DrugTheGuide
Pharmacokinetics

Michaelis-Menten Kinetics

Non-linear, saturable pharmacokinetics where drug elimination rate becomes concentration-dependent once a metabolic enzyme is saturated. Characterised by the parameters Vmax and Km. Phenytoin is the archetypal clinical example.

Definition and Equation

In first-order kinetics (the norm for most drugs), a constant fraction of the drug present is eliminated per unit time — so half-life is independent of dose. In Michaelis-Menten kinetics, the enzyme responsible for elimination can become saturated at therapeutic concentrations, so the elimination rate reaches a maximum (Vmax) and no longer increases proportionally with concentration.

The rate of elimination follows:

v = Vmax × C / (Km + C)

Where:

  • v = rate of elimination (mg/h or mg/day)
  • Vmax = maximum elimination rate when enzyme is fully saturated
  • C = current drug concentration
  • Km = Michaelis constant = concentration at which v = Vmax/2 (reflects enzyme affinity — lower Km = higher affinity)

At very low concentrations where C ≪ Km, the equation simplifies to v ≈ Vmax/Km × C — first-order behaviour. At very high concentrations where C ≫ Km, v ≈ Vmax — zero-order (constant amount eliminated per time, regardless of concentration). Most drugs with MM kinetics operate in the transition zone at therapeutic concentrations. See NCBI StatPearls: pharmacokinetics ↗ for a mathematical derivation.

Phenytoin: The Archetypal MM Drug

Phenytoin (Dilantin) is the most clinically important example of Michaelis-Menten kinetics. It is metabolised by CYP2C9 (primary) and CYP2C19, which saturate within the therapeutic range (10–20 mg/L).

Daily dose Steady-state Css Clinical note
200 mg/day ~5 mg/L Sub-therapeutic in most patients
250 mg/day ~10 mg/L Low therapeutic — approaching saturation
300 mg/day ~15 mg/L Mid-therapeutic — enzyme significantly saturated
350 mg/day ~20 mg/L Upper therapeutic — small dose change, large Css change
400 mg/day ~35 mg/L Toxic range — nystagmus, ataxia, diplopia

This dose-disproportionate concentration response is the clinical danger. The accumulation factor concept applies differently here — steady state cannot be predicted from single-dose kinetics alone without knowing Km and Vmax. Phenytoin TDM: measure free (unbound) phenytoin in hypoalbuminaemia or renal failure patients, as protein binding (>90% to albumin) alters total vs active concentration. See PubMed: phenytoin non-linear dosing ↗.

Other Drugs with Non-Linear Kinetics

  • Ethanol: alcohol dehydrogenase saturates rapidly. After initial distribution, elimination is approximately zero-order (~15 mg/dL/h in most adults). This is why blood alcohol concentration decreases linearly over time.
  • High-dose aspirin: at anti-inflammatory doses (>1 g), glycine conjugation is saturated; elimination becomes dose-dependent with prolonged t½. At analgesic/antipyretic doses, aspirin follows first-order kinetics.
  • Fluorouracil (5-FU): at high doses, dihydropyrimidine dehydrogenase (DPD) saturation causes non-linear kinetics. DPD deficiency (DPYD gene variants) is additionally dangerous — see pharmacogenomics context at CPIC DPYD guideline ↗.
  • Saturable renal secretion: penicillin, cephalosporins, and methotrexate can show non-linear renal elimination at high doses due to saturation of OAT transporters. Background on renal dosing: renal dosing adjustments guide.

FAQ

What is Michaelis-Menten kinetics in pharmacokinetics?
Michaelis-Menten (MM) kinetics — also called non-linear, saturable, or capacity-limited pharmacokinetics — describes drug elimination where the rate of elimination increases non-proportionally with drug concentration. Unlike first-order kinetics (where half-life is constant), MM kinetics arise when the drug saturates a metabolic enzyme, transporter, or binding site. The elimination rate follows: v = Vmax × C / (Km + C), where Vmax is the maximum elimination rate and Km is the drug concentration at which the elimination rate is half of Vmax.
Which drugs show Michaelis-Menten pharmacokinetics?
Phenytoin is the classic clinical example: at low concentrations it follows approximately first-order kinetics, but at therapeutic concentrations (10–20 mg/L) it saturates CYP2C9/CYP2C19, transitioning to near-zero-order kinetics. Small dose increases in phenytoin can produce disproportionately large plasma concentration increases and toxicity. Other examples include: ethanol (alcohol dehydrogenase saturation), high-dose aspirin (glycine conjugation saturation), fluorouracil (at high doses), and some drugs with active tubular secretion (saturable renal transporters). Drugs with zero-order kinetics behave as if V=0 and Km>>C, eliminating at a constant amount per time unit regardless of concentration.
How does saturable kinetics affect drug dosing and safety?
With Michaelis-Menten kinetics, the half-life is not constant — it increases as concentration rises (because elimination is increasingly saturated). This means: (1) small dose increases can cause disproportionately large concentration increases and toxicity at therapeutic concentrations; (2) time to steady state is concentration-dependent (longer at higher doses); (3) loading doses must be used with greater caution; (4) TDM is essential for drugs with saturable kinetics. For phenytoin, an increase in daily dose from 300 to 350 mg may raise the plasma concentration from 10 to 20 mg/L — doubling it — due to saturation of elimination.
How do Km and Vmax relate to drug metabolism?
Km (Michaelis constant) is the drug concentration at which the enzymatic elimination rate is half-maximal (Vmax/2). A low Km means the enzyme has high affinity — saturation occurs at low concentrations. Vmax is the maximum rate of elimination when the enzyme is fully saturated. For phenytoin, the typical Km is 5-10 mg/L and Vmax is approximately 7 mg/kg/day. These parameters are used in the Michaelis-Menten dose-rate equation: DR = Vmax × Css / (Km + Css), where DR is the dose rate at steady state and Css is the steady-state concentration.