A quantitative model of myosin phosphorylation and the photomechanical response of the isolated sphincter pupillae of the frog iris.

The time courses of isometrically recorded photomechanical responses of isolated sphincter pupillae of Rana pipiens can be accurately predicted by a set of differential equations derived from phosphorylation theory of smooth muscle contraction. We compared actual light-stimulated contractions with calculated ones over a wide range of stimulus intensities (56-fold) and durations (0.4-4.0 s). The hypothetical Ca++-calmodulin-myosin light chain kinase cascade acts as a "valve" to control the flow of ATP through a phosphorylation-dephosphorylation cycle. When the rate of flow of ATP through the phosphorylation-dephosphorylation cycle is increased, the percentage of phosphorylated myosin increases. The time courses of the concentrations of phosphorylated myosin during different responses are seen to be functions of the time courses of the opening and closing of the coupling cascade "valve." The calculations predict experimentally measurable intermediate variables, which can aid the investigation of the application of quantitative phosphorylation theory to amphibian sphincter pupillae and to smooth muscle in general.