Effect of the number of molecules on the energetic efficiency in molecular motors using the Flashing Ratchet model

In this paper, we analyze the N-motor model based on the Flashing Ratchet model. There are two types of models. One of them consists of the Langevin equation and the other consists of the Fokker–Planck equation. By using the former equation, we calculate the velocity of N-motor models, and find several dependencies on the number of motors. We also find analytical expressions of the velocity as a function of the number of motors, which contribute to understanding the cooperativity of motors. In the latter equation, we modify the previously proposed N-motor model and develop methods to calculate the velocity, efficiency, and dissipation rates of the model. Specifically, we analyze single-particle, 2-particle, and infinite-particle molecular motor models. We show that the efficiency increases as the number of motors increases depending on the dissipation rates.