Generation of continuous ligand–macromolecule binding isotherms. Use of exponential concentration gradients

Continuous exponential concentration gradients, accurate, precise, and reproducible to better than 1% over at least a 10³–10⁴ concentration range, can be easily produced. In fact, it appears that these gradients may be substantially better than this. Such gradients have been used to generate a continuous ligand binding isotherm for the system Mg⁺⁺ + Eriochrome Black T over a 10⁶ ligand concentration range. This continuous isotherm is shown to be sufficiently precise to provide a first derivative function Γ(y), which is precise to 0.4%. The moments of Γ(y) were calculated and found to be extremely accurate. For example, the second moment about the mean was calculated to be 3.32 and 3.30 for two different experiments compared to a theoretical value of 3.29. The general application of these techniques to generate continuous ligand binding isotherms is discussed.