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

细胞细长霉菌盘形盘基钢（Dictyostelium disideum, d.d.）是生物学中研究模式形成和发育的重要模式生物。当营养物质被剥夺时，D.d.细胞通过对趋化剂cAMP的趋化反应聚集，然后发育成多细胞子实体。细胞通过自发释放cAMP脉冲启动这一过程。其他细胞对引诱物的刺激作出反应，向其来源移动并传递信号。结果，圆形和螺旋形波形随时间形成，其周期为几分钟。在自然环境中，这种聚集发生在森林土壤中，并可能受到水流的影响。我们早期在一群信号dd细胞中对流驱动波的研究表明，外部流可以显著改变波的产生过程。在本项目的实验部分，我们旨在研究流驱动波对细胞迁移和D.d.细胞聚集模式的影响。我们试图回答的一些问题如下：1)水流对d.d.d细胞的时空格局形成和细胞迁移的影响是什么？2)在细胞信号传导的早期阶段，流动驱动波的存在如何影响后期D.d.细胞的聚集模式？3)流量对森林土壤中这些生物的生态是否起重要作用？此外，我们计划系统地研究外部cAMP脉冲存在下的自组织流驱动波，以探索系统响应锁定于外部cAMP注入频率的参数区域。在强迫振荡系统中，显示锁相响应区域的图称为阿诺德舌图。这将是首次探索在饥饿下经历发育途径的生命系统的完整阿诺德舌头图。在平行理论工作中，我们希望将二维martiel - goldbetter模型的模拟扩展到三维，并研究三维中cAMP的扩散对流动驱动波的作用。我们还打算在模拟中包括趋化细胞运动，以研究在流驱动波存在下细胞群的分布。此外，我们将进行广泛的数值模拟，以找到阿诺德图不同区域之间的过渡线，并将结果与实验结果进行比较。

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.