Collective Transport of Coupled Brownian Motors with Low Randomness

The transport properties of coupled Brownian motors in rocking ratchet are investigated via solving Langevin equation. By means of velocity, diffusion coefficient, and their ratio （Peclet number）, different features from a single particle have been found. In the regime of low-to-moderate D, the average velocity of elastically coupled Brownian motors is larger than that of a single Brownian particles; the Peclet number of elastically coupled Brownian motors is peaked functions of intensity of noise D but the Peclet number of a single Brownian motor decreases monotonously with the increase of a single Brownian motor. The results exhibit an interesting cooperative behavior between coupled particles subjected to a rocking force, which can generate directed transport with low randomness or high transport coherence in symmetrical periodic potential.     

A composite micromotor driven by self-thermophoresis and Brownian rectification

Brownian motors and self-phoretic microswimmers are two typical micromotors, for which thermal fluctuations play different roles. Brownian motors utilize thermal noise to acquire unidirectional motion, while thermal fluctuations randomize the self-propulsion of self-phoretic microswimmers. Here we perform mesoscale simulations to study a composite micromotor composed of a self-thermophoretic Janus particle under a time-modulated external ratchet potential. The composite motor exhibits a unidirectional transport, whose direction can be reversed by tuning the modulation frequency of the external potential. The maximum transport capability is close to the superposition of the drift speed of the pure Brownian motor and the self-propelling speed of the pure self-thermophoretic particle. Moreover, the hydrodynamic effect influences the orientation of the Janus particle in the ratched potential, hence also the performance of the composite motor. Our work thus provides an enlightening attempt to actively exploit inevitable thermal fluctuations in the implementation of the self-phoretic microswimmers.     

Brownian motors in the low-energy approximation: Classification and properties

We classify Brownian motors based on the expansion of their velocity in terms of the reciprocal friction coefficient. The two main classes of motors (with dichotomic fluctuations in homogeneous force and periodic potential energy) are characterized by different analytical dependences of their mean velocity on the spatial and temporal asymmetry coefficients and by different adiabatic limits. The competition between the spatial and temporal asymmetries gives rise to stopping points. The transition through these points can be achieved by varying the asymmetry coefficients, temperature, and other motor parameters, which can be used, for example, for nanoparticle segregation. The proposed classification separates out a new type of motors based on synchronous fluctuations in symmetric potential and applied homogeneous force. As an example of this type of motors, we consider a near-surface motor whose two-dimensional motion (parallel and perpendicular to the substrate plane) results from fluctuations in external force inclined to the surface.     

分子马达与布朗马达

综述了有关分子马达,主要是肌球蛋白马达和动蛋白马达的实验研究进展情况,并对理论模型,特别是近年来广为流行的布朗马达模型作了介绍和评论。最后展望了这一领域的发展前景及其所面临的挑战性问题。     

Performance characteristics of Brownian motors

Brownian motors are nonequilibrium systems that rectify thermal fluctuations to achieve directed motion, using spatial or temporal asymmetry. We provide a tutorial introduction to this basic concept using the well-known example of a flashing ratchet, discussing the micro- to nanoscopic scale on which such motors can operate. Because of the crucial role of thermal noise, the characterization of the performance of Brownian motors must include their fluctuations, and we review suitable performance measures for motor coherency and efficiency. Specifically, we highlight that it is possible to determine the energy efficiency of Brownian motors by measuring their velocity fluctuations, without detailed knowledge of the motor function and its energy input. Finally, we exemplify these concepts using a model for an artificial single-molecule motor with internal degrees of freedom.     

带反馈的分数阶耦合布朗马达的定向输运

研究具有幂律记忆性的带反馈耦合布朗马达的定向输运现象, 引入分数阶理论, 建立了带反馈的分数阶耦合布朗马达模型, 利用分数阶差分法求得模型数值解并分析了模型参数对合作定向输运性质的影响. 仿真结果表明, 系统的记忆性通过影响带反馈的棘齿势的打开和闭合而影响粒子的定向输运, 即当系统的阶数在较小的范围内, 系统的记忆性会使带反馈的棘齿势的开关频率增加, 从而增大定向流速; 当系统其他参数(势垒高度、噪声强度等)固定时, 输运速度随着阶数的变化出现广义随机共振现象.     

