Smo inactivation catalyzed by Ptc1. In this simulation two reactions are used, one for activation from a precursor and one for deactivation of Smo. Activation occurs spontaneously at a constant rate. The inverse deactivation reaction is catalyzed by Ptc1 and is much faster when sufficient Ptc1 is present. Here Ptc1 is an essential catalyst: in its absence the deactivation reaction does not occur and Smo is continuously activated and maintained at a high level. Smo concentrations were set to be in the range of 0.0 to 10.0 nM. The concentration of Ptc1 is given as a fraction of Smo concentration. The vertical dashed lines indicate the concentration range over which the maximum inactivation rate is attained. The rules for this model include only two reactions. Reaction 1: Smo activation is proportional to the substrate concentration, Smo_inactive. The product is Smo and the rate constant is 1.0e-5. Reaction 2: Smo (active) is the substrate, Smo_inactive is the product, and Ptc1 is an activator. The rate is computed by harmonic averaging of the outcomes for the following rules: the rate is proportional to Smo concentration; the rate is zero when Ptc1 is zero or very low, and very high when Ptc1 is low or greater.