Analysis of parameter resolution from derivatives of binding isotherms

Examination of binding information in the form of derivative (or finite difference) measurements is explored (1) experimentally by a thin-layer optical procedure (Dolman, D. & Gill, S. J. (1978) Anal. Biochem. 87, 127–134) and (2) theoretically by simulation in order to determine the influence of the number of data points and their standard error upon the resolvability of binding parameters in cooperative and non-cooperative systems. The data is described by the difference in optical absorbance divided by the change in the logarithm of the ligand activity and each data point is assumed to be influenced by a random error with a given variance. It is found that increasing the number of data points, which in turn effectively reduces the magnitude of the observed absorbance changes, results in an increase in the uncertainty of the resolved parameters of the system. The effect is verified by both experimental and simulation studies. Thus one is led to suggest that fewer measurements for the change of absorbance with larger magnitudes produces the most favorable situation for parameter resolution when the data is in the form of finite difference measurements.