Single-polymer Brownian motor: a simulation study

Memory effects in spiral diffusion of rotary self-propellers

The coupling of deterministic rotary motion and stochastic orientational diffusion of a self-propeller leads to a spiral trajectory of the expected displacement. We extend our former analysis of spiral diffusion [Phys. Rev. E 94, 030601(R) (2016)10.1103/PhysRevE.94.030601] in the white-noise limit to a more realistic scenario of stochastic noise with Gaussian memory and orientational fluctuations driven by an Ornstein-Uhlenbeck process. A variety of dynamical regimes including crossovers from ballistic to diffusive to ballistic in the angular dynamics are determined by the inertial timescale, orientational diffusivity, and angular speed.

Transport of coupled particles in rough ratchet driven by Lévy noise

This paper studies the transport of coupled particles in a tilted rough ratchet potential. The relationship between particles transport and roughness, noise intensity, external force, coupling strength, and free length is explored numerically by calculating the average velocity of coupled particles. Related investigations have found that rough potential can accelerate the process of crossing the barrier by increasing the particles velocity compared with smooth potential. It is based on the fact that the roughness on the potential surface is like a "ladder," which helps particles climb up and blocks them from sliding down. Moreover, superimposing an appropriate external force on the coupled particles or strengthening the Lévy noise leads to the particles velocity to increase. It is worth emphasizing that when the external force is selected properly, an optimal roughness can be found to maximize the particles velocity. For a given roughness, an optimal coupling coefficient is discovered to match the maximum velocity. And once the coupling coefficient is greater than the optimal value, the particles velocity drops sharply to zero. Furthermore, our results also indicate that choosing an appropriate free length between particles can also speed up transport.

Polymer-Based Accurate Positioning: An Exact Worm-like-Chain Study

Precise positioning of molecular objects from one location to another is important for nanomanipulation and is also involved in molecular motors. Here, we study single-polymer-based positioning on the basis of the exact solution to the realistic three-dimensional worm-like-chain (WLC) model. The results suggest the possibility of a surprisingly accurate flyfishing-like positioning in which tilting one end of a flexible short polymer enables positioning of the other diffusing end to a distant location within an error of ∼1 nm. This offers a new mechanism for designing molecular positioning devices. The flyfishing effect (and reverse process) likely plays a role in biological molecular motors and may be used to improve speed of artificial counterparts. To facilitate these applications, a new force-extension formula is obtained from the exact WLC solution. This formula has an improved accuracy over the widely used Marko-Siggia formula for stretched polymers and is valid for compressed polymers too. The new formula is useful in analysis of single-molecule stretching experiments and in estimating intramolecular forces of molecular motors, especially those involving both stretched and compressed polymer components.

Inchworm bipedal nanowalker

Nanowalkers take either inchworm (IW) or hand-over-hand (HOH) gait. The IW nanowalkers are advantageous over HOH ones in force generation, processivity and high-density integration, though both gaits occur in intracellular nanowalkers from biology. Artificial IW nanowalkers have been realized or proposed, but all rely on different 'head' and 'tail' to gain an adventitious direction. Here we report an inherently unidirectional IW nanowalker that is a biped with two identical legs (i.e., indistinguishable 'head' and 'tail'). This walker is made of DNA, and driven by a light-powered G-quadruplex engine. The directional inchworm motion is confirmed by operating the walker on a DNA duplex track that is designed to show a distinctive fluorescence pattern for IW walkers as compared to HOH ones. Interestingly, this walker exhibits stride-controlled IW-to-HOH gait switch and direction reversal when the track's periodic binding sites have wider and wider separation. The results altogether present an integrated mechanism for implementing nanowalkers of different gaits and directions on molecular tracks, optical potentials or even solid-state surfaces.

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.

