The role of intracellular signaling in the stripe formation in engineered Escherichia coli populations

Recent experiments showed that engineered Escherichia coli colonies grow and self-organize into periodic stripes with high and low cell densities in semi-solid agar. The stripes develop sequentially behind a radially propagating colony front, similar to the formation of many other periodic patterns in nature. These bacteria were created by genetically coupling the intracellular chemotaxis pathway of wild-type cells with a quorum sensing module through the protein CheZ. In this paper, we develop multiscale models to investigate how this intracellular pathway affects stripe formation. We first develop a detailed hybrid model that treats each cell as an individual particle and incorporates intracellular signaling via an internal ODE system. To overcome the computational cost of the hybrid model caused by the large number of cells involved, we next derive a mean-field PDE model from the hybrid model using asymptotic analysis. We show that this analysis is justified by the tight agreement between the PDE model and the hybrid model in 1D simulations. Numerical simulations of the PDE model in 2D with radial symmetry agree with experimental data semi-quantitatively. Finally, we use the PDE model to make a number of testable predictions on how the stripe patterns depend on cell-level parameters, including cell speed, cell doubling time and the turnover rate of intracellular CheZ.Author summary: One of the central problems in biology is to understand the underlying mechanisms responsible for spatial pattern formation in complex systems. This is a difficult task because the essential mechanisms for pattern formation often involve multiple space and time scales and are often buried in overwhelmingly complex physiological details. Recently, synthetic biology has made it possible to investigate strategies of pattern formation in relatively simpler, but still complex, systems. Here we develop multiscale models to help explain the role of intracellular signaling in the formation of stripe patterns in engineered E. coli colonies.