Non Linear Pharmacokinetics | Michaelis Menton Equation | Unit 5 Biopharmaceutics 6th Semester
This lecture covers Unit 5 of Biopharmaceutics and Pharmacokinetics, focusing on Non-Linear Pharmacokinetics and the Michaelis-Menten equation. The instructor explains the differences between linear (first-order) and non-linear (zero-order/mixed-order) pharmacokinetics, and derives three key conditions from the Michaelis-Menten equation. Several drug examples like Phenytoin and Valproic Acid are discussed as real-world cases of non-linear behavior.
Summary
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).
Key Insights
- The instructor explains that in non-linear pharmacokinetics, increasing the dose does not proportionally increase elimination rate — at high concentrations, elimination becomes constant (zero-order), meaning drug accumulates in the body and can cause toxicity.
- The instructor derives that when Km >> C in the Michaelis-Menten equation, the system behaves like first-order (linear) pharmacokinetics, where doubling the dose approximately doubles plasma concentration and elimination rate.
- The instructor argues that when Km << C, the Michaelis-Menten equation reduces to -dC/dt = Vmax, indicating zero-order kinetics where elimination rate is completely independent of drug concentration, making even small dose increases potentially toxic.
- The instructor identifies saturable metabolism as a key cause of non-linear pharmacokinetics, explaining that when metabolizing enzymes become saturated at high drug concentrations, clearance decreases and half-life increases because the drug cannot be eliminated efficiently.
- The instructor notes that in non-linear pharmacokinetics, half-life is not constant — unlike first-order kinetics where half-life remains fixed (e.g., always 4 hours), non-linear drugs may take 4 hours for the first halving but only 2 hours for the next, making dosing prediction unreliable.
Topics
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