Collective ratchet effects and reversals for active matter particles on quasi-one-dimensional asymmetric substrates

Using computer simulations, we study a two-dimensional system of sterically interacting self-mobile run-and-tumble disk-shaped particles with an underlying periodic quasi-one-dimensional asymmetric substrate, and show that a rich variety of collective active ratchet behaviors arise as a function of particle density, activity, substrate period, and the maximum force exerted by the substrate. The net dc drift, or ratchet transport flux, is nonmonotonic since it increases with increased activity but is diminished by the onset of self-clustering of the active particles. Increasing the particle density decreases the ratchet transport flux for shallow substrates but increases the ratchet transport flux for deep substrates due to collective hopping events. At the highest particle densities, the ratchet motion is destroyed by a self-jamming effect. We show that it is possible to realize reversals of the direction of the net dc drift in the deep substrate limit when multiple rows of active particles can be confined in each substrate minimum, permitting emergent particle-like excitations to appear that experience an inverted effective substrate potential. We map out a phase diagram of the forward and reverse ratchet effects as a function of the particle density, activity, and substrate properties.

Translocation of a granular chain in a horizontally vibrated saw-tooth channel

We study the translocation mechanism of a granular chain in a horizontally vibrated saw-tooth channel using MD simulations and macro-scale experiments and show that the translocation speed is independent of the chain length as long as the chain length is larger than the spatial period of the saw-tooth. With the help of simulation, we explore the effect of geometry of the container and frequency and amplitude of vibration as well as chain flexibility on the chain drift speed. We observe that the most efficient transport is achieved when one of the channel walls is shifted with respect to the other wall by an amount equal to half the spatial period of the saw-tooth. We define a persistence length for the chain and show that the translocation speed depends on the ratio of persistence length over the spatial period of the saw-tooth. The optimum translocation occurs when this ratio is about 0.4. We also determine the optimum saw-tooth angle for the translocation of the chain as well as the optimum distance between the two walls. Some properties of this system are similar to those of polymer systems.

Ratchet rectification effect on the translocation of a flexible polyelectrolyte chain

We report a three dimensional Langevin dynamics simulation of a uniformly charged flexible polyelectrolyte chain, translocating through an asymmetric narrow channel with periodically varying cross sections under the influence of a periodic external electric field. When reflection symmetry of the channel is broken, a rectification effect is observed with a favored direction for the chain translocation. For a given volume of the channel unit and polymer length, the rectification occurs below a threshold frequency of the external periodic driving force. We have also observed that the extent of the rectification varies non-monotonically with increasing molecular weight and the strength of geometric asymmetry of the channel. Observed non-monotonicity of the rectification performance has been interpreted in terms of a competition between two effects arising from the channel asymmetry and change in conformational entropy. An analytical model is presented with predictions consistent with the simulation results.

Self-Propelled Nanomotors Autonomously Seek and Repair Cracks

Biological self-healing involves the autonomous localization of healing agents at the site of damage. Herein, we design and characterize a synthetic repair system where self-propelled nanomotors autonomously seek and localize at microscopic cracks and thus mimic salient features of biological wound healing. We demonstrate that these chemically powered catalytic nanomotors, composed of conductive Au/Pt spherical Janus particles, can autonomously detect and repair microscopic mechanical defects to restore the electrical conductivity of broken electronic pathways. This repair mechanism capitalizes on energetic wells and obstacles formed by surface cracks, which dramatically alter the nanomotor dynamics and trigger their localization at the defects. By developing models for self-propelled Janus nanomotors on a cracked surface, we simulate the systems' dynamics over a range of particle speeds and densities to verify the process by which the nanomotors autonomously localize and accumulate at the cracks. We take advantage of this localization to demonstrate that the nanomotors can form conductive "patches" to repair scratched electrodes and restore the conductive pathway. Such a nanomotor-based repair system represents an important step toward the realization of biomimetic nanosystems that can autonomously sense and respond to environmental changes, a development that potentially can be expanded to a wide range of applications, from self-healing electronics to targeted drug delivery.

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.

Force generation by granular chains moving randomly on periodic ratchet plates

A variation of the Brownian ratchet mechanism for the force generated by the combination of the random motion and the ratchet structure is proposed and simulated with granular chains moving randomly on periodic ratchet plates. The present mechanism differs from the flashing ratchet model of the kinesin-microtubule molecular motor. When the bead chain bounces against the periodic ratchet, the chain as a whole will gain an impulse in the direction of the long side (the side with smaller slope). The observed behaviors of the simulating system, including (i) the force-velocity relation, (ii) the stall force as a function of the number of chains, (iii) the increase of velocity with the excitation, and (iv) the appearance of steps at low velocity and its distribution function, are similar to the corresponding ones of the kinesin-microtubule system.

