Pattern formation in growing populations of motile bacteria

Biological pattern formation is one of the most intriguing phenomena in nature. Simplest
examples of such patterns are represented by travelling waves and stationary periodic patterns
which occur during various biological processes including morphogenesis and population
dynamics. Formation of these patterns in populations of motile microorganisms such as
Dictyostelium discoideum and E. coli have been shown in several experimental studies.
Conditions for formation of various types of patterns are commonly addressed in mathematical
studies of dynamical systems containing diffusion and advection terms. In project,
we show spatio-temporal patterns formed by growing populations of chemotactically active
bacteria. First, we show formation of travelling wavefronts and Turing patterns in a one-species
population. We show that Turing patterns form when bacteria produce chemical which is a
strong attractant. We then move on to a system of two interacting bacterial populations, one of
which produces a chemotactic agent for another. Our analysis and numerical simulations show
that in this case Turing patterns form when the chemical acts as a repellent. Study of conditions
for formation of Turing patterns is done using linear stability analysis while their characteristics
(amplitude and wavelength) are found using Fourier series. Analytical results are also supported
by means of numerical simulations.