Shape, shear, search and strife; mathematical models of bacteria

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Biological pattern formation is one of the most intriguing phenomena in nature. Simplestexamples of such patterns are represented by travelling waves and stationary periodic patternswhich occur during various biological processes including morphogenesis and populationdynamics. Formation of these patterns in populations of motile microorganisms such asDictyostelium discoideum and E. coli have been shown in several experimental studies.Conditions for formation of various types of patterns are commonly addressed in mathematicalstudies of dynamical systems containing diffusion and advection terms. In project,we show spatio-temporal patterns formed by growing populations of chemotactically activebacteria. First, we show formation of travelling wavefronts and Turing patterns in a one-speciespopulation. We show that Turing patterns form when bacteria produce chemical which is astrong attractant. We then move on to a system of two interacting bacterial populations, one ofwhich produces a chemotactic agent for another. Our analysis and numerical simulations showthat in this case Turing patterns form when the chemical acts as a repellent. Study of conditionsfor 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 supportedby means of numerical simulations.