These ligand-receptor binding reactions are converted into ODEs by applying mass action kinetics with the pseudo-steady state approximation. This assumes that the cellular response to signals is much slower than that of ligand-receptor binding. The π terms in are derived by finding the ratio of the ligand-receptor complex to the unbound ligand. generalizes these equations to obtain ligand concentrations for the formulaic π terms. Rather than deriving π terms from each ligand-receptor binding combination, assumes that Hill functions represent stimulation and inhibition of cell activity due to the presence of a signaling factor X. Readers are referred to and for full derivation details. There are two forms of these Hill functions : one for activating signaling factors