionic current can be obtained that depends on ions size and cycle frequency, consistently with the entropic ratchet mechanism.