In enzyme kinetics V_max is the maximum rate of the enzymatic reaction. For drug metabolism in vivo, V_max is the maximum rate of drug metabolism by a specific pathway.V_max has units of amount per time and can also have units of concentration per time.

The maximum rate of drug metabolism is dependent on the amount of enzyme available for drug metabolism via a specific pathway. Enzyme induction results in increasing the amount of the enzyme and V_max.

Diseases that affect the liver (the primary organ for drug metabolism) may result in decreasing the metabolic capacity for metabolic pathways and decreases V_max. Also, V_max may depend on the size of the patient. Children may have lower V_max compared to adults.

It is the Michaelis-Menten constant. It is a qualitative characteristic of how an enzyme interacts with the substrate and is independent of the enzyme concentration. K_m is equal to the substrate conc when the reaction rate is half its maximum value (1/2 V_max).

K_m has units of concentrations (amount/volume).

Conditions such as the presence of a competitive inhibitor can result in increasing K_m. This is because at any given drug conc the rate of drug metabolism is slower in presence of a competitive inhibitor compared to the rate in absence of the inhibitor.

Enzyme induction results in increasing the metabolic capacity of the enzyme system. This can happen by a wide variety of agents known as enzyme inducers. Enzyme inducers usually increase enzyme synthesis leading to an increase in the total amount of the enzyme and an increase in the metabolic capacity of the metabolic pathway.

The effect of enzyme induction on drug metabolism depends on the drug and the inducer. Some inducers are specific for a certain sub-family of CYP-450 which will affect all the drugs metabolized by that particular CYP-450 sub-family.

Drugs that are metabolized by high capacity metabolic pathways (high extraction ratio drugs, or drugs that have high intrinsic metabolic clearance) will not be affected significantly by enzyme induction. On the other hand, enzyme induction significantly affects the rate of metabolism of drugs that have low intrinsic metabolic clearance (low extraction ratio drugs).

Competitive inhibitors of drug metabolism are compounds that can compete with the drug for the same metabolic pathway. Competitive inhibitors can be other drugs, metabolites, endogenous or exogenous compounds.

In absence of the inhibitor the drug is the only compound that is metabolized by its specific enzyme system. In presence of the inhibitor, the inhibitor compete with the drug for the same enzyme system.

At any given drug conc, the rate of drug metabolism is slower in presence of the inhibitor compared to when only the drug is present. The extent of inhibition depends on the drug and the inhibitor and the relative affinity of the drug and the inhibitor for the metabolizing enzyme.