Mathematical Tools for Developmental Signaling Networks

描述（由申请人提供）：从简单的成群变形虫原生动物到人类胚胎，生物系统发展的关键是模式。细胞内的信号网络可以通过细胞膜相互作用产生模式，作为局部相互作用的涌现特性。实验生物学家已经开发了一系列令人印象深刻的工具来探测发育信号机制，然而，即使是相对简单的信号网络的复杂性也决定了特定分子或遗传干预与由此产生的组织水平模式之间的关系将难以直观理解。本研究的目标是设计一个建模框架，分层混合系统，以及伴随的数学分析和计算工具，以询问所提出的导致模式的信号网络的属性。混合系统不断发展，并且具有阶段性操作，可以表示不同机制，控制规律或控制动态的逻辑开关。与连续模型相比，混合系统模型具有分析和计算方面的优势，因为它们可以将大型复杂系统表示为由较小的、相互作用的连续子系统组成的系统，这样更容易分析。本研究的实验平台将是一种称为平面细胞极性（PCP）的机制，它使膜平面内的上皮细胞极化。在果蝇中，PCP与其他机制相互作用，产生翅膀上的毛发，腿上的分割和关节形成：PCP的突变导致毛发和关节模式扭曲。在人类中，PCP的中断似乎会导致先天性耳聋综合征和神经管闭合缺陷，从而导致脊柱裂和相关疾病。因此，提出的研究目的是：(1)开发层次混合系统的数学建模和分析工具，(2)将这些工具应用于果蝇PCP问题。长期目标是利用这项研究最终帮助理解人类相应的信号传导。

DESCRIPTION (provided by applicant): Key to the development of biological systems, from simple swarming amoeboid protozoans, to human embryos, is patterning. Signaling networks within cells can interact with each other across cell membranes to produce patterns as emergent properties of Iocal interactions. Experimental biologists have developed an impressive array of tools to probe developmental signaling mechanisms, however, the complexity of even relatively simple signaling networks dictates that the relationship between a specific molecular or genetic intervention and the resulting tissue level pattern will defy intuitive understanding. The goal of this proposed research is to design a modeling framework, hierarchical hybrid systems, and accompanying mathematical analysis and computational tools, to interrogate the properties of proposed signaling networks which cause patterning. Hybrid systems evolve continuously, as well as have a phased operation which can represent the logical switching on and off of different mechanisms, control laws, or governing dynamics. Hybrid system models have analytic and computational advantages over continuous models, because they can be used to represent large complex systems as systems of smaller, interacting continuous subsystems, which are easier to analyze. The testbed for this study will be a mechanism called planar cell polarity (PCP) which polarizes epithelial cells within the plane of the membrane. In Drosophila, PCP interacts with other mechanisms which produce hairs on the wing, and segmentation and joint formation in the legs: mutations in PCP induce distorted hair and joint patterns. In humans, disruptions in PCP appear to result in congenital deafness syndromes and neural tube closure defects leading to spina bifida and related conditions. The aims of the proposed research are thus to (I) develop mathematical modeling and analysis tools for hierarchical hybrid systems, and (2) apply these to problems in PCP in Drosophila. The long term goals are to use this research to eventually aid in understanding the corresponding signaling in humans.