Diffusion Model of Phenotype Evolution in Helicobacter pylori

Abstract: Helicobacter pylori are bacteria that colonize the human stomach and are associated with diseases of the upper gastrointestinal tract. About half of the world's population is colonized with H. pylori. Because colonization appears to confer benefits (reduced risk of esophageal diseases) as well as costs (increased risk of peptic ulcer disease and gastric adenocarcinoma), it is important to understand the biology of host-microbial interaction. Examination of the selective pressures on H. pylori provide a model for evolution of Lewis antigen phenotypes during the colonization of a human host. A nonlinear diffusion equation model of Lewis antigen expression in H. pylori will be presented. The model incorporates the following key elements: H. pylori strains are highly diverse and continued variation is occuring during colonization; (2) H. pylori Lewis expression varies during colonization and host characteristics select for particular phenotypes; and (3) H. pylori strains have substantial ability to mutate and to recombine DNA with other H. pylori strains, thus providing opportunity for quasi-species development. The model has the form

where u(y,t) is the density of bacteria with respect to Lewis antigen type y, corresponds to the rate of mutation, is the selection coefficient, is the crowding parameter, and H is the recombination operator. Model simulations will be compared to data.