Gnarled-Trunk Evolutionary Model of Influenza A Virus Hemagglutinin

Human influenza A viruses undergo antigenic changes with gradual accumulation of amino acid substitutions on the hemagglutinin (HA) molecule. A strong antigenic mismatch between vaccine and epidemic strains often requires the replacement of influenza vaccines worldwide. To establish a practical model enabling us to predict the future direction of the influenza virus evolution, relative distances of amino acid sequences among past epidemic strains were analyzed by multidimensional scaling (MDS). We found that human influenza viruses have evolved along a gnarled evolutionary pathway with an approximately constant curvature in the MDS-constructed 3D space. The gnarled pathway indicated that evolution on the trunk favored multiple substitutions at the same amino acid positions on HA. The constant curvature was reasonably explained by assuming that the rate of amino acid substitutions varied from one position to another according to a gamma distribution. Furthermore, we utilized the estimated parameters of the gamma distribution to predict the amino acid substitutions on HA in subsequent years. Retrospective prediction tests for 12 years from 1997 to 2009 showed that 70% of actual amino acid substitutions were correctly predicted, and that 45% of predicted amino acid substitutions have been actually observed. Although it remains unsolved how to predict the exact timing of antigenic changes, the present results suggest that our model may have the potential to recognize emerging epidemic strains.