Simple model of smooth muscle myosin phosphorylation and dephosphorylation as rate-limiting mechanism

A simple mathematical treatment of the model proposed by others in which a dynamic balance between Ca++ -dependent phosphorylation and Ca++-independent dephosphorylation of myosin controls the activation of smooth muscle contractility is presented. The parameters of the model can be computed from the experimentally observed stable force-[Ca++] relationship. A simple extension of the model to the case of time-dependent activation yields an expression that quantitatively predicts the measured dependence of the rate of isometric tension development on the activating free [Ca++]. The parameters of the mechanical model, which are derived from the rate constants for phosphorylating and dephosphorylating enzyme activities, are in reasonable agreement with the constants measured directly in purified protein systems. In addition, the model predicts values for several parameters that have not yet been experimentally measured, such as the ratio of kinase and phosphatase activities, the maximum extent of myosin phosphorylation, and the kinase turnover number.