Regression analysis of simulated radio-ligand equilibrium experiments using seven different mathematical models

The objective of this study was to investigate the conditions for regression analysis of data from equilibrium experiments. One important issue was to recognize that Kd and the binding site concentration (A) are not of equal nature, although both are parameters in the regression analysis. Whereas Kd approximates to a true constant, A is subject to experimental variation due to pipetting errors and in solid-phase experiments also to uneven coating properties. While recognizing that the ideal assumptions for ordinary regression analysis are poorly satisfied, different regression models were evaluated by extensive simulations. It was first established by a 'worst case' investigation that a limited error (8%) in the dependent variable is not critical for the results obtained at curve-fitting to Langmuir's equation. Seven different equations were compared for the calculation of data representing a solid-phase equilibrium experiment with statistical but no systematic errors. All the equations are rearrangements of the law of mass action. In this setting the Scatchrd plot gave the best result, but also the double reciprocal and the Woolf plots worked well in weighted analysis. Langmuir's equation gave the best result of the 4 nonlinear regression models tested. The influence of one type of systematic error was also investigated. This assumed that 10% of the label was positioned on particles other than the functional ligand molecules. This systematic error was amplified, which resulted in a substantial bias. The calculated Kd-values varied slightly with the regression method used and were almost 24% too high in the best methods.