Implementation and refinement of the algorithm underlying the FLEXIFIT method was completed, resulting in two completed FORTRAN programs, FLEXIFIT v2.1 and FLEXIFIT v3.1. This method combines the advantages of empirical, nonparametric methods with those of traditional parametric modeling approaches. It seeks to characterize the common shape of a family of curves, and then to assess differences between curves via four linear scaling parameters. A substantial theoretical difficulty had been finding an estimate for the effective """"""""degrees of freedom"""""""" for the residual sum of squares after estimating the shape and four additional parameters. The theoretical solution involves calculation of the trace of a matrix. An efficient means for this calculation has now been incorporated into the FLEXIFIT program. Further, the new algorithm for minimization of a penalized sum of squares has been implemented. Tests show it to be much more stable than previous algorithms to changes in initial estimates. A second phase of the study of optimal design for ligand binding has been completed, with a compilation of designs for two-ligand experiments. Unlike the earlier designs for a single ligand, no universal rules or patterns emerged to describe such designs. Application of the sequential refinement of designs technique has been accomplished for a glucocorticoid receptor assay, resulting in an assay design requiring only a single animal rather than 15. New investigations were begun into the problems of analysis of hormone pulsatile data, specifically finding optimal estimates for the number of pulses in a convolved binomial-gaussian process. Substantial progress was made in finding algorithms for calculating the two-dimensional discrete and continuous affinity distribution from a family of binding curves. A theoretical link between these two problems was found utilizing a new algorithm for smooth, constrained numerical deconvolution.
