Mathematical Tools for Developmental Signaling Networks

描述(申请人提供)：从简单的成群的变形虫原生动物到人类胚胎，生物系统发展的关键是图案化。细胞内的信号网络可以跨越细胞膜相互作用，以产生作为局部相互作用的紧急特性的模式。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索发育信号机制，然而，即使是相对简单的信号网络的复杂性也决定了特定的分子或基因干预与由此产生的组织水平模式之间的关系将违反直观的理解。这项拟议的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，以询问拟议的信令网络的属性，导致模式。混杂系统不断进化，具有阶段性运行，可以代表不同机构、控制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上的优势，因为它们可以用来将大型复杂系统表示为更小的、相互作用的连续子系统的系统，从而更容易分析。这项研究的试验台将是一种名为平面细胞极化(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，这些机制产生翅膀上的毛发，以及腿上的分段和关节形成：PCP的突变导致扭曲的毛发和关节模式。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，拟议研究的目的是(I)为分层混合系统开发数学建模和分析工具，以及(2)将这些工具应用于果蝇PCP中的问题。长期目标是利用这项研究最终帮助理解人类体内的相应信号。

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.