Flow-driven waves, Phase-Locked patterns and Arnold-tongues during aggregation of Dictyostelium discoideum

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The cellular slim mold Dictyostelium discoideum (D.d.) is a valuable model organism to study pattern formation and development in biology. When deprived of nutrients, D.d. cells aggregate by a chemotactic response to the chemoattractant cAMP and then develop to form multicellular fruiting bodies. The cells initiate the process by the spontaneous release of cAMP pulses. The other cells respond to the attractant stimulation by moving towards its source and by relaying the signal. As a result, circular and spiral wave patterns form with time which have a periodicity of few minutes. In the natural environment, this aggregation occurs in forest soil and may be subject to water flow. Our earlier work on flow-driven waves in a colony of signaling D.d. cells has shown that the external flow can significantly change the wave generation processes. In the experimental part of this project, we aim to investigate the effect of flow-driven waves on cell migration and the aggregation pattern of D.d. cells. Some of the questions we seek to answer are as follows: 1) What are the effects of water flow on the spatiotemporal pattern formation and cell migration of D.d. cells? 2) How does the presence of flow-driven waves in early stages of cell signaling influence the aggregation pattern of D.d. cells in later times? 3) Does flow play any significant role on the ecology of these organisms in the forest soil? Furthermore, we plan to systematically study self-organized flow-driven waves in the presence of external pulses of cAMP to explore the regions of parameters where the system response is locked to the injection frequency of external cAMP. In forced oscillatory systems, the map exhibiting regions of phase-locked responses is called Arnold tongues diagram. This would be the first effort to explore the complete Arnold tongues diagram for a living system that undergoes a developmental pathway under starvation. In the parallel theoretical work, we would like to extend our two-dimensional simu- lations of Martiel-Goldbeter model to three dimensions and investigate the role of diffusion of cAMP in three dimensions on flow-driven waves. We also aim to include chemotactic cell movement in the simulations to study the distribution of cell population in the presence of flow-driven waves. Furthermore, we will perform extensive numerical simulations to find the transition lines between different regions of the Arnold diagram and compare the results with the experimental findings.