A Simple Model of Multivalent Adhesion and Its Application to Influenza Infection

Adhesion between biological surfaces, which is typically the result of molecular binding between receptors on one surface and ligands on another, plays a fundamental role in biology and is key to the infection mechanisms of certain viruses, including influenza. The physiological outcome of adhesion depends on both the number of bound cells (or viruses, or other biological particles) and the properties of the adhesion interface that is formed, including the equilibrium number of receptor-ligand connections. Here, we introduce a quantitative model for biological adhesion by adapting thermodynamic models developed for the related problem of multivalent molecular binding. In our model, adhesion affinity is approximated by a simple, analytical expression involving the numbers of ligands and receptors at the interface. Our model contains only two fitting parameters and is simple to interpret. When applied to the adhesion between the hemagglutinin ligands on influenza viruses and the sialic acid receptors on biosensors or on host cells, our model generates adhesion affinities consistent with experimental measurements performed over a range of numbers of receptors, and provides a semiquantitative estimate of the affinity range of the hemagglutinin-sialic acid interaction necessary for the influenza virus to successfully infect host cells. The model also provides a quantitative explanation for the experimental finding that a mutant avian virus gained transmissibility in mammals despite the mutations conferring only a less than twofold increase in the affinity of its hemagglutinin for mammalian receptors: the model predicts an order-of-magnitude improvement in adhesion to mammalian cells. We also extend our model to describe the competitive inhibition of adhesion: the model predicts that hemagglutinin inhibitors of relatively modest affinity can dramatically reduce influenza virus adhesion to host cells, suggesting that such inhibitors, if discovered, may be viable therapeutic agents against influenza.