Asymmetric Periodic Potential Research Articles

Towards Nanopore Sequencing: Comparing Experimental Results with Computational Modeling of DNA Interactions with α-Hemolysin

The ability to discriminate current modulations produced by various nucleotides while single stranded DNA is being electrophoretically driven through a biological nanopore offers a simple and inexpensive technique for DNA sequencing. However, to realize the potential of nanopore sequencing, the molecular mechanism of DNA movement through the pore and the interactions of nucleotides with various pore residues have to be well characterized. Here, we applied computational approaches through atomistic Molecular Dynamics (MD) and Grand-Canonical Monte-Carlo/Brownian Dynamics simulations to investigate DNA translocation and interactions with the biological nanopore α-Hemolysin (αHL) and compared results with data obtained from experiments. Equilibrium and non-equilibrium (accounting for an electric field acting on a system) MD simulations of all-atom models of homopolymeric DNA (polydA or polydC) translocating through both wild-type and mutant αHL pores provided results that qualitatively match the contrast in ionic current blockade produced between the bases in experimental studies. Additionally, atomistic Free Energy Simulations with the “swarm-of-trajectories” method provides the first computational insight into the potential energy landscape governing DNA conformational dynamics within the pore, which agree with experiments indicating an asymmetric periodic potential. Finally, a truncated model of the αHL pore, in which the extra-membrane vestibule is removed, has been generated and compared to the full protein. This simple model will allow longer simulation times, providing richer information on the dynamics of DNA translocation as well as a more accurate evaluation of ion conductance. The combined theory/experimental analysis of targeted modifications of different sensing regions within the pore allows the assessment of different factors (e.g. steric, electrostatic and van-der-Waals contributions to binding) governing specificity of pore-nucleotide interactions. The development of such in silico models will enable prediction of residues for site-directed mutagenesis yielding ideal pore properties for sequencing.

Brownian motors and stochastic resonance

We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.

Brownian motion in a complex asymmetric periodic potential under colored-noise action

Brownian motion in a complex asymmetric periodic potential under colored-noise action

Random Long-Range Interaction Induced Synchronization in Coupled Networks of Inertial Ratchets

We investigate how the random long-range interactions affect the synchronization features in networks of inertial ratchets, where each ratchet is driven by a periodic time-dependent external force, under the influence of an asymmetric periodic potential. It is found that for a given coupling strength C, the synchronization of the coupled ratchets is induced as the fraction of random long-range interactions p increases and the ratchet networks reach full synchronization for a larger p. It is also found that the system reaches synchronization more effectively for a stronger coupling strength.

Directed transport driven by correlated two-state noises

The transport of overdamped Brownian particles in an asymmetric periodic potential was investigated in the presence of temporally asymmetric correlated two-state noise and a load. It was found that the interplay between temporal asymmetry and spatial asymmetry can bring about some peculiar phenomena. A reversal of the current will occur when the parameters are suitably chosen. A value of the potential height exists at which the current takes its maximal value. For very large values of the correlated time, the variation of the current is independent of the correlated time. Remarkably, we also observed that the correlated time cannot affect the value of the load at which the current reverses its direction.

Sorting of Brownian rods by the use of an asymmetric potential

We present here a method for sorting nanometer scale brownian rods by using a switching asymmetric periodic potential. A two stage sorting process is used to isolate particles with specific dimensions, with acceptable sorting times as well as realizable potential barrier lengths. The method was tested using computer simulations. The ability to sort the nanometer scale anisotropic particles, such as gold nanorods, portends important applications in large scale data recording, photothermal surgery, and bioimaging.

Spatially chaotic distribution of atoms in Bose-Einstein condensate systems

In this paper, we study the spatially chaotic distribution of atoms in a Bose-Einstein condensate system, trapped in an asymmetric periodic potential. For a constant phase of condensate, without atom currents in the system, the space distributed structure of condensated atoms can be described by an undamped Duffing equation with double drivers. Through theoretical analyses, the Mel'nikov chaotic criterion for the system with a repulsive interatomic interaction is presented. Numerical simulations show that an increasing chemical potential can exert considerable suppression on the chaotic distribution of condensated atoms and even completely eliminate chaos. For a system with an attractive interatomic interaction, under some specific parametric conditions, adjusting the ratio between optical lattice potential amplitudes will force the condensated atoms from a periodic state into a spatially chaotic distribution; with the increase of chemical potential, the spatially chaotic distribution is completely suppressed.

Transport of overdamped Brownian particles driven by ac forces and time-delayed feedback

Transport of the overdamped Brownian particles in an asymmetric periodic potential is investigated in the presence of ac driving forces and time-delayed feedback. Using Brownian dynamics simulations, we obtain the average velocity of the particles. We found that it is possible to enhance the average velocity remarkably through increasing the delay time. For a large value of the delay time, the average velocity becomes independent of the delay time. Especially, for small values of noise intensity, there exists a threshold value of noise intensity below which no directed transport can be obtained. We can also observe current reversals by changing the parameters.

