[en] Some kinds of muscles can oscillate spontaneously, which is related to the dynamic instability of the collective motors. Based on the two-state ratchet model and with consideration of the motor stiffness, the dynamics of collective myosin II motors are studied. It is shown that when the motor stiffness is small, the velocity of the collective motors decreases monotonically with load increasing. When the motor stiffness becomes large, dynamic instability appears in the force–velocity relationship of the collective-motor transport. For a large enough motor stiffness, the zero-velocity point lies in the unstable range of the force–velocity curve, and the motor system becomes unstable before the motion is stopped, so spontaneous oscillations can be generated if the system is elastically coupled to its environment via a spring. The oscillation frequency is related to the motor stiffness, motor binding rate, spring stiffness, and the width of the ATP excitation interval. For a medium motor stiffness, the zero-velocity point lies outside the unstable range of the force–velocity curve, and the motion will be stopped before the instability occurs. (paper)

[en] Cytoskeleton is a network of filamentous proteins, such as actin filaments and microtubules. We propose a continuum cooperative hydrolysis model which possesses exactly analytical solution to describe the dynamics of filament. The results show that the cooperativity leads to non negative-exponential distribution of T (ATP or GTP) subunits. As an application, we investigate the treadmilling phenomenon using our model. It is shown that the cooperativity remarkably affects the length of filament. (paper)

[en] We proposed a modified ratchet model including power-stroke and elastic coupling to study the efficiency of collective non-processive motors such as myosin II in muscle. Our theoretical results are in good agreement with the experimental data. Our study not only reveals that the maximum efficiency depends on elasticity and is independent of transition rates but also indicates that the parameters fitted to fast muscle are different from those fitted to a slow one. The latter may imply that the structure of the fast muscle is different from that of the slow one. The main reason that our model succeeds is that velocity in this model is an independent variable. (paper)

[en] Membrane tubes are important functional elements for living cells. Experiments have found that membrane tubes can be extracted from giant lipid vesicles by groups of kinesin. How these motors cooperate in extracting the membrane tube is a very important issue but still unclear so far. In this paper, we propose a cooperation mechanism called two-track-dumbbell model, in which kinesin is regarded as a dumbbell with an end (tail domain) tethered on the Quid-like membrane and the other end (head domain) stepping on the microtubule. Taking account of the elasticity of kinesin molecule and the excluded volume effect of both the head domain and the tail domain of kinesin, which are not considered in previous models, we simulate the growth process of the membrane tube pulled by kinesin motors. Our results indicate that in the case of strong or moderate exclusion of motor tails, the average number of motors pulling the tube can be as high as 9 and thus motors moving along a single microtubule protofilament can generate enough force to extract membrane tubes from vesicles. This result is different from previous studies and may be tested by future experiments. (interdisciplinary physics and related areas of science and technology)