HA ^x models in systematic representation. Blue circles, ligand; white circles, empty binding site. The set of closed–open isomerizations on the bottom is valid for all HA^x models at an equal degree of liganding. For open channels with incomplete occupation of the binding sites, the ligands are drawn below the channel cartoon to illustrate that there is more than one option for occupancy. The K_x indicate the equilibrium association constants corresponding to Tables S1, S2, S3, and S4. (A) HA² model. (B) HA³ model. (C) HA⁴ model. (D) HA⁵ model. In the HA⁵ model, the K_x were omitted for clarity but are provided by Table S4.