Mitochondrial cytochrome c oxidase: Mechanism of action and role in regulating oxidative phosphorylation: Reply to Pannala, Beard, and Dash

to the editor: We are pleased that the authors have read our paper (2) and consider it of sufficient importance to critique it (1). There is an error in our program: the rate constants k_4a and k_4b are interchanged in Eq. A15. The error was introduced before fitting of the equations to the cytochrome c oxidase data. Fortunately, Eq. A15 is only used for calculating the turnover number for cytochrome c, and the turnover number is not used in any other calculations.

When Eq. A15 is corrected and the model is refitted to the cytochrome c oxidase data, the values of 5 of the rate constants are slightly decreased (Table 1). The original equation and constants (column 2) fit to the cytochrome c oxidase data is the same, within experimental error, as the corrected equation and the constants in column 3. Because the two different calculations yield the same dependence of cytochrome c oxidase activity on energy state, pH, and Po₂, application of the fitted equations to other metabolic systems is not affected.

Table 1.

Original and re-estimated constants for fit to the data

Constant	Value in Our Paper	Value after Correction
k 1	8 × 109 M−1s−1	8 × 109 M−1s−1
k 1r	8 × 107 M−1s−1	8 × 107 M−1s−1
k 2	6 × 108 M−1s−1	6 × 108 M−1s−1
k 2r	1 × 101 s−1	1 × 101 s−1
K 3	2 × 106 M−1	2 × 106 M−1
K 5	1 × 1025	1 × 1025
k 4a	2.5 × 108 M−1s−1	2 × 107 M−1s−1
k 4b	8 × 107 M−1s−1	3 × 108 M−1s−1

The same equations were fit to similar data, so why are the values of the constants obtained by Pannala et al. so different from ours? The principal reason is our requirement that any constant used in fitting be consistent with available experimental data. For example, the value of k₂, the rate constant for the bimolecular reaction of O₂ with cytochrome c oxidase, has been experimentally measured to be between 10⁸ and 10⁹ M⁻¹s⁻¹ so k₂ was constrained to values within this range. Their table shows a k₂ value of 5.8 × 10¹¹ M⁻¹s⁻¹, exceeding the measured values by ∼1,000-fold and the diffusion limit by 50-fold.

We apologize for the error in Eq. A15 but assure readers that correcting it introduces only the small changes in the values assigned to the rate constants as shown in Table 1. The calculated dependence of cytochrome oxidase activity on its regulatory parameters and the evidence for its central role in setting and maintaining metabolic homeostasis is unchanged. Discussion is encouraged (wilsondf@mail.med.upenn.edu).

Also, the sign for k_4a·c_r·III in eq. A1 should be − and not + (typing error).

AUTHOR CONTRIBUTIONS

Author contributions: D.F.W. and S.A.V. conception and design of research; D.F.W. performed experiments; D.F.W. analyzed data; D.F.W. drafted manuscript; D.F.W. edited and revised manuscript; D.F.W. and S.A.V. approved final version of manuscript.

DISCLOSURES

Conflict of interest statement: No conflicts of interest, financial or otherwise, are declared by the author(s).