Mathematical analysis and modeling of Notch signaling in zebrafish somitogenesis

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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.