Assembly systems in molecular biology: A graph theory of genetic complementation between two related species

In this report I discuss the interpretation of the data of genetic complementation in vivo of assembly systems between two related species, such as the complementation of structural proteins between related bacteriophages. It is suggested that such experiments reveal interactions between gene products that are overlooked in many other experiments. A mathematical model based on the graph theory is presented, assuming that the assembly system consists of gene products and interactions between them. The model shows that information from the complementation experiment is limited to those interactions which are mismatching if the interacting gene products are produced by different species. Moreover, it shows that the number and positions of mismatching interactions cannot always be determined uniquely by the data of complementation. However, there is a mathematical method by which one can calculate all the possible solutions for the number and positions of mismatching interactions from experimental data. Actual calculation is performed for a simple example. Thus, the model clarifies validity and limitation of complementation experimiments between related species.