Graded Dose-Response Curves and Sigmoid Shape

A graded dose-response curve plots the magnitude of a continuously variable response in a single biological system against the dose or concentration of a drug. When the dose axis is logarithmic, the relationship typically takes a characteristic sigmoid (S-shaped) form: little effect at very low doses, a steep near-linear rise over an intermediate range, and a plateau as the maximal effect is approached.

Definition

A graded dose-response curve is a plot of the continuously graded magnitude of a pharmacological effect in an individual system against drug dose or concentration, conventionally drawn on a logarithmic dose axis where it assumes a sigmoid shape bounded by a baseline and a maximal effect (Emax).

Scope

This topic covers the construction and reading of graded dose-response curves, why the logarithmic dose axis produces a sigmoid, the meaning of the lower and upper asymptotes and the steep mid-range, and how the curve differs from the population-based quantal form. It is reference-educational and gives no dosing guidance.

Core questions

• What does a graded dose-response curve measure, and how does it differ from a quantal curve?
• Why does plotting effect against the logarithm of dose produce a sigmoid shape?
• What do the lower asymptote, steep mid-range, and upper plateau of the curve represent?
• How are potency and maximal effect read off a graded curve?

Key concepts

• Graded (continuous) response
• Logarithmic dose axis
• Sigmoid shape
• Lower and upper asymptotes
• Maximal effect (Emax)
• Steep mid-range and curve position
• Linear (arithmetic) versus semi-log plotting

Mechanisms

In a graded response the effect varies continuously with dose, reflecting the increasing fraction of target molecules engaged and the downstream transduction of that engagement into a measurable output. On an arithmetic dose axis the curve is a rectangular hyperbola rising toward a maximum; transforming the dose axis to a logarithm stretches the low-dose region and compresses the high-dose region, converting the hyperbola into a symmetric sigmoid. The lower asymptote corresponds to baseline with negligible target occupancy, the steep central region to the range where small changes in log dose produce large changes in effect, and the upper plateau to the maximal effect the system can produce once occupancy or a downstream step is saturating. The position of the curve along the dose axis reflects potency, while the height of the plateau reflects efficacy; standardised terminology for these features is set by the IUPHAR committee, and the sigmoid is formalised by the Hill equation.

Clinical relevance

The graded dose-response curve is the conceptual tool by which the relationship between exposure and the intensity of a drug effect is described and compared across drugs. This entry presents it for educational reference; it characterises how effects scale with dose and is not a basis for selecting doses in patients.

History

The graded dose-response curve emerged from early receptor-occupancy theory, which linked the fraction of receptors occupied to the size of the response. The use of a logarithmic dose axis to linearise the steep mid-range became standard practice in quantitative pharmacology, and Colquhoun's history traces how occupancy models and curve-fitting consolidated the modern graded curve.

Key figures

• Archibald Vivian Hill
• Terry Kenakin
• David Colquhoun

Seminal works

• neubig-2003
• colquhoun-2006

Frequently asked questions

Why is a dose-response curve sigmoid when plotted on a log dose axis?

On an arithmetic axis the underlying relationship is a saturating hyperbola; taking the logarithm of dose stretches the low-concentration range and compresses the high-concentration range, turning the hyperbola into a symmetric S-shaped curve with an easily identified half-maximal point.

What does the plateau at the top of a graded curve represent?

It represents the maximal effect (Emax) the system can produce: beyond this point adding more drug does not increase the response, because the target is fully engaged or a downstream step has become rate-limiting.