  Bacterial cells navigate around their environment by directing their movement
along chemical gradients. This process, known as chemotaxis, can promote the
rapid expansion of bacterial populations into previously unoccupied
territories. However, despite numerous experimental and theoretical studies on
this classical topic, chemotaxis-driven population expansion is not understood
in quantitative terms. Building on recent experimental progress, we here
present a detailed analytical study that provides a quantitative understanding
of how chemotaxis and cell growth lead to rapid and stable expansion of
bacterial populations. We provide analytical relations that accurately describe
the dependence of the expansion speed and density profile of the expanding
population on important molecular, cellular, and environmental parameters. In
particular, expansion speeds can be boosted by orders of magnitude when the
environmental availability of chemicals relative to the cellular limits of
chemical sensing is high. As analytical understanding of such complex
spatiotemporal dynamic processes is rare, the results derived here provide a
mathematical framework for further investigations of the different roles
chemotaxis plays in diverse ecological contexts.
