Fig. 2.

Modification of quinone E_ms by proton or protein binding. a Energetics of coupled electron and proton transfer. X is a base associated with a quinone binding site. When X is neutral the E_m for Q is E_m,0; when Q is neutral the pK_a for X is pK_a,0. Favorable interactions between X⁺ and Q^•− raise the E_m for Q by −ΔΔG°/nF. The same interaction stabilizes XH⁺, raising the pK_a by ΔΔG°/2.3RT. A ΔΔG° of −1.36 kcal/mol shifts the E_m up by 58 mV and the pK_a up by 1 pH unit. If the pK_a of X remains below the pH in the presence of Q^•− then X will never be protonated and E_m=E_m,0. If the pH is below the pK_a of X with Q oxidized, XH⁺ will be present throughout the reaction and the observed E_m will be E_m=E_m,0−ΔΔG°/F. In this case the reduction of Q feels the full stabilization by the adjacent base. In either case the reaction is pH independent. However, if the pH is at least ≈2 pH units below the pK_a with Q and ≈2 pH units above the pK_a in the presence of Q^•− (i.e. ΔΔG° >≈5.4 kcal/mol) then binding ≈1 proton will be coupled to electron transfer (when the pH is 2 pH units below the pK_a X will remain 1% protonated; when the pH is 2 pH units above the pK_a X will remain 1% XH⁺. Thus, on average 0.98 more protons will be bound). The resultant E_m will be E_m,0− [ΔΔG°+(pH−pK_a,0)/2.3RT]/F. The free energy needed to protonate X at this pH is (pH−pK_a,0)/2.3RT. It is this term which leads to the classic 60 meV/pH unit E_m shift with pH indicative of 1 proton bound/electron. The cost of rearranging the surroundings diminishes the E_m shift from that found if XH⁺ were present at the start of the reaction. If pK_a,0 for X is near the pH even a small ΔΔG° of interaction with a more distant Q^•− will lead to substoichiometric changes in protonation of X, leading to a pH dependence smaller then 60 mV/pH unit. b The relationship between the thermodynamics of quinone binding and quinone electrochemistry. If the E_m is more positive in the quinone binding site then the semiquinone is bound more tightly then the quinone. ΔΔG°_bind is 2.3RT(logK_dQ^•−− logK_dQ)