Pore-forming toxins are polymeric cytotoxins used by both bacteria and the immune system that kill cells by forming pores on the cell membrane. Experiments that track the formation of a single pore reveal that pore formation is surprising fast, yet partially-formed pores are not seen. In this paper, we developed a model for pore formation that explains those observations. Moreover, our mathematical model provides insights to hindering the action of pore-forming toxins in bacteria.

We analysed the Cahn-Hilliard Equation with degenerate mobility using formal matched asymptotics. The analysis showed that the long-time sharp interface limit is not given by the so-called surface diffusion model, as was assumed in all previous literature. 

Using a simple heuristic argument, we showed the physical reasons underlying why degenerate mobilities in Cahn-Hilliard equation are insufficient to capture surface diffusion.