The molecular statistics of an enzyme action

Until recently no exact figures were available concerning the rate of transformation of the enzyme-substrate compound. For example, while Willstätter and Pollinger's (1923) best peroxidase preparation could activate over 2000 times its weight of H2 O2 per second under favourable conditions, neither its degree of purity nor its molecular weight is known. Hence such calculations as that of Haldane (1930, p. 176) based on this work are necessarily very rough. Zeile and Hellström (1930) have found that horse-liver catalase is an iron-porphyrin compound with a spectrum resembling that of alkaline hæmatin, and that its amount, reckoned in milligrams of combined iron, can be measured photometrically with great accuracy by converting it into pyridine-hæmochromogen. Thus, although it has not been obtained pure, one can now estimate the activity of a molecule of catalase. In what follows the assumption is made that each molecule of catalase contains only one atom of iron. If this is not so, as in the case of hæmoglobin, where the molecule contains four iron atoms, the calculations given below are true, not for the molecule as a whole, but for each of the active centres on it, since the iron-porphyrin complex is clearly the active centre, as shown by the effects of cyanide. Zeile and Hellström worked at 0° C. and the optimalp h of 6⋅6, with 0⋅01 M. H2 O2 , which disappears according to the unimolecular law, and express their results as unimolecular velocity constants per milligram Fe per litre. Their unit of time is a minute. Moreover, an examination of Zeile's (1930) protocols shows that he employs decimal instead of natural logarithms. Hence to reduce the published velocity constants to the normal unit, they must be multiplied by 2⋅3026/60, or 0⋅03838. For horse-liver catalase solutions containingx mg. Fe per litre., Zeile and Hellström found a unimolecular velocity constant of 2513x , the standard error being only 86x ; or neglecting one rather dubious figure, the velocity constant is 2531 ± 63x . Zeile (1931) found a rate of about 8000x for a catalase prepared from seedlings, but the error is considerably greater. In ordinary units the constant for liver catalase is 97⋅14x, i. e. , mg. Fe destroys 0⋅9714 gram-molecule of H2 O2 per second, in 0⋅01 M. solution, and 1 gram-molecule of enzyme destroys 5⋅42 × 104 gram-molecules of H2 O2 per second. In other words a molecule of enzyme destroys 5⋅42 × 104 substrate molecules per second at 0° C. and 10-2 M. substrate concentration. Under the same conditions plant catalase destroys about 1⋅7 × 105 substrate molecules per molecule per second.