Mathematical analysis and modeling of Notch signaling in zebrafish somitogenesis

许多生物过程需要细胞通讯来协调多细胞的行动，以产生适当的集体结果。信号细胞通过信号传导途径向邻近的靶细胞传递信号。这个过程包括细胞内和细胞间的反应。一个典型的例子是体细胞发生中的Notch信号。体细胞发生是脊椎动物细胞分化成身体轴部分的过程。Notch信号通过Notch蛋白与其配体的结合传递信号，调节细胞的集体行为。然而，由于脊椎动物胚胎的复杂性，在实验和计算上验证Notch信号的详细机制仍然很困难。对这些微观和宏观动态的分析需要高维晶格系统来包含空间信息并保持细胞的个性。然而，由于高维系统的复杂性，多单元动力学的分析结果是有限的。我提出的研究计划的长期目标是研究细胞内和细胞间反应如何调节细胞信号的集体细胞行为；我的小组将研究反应函数、系统网络和子系统的耦合类型如何影响整个系统的动力学。因此，在这个发现基金（DG）周期中，将建立一个数学和计算框架来研究斑马鱼体细胞发生中的Notch信号传导机制。对于数学家来说，影响将是构建细胞信号传导的广义模型和分析工具，使这些模型能够轻松扩展到研究其他细胞通信。为了研究集体细胞行为，我们将发展数学理论来克服高维系统中的挑战。将发现不同类型模型之间的联系，以扩展这些模型的好处。数学分析将描述动力学及其因果关系，以探索Notch信号如何协调集体结果。对于实验学家和生物学家来说，我们分析的标准将为通过预测胚胎成分的大小来帮助克服实验限制提供方法。计算结果将用于指导实验设计，可以在斑马鱼胚胎中进行操作，直接测试数学参数。总的来说，将建立一个广义的数学和计算框架来研究子系统和整个系统之间的关系，用于一般的细胞通信，适应时间和空间尺度的差异。重要的是，该项目为交叉训练新一代科学家提供了一个理想的环境，以获取和发展方法，结合数学，计算和生物学，以克服每个学科的局限性。

Many biological processes require cellular communication to coordinate multiple-cell actions for generating proper collective outcomes. The communication consists of signaling pathways in which signaling cells transmit signals to neighboring target cells. This process involves intracellular and intercellular reactions. A representative example is Notch signaling in somitogenesis. Somitogenesis is the process, in vertebrates, through which cells differentiate into segments of the body axis. Notch signaling transmits signals, through the binding between Notch protein and its ligands, to regulate collective cell behavior. However, it remains experimentally and computationally difficult to verify the detailed mechanisms of Notch signaling, due to the complexity of vertebrate embryos. Analysis of these microscopic and macroscopic dynamics requires high dimensional lattice systems to include space information and preserve the individuality of cells. However, analytic results for multiple-cell dynamics are limited, due to the complexity of high-dimensional systems. The long-term goal of my proposed research program is to investigate how the intracellular and intercellular reactions regulate the collective cell behavior of cellular signaling; my group will investigate how the reaction functions, system networks, and coupling types of subsystems affect the dynamics of the whole system in general. Hence, in this Discovery Grant (DG) cycle, a mathematical and computational framework will be built to investigate the mechanisms of Notch signaling in zebrafish somitogenesis. For mathematicians, the impact will be the construction of generalized models and analytical tools for cell signaling, enabling easy extension of these models to investigate other cellular communications. In order to investigate the collective cell behaviors, we will develop mathematical theories to overcome challenges in high dimensional systems. Connections between different types of models will be discovered to extend the benefits of these models. Mathematical analysis will characterize dynamics and their causal relation to explore how Notch signaling coordinates collective outcomes. For experimentalists and biologists, the criteria from our analysis will provide methods to help overcome experimental limitations by predicting the magnitude of embryonic components. Computational findings will be used to guide experimental designs that can be manipulated in zebrafish embryos to directly test mathematical parameters. Overall, a generalized mathematical and computational framework will be built to investigate the relation between subsystems and the whole system, for general cellular communication, accommodating differences in time and space scales. Importantly, this program provides an ideal environment for cross-training a new generation of scientists to acquire and develop methodologies, combining mathematics, computation, and biology, to overcome limitations in each discipline.