The influenza virion is characterized by two surface proteins, hemagglutinin (HA) and neuraminidase (NA). The changes in their surface antigenic sites have given rise to several subtypes – H1 to H16 for the hemagglutinin and N1 to N9 for the neuraminidase, and each influenza strain is identified with these subtypes such as the H5N1, H7N9, etc. Of the 16 x 9 combinations possible, only certain combinations are observed to proliferate in the wild, such as the H1N1, H3N2, H5N1, etc. This interdependence of the HA and NA on certain subtypes have been noticed, and experimentally demonstrated, but the underlying cause or its systematics have been unknown.

We have hypothesized that the base distribution characteristics of the HA and NA constitute a coupling between them. We estimate the coupling strength by measuring the distance in graph radii between the two genes in a graphical representation scheme. We found that this distance was characteristic of each subtype combination and forced combinations with a different HA or NA subtype led to widely different values, which by our hypothesis, and the experimental findings of Zhang et al, implied unstable combinations.

This hypothesis implies that given a stable subtype of pathogenic influenza, we can estimate using the coupling constants which other subtype combinations could emerge through reassortment. Thus in the case of the H5N2 strain which had an epidemic form in North America in 2015, we have calculated the consequences of altering the NA component. We found that only H5N4 and H5N9 combinations could match the coupling strength of the H5N2, thus implying that the next epidemics could arise from these combinations rather than other subtypes of H5. This allows for more focused monitoring of emerging flu strains for epidemic potential.