HETEROGENEITY ANALYSIS FOR BINDING DATA USING AN ADAPTED SMOOTHING SPLINE TECHNIQUE

Heterogeneity analysis is a helpful tool to select a proper model for the description of ion binding to polyfunctional ligands. Two approaches of heterogeneity analysis are discussed: the local isotherm approximation (LIA) method and the differential equilibrium function (DEF) method. For both methods, the approximate distribution function of a given ligand system is a series of derivatives of the experimentally obtained binding function. To obtain reliable derivatives, a smoothing spline routine is adapted for the present problem. The smoothing parameter of the spline is determined by a generalized cross-validation criterion in combination with physical constraints derived from the binding function. With the thus obtained spline function, the distribution is calculated. Error bars for the obtained distribution function can be calculated using the variance in the spline function. The error bars indicate whether peaks in the distribution are significant. The methodology ia applied to a synthetic data set to illustrate its capabilities and limitations and is applied to copper binding to humic materials (data set of Hansen et al.) to illustrate its use in practice. The quality of the calculated distribution function depends on the experimental error in the data, the number of data points, and the binding range. On the basis of the calculated distribution function, a binding model can be selected.