[22] Simultaneous analysis for testing of models and parameter estimation

This chapter describes the application of the least-squares method by providing two examples of current problems, which benefit from simultaneous analyses. The two examples are the linear extrapolation method for determination of protein unfolding free energy changes and the individual site binding approach for the determination of protein–DNA interaction free energy changes. In the former case, it is found that by properly formulating the model to apply the least-squares criterion to baseline extensions and extrapolation of free energy changes, more realistic limits to the estimate of the unfolding free energy change are obtained. Simultaneous analysis of the effects of different denaturants increases the precision of the estimates and provides confidence in some of the assumptions of the model. In the later case, the proper combination of data for binding of a repressor ligand to a multisite operator DNA and to reduced valency mutants is necessary to resolve all of the interaction free energy changes. The chapter introduces nonlinear least-squares techniques, which provide direct means of analysis for complex models and illustrates by example the powerful technique of simultaneous analysis for resolving parameters and testing the adequacy of the model used by the investigator.