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.

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.

A first-order process is a process that has a rate proportional to the amount of the reactant involved in this process.

For example, if the dg elimination rate is proportional to the amount of the drug in the body, this means that this drug is eliminated by a first-order process. The proportionality constant is the first-order elimination rate constant. i.e.

Elimination rate = elimination rate constant x drug amount

The rate of drug elimination decreases with time because the amount of the drug remaining decreases with time.

A zero-order process is a process that has a constant rate. The rate of the zero-order process does not depend on the amount of the reactant involved in the process.

If the elimination of a drug follows zero-order kinetics, this means that there is a constant amount of the drug eliminated per unit time, regardless of the administered dose.

Because the rate of drug elimination is constant (zero-order elimination) the fraction of the dose eliminated per unit time after administration of a large dose, is much smaller than the fraction of the dose eliminated per unit time after administration of smaller doses.