分数阶布朗马达在闪烁棘齿势中的合作输运现象

引入分数阶微积分理论,建立耦合分数阶布朗马达在闪烁棘齿势中的合作输运模型, 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. 发现在具有记忆性的分数阶棘齿系统中, 系统阶数与粒子间耦合强度不仅可影响粒子链输运速度, 还可使粒子链出现与整数阶方向相反的定向流; 在阶数固定下, 定向输运速度将随参数(噪声强度、耦合强度、棘齿势峰值高度)变化出现广义随机共振现象. 关键词： 分数阶布朗马达 闪烁棘齿势 合作定向输运 广义随机共振     

A prototype of a rationally designed chemically powered Brownian motor

The design and development of a molecular system functioning as a prototype of a Brownian motor is presented. The road towards the molecular motor is illustrated with previous attempts preparing other mechanical devices, such as a molecular brake and a molecular ratchet. Thermal and chemical energy are used to achieve unidirectional rotation in the Brownian motor. The similarities of synthetic molecular devices with biological – microscopic – and mechanical – macroscopic – systems and the perils of extrapolating macroscopic principles to the molecular level are also discussed. Received: 15 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Active Brownian motion models and applications to ratchets

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.     

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.     

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.     

Fractional motions

Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.     

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.     

分数阶双头分子马达的欠扩散输运现象

研究具有幂律记忆性的细胞液中双头分子马达的定向输运现象,选取幂函数作为广义Langevin方程的阻尼核函数,建立了分数阶过阻尼耦合Brown马达模型,讨论了阶数及耦合系数对双头分子马达定向输运速度的影响. 仿真结果表明,分数阶过阻尼双头分子马达也会产生定向输运现象,并且在某些阶数下会产生整数阶情形所不具有的反向定向流. 当噪声强度固定时,输运速度随着阶数以及耦合系数的变化均会出现广义随机共振现象. 特别地,研究发现双头分子马达在记忆闪烁棘轮势中具有某些单头分子马达所不具备的运动特性,定向流的大小和方向由噪声与双头间作用力相互耦合控制. 关键词： 分数阶双头分子马达 欠扩散 定向输运 广义随机共振     

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.     

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.     

Controllable 3D atomic Brownian motor in optical lattices

We study a Brownian motor, based on cold atoms in optical lattices, where atomic motion can be induced in a controlled manner in an arbitrary direction, by rectification of isotropic random fluctuations. In contrast with ratchet mechanisms, our Brownian motor operates in a potential that is spatially and temporally symmetric, in apparent contradiction to the Curie principle. Simulations, based on the Fokker-Planck equation, allow us to gain knowledge on the qualitative behaviour of our Brownian motor. Studies of Brownian motors, and in particular ones with unique control properties, are of fundamental interest because of the role they play in protein motors and their potential applications in nanotechnology. In particular, our system opens the way to the study of quantum Brownian motors.     

涨落作用下周期驱动的分数阶过阻尼棘轮模型的混沌输运现象

考虑涨落作用下周期驱动的过阻尼分数阶棘轮模型, 通过模型的数值求解, 研究确定性棘轮的混沌特性与噪声的作用对输运行为的影响, 进而讨论过阻尼分数阶分子马达反向输运的机理. 分析表明: 随着势垒高度、 势不对称性与模型记忆性的变化, 随机棘轮的反向输运并不必然地要求确定性棘轮也反向输运; 随着模型阶数的减小, 亦即分数阻尼介质记忆性的增强, 确定性棘轮在反向输运之前会经历一个周期倍化导致的混沌状态, 但在噪声作用下, 反向流的发生会提前, 即混沌状态的确定性棘轮在噪声的作用下即可进行反向输运. 也就是说, 噪声能定性地改变棘轮的输运状态: 从无噪声时的混沌运动到有噪声时的定向输运. 这是过阻尼随机棘轮反向输运的一种机理, 也是噪声在定向输运过程中发挥积极作用的一个体现.     

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。     

Intracellular transport of single-headed molecular motors KIF1A

Motivated by experiments on single-headed kinesin KIF1A, we develop a model of intracellular transport by interacting molecular motors. It captures explicitly not only the effects of adenosine triphosphate hydrolysis, but also the ratchet mechanism which drives individual motors. Our model accounts for the experimentally observed single-molecule properties in the low-density limit and also predicts a phase diagram that shows the influence of hydrolysis and Langmuir kinetics on the collective spatiotemporal organization of the motors. Finally, we provide experimental evidence for the existence of domain walls in our in vitro experiment with fluorescently labeled KIF1A.     

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.     

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.     

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.     

A non-Markov ratchet model of molecular motors：processive movement of single-headed kinesin KIF1A

A fluctuating ratchet model of non-Markov process is presented to describe the processive movement of molecular motors of single-headed kinesin KIF1A,where the fluctuation perturbation to the local potential is introduced and the detailed ATPase pathway of the motor is included. The theoretical results show good quantitative agreement with the previous experimental ones.