<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>

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Biomolecular motors are a big family of protein, and play a very important role in transporting the organelles within cells. They can also convert chemical energy into mechanical energy. In order to study the dynamic mechanism of molecular motors in depth, a great many of Brownian ratchet models such as double-temperature ratchet, feedback control ratchet, and hand-over-hand ratchet have been proposed. By investigating different kinds of ratchets, it is better to comprehend the directed transport of Brownian particles and obtain an insight into the transport process in biomedicine. Especially, the investigation of Brownian ratchets can also be used for improving the accurate drug delivery and effectively utilizing the medicine.Until now, the directed transport of ratchet has aoused the interest of researchers. It is found that a certain driving phase can lead to the current reversal of the underdamped ratchets in theory. A large number of experiments have shown that most of the biomolecular motors in cells are enzyme protein macromolecules and they can carry the “cargos” to implement the directed transport. Interestingly, molecular motors have high efficiency usually, and some of them can even reach an efficiency close to 100% in experiment. Nevertheless, it is found that the energy conversion of Brownian motors is low as indicated by calculating the rate between the effective work of particles and the input energy of ratchets. According to a comparison between the experimental results and theoretical analyses, it is well known that the efficiency of ratchets is still far from the actual motor efficiency measured experimentally. Therefore, how to increase the efficiency of molecular motor which is pulled by loads is still a very important research topic. Owing to the fact that the molecular motors are influenced by the cellular environment during the hydrolysis of ATP in the organism, the catalytic cycles of the coupled motor proteins are out of phase. This gives us an inspiration for establishing the corresponding feedback pulsing ratchet.Due to the effect of the feedback pulse on coupled ratchets, the directed transport character of pulsing ratchets when they drag loads is explored in the present work. And the directed transport, diffusion and energy conversion efficiency of coupled particles are discussed systematically. It can be observed that the directed transport of the feedback pulsing ratchets would be futher facilitated by adjusting suitable free length and coupling strength. Meanwhile, the energy conversion efficiency of coupled particles can obtain a maximum value under a certain free length and coupling strength. In particular, there is the current reversal in an evolutive cycle under a certain pulse. Moreover, the diffusion of coupled particles can be suppressed effectively by modulating the pulsing phase, thus the corresponding directed transport of pulsing ratchets can be facilitated. In addition, the energy conversion of feedback ratchets can also be improved if the load is appropriate. The current reserval obtained in this paper can be applied to the particle separation. On the other hand, these results provide some great experimental inspirations in the aspect of medical delivery.