Limited diffusion and spatial association of reactants can increase the Hill coefficient, k . Simulations shown from the computer package Smoldyn, based on the reaction scheme in Eqs. (9,10). The concentration of the input signal, S, is the number of molecules per unit volume. The other concentrations are set to N=X=100. Diffusion rates are 10-5 for all molecules. I ran three replicates for each input concentration, S. Each circle shows the average of the three replicates. For each panel (a – f), I fit a Hill equation curve to the observations, denoting the output as the relative saturation level, A/N=sat[Sk/(mk+Sk)]. The fitted parameters are: k, the Hill coefficient; m, the input signal concentration that yields one-half of maximum saturation; and “sat”, the maximum saturation level at which the output is estimated to approach an asymptotic value relative to the maximum theoretical value of one, at which all N has been transformed into A. Because of limited diffusion, actual saturation can be below the theoretical maximum of one. Panels (b) and (c) are limited to output responses far below the median, because the simulations take too long to run for higher input concentrations.