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 approach es of heterogeneity analysis are discussed: the local isotherm approxi mation (LIA) method and the differential equilibrium function (DEF) me thod. For both methods, the approximate distribution function of a giv en ligand system is a series of derivatives of the experimentally obta ined binding function. To obtain reliable derivatives, a smoothing spl ine routine is adapted for the present problem. The smoothing paramete r of the spline is determined by a generalized cross-validation criter ion 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 c alculated using the variance in the spline function. The error bars in dicate whether peaks in the distribution are significant. The methodol ogy ia applied to a synthetic data set to illustrate its capabilities and limitations and is applied to copper binding to humic materials (d ata set of Hansen et al.) to illustrate its use in practice. The quali ty 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.