Collective mechanism of molecular motors and a dynamic mechanical model for sarcomere

A non-equilibrium statistical method is used to study the collective characteristics of myosin II motors in a sarcomere during its contraction. By means of Fokker-Planck equation of molecular motors, we present a dynamic mechanical model for the sarcomere in skeletal muscle. This model has been solved with a numerical algorithm based on experimental chemical transition rates. The influences of ATP concentration and load on probability density, contraction velocity and maximum active force are discussed respectively. It is shown that contraction velocity and maximum isometric active force increase with the increasing ATP concentration and become constant when the ATP concentration reaches equilibrium saturation. Contraction velocity reduces gradually as the load force increases. We also find that active force begins to increase then decrease with the increasing length of sarcomere, and has a maximum value at the optimal length that all myosin motors can attach to actin filament. Our results are in good agreement with the Hill muscle model.