Initial values of R b and R t for fitting with control data were set at the minimum and maximum values of the response, while initial values of R b and R t were set at the minimum and maximum values of the percentage activity. During the fitting procedure, these parameters were restricted to their initial values plus/minus a quarter of the data range. For x 50 , the initial value was set to be observed concentration with the response closest to the mean of the minimum and maximum response. The initial Hill slope was set to 1. x 50 and H were restricted to the range from -50 to 0 and from 0 to 50, respectively. Optimization was performed until the absolute difference in the log likelihood was less than a tolerance of 1 × 10 4 .