Chemical synthesis of [32P]pyrophosphate with high specific activity

Graphical methods have traditionally been the principal means for estimation of parameters (e.g., affinity constants, cooperativity parameters, and concentrations of receptor sites) in enzymology and ligand-binding problems. The present report provides a review of these methods as well as new results, as applied to three coordinate systems popularly used in ligand-binding studies: $\text{B}\text{F}$ vs [Bound]. $\text{B}\text{F}$ vs [Free], and $\text{B}\text{F}$ vs [Total]. We consider two extremely general models, the statistical mechanical model and the Adair model for equilibrium ligand binding. We also consider a very specialized case of receptor interaction wherein the equilibrium constannt of dissociation is linearly related to receptor occupancy. We collect previously described equations and derive new ones, to enable the user to estimate the parameters of the models in terms of relatively easily measurable graphical characteristics. We have evaluated the performance of these methods in representative cases using Monte Carlo studies. The results indicate the kind of precision and accuracy which can be obtained with typical experimental designs. Depending upon the magnitude of experimental error, the graphical methods can provide dependable values for the binding parameters. However, in general, the results obtained by the graphical methods should be regarded as reasonable initial estimates for further refinement by weighted nonlinear least-squares curve fitting.