Table 1.

Partial processes and kinetic parameters for Q_o-site model

Reaction equation	Rate constants		kforward	kreverse	Keq
EFeS.c1.bL.bH + QH2 Ý EFeS.c1.bL.bH .QH2	konQH	koff	500×[QH2]	5×103	10	a
EFeS.c1.bL.bH .QH2 Ý EFeS.c1.bL.bH .QH-H	kproton	k−proton	107	1012	10−5	b
EFeS.c1.bL.bH .QH-H Ý EFeS−.c1.bL.bH .SQ(d)	k1	k−1	1.65×108	3.25×105	510	c
EFeS−.c1.bL.bH .SQ(d) Ý EFeS.c1−.bL.bH .SQ(d)	k5	k−5	108	3×108	0.33	d
EFeS.c1−.bL.bH .SQ(d) + Aox Ý EFeS.c1.bL.bH .SQ(d) + Ared	k3	k−3	107	105	100	e
EFeS.c1.bL.bH .SQ(d) Ý EFeS.c1.bL−.bH .Q(d)	k2d	k−2d	1.2×103	0.192	6250	f
EFeS.c1.bL−.bH .Q(d) Ý EFeS.c1.bL.bH − .Q(d)	k4	k−4	106	6250	160	g
EFeS.c1.bL.bH .SQ(d) Ý EFeS.c1.bL.bH .SQ(p)	kdiff	k−diff	107	107	1	h
EFeS.c1.b− L.b−H .SQ(d) Ý EFeS.c1.b− L.b−H .SQ(p)	kdiff3	k−diff3	106	108	0.01	h
EFeS.c1.bL.bH .SQ(p) Ý EFeS.c1.bL−.bH .Q(p)	k2p	k−2p	4.3×109	6.9×105	6250	i
EFeS.c1.bL−.bH .Q(p) Ý EFeS.c1.bL.bH− .Q(p)	k4	k−4	106	6250	160	g
EFeS.c1.bL.bH − .Q(p) Ý EFeS.c1.bL.bH− .Q(d)	kdiff	k−diff	107	107	1	h
EFeS.c1.bL.bH− .Q(d) Ý EFeS.c1.bL.bH − + Q	koff	konQ	5×103	50×[Q]	1	j
EFeS.c1.bL.bH − + QH2 Ý EFeS.c1.bL.bH−.QH2	koff	konQH	500×[QH2]	5×103	10	k

Notes:

The model represents the essential processes of the Q_o-site reaction, constrained by antimycin to prevent the Q_i-site reaction so that flux out of the b-heme chain is inhibited. The full complement of redox centers is included, and an additional acceptor (by default in 6-fold excess over the complex) of E_m,7 420 mV to simulate the driving force available from the rest of the chain. For simplicity, it is assumed that all components retain the E_m,7 values determined by redox titration. The reactions shown are appropriate to the first turnover of the Q_o-site. The model allows simulation of the second turnover, and uses the same rate constants for similar processes (see Supplementary Information for details).

^a)The value for k_onQH shown is that suggested in [ 31], with the initial [QH₂] given as 200 (no units), to give an apparent first-order rate constant of 5×10⁴ s⁻¹. In chromatophores at saturating QH₂, the exchange of Q and QH₂ has no appreciable contribution to the kinetics [72], indicating that these reactions are all rapid compared to the rate limiting step. The second-order rate constant determined in situ was ~2 × 10⁵ M⁻¹s⁻¹ [74], estimated from the observed rate at ~10 mM QH₂ in the membrane. The diffusion-limited rate constant would be considerably higher. The displacement of the apparent E_m due to formation of the ES₁-complex shows a tighter binding of QH₂ than Q by a factor ~10.

^b)Rates for H⁺ exchange along H-bonds have been variously estimated on the range 10¹¹ to 10¹³s⁻¹ [123–125]. We have used a value of 10¹² s⁻¹ for k_−proton, the more rapid of the two rate constants, but any choice in the range shown experimentally would give the same kinetics overall. The ratio of rate constants gives the probability for finding the H⁺ in a position favorable for electron transfer (the equilibrium constant for distribution along the H-bond), derived from the difference in pK values between donor (the −OH of QH₂, pK >11.5) and acceptor groups (the N_ε of His-152 (His-161 in mitochondrial sequences) of the oxidized ISP, with pK_ox1 ~7.6). At saturating QH₂, electron transfer occurs from the ES₁-complex, and the value for pK_ox1 would be less than in the isolated ISP because of the binding free-energy [8]. A value of 6.5 is used in the simulation (a ΔpK of 10⁵).

