Dose-Response Curve

Plotted against the logarithm of concentration, most pharmacological responses trace a symmetrical sigmoid. Three parameters describe it: the maximum, the concentration producing half of that maximum, and the slope, which reflects how steeply the response rises through the middle of the range. With a standard slope of one, moving the response from ten per cent to ninety per cent takes an eighty-one-fold change in concentration, which is why log axes are used and why a curve drawn on a linear axis misleads. Steeper slopes compress that span; shallower slopes stretch it.

Clinical dose-ranging aims to find the same shape in patients. In the 72-week SURMOUNT-1 trial, tirzepatide at 5, 10 and 15 mg weekly produced progressively greater weight loss, a graded relationship across three doses rather than an all-or-nothing effect. Every efficacy curve has an adverse-event curve beside it, and for incretin agents the gastrointestinal one rises with dose as well, which is why trials titrate. Not all curves are monotonic; some hormonal and immune responses are bell-shaped, with high concentrations producing less effect than intermediate ones.

The relationship between the two curves is what makes a dose choosable. Where the efficacy curve has flattened and the tolerability curve has not, further escalation buys adverse events and little else. A steep slope narrows the margin for error, because small differences in exposure translate into large differences in effect.

The error worth naming is the two-point dose-response, where a compound tested at exactly two concentrations is said to show a dose-dependent effect. Two points fit nothing and cannot detect a plateau or a bell. The other is treating a cell-culture concentration axis as if it were a dose axis; the concentration bathing a monolayer for 48 hours has no fixed relationship to anything achievable in plasma.