  Influenza viruses enter a cell via endocytosis after binding to the surface.
During the endosomal journey, acidification triggers a conformational change of
the virus spike protein hemagglutinin (HA) that results in escape of the viral
genome from the endosome to the cytoplasm. A quantitative understanding of the
processes involved in HA mediated fusion with the endosome is still missing. We
develop here a stochastic model to estimate the change of conformation of HAs
inside the endosome nanodomain. Using a Markov-jump process to model the
arrival of protons to HA binding sites, we compute the kinetics of their
accumulation and the mean first time for HAs to be activated. This analysis
reveals that HA proton binding sites possess a high chemical barrier, ensuring
a stability of the spike protein at sub-acidic pH. Finally, we predict that
activating more than 3 adjacent HAs is necessary to prevent a premature fusion.
