Dose-response

Why can the same substance be a medicine at one dose and a poison at another?

We talk as though the world divided into medicines and poisons, and as though the label belonged to the substance. But botulinum toxin, among the most lethal substances known, is injected into faces by the million; water, which nothing could be more innocent, has killed people who drank too much of it too fast. Paracelsus put it in the sixteenth century: the dose makes the poison. If that is right, then "is this substance harmful?" is a badly formed question. What is the well-formed one?

Start with what a substance actually does in a body. It binds something — a receptor, an enzyme, a transporter — and the fraction of those targets occupied rises with concentration. At very low concentrations almost nothing is occupied and almost nothing happens; as concentration climbs, occupancy climbs and the effect with it; eventually the targets saturate and further dose adds no more. So dose and effect are related not by a line but by a curve that starts flat, rises steeply, and flattens again.

Now ask the question that opens everything: does a substance have one such curve? It rarely does. Most molecules bind more than one thing, and even a perfectly selective one produces different consequences in different tissues at different concentrations. So think of at least two curves on the same dose axis — one for the effect you want, one for the effect you do not.

If those two curves sat on top of each other, the substance would be useless: no dose could give you benefit without harm. What makes something a medicine is that they are separated — the wanted effect rises at lower doses than the unwanted one. The gap between them is the therapeutic window, and the whole discipline of dosing is the business of landing inside it.

This immediately explains the puzzle. Nothing about the molecule changes between the medicinal dose and the toxic one. You have simply moved along the axis from a region where the first curve has risen and the second has not, into a region where both have.

How wide is the gap? Very wide for some things — paracetamol at a gram is routine, while liver injury needs many times that. Very narrow for others: digoxin's useful serum concentration sits at roughly 0.5 to 2 nanograms per millilitre, and toxicity begins essentially where that ends. Warfarin and lithium are similar, and those are precisely the drugs that get blood-level monitoring.

So how do we measure the harmful curve? The classical instrument is LD50, the dose that kills half of a test population. Its virtue is being a single comparable number, and that virtue is also its defect. It records one endpoint — death — and is silent on everything short of it: organ damage, developmental harm, cancer decades later. It is a median, so it says nothing about the person at the sensitive tail. It is measured in a species that is not us, by a route that may not be ours. And it reports a point on the curve, not the curve's slope — two substances with identical LD50 values can differ enormously in how steeply harm rises with dose, which is exactly what determines how much a mistake costs. It survives because blunt and comparable beats sharp and unavailable.

One more wrinkle, flagged as contested rather than asserted. Some studies report that a substance harmful at high doses is mildly beneficial at very low ones — an effect called hormesis, thought to reflect the mobilising of stress-response systems. It is well documented in some laboratory systems. It is also routinely overstated, generalised far beyond the evidence, and used to argue that low doses of things like radiation or alcohol are good for you. Treat it as a real but narrow and disputed phenomenon, not as a general rule about low doses.

Three refinements worth making explicit.

First, dose is not the same as amount taken. What matters at the target is concentration over time, which depends on absorption, distribution, metabolism and excretion. Two people swallowing identical tablets can reach very different concentrations — through kidney function, liver enzyme variation, body size, age, or interaction with another drug. The therapeutic window is a property of the pair, substance and person, not of the substance alone.

Second, "the dose makes the poison" is a claim about dose being decisive, not a claim that every substance has a safe dose. For some effects, particularly certain carcinogens, whether a genuinely harmless threshold exists is disputed and regulators often assume none; and for a few substances the useful window is so narrow or so far below the toxic range as to be practically empty.

Third, do not read the window as a cliff with safety on one side. Both curves are gradual. The edge of the therapeutic window is a probability changing, not a switch flipping — which is why dosing errs low, and why a drug with a narrow window is dangerous even when the prescribed dose is correct.

• How pharmacokinetics turns a swallowed tablet into a concentration-over-time curve at the target.
• Why the linear-no-threshold model is still argued about for low-dose radiation and chemical carcinogens.

Every term the collection defines is gathered in the glossary.