A dynamic model of skeletal muscle is developed to describe its activation kinetics and contraction dynamics based on the collective working mechanism of myosin II motors with a statistical mechanics method.According to the structure of sarcomeres arranged in series and in parallel,the mechanical properties of skeletal muscle are studied.This model reveals the relations between action potential and muscle characteristics.It is shown that calcium concentration in sarcoplasmic(SP) increases linearly with the increasing stimulation frequency and gradually reaches saturation.Active force and contraction velocity follow the trend of calcium concentration and reach a peak value at the maximum stimulation frequency.Contraction velocity is inversely proportional to the load while the contraction power increases to maximum and then reduces to zero with the increasing load.These properties are consistent with published physiological experimental results of skeletal muscle.
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.