Deterministic inhomogeneous inertia ratchets

We study the deterministic dynamics of a periodically driven particle in the underdamped case in a spatially symmetric periodic potential. The system is subjected to a space-dependent friction coefficient, which is similarly periodic as the potential but with a phase difference. We observe that frictional inhomogeneity in a symmetric periodic potential mimics most of the qualitative features of deterministic dynamics in a homogeneous system with an asymmetric periodic potential. We point out the need of averaging over the initial phase of the external drive at small frictional inhomogeneity parameter values or analogously low potential asymmetry regimes in obtaining ratchet current. We also show that at low amplitudes of the drive, where ratchet current is not possible in the deterministic case, noise plays a significant role in realizing ratchet current.

OPTIMAL DIRECTED CURRENT OF A BROWNIAN MOTOR UNDER A NON-GAUSSIAN NOISE GENERATED BY A MULTIPLICATIVE PROCESS

Unidirectional motion is achieved when a particle, moving under the influence of an underlying noise source, is subjected to a ratchet asymmetric periodic potential. Here, we investigate how deviations from the Gaussian nature of the noise distribution function impacts the average particle's current. The input noise is considered to be produced by a Langevin process including both multiplicative and additive random noise sources. The resulting input random signal has a power-law amplitude distribution and a finite correlation time. These features are controlled by the average of the multiplicative noise. We show that the average particle's velocity depends non-monotonically on the degree of non-Gaussianity of the input noise. It exhibits a maximum at an intermediate value of the effective power-law exponent that characterizes the asymptotic decay of the noise probability distribution function.

A model for processive movement of single-headed myosin-IX

It is puzzling that in spite of its single-headed structure, myosin-IX can move processively along actin. Here, based on the experimental evidence that the strong binding of myosin to actin in rigor state induces structural changes to several local actin monomers, a Brownian ratchet model is proposed to describe this processive movement. In the model, the actin plays an active role in the motility of single-headed myosin, in contrast to the common belief that the actin acts only as a passive track for the motility of the myosin. The unidirectional movement is due to both the asymmetric periodic potential of the myosin interacting with actin and the forward Stokes force induced by the relative rotation of the neck domain to the motor domain, while the processivity is determined by the binding affinity of the myosin for actin in ATP state. This gives a good explanation to the high processivity of myosin-IX, which results from its high binding affinity for actin in ATP state due to the presence of unique loop 2 insertion or N-terminal extension. The experimental results on the motility of myosin-IX such as the step size, large forward/backward stepping ratio, run length, stall force, etc, are explained well.

Phase synchronization for two Brownian motors with bistable coupling on a ratchet

We study phase synchronization for a walker on a ratchet potential. The walker consist of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the deterministic and the stochastic dynamics of the center of mass of the walker in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of external periodic forcing. This oscillator has an intrinsic frequency that can be entrained with the frequency of the external driving. We introduced a linear phase through a set of discrete time events and the associated average frequency, and show that this frequency can be synchronized with the frequency of the external driving. In this way, we can properly characterize the phenomenon of synchronization through Arnold tongues and show that the local maxima in the average velocity of the center of mass of the walker, both in the deterministic case and in the presence of noise, correspond to the borders of these Arnold tongues. In this way, we established a connection between optimal transport in ratchets and the phenomenon of phase synchronization.

Directed transport driven by Lévy flights coexisting with subdiffusion

Transport of the Brownian particles driven by Lévy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination techniques, we obtain the group velocity which can measure the transport. It is found that the group velocity increases monotonically with the subdiffusive index and there exists an optimal value of the Lévy index at which the group velocity takes its maximal value. There is a threshold value of the subdiffusive index below which the ratchet effects will disappear. The nonthermal character of the Lévy flights and the asymmetry of the potential are necessary to obtain the directed transport. Some peculiar phenomena induced by the competition between Lévy flights and subdiffusion are also observed. The pseudonormal diffusion will appear on the level of the median.

Current reversal and mass separation of inertial Brownian motors in a two-noise ratchet

Transport of an inertial Brownian motor moving in an asymmetric periodic potential driven by an external force and correlated noises is investigated. Using the numerical algorithm, the asymptotic mean velocity (AMV) for characterizing directed transport is obtained. The effects of the external driving force f and the correlation λ between the two noises on the AMV are discussed. The results manifest: (1) the external driving force and the correlation between the two noises can lead to the phenomena like current reversal. (2) The competitions among the external driving force and the correlation between the two noises are necessary for current reversal, i.e., f λ > 0 . (3) Different directions of transport are found for different masses of the Brownian particles under the condition f λ > 0 . Therefore a theoretical study is suggested for separating Brownian particles according to their different masses in the ratchet system.

