Investigation on the directional transportation of coupled Brownian motors with asymmetric friction

Abstract

<sec>Biological molecular motors exist in cells widely. They can make use of intracellular free energy to complete all kinds of internal biological transports by transforming chemical energy into mechanical energy. The kind of directional movement of biological molecular motors plays a very important role in intracellular material transportation. In order to study the transport mechanism of molecular motors further, a large number of ratchet models are proposed, such as rocking ratchets and flashing ratchets. By investigating various kinds of ratchets we can not only understand the directional movement mechanism of Brownian particles, but can find suitable conditions in which the performance of Brownian motors’ directional transportation could be enhanced. Meanwhile, the investigation of ratchets could also be applied in manufacturing nanometer devices.</sec><sec>At present, the directional transportation of Brownian ratchet has attracted extensive interests of researchers. In general, most friction factors of Brownian ratchet models are considered unit. In fact, the concentration of solutions and cell fluid impurity affect the actual frictional damping conditions, so the real frictional coefficient of Brownian motors is often changed. In addition, lots of experimental studies have shown that the movement of Brownian motors is collectively directed motion and the kind of directional movement is induced by intermolecular coupling interaction. As a result, it is more valuable to investigate the transporting performance of coupled Brownian particles that existed in different frictional damping conditions. In order to enhance the transporting performance of Brownian ratchet in different frictional damping conditions, we discuss how the frictional damping factor influences the directional movement of coupled Brownian particles deeply when Brownian particles drag loads.</sec><sec> In this paper, we established the overdamped frictional ratchets, and then we investigated how frictional damping coefficient ratio, coupling strength and external force amplitude affect the transportation of coupled Brownian ratchets. On the basis of the investigation, some interesting results are found. The directional transport of frictional ratchets can be promoted by adjusting the frictional damping factor. Besides, the transportation can obtain the maximum under the appropriate friction factor case. In addition, under certain frictional damping condition, the directional transportation of the friction ratchets present multi-peak structure as the external force amplitude increases. Meanwhile, the appropriate free length and coupling strength can also enhance the transportation characteristic of frictional ratchets. All conclusions obtained in this paper can not be applied in selecting suitable frictional damping conditions experimentally to improve the directional transportation of coupled Brownian ratchets, but they can also be used in developing and manufacturing nanometer devices.</sec>

Rotation-translation coupling of a double-headed Brownian motor in a traveling-wave potential

“…Similarly, when a Brownian motor moves in a periodic potential, there are various random fluctuations such as the thermal fluctuation. Gaussian noises are commonly selected to model the thermal fluctuation [47][48][49][50]. In a Gaussian distribution the tails of the probability density fall off exponentially, and the mean squared displacement in the passive motion grows linearly with time.…”