Non Linear Pharmacokinetics | Michaelis Menton Equation | Unit 5 Biopharmaceutics 6th Semester

The lecture begins by contrasting linear and non-linear pharmacokinetics. In linear (first-order) pharmacokinetics, all ADME parameters (Absorption, Distribution, Metabolism, Excretion) change proportionally with dose — increasing the dose proportionally increases plasma concentration, distribution, and elimination. In non-linear pharmacokinetics, these parameters do not change proportionally with dose, meaning doubling the dose may not double plasma concentration or elimination rate.

The instructor outlines key differences between linear and non-linear systems: in linear systems, clearance is constant, half-life is constant, AUC is proportional to dose, and elimination rate increases with dose. In non-linear systems, clearance changes with dose, half-life varies, AUC shows disproportional changes, and elimination rate becomes constant at high concentrations (zero-order behavior).

Four main causes of non-linear pharmacokinetics are discussed: (1) Saturable Metabolism — metabolizing enzymes (e.g., CYP enzymes) become saturated at high drug concentrations, reducing clearance and increasing half-life; (2) Saturable Absorption — carrier-mediated transport systems become saturated, reducing bioavailability; (3) Saturable Plasma Protein Binding — plasma proteins like albumin become saturated, increasing free drug concentration and risk of toxicity or side effects; (4) Enzyme Induction/Inhibition — auto-induction or inhibition of metabolizing enzymes alters drug metabolism rates unpredictably.

The Michaelis-Menten equation is then presented: -dC/dt = Vmax × C / (Km + C), where dC/dt is the rate of change in drug concentration (elimination), Vmax is the maximum elimination rate, C is plasma drug concentration, and Km is the Michaelis-Menten constant. Three interpretive conditions are derived: (1) When Km = C, the system follows mixed-order kinetics (-dC/dt = Vmax/2), requiring careful dose management; (2) When Km >> C, Km + C approximates Km, yielding -dC/dt = Vmax × C/Km, representing first-order (linear) kinetics where elimination is proportional to concentration; (3) When Km << C, Km + C approximates C, yielding -dC/dt = Vmax, representing zero-order kinetics where elimination rate is constant regardless of dose, posing significant toxicity risk if dose is increased.

The lecture closes with drug examples: Phenytoin (saturable CYP metabolism), Theophylline (saturable metabolism), Valproic Acid (saturable protein binding), Gabapentin (saturable absorption), and Carbamazepine (auto-induction).