Collaborative Research: Analysis of spatiotemporal signal processing in developmental patterning

胚胎发育是由高度调控的基因表达的空间和时间模式驱动的。这些模式是在一个连续的过程中出现的，简单的模式为分子网络提供输入，分子网络反过来将这些输入转换为更复杂的输出。由于分子研究的最新进展，这些网络现在可以在机理水平上建模。探索复杂的力学模型在很大程度上依赖于计算技术的使用；同时，大型模型的行为通常可以通过分析简化的模型来理解，这为计算实验和真实实验之间提供了一座“桥梁”。用于分析发育模式中信号处理的动力学的严格的数学技术尚未开发出来。为此，PI建议采用一些分析方法来研究构图网络中的时空动力学。这些方法严重依赖于变分法的技术，将应用于果蝇卵上皮模式形成的背景下，这是一个已经建立的实验模型，用于研究简单的输入如何在发育中建立复杂的空间模式。拟议的分析和计算工作将以私人投资机构在上一个供资期间获得的建模和实验结果为基础。在这一应用的框架内，PI将专注于具有正反馈回路的二维图案网络的信号处理。拟议的研究与表皮生长因子受体(EGFR)介导的图案形成实验工作密切相关，EGFR是跨物种上皮组织的关键调节因子。鉴于EGFR信号的高度保守性和诱导模式事件的普遍性，PI的工作将为一大类发展问题提供见解。此外，本建议所发展的数学技巧将适用于以非线性抛物型偏微分方程式为模型的各种问题。这项研究与PIS的教育努力密切相关，包括进一步发展关于细胞通信系统的数学生物学的本科生和研究生课程，以及对NJIT和普林斯顿的数学和工程研究生和本科生进行跨学科培训。

Embryonic development is driven by highly regulated spatial and temporal patterns of gene expression. These patterns emerge in a sequential process, with simple patterns providing inputs to molecular networks, which, in turn, transform these inputs into more complex outputs. Due to the recent advances in the molecular studies of development, these networks can now be modeled at mechanistic level. Exploring complex mechanistic models is critically dependent on the use of computational techniques; at the same time, the behavior of large-scale models can often be understood through analysis of simplified models, providing a "bridge" between computational and real experiments. Rigorous mathematical techniques for analyzing the dynamics of signal processing in developmental patterning are yet to be developed. To this end, the PIs propose to pursue a number of analytical approaches for studying the spatiotemporal dynamics in patterning networks. These approaches, which rely heavily on the techniques from the calculus of variations, will be applied in the context of epithelial pattern formation in the Drosophila egg, an established experimental model for studying how simple inputs establish complex spatial patterns in development. The proposed analytical and computational work will build on the modeling and experimental results obtained by the PIs during the previous funding period. Within the framework of this application, the PIs will focus on signal processing by two-dimensional patterning networks with positive feedback loops.The proposed research is closely linked to the experimental work on pattern formation mediated by the Epidermal Growth Factor Receptor (EGFR), a key regulator of epithelial tissues across species. Given the highly conserved nature of EGFR signaling and the generality of inductive patterning events, the work of the PIs will provide insights into a large class of development problems. In addition, the mathematical techniques developed in this proposal will be applicable to a wide range of problems modeled by nonlinear parabolic partial differential equations. This research is strongly aligned with the educational effort of the PIs that involves further development of undergraduate and graduate courses on mathematical biology of cell communication systems and interdisciplinary training of mathematics and engineering graduate and undergraduate students at NJIT and Princeton.