Pattern Formation in the Microbial World: Dictyostelium Discoideum

Abstract

Over the past few decades, there has been significant progress made towards understanding how non-equilibrium systems can generate interesting spatial patterns. These patterns range from the dendritic, sometimes fractal, morphologies seen in diffusively unstable interface motion [668] to the selforganized nonlinear waves in excitable dynamics [669] to the interacting localized structures which occur in Turing-unstable media [670]. In each of these examples, we have in place reasonably accurate theoretical models that allow us, by combining numerical simulation with mathematical analysis, to assess the importance of different parameters and make predictions for future experiments. While much work needs to be done and new surprises undoubtedly lie in wait, we are confident that the framework being used to study these processes is ultimately capable of resolving any issues that arise in this field.