Charge ratchet from spin flip: Space-time symmetry paradox

Traditionally the charge ratchet effect is considered as a consequence of either the spatial symmetry breaking engineered by asymmetric periodic potentials, or time asymmetry of the driving fields. Here we demonstrate that electrically and magnetically driven quantum dissipative systems with spin-orbit interactions represent an exception from this standard idea. In contrast to the so far well established belief, a charge ratchet effect appears when both the periodic potential and driving are symmetric. We show that the source of this paradoxical charge ratchet mechanism is the coexistence of quantum dissipation with the spin-flip processes induced by spin-orbit interactions.

Directional motion, current reversal and mass separation in an asymmetrical periodicpotential

Fluctuation-induced transport in an asymmetric periodic potential driven by a staticbias and correlated noises is investigated for the overdamped and underdampedcases. Using both theoretical predictions and numerical simulations, we study thesteady current of an overdamped Brownian particle moving in the potential. It isshown that an asymmetric periodic potential driven by a static bias and thecorrelated noises is simultaneously able to exhibit directional transport and currentreversal. For the underdamped case, we examine the dynamics at various inertialstrengths by means of direct simulations of the stochastic differential equations. Weespecially focus on the influence of inertial terms in the particle dynamics for thenoise-induced, directed current. It is found that the inertial ratchet possesses currentreversals as a function of the mass of the particle; thus an efficient scheme forseparating different species of particles according to their different masses is suggested.

Current inversion in an asymmetric periodic potential driven by cross-correlated white noise sources

With both theoretical approximation and numerical simulations, we study steady current of a Brownian particle moving in an asymmetric periodic potential driven by cross-correlation between multiplicative and additive noises. The effects of the asymmetric parameter of the potential, the multiplicative noise intensity, the additive noise intensity and the correlated strength between multiplicative and additive noises are discussed. We find current reversal with respect to a variation of the asymmetric parameter or the correlated strength. It is also shown that the direction of the steady current is controlled by multiplicative or additive noise intensity, but they are not sufficient conditions for current reversal.

Rocking ratchets in nanostructured superconducting–magnetic hybrids

Two rectification mechanisms in vortex lattice dynamics in Nb films have been studied.These two effects are based on ratchet effects, that is, an ac driving force inducesa net dc vortex flow. In our case, an input ac current applied to the Nb films,grown on top of arrays of Ni nanotriangles, yields an output dc voltage. These tworectification effects occur when the vortex lattice moves in periodic asymmetricpotentials. These pinning potentials are induced by the array of Ni triangles. In oneconfiguration (longitudinal effect) the driven force is applied perpendicular to the trianglereflection symmetry axis; in the second one (transverse effect) the input current isinjected parallel to the triangle reflection symmetry axis. In the framework ofthe rocking ratchet mechanism, the appropriate Langevin equation allows us tomodel the experimental data, taking into account the vortex–vortex interaction.

Interplay between quantum dissipation and an in-plane magnetic field in the spin ratchet effect

We investigate the existence of the pure spin ratchet effect in a dissipative quasi-one-dimensional system with Rashba spin-orbit interaction. The system is additionally placed into a transverse uniform stationary in-plane magnetic field. It is shown that the effect exists at low temperatures and pure spin currents can be generated by applying an unbiased ac driving to the system. An analytical expression for the ratchet spin current is derived. From this expression it follows that the spin ratchet effect appears as a result of the simultaneous presence of the spin-orbit interaction, coupling between the orbital degrees of freedom and spatial asymmetry. In this paper we consider the case of a broken spatial symmetry by virtue of asymmetric periodic potentials. It turns out that an external magnetic field does not have any impact on the existence of the spin ratchet effect but it influences its efficiency, enhancing or reducing the magnitude of the spin current.

Processivity of single-headed kinesin motors

The processive movement of single-headed kinesins is studied by using a ratchet model of non-Markov process, which is built on the experimental evidence that the strong binding of kinesin to microtubule in rigor state induces a large apparent change in the local microtubule conformation. In the model, the microtubule plays a crucial active role in the kinesin movement, in contrast to the previous belief that the microtubule only acts as a passive track for the kinesin motility. The unidirectional movement of single-headed kinesin is resulted from the asymmetric periodic potential between kinesin and microtubule while its processivity is determined by its binding affinity for microtubule in the weak ADP state. Using the model, various experimental results for monomeric kinesin KIF1A, such as the mean step size, the step-size distribution, the long run length and the mean velocity versus load, can be well explained quantitatively. This local conformational change of the microtubule may also play important roles in the processive movement of conventional two-headed kinesins. An experiment to verify the model is suggested.