Currents in defective coupled ratchets

Transport phenomena in a one-dimensional system of interacting particles is studied. This system is embedded in a periodic and left-right asymmetric potential driven by a force periodic in time and space. When the density (number of particles per site) is an integer, directional current of the particles is collective; that is, it involves the whole system since all the sites are equivalents. On the other hand, when the system has a defect, a new localized or noncollective current appears due to the migration of defects from one site to another. We show here how this "defective" (defects generated) current can be controlled by white noise.

Single-layer metal-on-metal islands driven by strong time-dependent forces

Nonlinear transport properties of single-layer metal-on-metal islands driven with strong static and time-dependent forces are studied. We apply a semiempirical lattice model and use master-equation and kinetic Monte Carlo simulation methods to compute observables such as the velocity and the diffusion coefficient. Two types of time-dependent driving are considered: a pulsed rotated field and an alternating field with a zero net force (electrophoretic ratchet). Small islands up to 12 atoms were studied in detail with the master-equation method and larger ones with simulations. Results are presented mainly for a parametrization of Cu on Cu(001) surface, which has been the main system of interest in several previous studies. The main results are that the pulsed field can increase the current in both diagonal and axis direction when compared to static field, and there exists a current inversion in the electrophoretic ratchet. Both of these phenomena are a consequence of the coupling of the internal dynamics of the island with its transport. In addition to the previously discovered "magic size"effect for islands in equilibrium, a strong odd-even effect was found for islands driven far out of equilibrium. Master-equation computations revealed nonmonotonous behavior for the leading relaxation constant and effective Arrhenius parameters. Using cycle optimization methods, typical island transport mechanisms are identified for small islands.

Time-dependent motor properties of multipedal molecular spiders

Molecular spiders are synthetic biomolecular walkers that use the asymmetry resulting from cleavage of their tracks to bias the direction of their stepping motion. Using Monte Carlo simulations that implement the Gillespie algorithm, we investigate the dependence of the biased motion of molecular spiders, along with binding time and processivity, on tunable experimental parameters, such as number of legs, span between the legs, and unbinding rate of a leg from a substrate site. We find that an increase in the number of legs increases the spiders' processivity and binding time but not their mean velocity. However, we can increase the mean velocity of spiders with simultaneous tuning of the span and the unbinding rate of a spider leg from a substrate site. To study the efficiency of molecular spiders, we introduce a time-dependent expression for the thermodynamic efficiency of a molecular motor, allowing us to account for the behavior of spider populations as a function of time. Based on this definition, we find that spiders exhibit transient motor function over time scales of many hours and have a maximum efficiency on the order of 1%, weak compared to other types of molecular motors.

Dynamics of a polymer in a Brownian ratchet

We have used Brownian dynamics simulations to study the dynamics of a bead-and-spring polymer subject to a flashing ratchet potential. To elucidate the role of hydrodynamic (HD) interactions, simulations were carried out for the cases where HD interactions are present and when they are absent. The average speed of the polymer and its conformational properties were examined upon variation in the polymer length, N, and the ratchet spatial period, L. Two distinct dynamical regimes were evident. In the low-N/high-L regime, the velocity decreases with increasing N, and center-of-mass diffusion is a key part of the motional mechanism. By contrast, in the high-N /low-L regime, the velocity is insensitive to variation in N, and motion is achieved via the coupling of internal modes to the cycling of the ratchet potential. The location of the regimes is correlated with the average conformational state of the polymer. Incorporating HD interactions increases the average polymer velocity for all polymer lengths and ratchet spatial periods considered. The dynamical behavior of polymers in the low-N/high-L regime can be understood using simple a theoretical model that yields quantitatively reasonable predictions of the polymer velocity.

