Markov state model describing the binding and unbinding of ATP to P2X2a and P2X2b receptors. The model, Eqs. 1–16, was developed from the scheme for P2X7 (Yan et al., 2010). Each state in this scheme represents the fraction of receptors that belong to a given state. C_i, i = 1,2,3,4, are closed states, whereas Q₁, Q₂ (with conductance g₁₂) are open states, and Q₃, Q₄ (with conductance g₃₄) are dilated states; i.e., their conductances satisfy g₁₂ < g₃₄. The states D_i (top row), i = 1,2,3,4, are the Ca²⁺-independent desensitized states, whereas the states $Dic$ (bottom row) are the Ca²⁺-dependent desensitized states. Open circles on each state represent unoccupied ATP-binding sites, and closed circles represent occupied sites. The forward and backward rates in the top and bottom rows (i.e., the desensitized rows) are identical to those in the middle rows. L_i, i = 1,2,3,4,5, are the transition rates between the four rows, where L₄, L₅ are the rates of transition between open and dilated states, and L₁, L₂, L₃ are the desensitization rates. Note that L₂ depends on [Ca²⁺]_i via the toggle switch shown in Fig. 2.