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Influenza virus evolves to escape from immune system antibodies that bind toit. We used free energy calculations with Einstein crystals as reference statesto calculate the difference of antibody binding free energy ($\Delta\Delta G$)induced by amino acid substitution at each position in epitope B of the H3N2influenza hemagglutinin, the key target for antibody. A substitution withpositive $\Delta\Delta G$ value decreases the antibody binding constant. Onaverage an uncharged to charged amino acid substitution generates the highest$\Delta\Delta G$ values. Also on average, substitutions between small aminoacids generate $\Delta\Delta G$ values near to zero. The 21 sites in epitope Bhave varying expected free energy differences for a random substitution.Historical amino acid substitutions in epitope B for the A/Aichi/2/1968 strainof influenza A show that most fixed and temporarily circulating substitutionsgenerate positive $\Delta\Delta G$ values. We propose that the observed patternof H3N2 virus evolution is affected by the free energy landscape, the mappingfrom the free energy landscape to virus fitness landscape, and random geneticdrift of the virus. Monte Carlo simulations of virus evolution are presented tosupport this view.

Predicting Fixation Tendencies of the H3N2 Influenza Virus by Free Energy Calculation