Introduction to the physics of Brownian motors

A detailed introduction to directed transport in Brownian motors occurring in spatially periodic systems far from equilibrium is presented. We elucidate the prominent physical concepts and novel phenomena with a representative dissipative Brownian motor dynamics. Its main ingredient is a thermal noise with time-dependent temperature modulations that drive the system out of thermal equilibrium in a spatially asymmetric (ratchet-) potential. Yet, this asymmetric setup does not exhibit a concomitant obvious bias into one or the other direction of motion. Symmetry conditions for the appearance (or not) of directed current, its reversal upon variation of certain parameters, and various other generic features and applications are discussed. In addition, we provide a systematic classification scheme for Brownian motor models and review historical landmark contributions to the field. Received: 9 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Symmetric linear potential and imperfect Brownian ratchet in molecular motor function

Biomolecular motors are tiny engines that transport materials at the microscopic level within biological cells. In recent years, Elston and Peskin et al have investigated the effect of the elastic properties of the tether that connects the motor to its cargo at the speed of the motor. In this paper we extend their work and present a tether in the form of symmetric linear potential.Our results show that when the driving mechanism is an imperfect Brownian ratchet, the average speed decreases as the stiffness of the tether increases in the limit of large motor diffusion coefficient, which is similar to the results of Elston and Peskin.However, a threshold for the stiffness of the tether connecting the motor to its cargo is found in our model. Only when the tether is stiffer than the threshold can the motor and its cargo function co-operatively, otherwise, the motor and its cargo depart from each other. This result is more realistic than that of the spring model of Elston and Peskin.     

过阻尼布朗棘轮的斯托克斯效率研究

根据随机能量理论解析得到阻尼环境中布朗粒子的概率流和斯托克斯效率,并进一步研究布朗粒子的输运性能.详细讨论了空间的不对称性、外偏置力及外势结构等对棘轮定向输运的影响.研究发现,合适的外偏置力能使棘轮的定向输运达到最强.通过调节外势的不对称性可使棘轮中粒子的运动反向,当选择合适的空间不对称性时布朗粒子的反向输运可获得最强.此外,一定条件下合适的外势高度也能增强棘轮输运,且能使粒子克服黏滞阻力的斯托克斯效率达到最大.所得结论能够启发实验上设计合适的外势及外偏置来优化布朗棘轮的定向输运性能,并为生物纳米器件的研制提供一定的理论参考.     

The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor

Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.     

Double-temperature ratchet model and current reversal of coupled Brownian motors

On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we propose a double-temperature ratchet model of coupled motors to reveal the dynamical mechanism of cooperative transport of motors with two heads, where the interactions and asynchrony between two motor heads are taken into account. We investigate the collective unidirectional transport of coupled system and find that the direction of motion can be reversed under certain conditions. Reverse motion can be achieved by modulating the coupling strength, coupling free length, and asymmetric coefficient of the periodic potential, which is understood in terms of the effective potential theory. The dependence of the directed current on various parameters is studied systematically. Directed transport of coupled Brownian motors can be manipulated and optimized by adjusting the pulsation period or the phase shift of the pulsation temperature.     

Stochastic mechano-chemical kinetics of molecular motors: A multidisciplinary enterprise from a physicist’s perspective

A molecular motor is made of either a single macromolecule or a macromolecular complex. Just like their macroscopic counterparts, molecular motors “transduce” input energy into mechanical work. All the nano-motors considered here operate under isothermal conditions far from equilibrium. Moreover, one of the possible mechanisms of energy transduction, called Brownian ratchet, does not even have any macroscopic counterpart. But, molecular motor is not synonymous with Brownian ratchet; a large number of molecular motors execute a noisy power stroke, rather than operating as Brownian ratchet. We review not only the structural design and stochastic kinetics of individual single motors, but also their coordination, cooperation and competition as well as the assembly of multi-module motors in various intracellular kinetic processes. Although all the motors considered here execute mechanical movements, efficiency and power output are not necessarily good measures of performance of some motors. Among the intracellular nano-motors, we consider the porters, sliders and rowers, pistons and hooks, exporters, importers, packers and movers as well as those that also synthesize, manipulate and degrade “macromolecules of life”. We review mostly the quantitative models for the kinetics of these motors. We also describe several of those motor-driven intracellular stochastic processes for which quantitative models are yet to be developed. In part I, we discuss mainly the methodology and the generic models of various important classes of molecular motors. In part II, we review many specific examples emphasizing the unity of the basic mechanisms as well as diversity of operations arising from the differences in their detailed structure and kinetics. Multi-disciplinary research is presented here from the perspective of physicists.     

