Collaborative Research: Analysis of spatiotemporal signal processing in developmental patterning

胚胎发育受基因表达的高度调控的空间和时间模式驱动。 这些模式在一个连续的过程中出现，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化为更复杂的输出。 由于最近的进展，在发展的分子研究，这些网络现在可以在机制水平建模。 探索复杂的机械模型是关键依赖于使用计算技术，在同一时间，大规模的模型的行为往往可以通过分析简化模型，提供了一个“桥梁”之间的计算和真实的实验。用于分析发育模式中信号处理动态的严格数学技术还有待开发。 为此，PI提出了一些分析方法来研究图案网络中的时空动态。 这些方法在很大程度上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，这是一个建立的实验模型，用于研究简单的输入如何在发展中建立复杂的空间模式。 拟议的分析和计算工作将建立在上一个资助期内由PI获得的模型和实验结果的基础上。 在这个应用程序的框架内，PI将专注于通过具有正反馈回路的二维图案网络进行信号处理。拟议的研究与表皮生长因子受体（EGFR）介导的图案形成的实验工作密切相关，EGFR是跨物种上皮组织的关键调节因子。 鉴于EGFR信号转导的高度保守性和诱导模式化事件的普遍性，PI的工作将为一大类发育问题提供见解。 此外，在这个建议中开发的数学技术将适用于广泛的问题建模的非线性抛物型偏微分方程。 这项研究与PI的教育工作密切相关，包括进一步开发细胞通信系统数学生物学的本科生和研究生课程，以及NJIT和普林斯顿大学数学和工程研究生和本科生的跨学科培训。

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.