Center for Computational and Theoretical Biology, University of Würzburg, Würzburg, Germany.
J Math Biol. 2023 Sep 7;87(4):54. doi: 10.1007/s00285-023-01959-9.
During development, spatio-temporal patterns ranging from checkerboard to engulfing occur with precise proportions of the respective cell fates. Key developmental regulators are intracellular transcriptional interactions and intercellular signaling. We present an analytically tractable mathematical model based on signaling that reliably generates different cell type patterns with specified proportions. Employing statistical mechanics, We derived a cell fate decision model for two cell types. A detailed steady state analysis on the resulting dynamical system yielded necessary conditions to generate spatially heterogeneous patterns. This allows the cell type proportions to be controlled by a single model parameter. Cell-cell communication is realized by local and global signaling mechanisms. These result in different cell type patterns. A nearest neighbor signal yields checkerboard patterns. Increasing the signal dispersion, cell fate clusters and an engulfing pattern can be generated. Altogether, the presented model allows us to reliably generate heterogeneous cell type patterns of different kinds as well as desired proportions.
在发育过程中，会出现从棋盘状到吞噬状的时空调控模式，具有各自细胞命运的精确比例。关键的发育调节剂是细胞内转录相互作用和细胞间信号传递。我们提出了一种基于信号传递的可分析处理的数学模型，该模型可以可靠地生成具有指定比例的不同细胞类型模式。我们利用统计力学，为两种细胞类型推导出了一个细胞命运决策模型。对所得动力学系统的详细稳态分析得出了生成空间异质模式的必要条件。这使得细胞类型比例可以通过单个模型参数来控制。细胞-细胞通讯是通过局部和全局信号机制实现的。这些导致了不同的细胞类型模式。最近邻信号产生棋盘状模式。增加信号分散度，可以产生细胞命运簇和吞噬模式。总之，所提出的模型使我们能够可靠地生成不同种类的异质细胞类型模式以及所需的比例。
