Nonlinear PK modelling

A drug is "linear" when its behaviour scales predictably with dose: double the dose, double the concentration in blood, because the body clears it at a constant rate — water through a fixed pipe. Most drugs, at normal doses, work this way, and the maths describing them is simple, clean exponentials.

Some drugs break that assumption, because the enzymes metabolising them saturate. Once those enzymes are working at full capacity, more drug doesn't mean faster clearance — it just piles up disproportionately. This is nonlinear PK, and the standard maths for it — Michaelis-Menten kinetics — is the same maths used to describe saturating enzyme behaviour in biochemistry generally.

A few other routes into nonlinearity, beyond enzyme saturation:

• Saturable protein binding — a drug binds blood proteins that have limited capacity; past that limit, more of the drug is free and active.
• Saturable transport — the transporters that move a drug into cells get overwhelmed at high concentration.
• Target-mediated drug disposition (TMDD) — common in biologics: the drug binds its target so tightly and specifically that the target itself becomes a major route of clearance.
• Auto-induction or auto-inhibition — the drug changes the activity of the enzymes that metabolise it, over time, altering its own PK as treatment continues.

Phenytoin (epilepsy), warfarin (anticoagulation), and most monoclonal antibodies are nonlinear. Dosing a nonlinear drug as if it were linear — assuming the safe, well-tolerated response at a low dose will scale smoothly to a higher one — is a real way to hurt someone.

Where it sits in development#

Nonlinear PK modelling gets called in wherever a drug's behaviour looks unusual, rather than as a routine step every drug goes through. It matters most acutely during Phase I dose escalation — the step where a trial moves from a safe low dose toward a therapeutic one — because an undetected nonlinearity is exactly what makes that transition dangerous.

What's actually settled, and what isn't#

Michaelis-Menten kinetics for small molecules has been textbook material since the 1970s — phenytoin and ethanol are the standard teaching examples. What's genuinely still being built:

• TMDD models for next-generation biologics — bispecific and trispecific antibodies, antibody-drug conjugates — where the existing models, built for simple single-target antibodies, don't hold once a drug binds two targets at once.
• Gene and cell therapy PK is close to a blank page: how a viral vector distributes through the body, gets taken up by cells, and is cleared doesn't have an established modelling tradition to draw on yet.
• Predicting nonlinearity onset ahead of time — at what dose does a given drug stop behaving linearly — is currently mostly discovered after the fact, in a trial, rather than predicted beforehand from the molecule's properties.
• Nonlinear PK in sick patients — inflammation, organ failure, a large tumour burden all plausibly change where saturation kicks in, but the patients most likely to need the drug are exactly the ones usually excluded from the studies that build these models.

As with the other notes in this pillar, I'm not going to attach a confidence percentage to how "solved" this field is — that's a judgement call, not a number I can source.