Monotone Input/Output Systems in Mathematical Biology

本项目主要研究单调输入/输出系统在数学生物学中的应用。单调i/o系统起源于对有丝分裂原激活的蛋白激酶级联和其他细胞信号网络的分析，但后来被证明在各种其他生物模型的研究中很有用。他们的理论过去和现在都是根据具体生物模型的分析而发展起来的。工作包括：(a)在以往单调和几乎单调i/o系统工作的基础上，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，包括对记忆、开关行为、振荡和其他动态特性的研究；(b)发展一个理论和实践框架，利用定性和定量技术相结合的方法分析生物分子网络，特别是研究作为可能动态行为约束的网络拓扑，以及研究结构和参数之间的相互作用，方法是将系统分解为行为良好的构件组件，如单调子系统；并且仅使用这些子系统的输入/输出数据来描述全局行为。生物科学正处于革命性的发展之中。几乎每天都有新的发现，新的组织原理的建议，有希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，迫切需要新的基础数学和系统级知识。这项工作涉及由这些发展引起的数学问题。

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.