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<sec>Molecular motor is a kind of protein macromolecule, which moves along the microfilament or microtubule in cell directionally and participates in all kinds of intracellular life activities fully. In order to study the directional motion of molecular motor, a series of ratchet models have been proposed. However, the potentials used in most of the ratchet models are smooth sawtooth potential or harmonic potential. Recently, the experimental studies show that intracellular impurities, spatial inhomogeneity or the folding process of protein can yield deviation from a smooth ratchet profile. This kind of deviation will roughen the known smooth potential. In fact, the roughness of potential is not only closely related to the properties of protein, but also has an important implication in transition rate. Therefore, the rough ratchet will be used to simulate the interaction between molecular motor and trajectory in this work. In addition, experimental researches show that there is a class of molecular motor that can move directionally without dragging load in organism. According to the theory presented by Wang and Oster (Wang H, Oster G 2002 <i>Europhys. Lett.</i> <b>57</b> 134), the directional transport capability of this kind of motor can be investigated by means of Stokes efficiency. The higher the Stokes efficiency of the motor, the stronger the ability of the motor to use external input energy for directional motion.</sec><sec>Here in this work, the overdamped Brownian transport of the two harmonically interacting particles is investigated, and the performance of transport is analyzed by studying the mean velocity and Stokes efficiency of the dimer induced by the introduction of roughness into the potential profile. The influences of the amplitude of perturbation, the wavenumber, the coupling strength and the free length of coupled Brownian particles on the directional transport performance are discussed in detail. According to the structure of ratchet, it is found that the roughness can either restrain or enhance the ratchet performance. It is shown that the appropriate amplitude and wavenumber of rough ratchet can promote the directional transport and enhance the Stokes efficiency of coupled Brownian particles. Moreover, one can distinguish between the optimal value of the coupling strength and free length that leads to a local maximum current. In addition, the directional transport of rough ratchet can be reversed by modulating the suitable coupling strength and free length. The conclusions obtained in this paper can provide theoretical guidance for understanding the motion behavior of molecular motor in experiment, and can also provide experimental inspiration for developing the nanometer machines and realizing the particle separation technology.</sec>
<sec>Molecular motor is a kind of protein macromolecule, which moves along the microfilament or microtubule in cell directionally and participates in all kinds of intracellular life activities fully. In order to study the directional motion of molecular motor, a series of ratchet models have been proposed. However, the potentials used in most of the ratchet models are smooth sawtooth potential or harmonic potential. Recently, the experimental studies show that intracellular impurities, spatial inhomogeneity or the folding process of protein can yield deviation from a smooth ratchet profile. This kind of deviation will roughen the known smooth potential. In fact, the roughness of potential is not only closely related to the properties of protein, but also has an important implication in transition rate. Therefore, the rough ratchet will be used to simulate the interaction between molecular motor and trajectory in this work. In addition, experimental researches show that there is a class of molecular motor that can move directionally without dragging load in organism. According to the theory presented by Wang and Oster (Wang H, Oster G 2002 <i>Europhys. Lett.</i> <b>57</b> 134), the directional transport capability of this kind of motor can be investigated by means of Stokes efficiency. The higher the Stokes efficiency of the motor, the stronger the ability of the motor to use external input energy for directional motion.</sec><sec>Here in this work, the overdamped Brownian transport of the two harmonically interacting particles is investigated, and the performance of transport is analyzed by studying the mean velocity and Stokes efficiency of the dimer induced by the introduction of roughness into the potential profile. The influences of the amplitude of perturbation, the wavenumber, the coupling strength and the free length of coupled Brownian particles on the directional transport performance are discussed in detail. According to the structure of ratchet, it is found that the roughness can either restrain or enhance the ratchet performance. It is shown that the appropriate amplitude and wavenumber of rough ratchet can promote the directional transport and enhance the Stokes efficiency of coupled Brownian particles. Moreover, one can distinguish between the optimal value of the coupling strength and free length that leads to a local maximum current. In addition, the directional transport of rough ratchet can be reversed by modulating the suitable coupling strength and free length. The conclusions obtained in this paper can provide theoretical guidance for understanding the motion behavior of molecular motor in experiment, and can also provide experimental inspiration for developing the nanometer machines and realizing the particle separation technology.</sec>
<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>
<sec>Biomolecular motor is a kind of protein macromolecule widely existing in cells. It can convert the chemical energy contained in ATP molecules into mechanical motion, and then continuously provide power for the material transport process. In order to further study the directional transport of molecular motors, the Brownian ratchet model is established based on Brownian motion theory. However, most of the considerations in previous studies are devoted to the motion of Brownian particles under the condition of unit friction damping. In order to further study the influence of medium damping on the directional motion of Brownian particles, our group further study the directional transport of Brownian ratchets in different damping environments, and find that the suitable friction damping coefficient ratio can increase the center-of-mass mean velocity of the coupled Brownian particle. It should be pointed out that the above studies of Brownian ratchets consider the motion of Brownian particles under the condition of uniform spatial friction. In fact, the cell environment in organism is very complex, and the concentration and impurities in the cell change all the time. The medium damping of molecular motor is not always fixed, so choosing the space non-uniform friction condition to study the directional motion of coupled Brownian particles under different damping environments can better understand the directional transport characteristics of friction ratchets. In addition, other point of interest in the research of biomolecular motors is the high efficiency of energy conversion. Experimental results show that the energy conversion efficiencies of most molecular motors are more than 70%, and the efficiencies of some motors are even close to 100%. However, by comparing the experimental results with the theoreticalstudies, it can be found that the efficiency calculated by ratchet model is much lower than that measured in experiment. Therefore, in this paper, the directional motion of coupled Brownian particles in the space non-uniform friction environment is studied in depth, and the energy conversion efficiency of Brownian particles is further discussed.</sec><sec>The results show that the center-of-mass mean velocity varying with the amplitude of the friction coefficient presents a multi-peak structure. This conclusion shows that friction damping does not always hinder the directional motion of coupled particles, and the frictional environment under certain conditions can also enhance the directional transport of coupled Brownian particles. At the same time, the change of the energy conversion efficiency of friction ratchets is similar to that of the center-of-mass mean velocity, which means that the proper friction damping can also enhance the transport performance of the friction ratchets. In addition, under the condition of small friction amplitude, the flow reversal of friction ratchet can be induced by external force amplitude, external potential asymmetry and spatial phase difference. The conclusions obtained in this paper can not only help people understand the directional transport performance of coupled particles in a spatially non-uniform friction environment, but also provide theoretical inspiration for particle separation and screening technology and the design of artificial nanomachines.</sec>
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