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.

Molecular motors in life activities of cell are known to operate efficiently.They could convert molecular-scale chemical energy into macroscopic-scale mechanical work with high efficiency.In order to acquire the transport mechanism of the molecular motor,the Brownian ratchet has been proposed to explore the property of directed transport and energy conversion.There are different kinds of Brownian ratchet models like flashing ratchets,rocking ratchets,and time-asymmetric ratchets and so on.Through investigating the performance of Brownian ratchet moving in periodic potential,the directed transport of ratchet could be explained,and the effective usage of ratchet energy for directed transport could also be improved.Recently,optimizing the transport of Brownian ratchet has aroused the interest of researchers.It is found that the viscous resistance could reinforce the directed transport of the Brownian particle in damping liquid.Meanwhile,a large number of conclusions indicate that the transport of Brownian ratchets would be enhanced if the asymmetry of the potential is changed.Those results show that the influences of the external potential and the damping force on the particle flow cannot be neglected.Hence in this paper,the effects of the potential structure and the temperature of heat bath on transport are discussed. Furthermore,how to use the ratchet energy effectively has been investigated in recent years.When the Brownian motor operates with load,the input energy is reduced.More importantly,the energy transformation efficiency defined as the ratio of the useful work done against the load to the input energy is assumed to be a zero value in the absence of load.With the help of stochastic energetic theory proposed by Sekimoto,the Stokes efficiency has been used to explore the performance of the Brownian ratchet.So far,the numerical solution has been used extensively in most theoretical investigations.Nevertheless,in our work,the Stokes efficiency is discussed analytically for explaining the mechanism of directed transport.We consider the transport performance of the Brownian ratchet described by the Fokker Planck equation which is corresponding to the Langevin equation under time-varying external force and thermal noise.Mainly, the effects of potential asymmetry,external force,height of the barrier,and intensity of the thermal noise on transport are discussed in detail.It is found that the transport direction of Brownian ratchet will be reversed under the condition of appropriate potential structures,and the probability current can reach a maximal value by changing the asymmetry of potential.It is worthwhile to point out that the performance of directed transport of the ratchet can be improved when an appropriate amplitude of the external force is applied.Meanwhile,there is an optimal value of the barrier height at which the Stokes efficiency reaches a maximal value and the directed transport of ratchet is enhanced.Through our conclusions,the ratchets of different structures could be designed for improving the transport property of Brownian motor.And the results have helpful theoretical guidance not only in the aspect of medical delivery but also in the control of nano-devices.