Nonlinear (Saturable) Kinetics
On this page
Direct answer
Nonlinear kinetics means elimination switches from first-order (constant fraction removed per hour) to zero-order (constant amount removed) as drug levels approach the saturation point of metabolising enzymes, best described by Michaelis-Menten kinetics: rate of metabolism = (Vmax × C) / (Km + C), where Vmax is the maximum elimination capacity and Km the concentration at half-maximal metabolism. Phenytoin is the textbook example — its Km of roughly 4-40 mg/L sits inside the therapeutic window of 10-20 mg/L, so a 20 percent dose increase can double levels and produce nystagmus, ataxia and lethargy. Ethanol at social-to-toxic doses, high-dose salicylate, theophylline near toxic levels and fluoxetine's auto-inhibition follow the same saturation logic, demanding level-guided, small-step dose changes.
What you must remember
- Michaelis-Menten equation: metabolism rate = Vmax × C / (Km + C); at concentrations well below Km it behaves first-order, and near or above Vmax it becomes zero-order — the equation is quotable exam currency.
- Phenytoin numbers: Km about 4-40 mg/L, Vmax roughly 300-1,000 mg/day in adults; therapeutic window 10-20 mg/L; the fatal trap is increasing 300 mg daily to 400 mg and sailing past 30 mg/L within days.
- Clinical signatures of nonlinearity: half-life rises with dose, area under the curve increases disproportionately (doubling dose can quadruple AUC), steady state arrives unpredictably late, and small adherence lapses cause wild level swings.
- Ethanol: zero-order at about 7-10 g (roughly a drink's worth of alcohol) metabolised per hour; a linear falling blood-alcohol line is the court-room application.
- Salicylate: therapeutic anti-inflammatory doses push clearance into nonlinear renal and metabolic handling, so poisoning escalates both toxic effect and half-life at the same time.
- Other examples worth naming: theophylline at high concentrations, high-dose diazepam's desmethyldiazepam accumulation, fluoxetine auto-inhibition of CYP2D6, voriconazole (supratherapeutic doses give less than proportional levels — and CYP2C19 genetics add scatter).
- Monitoring doctrine: for phenytoin, change doses by 25-50 mg steps and recheck levels after an adequate interval (1-2 weeks or longer near saturation); free (unbound) phenytoin matters in hypoalbuminaemia and uraemia.
- Interpretation anchor: 90 percent of steady state takes about 5 half-lives — but only when half-life is constant; in saturable drugs the "wait and see" interval itself lengthens as levels climb.
A phenytoin titration gone wrong
A 60 kg woman with focal epilepsy is seizure-free on phenytoin 300 mg daily, but her level reads 8 mg/L and she reports auras. The registrar, reasoning linearly, doubles the dose to 600 mg; ten days later she is nystagmic, ataxic and drowsy, and the level returns 42 mg/L. The pharmacokinetic autopsy: her Km sits near 10 mg/L, so the jump from 8 to beyond Km pushed metabolism toward Vmax, where each extra milligram persists far longer; the apparent half-life stretched from roughly 20 hours toward days, and accumulation continued well past the usual five-half-life expectation. The correct move was 325 or 350 mg with a level after two weeks. Recovery follows the same asymmetry — stopping the drug entirely drops levels slowly through the saturated range, then more quickly once below Km, which is why phenytoin-toxic patients are observed rather than dialysed (high protein binding and a huge Vd keep it out of the dialyser). This single case carries the whole lesson of the topic: with saturable drugs, dose is changed in whispers, and the level — never arithmetic — adjudicates.
How the exam frames it
Questions test three instincts. First, recognition: a stem describing disproportionate toxicity after a modest dose increase, or a half-life that changes with dose, signals saturation — name phenytoin and write the Michaelis-Menten equation. Second, plotting: sketch dose versus steady-state concentration — linear below Km, then rocket ascent as intake approaches Vmax (levels then climb without ceiling). Third, contrasting lists: capacity-limited metabolism (phenytoin, ethanol, salicylate) versus flow-limited (propranolol, where hepatic blood flow governs clearance) versus saturable plasma protein binding (ceftriaxone, valproate at high levels) — three different "nonlinearities" that students blur at their peril. A favourite one-liner: why does zero-order kinetics have no true half-life? Because half-life is defined for exponential decay, and a constant-amount decline gives a half-life that grows as concentration falls.
Frequently asked questions
What is the Michaelis-Menten equation applied to drug elimination?
Rate = Vmax × C / (Km + C), describing metabolism that is first-order at low concentrations and zero-order once enzymes saturate.
Why can a small phenytoin dose increase cause toxicity?
Phenytoin's Km lies within the therapeutic range, so metabolism saturates as levels climb; a 20-30% dose increment can raise levels several-fold.
How do steady state and half-life behave in nonlinear kinetics?
Both become dose-dependent — half-life lengthens and steady state is delayed unpredictably as concentrations approach saturation, defying the fixed 5-half-life rule.
Which common substances show zero-order elimination?
Ethanol (about 7-10 g/hour) at usual drinking levels, phenytoin near the therapeutic ceiling, and high-dose salicylate are the classical examples.
What dosing strategy is safe for saturable drugs?
Small incremental changes (25-50 mg for phenytoin) with concentration monitoring after an adequate interval — never linear dose scaling.