Demonstration of a controllable three-dimensional Brownian motor in symmetric potentials

We demonstrate a Brownian motor, based on cold atoms in optical lattices, where isotropic random fluctuations are rectified in order to induce controlled atomic motion in arbitrary directions. In contrast to earlier demonstrations of ratchet effects, our Brownian motor operates in potentials that are spatially and temporally symmetric, but where spatiotemporal symmetry is broken by a phase shift between the potentials and asymmetric transfer rates between them. The Brownian motor is demonstrated in three dimensions and the noise-induced drift is controllable in our system.     

A simplified tether model for molecular motor transporting cargo

Molecular motors are proteins or protein complexes which function as transporting engines in biological cells. This paper models the tether between motor and its cargo as a symmetric linear potential. Different from Elston and Peskin's work for which performance of the system was discussed only in some limiting cases, this study produces analytic solutions of the problem for general cases by simplifying the transport system into two physical states, which makes it possible to discuss the dynamics of the motor--cargo system in detail. It turns out that the tether strength between motor and cargo should be greater than a threshold or the motor will fail to transport the cargo, which was not discussed by former researchers yet. Value of the threshold depends on the diffusion coefficients of cargo and motor and also on the strength of the Brownian ratchets dragging the system. The threshold approaches a finite constant when the strength of the ratchet tends to infinity.     

反馈脉冲棘轮的能量转化效率研究

研究了反馈脉冲棘轮的定向输运及能量转化效率.详细讨论了弹簧自由长度、耦合强度及脉冲相位等参量对耦合布朗粒子定向输运性能的影响.研究发现,一定自由长度和耦合强度都能促进反馈脉冲棘轮的定向输运,并能使耦合粒子拖动负载做功时的能量转化效率达到最大.此外,通过调节脉冲相位能使反馈棘轮在一个演化周期内获得两次流反转,且合适的相位还能增强反馈棘轮的定向输运.所得结论不仅可为实验上设计合适的反馈脉冲作用来优化棘轮的定向输运性能,而且还能为生物医疗上药物的精准投放提供一定的理论参考.     

Ratchet patterns sort molecular shuttles

Molecular shuttles based on microtubules propelled by motor proteins can be guided on surfaces by adsorbing motors in chemical patterns or by using open guiding channels. While chemical patterns can guide microtubules based on a Brownian ratchet mechanism, the rigidity of the microtubules limits guiding to features with dimensions on the order of their persistence length (5 mm). To achieve guiding on micron-scale dimensions, physical barriers are required which can exploit the forces exerted by multiple motors to bend tubules into tight radii of curvature. Microtubule guiding is illustrated for the case of a special ratchet pattern that is capable of sorting microtubules on the basis of the direction of their motion. Received: 3 December 2001 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Anomalous transport and diffusion phenomena induced by biharmonic forces in deformable potential systems

We study transport properties of an inertial Brownian motor which moves in a deformable Remoissenet-Peyrad periodic potential and is subjected to both a static bias force and time periodic driving biharmonic force. By modifying the shape of the potential, the anomalous transport is identified for a particular set of the system parameters. For a particular potential shape, the mean velocity of a particle is modified by going from negative to positive values according to the external bias force. These features also depend on both the biharmonic parameter and the phase-lag of two signals. A remarkable transition of the negative velocity depending on the shape of the potential is observed. We also focus on the efficiency of the motor and discuss velocity fluctuation. In addition, within selected system parameters, different types of diffusion particle such as subdiffusion, superdiffusion, normal diffusion, ballistic diffusion, hyperdiffusion and dispersionless transport phenomena are generated in the system.     

Rectifying fluctuations in an optical lattice

We have realized a Brownian motor by using cold atoms in a dissipative optical lattice as a model system. In our experiment the optical potential is spatially symmetric and the time symmetry of the system is broken by applying appropriate zero-mean ac forces. We identify a regime of rectification of forces and a regime of rectification of fluctuations, the latter corresponding to the realization of a Brownian motor.     

System Driven by Correlated Gaussian Noises Related with Disorder

A system driven by correlated Gaussian noises related with disorder is investigated. The Fokker-Planck equation （FPE） for the system is derived. Using the FPE derived, some systems driven by correlated Gaussian noises related with disorder can be investigated for Brownian motors, nonequilibrium transition, resonant activation, stochastic resonance, and so on. We only give one example： i.e., using the FPE derived, we study the resonant activation for a single motor protein model with correlated noises related to disorder. Since the correlated noise related to disorder usually exists with the friction, for the temperature, and so on, our results have generic physical meanings for physics, chemistry, biology and other sciences.