Waterloo, December 8 - 11, 2017
Most phages can only infect a limited set of strains within a bacterial species. Thus resistant bacteria may emerge. Bacterial resistance is generally due to loss of the receptor molecule to which a phage binds. Because this receptor is involved in bacterial metabolism, the phage-resistant bacteria are usually the weaker competitors than phage-sensitive bacteria for the limiting resource.
Recently Tzipilevich et al. discovered a phenomenon called ``acquisition of sensitivity", in which bacteria lacking phage receptors can become transiently sensitive to phage and get infected. This is caused by transfer of phage receptors to the resistant cells, released from phage-sensitive cells, mediated by membrane vesicles. Acquisition of sensitivity implies that the resistant mutant loses more competitiveness than that expected in the literature, so the persistence of the mutant bacteria becomes even less possible. In our work, using persistence theory and the numerical solver DDE-BIFTOOL, we analyze a delay system involving the acquisition of sensitivity to confirm this prediction.
We establish a threshold for survival and extinction: in the former case, it
is confirmed using Lyapunov functionals that the population approaches the
delay modified carrying capacity; in the later case the extinction is proved
by the fluctuation lemma. We further use the adaptive dynamics to conclude
that the evolutionary trend is to make the mean delay in growth as short as
possible. This confirms Hutchinson’s conjecture and fits biological evidence.