A generalized epistasis analysis as a method of reconstruction of developmental process and its application to drosophila dorso-ventral axis formation

Epistasis analysis has been used in molecular genetics to infer cause and effect relationships among loci that decide a developmental fate. In this paper, in order to investigate the logical background of the rule that relates epistasis and causal relation, a mathematical epistasis analysis is formulated. An “orderliness index” is introduced by which the cause-and-effect relation can systematically be extracted from genotype-phenotype data. This method is applied toDrosophila melanogasterdorso-ventral axis formation and it is shown that the method of reconstructing the framework of the causal relation between a locus and its sign (activation or inhibition) as an “orderliness diagram” from eight groups of the genes. From the diagram it can be seen that thedorsalgene works as a morphogen. The difference between orderliness diagrams of the dorsal and ventral sides of the embryo shows that the cells on the ventral side receive the signal and the fate of the cells on the dorsal side is default in the wild-type embryo.