Hyperbola

The shape of most binding curves for ligands interacting reversibly with a receptor or other target protein is hyperbolic. This is also true for the shape of most dose-response curves. Binding is saturable, reaching a maximum plateau at (theoretically) infinitely high ligand concentrations. The concentration of ligand at which binding is 50% of the maximum possible binding gives the KD for the binding interaction. The shape of the curve is described by the Hill-Langmuir equation. If hyperbolic data are instead plotted on a logarithmic concentration scale, the data appear sigmoidal.

(Left panel) Binding curves for three ligands with KD values of 10 µM (red), 30 µM (green) and 100 µM (blue). The three hyperbolic curves will all reach a common plateau at Bmax, while the three X-axis intercepts indicated reveal the KD values. (Right panel) The same data plotted on a logarithmic concentration axis convert hyperbolic data to sigmoids. The X-intercepts now indicate log KD values. The benefits of plotting on a logarithmic concentration axis are clear; binding curves for drugs with KD values that are significantly different can be plotted in their entirety on the same graph.

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An ABC of PK/PD Copyright © 2023 by Dr. Andrew Holt is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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