Translocation time of periodically forced polymer chains

In this work we study the presence of both a minimum and clear oscillations in the frequency dependence of the translocation time of a polymer described as a unidimensional Rouse chain driven by a spatially localized oscillating linear potential. The observed oscillations of the mean translocation time arise from the synchronization between the very mean translocation time and the period of the external force. We have checked the robustness of the frequency value for the minimum translocation time by changing the damping parameter, finding a very simple relationship between this frequency and the correspondent translocation time. The translocation time as a function of the polymer length has been also evaluated, finding a precise L2 scaling. Furthermore, the role played by the thermal fluctuations described as a gaussian uncorrelated noise has been also investigated, and the analogies with the resonant activation phenomenon are commented.

Characteristics of the polymer transport in ratchet systems

Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency, and nonuniform charge distributions. We also use currents in the nonequilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state (e.g., total and head-to-head lengths) of the polymers. Several numerical methods are used to solve the master equations and nonlinear optimization problems. The dominating transport mechanisms are found via graph optimization methods. The results show that small changes in the molecule structure and the environment variables can lead to large increases of the drift. The drift and the coherence can be amplified by using deterministic flashing potentials and customized polymer charge distributions. Identifying the dominating transport mechanism by graph analysis tools is found to give insight in how the molecule is transported by the ratchet effect.

Polymer deformation in Brownian ratchets: theory and molecular dynamics simulations

We examine polymers in the presence of an applied asymmetric sawtooth (ratchet) potential which is periodically switched on and off, using molecular dynamics (MD) simulations with an explicit Lennard-Jones solvent. We show that the distribution of the center of mass for a polymer in a ratchet is relatively wide for potential well depths U0 on the order of several kBT. The application of the ratchet potential also deforms the polymer chains. With increasing U0 the Flory exponent varies from that for a free three-dimensional (3D) chain, nu=35 (U0=0), to that corresponding to a 2D compressed (pancake-shaped) polymer with a value of nu=34 for moderate U0. This has the added effect of decreasing a polymer's diffusion coefficient from its 3D value D3D to that of a pancaked-shaped polymer moving parallel to its minor axis D2D. The result is that a polymer then has a time-dependent diffusion coefficient D(t) during the ratchet off time. We further show that this suggests a different method to operate a ratchet, where the off time of the ratchet, toff, is defined in terms of the relaxation time of the polymer, tauR. We also derive a modified version of the Bader ratchet model [Bader, Proc. Natl. Acad. Sci. U.S.A. 96, 13165 (1999)] which accounts for this deformation and we present a simple expression to describe the time dependent diffusion coefficient D(t). Using this model we then illustrate that polymer deformation can be used to modulate polymer migration in a ratchet potential.

Polymer dynamics in time-dependent periodic potentials

The dynamics of a discrete polymer in time-dependent external potentials is studied with the master equation approach. We consider both stochastic and deterministic switching mechanisms for the potential states and give the essential equations for computing the stationary-state properties of molecules with internal structure in time-dependent periodic potentials on a lattice. As an example, we consider standard and modified Rubinstein-Duke polymers and calculate their mean drift and effective diffusion coefficient in the two-state nonsymmetric flashing potential and symmetric traveling potential. Rich nonlinear behavior of these observables is found. By varying the polymer length, we find current inversions caused by the rebound effect that is only present for molecules with internal structure. These results depend strongly on the polymer type. We also notice increased transport coherence for longer polymers.

Dynamics of a dimer in a symmetric potential: ratchet effect generated by an internal degree of freedom

The one-dimensional dynamics of a dimer consisting of two harmonically coupled components is considered. The mutual distance between the dimer components plays the role of an internal degree of freedom. Both components are in contact with the same heat bath and are coupled to a spatially periodic, symmetric potential, whose amplitude is modulated periodically in time and whose coupling strength is different for the two components. In the absence of any external bias, a ratchet effect (directed transport) arises generically unless the mutual coupling of the dimer components tends to zero or infinity. In other words, the ratchet effect is generated by the internal degree of freedom. An accurate analytical approximation for the dimer's velocity and diffusion coefficient is obtained. The velocity of the system is maximized by adding an optimal amount of noise and by tuning the driving frequency to an optimal value. Furthermore, there exists an optimal coupling strength at which the velocity is the largest.

