Abstract
We report experimental and theoretical results for spatiotemporal pattern formation in cell populations, where the parameters vary in space and time due to mechanisms intrinsic to the system, namely Dictyostelium discoideum (D.d.) in the starvation phase. We find that different patterns are formed when the populations are initialized at different developmental stages, or when populations at different initial developmental stages are mixed. The experimentally observed patterns can be understood with a modified Kessler–Levine model that takes into account the initial spatial heterogeneity of the cell populations and a developmental path introduced by us, i.e. the time dependence of the various biochemical parameters. The dynamics of the parameters agree with known biochemical studies. Most importantly, the modified model reproduces not only our results, but also the observations of an independent experiment published earlier. This shows that pattern formation can be used to understand and quantify the temporal evolution of the system parameters.
Highlights
Pattern formation has been broadly studied in living and non-living systems over a large range of scales [1,2,3], e.g., animal coats, shells, butterfly wings [4], in dynamics of cardiac tissues [5], in chemical reactions like the Belusov-Zhabotinsky reaction [6]
We show that spatial heterogeneity of cell density and parameters combined with a specific temporal evolution of the system parameters semi-quantitatively reproduce the experimental results
We observed different patterns depending on the initial starvation times as shown in figure 1
Summary
Pattern formation has been broadly studied in living and non-living systems over a large range of scales [1,2,3], e.g., animal coats, shells, butterfly wings [4], in dynamics of cardiac tissues [5], in chemical reactions like the Belusov-Zhabotinsky reaction [6]. During the embryogenesis of the fruit fly Drosophila, the activation of different genes at different stages causes the spatial patterning [7] While these patterns can be visualized correlating these patterns with the changing dynamics of the system is challenging. The cells exhibit social behavior when they begin to starve [18] They secrete a chemical called cyclic adenosine monophosphate (cAMP) as a response to starvation. On failing to find nutrients, the slug develops into a fruiting body; the cells that form its stalk die and the cells at its top become spores [23]
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