^c)The forward rate constant is that for electron transfer from the weakly populated configuration in which the H⁺ is close to the histidine N_ε of His-152 (occupancy 10⁻⁵ used here, see (b)). The value for rate constant needed is therefore 10⁵-fold greater than the observed value. The value given here is that from a Marcus analysis using the distance dependence of Moser and colleagues [100], and λ = 0.935, distance 7.0 Å, and driving force ΔG^o/F = −0.16 V appropriate to the value for K_eq shown. The reverse rate constant is chosen to give a SQ occupancy in the range shown by experiment (~0.05 [30] and this work), after taking account of the occupancy of the intermediate state. It is assumed that the reaction is reversible only in the ES₁-complex configuration. After electron transfer, the H-bond to SQ would break, releasing the reduced ISP, which would rapidly rotate away from the ES-complex configuration to passes its electron to heme c₁.

^d)Removal of ISPH from interaction with Q_o-site, and oxidation to ISP_ox. The forward rate constant given is that for dissociation and movement of ISPH, since this would release SQ for further reaction. The equilibrium constant is that for oxidation of ISPH by cyt c₁, which is weakly unfavorable at pH 7.0.

^e)Second-order rate constant to represent oxidation of cyt c₁ by a pool of high-potential acceptor.

^f)The forward rate constant for oxidation of SQ in the domain distal from heme b_L. The value is that needed to match the observed rate in strains mutated at Glu-295 (v~40–80 QH₂/bc₁/s at pH 8.5 – 9), with a SQ occupancy ~0.05 [30], using the relation, v = k(occupancy).

^g)The rate constant for electron transfer from heme b_L to heme b_H. The forward rate constant was calculated using Marcus/Moser-Dutton analysis from the distance given by modeling. The reverse rate constant was chosen so that the equilibrium constant matches that calculated from E_m values. The value is similar to that determined from the rate of oxidation of heme b_H induced by generation of a membrane potential [126]. The kinetics of heme b_H reduction were not significantly changed by varying the value for k₄ over the range 10⁴ to 10⁶ s⁻¹, though a transient reduction of heme b_L (maximal occupancy 0.08) was seen when the lower value was used.

^h)An approximate value for k_diff is given by k ≈ 1/t = 2D /<x²>. Using x = 5×10⁻⁸ cm, D in the range 10⁻⁹ to 10⁻⁷ cm² s⁻¹ [119, 120], we find 0.8× 10⁶ <k_diff <0.8 × 10⁸ s⁻¹, assuming a 1- dimensional diffusion path, and diffusion in both directions from a starting position; if movement was constrained to the direction closer to heme b_L, the values would scale up. The value used in the simulation could be varied over the range 10⁸ – 10⁷ s⁻¹ without changing the overall rate of reaction. In all the simulations shown in which heme b_L was available in the oxidized form, the same value was used in forward and reverse directions. The limited range could be extended by applying a bias to the diffusional process. For example, bias would increase k_diff if there was a coulombic driving force for displacement of Q^.- by a positive field around heme b_L. Similarly, the occupancy of the distal domain by Q^.- could be constrained if k_−diff was increased by a negative field around ferroheme b_L. In the simulation, we implemented such an effect under conditions in which both b-hemes were reduced, but the only outcome affected was the distribution between SQ_d and SQ_p states. In the mechanism outlined in Fig. 8 we speculate that the change in charge on reduction would switch the field from +ve to −ve, but have not otherwise implemented that feature in the present models. For the neutral Q species, the same value for k_diff was used in both reaction directions. The value for k_diff was varied in the plots of Figs. 7–9, as indicated, to simulate impaired oxidation of SQ by mutation of Glu-295.

ⁱ⁾The forward rate constant for oxidation of SQ in the domain proximal to heme b_L. The value was calculated using the Moser-Dutton distance parameter, the distance to heme b_L shown by myxothiazol-containing structures, and the Marcus exponential term [8]. Both here, and in estimation of the complementary parameter for the distal domain, the reverse rate constant was calculated so as to be consistent with the equilibrium for the overall reaction and the other values for equilibrium constants used in the simulation.

^j)The values chosen reflect a 10-fold tighter binding for QH₂ than Q at the catalytic site. As noted in a), the actual value is conservative.

^k)Because of the 25 Å distance, and the neutral charged state of the binding species, it was assumed that the redox state of heme b_H did not affect the binding of Q or QH₂ at the Q_o-site.