Combinatorial complexity. The full combinatorial complexity of the described parts of insulin signaling is demonstrated. The insulin receptor can bind Insulin, Shc and IRS. IRS can bind four PI3K molecules, SHP2 and Grb2. Grb2 can bind SOS and phosphorylated SOS. This results in 35·5 = 1215 different complexes with IRS. For Shc and insulin binding to the receptor monomer there are seven and two possibilities, respectively. Altogether there are n = 2·7·(35·5 + 2) = 17038 different complexes of the receptor monomer. As the receptor is a dimer (k = 2) this setup allows = = 145, 155, 241 ≈ 1.5·108 different combinations. Free species contribute another 1215 + 10 + 1 + 1 + 1 = 1228 possible species: 1215 for the free IRS complexes, 10 for all combinations of Shc, Grb2 and SOS and one for insulin, PI3K and SHP2 each.