Synergic mechanism and fabrication target for bipedal nanomotors

Inspired by the discovery of dimeric motor proteins capable of undergoing transportation in living cells, significant efforts have been expended recently to the fabrication of track-walking nanomotors possessing two foot-like components that each can bind or detach from an array of anchorage groups on the track in response to local events of reagent consumption. The central problem in fabricating bipedal nanomotors is how the motor as a whole can gain the synergic capacity of directional track-walking, given the fact that each pedal component alone often is incapable of any directional drift. Implemented bipedal motors to date solve this thermodynamically intricate problem by an intuitive strategy that requires a hetero-pedal motor, multiple anchorage species for the track, and multiple reagent species for motor operation. Here we performed realistic molecular mechanics calculations on molecule-scale models to identify a detailed molecular mechanism by which motor-level directionality arises from a homo-pedal motor along a minimally heterogeneous track. Optimally, the operation may be reduced to a random supply of a single species of reagents to allow the motor's autonomous functioning. The mechanism suggests a distinct class of fabrication targets of drastically reduced system requirements. Intriguingly, a defective form of the mechanism falls into the realm of the well known Brownian motor mechanism, yet distinct features emerge from the normal working of the mechanism.

Self-organized escape of oscillator chains in nonlinear potentials

We present the noise-free escape of a chain of linearly interacting units from a metastable state over a cubic on-site potential barrier. The underlying dynamics is conservative and purely deterministic. The mutual interplay between nonlinearity and harmonic interactions causes an initially uniform lattice state to become unstable, leading to an energy redistribution with strong localization. As a result, a spontaneously emerging localized mode grows into a critical nucleus. By surpassing this transition state, the nonlinear chain manages a self-organized, deterministic barrier crossing. Most strikingly, these noise-free, collective nonlinear escape events proceed generally by far faster than transitions assisted by thermal noise when the ratio between the average energy supplied per unit in the chain and the potential barrier energy assumes small values.

General mechanism for inchworm nanoscale track walkers: Analytical theory and realistic simulation

Nanomotors capable of directed transportation along an unlimited linear track are being vigorously pursued both theoretically and experimentally. This study generalizes a previously proposed mechanism for nanoscale track walkers by explicitly treating key molecular details of the walker-track systems. An energy-diagram analysis identifies pathways of energy flow through the walker's movement cycle, and thereby enables us to develop an analytical theory for the track-walking mechanism. Realistic simulations of the walker's movement cycles are also conducted. The results show that the walker's directionality, run length, and speed depend critically on several key dimensional parameters of the walker-track systems. Most notably, the walker's performance as a function of the binding site interval of the track exhibits an oscillating pattern, which is accurately reproduced by the analytical theory. The wealth of nanocontrol mechanisms identified in the proposed track-walker systems not only provides a framework for optimizing performance of the walker, but also clarifies major requirements for future experimental implementation.

Analytical theory of the nonequilibrium spatial distribution of RNA polymerase translocations

A continuum Fokker-Planck model is considered for the RNA polymerase in the elongation phase, where the topology of a single free energy profile as a function of the translocation variable distinguishes the Brownian ratchet and power stroke mechanisms. The model yields a simple analytical stationary solution for arbitrary functional forms of the free energy. With the translocation potential of mean force estimated by the time-series data of the recent high-resolution single-molecule experiment [Abbondanzieri et al., Nature (London) 438, 460 (2005)], predictions of the model for the mechanical properties agree with experiments quantitatively with reasonable values of parameters. The evolution of the spatial distribution of translocation variable away from equilibrium with increasing nucleoside triphosphate concentration shows qualitatively different behavior in the two alternative scenarios, which could serve as an additional measurable signature of the underlying mechanism.

Mechanical coupling in flashing ratchets

We consider the transport of rigid objects with internal structure in a flashing ratchet potential by investigating the overdamped behavior of a rodlike chain of evenly spaced point particles. In one dimension, analytical arguments show that the velocity can reverse direction multiple times in response to changing the size of the chain or the temperature of the heat bath. The physical reason is that the effective potential experienced by the mechanically coupled objects can have a different symmetry than that of individual objects. All analytical predictions are confirmed by Brownian dynamics simulations. These results may provide a route to simple, coarse-grained models of molecular motor transport that incorporate an object's size and rotational degrees of freedom into the mechanism of transport.