The binding thermodynamic cycle in MelB_St. (a) Thermodynamic cycle of melibiose (Mel) and Na⁺ binding to MelB_St. A four-state model includes the apo state with a cavity possibly opening to periplasmic side [A], two binary complexes MelB_St/Na⁺ [B] and MelB_St/melibiose [C] with periplasmic open conformation, and the MelB_St/melibiose/Na⁺ ternary complex [D] with an occluded or partially occluded conformation. ΔΔG = −5 kJ/mol is the coupling energy (ΔG_[C]→[D] − ΔG_[A]→[B]) or ΔG_[B]→[D] − ΔG_[A]→[C]. The ΔH versus temperature plot for each binding step is displayed as indicated. (b) Energy conservation. The histogram shows that total free energy ΔG_Sum derived the ternary complex from the two paths (difference in the binding order) are similar at each temperature. ΔG_{Sum [A]→[B]→[D]} (left) = ΔG_{Sum [A]→[C]→[D]} (right), all approximately −35 kJ/mol within experimental errors.