Scheme 2. Illustration of Equation 38.

A hypothetical allostery graph shows how the label for the edge at the top, which links the vertical subgraphs at conformations c_k and c_l at the binding subset $S$, can be calculated from the quantities ${\mu }_S(A^{c_k})$ and ${\mu }_S(A^{c_l})$ and the edge label at the bottom. The ${\mu }_S$ quantities come from paths to the vertices in question from the respective reference vertices in the vertical subgraphs, as specified in Equation 30 and Scheme 1. The edge label at the bottom comes from the horizontal subgraph of empty conformations, $A_{\mathrm{\varnothing }}$. The vertical subgraphs $A^{c_k}$ and $A^{c_l}$ have the same structure and the paths are shown as the same in each subgraph, but they could be arbitrary paths because of the cycle condition at thermodynamic equilibrium (Equation 32). Once appropriate directions are taken, the two paths and the edges at the top and bottom constitute a large cycle in the allostery graph and Equation 38 is simply a rewriting of Equation 32 applied to this cycle.