Larger doses achieve higher initial drug conc. Higher conc results in lower clearance and longer half life. However at any conc, the rate of decline of the drug conc is similar, since Km and Vmax are constant.
Increasing the dose results in more than proportional increase in the steady state conc. It takes longer time to achieve steady state when larger doses are administered.
Doseis the administered dose of the drug (amount).
Vmaxis the maximum rate of drug metabolism (amount/time). In this example it is also the maximum rate of drug elimination since it is assumed that the drug is eliminated via a single pathway.
Kmis the Michaelis-Menten constant. It is the substrate concentration when the rate of the reaction is equal to half Vmax (amount/volume).
Km
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. Km is equal to the substrate conc when the reaction rate is half its maximum value (1/2 Vmax).
Km has units of concentrations (amount/volume).
Conditions such as the presence of a competitive inhibitor can result in increasing Km. 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.
Vmax
In enzyme kinetics Vmax is the maximum rate of the enzymatic reaction. For drug metabolism in vivo, Vmax is the maximum rate of drug metabolism by a specific pathway.Vmax 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 Vmax.
Diseases that affect the liver (the primary organ for drug metabolism) may result in decreasing the metabolic capacity for metabolic pathways and decreases Vmax. Also, Vmax may depend on the size of the patient. Children may have lower Vmax compared to adults.
