Incorporating dock, catch, and hold into a thermodynamic cycle. (A) Each of the three processes is a dimension of the cube. Dock is by diffusion alone, and both catch and hold require a protein conformational change. The scheme pertains only to events related to agonist binding rather than the full gating isomerization; states boxed with dotted lines lead directly to open-channel R* states. Front plane, catch and hold with agonists; backplane (gray), catch and hold with water only; left plane, encounter complexes. W–R corresponds to R in the scheme shown in Fig. 1 D. Thick lines represent the main dock–catch–hold activation sequence. (B) If agonists (A) and water (W) exchange only at encounter complexes, the cycle is 2-D. K and J are the LA and HA equilibrium association constants (forward direction given by arrow). There are three kinds of unliganded openings: after catch (E0) or with either water or agonist in the encounter complex (E0′ and E0″). From detailed balance, E1/E0 = λA/λW, where λ = Kd/Jd.