Analysis of binding in macromolecular complexes: a generalized numerical approach

In this work, we introduce a generalized, global numerical methodology for analysis of binding phenomena in complex macromolecular assemblies. On the basis of a numerical algorithm (EQS) to solve systems of simultaneous free energy equations, binding profiles of simple to highly complex interacting systems can be analyzed over any concentration region without any need to generate an analytical form to describe the data. The output of the numerical algorithm is the concentration of each individual species in solution, allowing the generation of all possible binding profiles of the system (e.g., protein saturation by ligand). We present here the application of this approach to the DNA-protein subunit-ligand interactions of the trp repressor system as a typical example. From a practical point of view, the analysis program is capable of the rapid and simultaneous analysis of multiple binding profiles in terms of internally consistent sets of free energies. Given both the enormous complexity, as well as the underlying subtlety, involved in the regulation of biological function, the present generalized approach to analyzing macromolecular binding should find wide applications.