A Traveling-Wave Solution for Bacterial Chemotaxis with Growth

Abstract

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.

arXiv comment27 pages main text, 34 pages Supplemental Information

References in corpus (10)

• Front propagation into unstable states
• Genetic drift at expanding frontiers promotes gene segregation
• Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
• Optimisations for quadrature representations of finite element tensors through automated code generation
• Efficient Assembly of H(div) and H(curl) Conforming Finite Elements
• Migration of chemotactic bacteria in soft agar: role of gel concentration
• Automating the Finite Element Method
• Automated code generation for discontinuous Galerkin methods
• Traveling Wave and Aggregation in a Flux-Limited Keller-Segel Model
• Benchmarking Domain-Specific Compiler Optimizations for Variational Forms

Cited by in corpus (5)

• Chemotactic smoothing of collective migration
• Cellular Sensing Governs the Stability of Chemotactic Fronts
• Influence of confinement on the spreading of bacterial populations
• Structured foraging of soil predators unveils functional responses to bacterial defenses
• Acceleration of Propagation in a chemotaxis-growth system with slowly decaying initial data