The mechanism of enzyme-inhibitor-substrate reactions has been analyzed from a theoretical standpoint and illustrated by data from the system cholinesterase-physostigmine-acetylcholine. This treatment is by no means limited to a single system but should be generally applicable to others of similar type.

Competitive enzyme-inhibitor-substrate systems show the same characteristic "zones of behavior" already demonstrated for non-competitive systems by Straus and Goldstein. These zones, three in number, determine the mathematical function which relates activity of an enzyme to concentration of an added substrate or inhibitor or both.

The effects of suboptimal substrate concentration in such systems have been considered, and the errors arising from various common simplifications of the descriptive equations have been pointed out.

The zone behavior phenomenon has been shown to be useful in determining the number of molecules of substrate or inhibitor combining reversibly with a single enzyme center.

The kinetics of competitive inhibition, dilution effect, combination of inhibitor or substrate with enzyme, and destruction of inhibitor or substrate by enzyme have been analyzed and experimentally verified, and absolute velocity constants have been determined.

Theoretical conclusions have been discussed from the standpoint of their physiological significance.

Specifically, it has been shown that:

1. The inhibition of cholinesterase by physostigmine is competitive. A single molecule of physostigmine or acetylcholine combines with one center of cholinesterase—n = 1; and the mechanism n = 2 has been. excluded. Numerical values of the constants for this system are as follows:

KI = 3.11 x 10–8

k1 (combination) = 8.3 x 105

k2 (dissociation) = 0.026

KS = 1.25 x 10–3

k3 (combination) = 260

k4 (dissociation) = 0.32

2. No definitive value can be assigned to E, the molar concentration of enzyme centers, but in 4.54 per cent dog serum, E < 1.8 x 10–8 (EI' < 0.58). The system therefore operates in (or nearly in) zone A at this concentration.

3. Competitive displacement of inhibitor by substrate and vice versa introduces considerable error in the usual 20 minute determination of the activity of an inhibited enzyme, unless properly corrected for.

4. Dissociation of the enzyme-inhibitor complex on dilution proceeds moderately slowly so that the full corrections for dilution cannot be applied unless time has been allowed for full dissociation.

5. Combination of physostigmine with cholinesterase is slow at all but large concentrations of inhibitor.

6. The destruction of physostigmine or acetylcholine by cholinesterase follows the predicted curve; kD for the destruction of physostigmine is found to be > 0.00182; kD for acetylcholine destruction is > 3500. There is no reason to assume inhibition of destruction by excess substrate or inhibitor.

7. The common assumption that enzymatic activity follows (or nearly follows) a monomolecular course is true only under limited conditions, which have been here defined. It is not valid, as a rule, for the enzymatic destruction of an inhibitor (e.g., physostigmine) and its application to such a case may lead to erroneous conclusions about the reaction mechanism.

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