用混合信号机制模拟双层组织中极性驱动的层模式
Modelling polarity-driven laminar patterns in bilayer tissues with mixed signalling mechanisms
摘要：
高分辨率实验方法的最新进展突出了细胞信号通路串扰和局部信号传导活动在许多生物系统的发展和疾病中的重要性。对多种信号通路的研究通常引入不同的细胞间通信方法，即基于接触的或扩散的信号传导，其产生对细胞行为的空间和时间依赖性。出于细胞机制，控制细胞命运的决定，在发展中的双层组织，我们使用动力系统加上多层图形分析的作用，信号极性和通路串扰的蛋白质活性的细颗粒图案的形成。具体来说，我们研究多层图边缘结构和权重如何影响双层结构中细胞的逐层（层）图案，这种结构常见于腺体组织中。给出了大尺度空间离散动力系统中齐次胞态存在、唯一和不稳定的充分条件。使用图形分割的模式模板生成商系统与单调动力系统的概念相结合的方法，我们利用广泛的降维提供存在条件所需的极性诱导细颗粒层模式与多个空间依赖的细胞内组件。然后，我们探索的商和大规模的动力系统之间的光谱联系，以扩展层流模式的标准，从存在到收敛足够大量的细胞极性在大规模的动力系统，独立的空间维度和组织中的细胞数量。
英文摘要：
Recent advances in high-resolution experimental methods have highlighted the significance of cell signal pathway crosstalk and localised signalling activity in the development and disease of numerous biological systems. The investigation of multiple signal pathways often introduces different methods of cell-cell communication, i.e. contact-based or diffusive signalling, which generates both a spatial and temporal dependence on cell behaviours. Motivated by cellular mechanisms that control cell-fate decisions in developing bilayer tissues, we use dynamical systems coupled with multilayer graphs to analyse the role of signalling polarity and pathway crosstalk in fine-grain pattern formation of protein activity. Specifically, we study how multilayer graph edge structures and weights influence the layer-wise (laminar) patterning of cells in bilayer structures, which are commonly found in glandular tissues. We present sufficient conditions for existence, uniqueness and instability of homogeneous cell states in the large-scale spatially discrete dynamical system. Using methods of pattern templating by graph partitioning to generate quotient systems in combination with concepts from monotone dynamical systems, we exploit the extensive dimensionality reduction to provide existence conditions for the polarity required to induce fine-grain laminar patterns with multiple spatially dependent intracellular components. We then explore the spectral links between the quotient and large-scale dynamical systems to extend the laminar patterning criteria from existence to convergence for sufficiently large amounts of cellular polarity in the large-scale dynamical system, independent of spatial dimension and number of cells in the tissue.
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