The detailed molecular mechanism for the reversible inhibition of mitochondrial respiration by NO has puzzled investigators: The rate constants for the binding of NO and O 2 to the reduced binuclear center Cu B͞a3 of cytochrome oxidase (COX) are similar, and NO is able to dissociate slowly from this center whereas O 2 is kinetically trapped, which altogether seems to favor the complex of COX with O 2 over the complex of COX with NO. Paradoxically, the inhibition of COX by NO is observed at high ratios of O 2 to NO (in the 40 -500 range) and is very fast (seconds or faster). In this work, we used simple mathematical models to investigate this paradox and other important biological questions concerning the inhibition of COX by NO. The results showed that all known features of the inhibition of COX by NO can be accounted for by a direct competition between NO and O 2 for the reduced binuclear center Cu B͞a3 of COX. Besides conciliating apparently contradictory data, this work provided an explanation for the so-called excess capacity of COX by showing that the COX activity found in tissues actually is optimized to avoid an excessive inhibition of mitochondrial respiration by NO, allowing a moderate, but not excessive, overlap between the roles of NO in COX inhibition and in cellular signaling. In pathological situations such as COX-deficiency diseases and chronic inflammation, an excessive inhibition of the mitochondrial respiration is predicted.mitochondrial respiration ͉ mathematical model ͉ cytochrome-oxidasedeficiency diseases ͉ inflammation ͉ excess capacity of cytochrome oxidase T he paradigm that the respiratory chain is regulated by ADP and O 2 was recently updated to include the reversible inhibition of cytochrome oxidase (COX) by nitric oxide (NO) (1-6). The physiological role and the detailed molecular mechanism of this inhibition, as well as the reason for the apparent excess content of COX compared with other mitochondrial complexes, are fundamental questions of mitochondrial biochemistry that remain unsolved. Concerning the mechanism, the problem is particularly puzzling because the known characteristics of COX inhibition by NO are difficult to conciliate with the available kinetic rate constants for this inhibition. On the one hand, COX is inhibited rapidly, within a time scale of seconds, with half-inhibition of respiration attained at O 2 ͞NO ratios in the 40-500 range (4, 7), which apparently indicates that the interaction of COX with NO is stronger than that of COX with O 2 and very fast. On the other hand, the rate constants for the binding of O 2 and NO with the fully reduced binuclear center (Cu B ͞a 3 ) of COX are similar [1.4 ϫ 10 8 (8) and 4 ϫ 10 7 to 1 ϫ 10 8 M Ϫ1 ⅐s Ϫ1 (9, 10), respectively] and NO dissociates slowly from this center (0.01-0.13 s Ϫ1 ) (11, 12), whereas the apparent dissociation rate constant of O 2 with COX is virtually zero because, during the initial steps of reduction of oxygen by COX, oxygen is kinetically trapped (8). Accordingly, several investigators have noticed th...