二维和三维双层结构中通过侧抑制确定层状模式分叉的代数框架
Algebraic framework for determining laminar pattern bifurcations by lateral-inhibition in 2D and 3D bilayer geometries
摘要：
细颗粒模式产生的阿曲他克林信号，已被研究使用静态单层细胞域。不幸的是，由于非线性动力系统的代数复杂性，分析结果仅限于少数细胞。在乳腺中观察到的Notch表达的同心图案的动机，我们结合了图形和控制理论的概念来表示细胞连接。由此产生的理论框架，使我们能够利用在2D和3D的多细胞双层结构的对称性，从而推导出的分析条件，驱动动力系统，以形成与制定细胞极性的层状图案。关键的是，条件是独立的精确的动力学细节，因此框架允许最大的一般性，在理解细胞的几何形状对图案的影响，在侧抑制系统。将分析条件应用于乳腺类器官表明，使用侧向抑制机制在静态双层内维持分层细胞类型需要强烈的细胞信号极性。此外，通过采用二维和三维细胞为基础的模型，我们强调，来自静态域的细胞极性条件有能力在动态环境中产生层状图案。然而，它们不足以维持图案时，受到实质性的形态扰动。与严格的信号极性诱导的细胞的数学含义一致，我们提出了一个粘附依赖性Notch-Delta生物过程，它有可能在发育中的乳腺类器官中启动双层分层。
英文摘要：
Fine-grain patterns produced by juxtacrine signalling, have been studied using static monolayers as cellular domains. Unfortunately, analytical results are restricted to a few cells due to the algebraic complexity of nonlinear dynamical systems. Motivated by concentric patterning of Notch expression observed in the mammary gland, we combine concepts from graph and control theory to represent cellular connectivity. The resulting theoretical framework allows us to exploit the symmetry of multicellular bilayer structures in 2D and 3D, thereby deriving analytical conditions that drive the dynamical system to form laminar patterns consistent with the formulation of cell polarity. Critically, the conditions are independent of the precise dynamical details, thus the framework allows for the utmost generality in understanding the influence of cellular geometry on patterning in lateral-inhibition systems. Applying the analytic conditions to mammary organoids suggests that intense cell signalling polarity is required for the maintenance of stratified cell-types within a static bilayer using a lateral-inhibition mechanism. Furthermore, by employing 2D and 3D cell-based models, we highlight that the cellular polarity conditions derived from static domains have the capacity to generate laminar patterning in dynamic environments. However, they are insufficient for the maintenance of patterning when subjected to substantial morphological perturbations. In agreement with the mathematical implications of strict signalling polarity induced on the cells, we propose an adhesion dependent Notch-Delta biological process which has the potential to initiate bilayer stratification in a developing mammary organoid.
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