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 Europhys. Lett. 57 134), 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.

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.