Monotone Input/Output Systems in Mathematical Biology

这个项目的重点是单调输入/输出系统作为数学生物学的工具。 单调输入/输出系统起源于分析促分裂原活化蛋白激酶级联和其他细胞信号网络，但后来被证明可用于研究各种其他生物模型。 他们的理论是并将继续发展，以回应具体的生物模型的分析。 工作内容包括：（a）在以前关于单调和几乎单调输入/输出系统的工作的基础上，提出和解决有关信号和调节生物分子网络的新的、生物学动机的数学问题，包括研究记忆、开关行为、振荡和其他动力学特性;（B）发展理论和实践框架，使用定性和定量技术相结合的方法分析生物分子网络，特别是研究网络拓扑作为对可能的动态行为的约束，以及研究结构和参数的相互作用，通过将系统分解为行为良好的构建块组件，如单调子系统，并且只使用这些子系统的输入/输出数据来表征全局行为。生物科学正处于革命性的发展之中。 事实上，每天都有新的发现，以及对新的组织原则的建议，这些原则有望改变对生命和疾病的基本理解。 伴随着这些进步，领先的生物学家已经认识到，新的基础生物学和系统级的知识是迫切需要的。 这项工作涉及的数学问题的动机，这些发展。

This project focuses on monotone input/output systems as a tool in mathematical biology. Monotone i/o systems originated in the analysis of mitogen-activated protein kinase cascades and other cell signaling networks, but later proved useful in the study of a broad variety of other biological models. Their theory was and continues to be developed in response to the analysis of concrete biological models. The work includes: (a) The formulation and solution of new, biologically-motivated mathematical problems concerning signaling and regulatory biomolecular networks, including the study of memory, switching behavior, oscillations, and other dynamical characteristics, built upon the foundations of previous work on monotone and almost-monotone i/o systems; (b) The development of a theoretical and practical framework for the analysis of biomolecular networks using a combination of qualitative and quantitative techniques, and in particular the study of network topology as a constraint on possible dynamic behaviors and the study of the interplay of structure and parameters, by breaking up systems into well-behaved building-blocks components such as monotone subsystems, and using only input/output data for these subsystems in order to characterize global behavior.The biological sciences are in the midst of revolutionary developments. Literally each day brings new discoveries, and proposals for novel organizing principles, which hold the promise of altering the fundamental understanding of life and diseases. Concomitant with these advances, leading biologists have recognized that new basic mathematcial and systems-level knowledge is urgently required. This work deals with mathematical questions motivated by these developments.