New techniques for analyzing the long-term behavior of intracellular networks

活细胞依靠微妙的细胞内网络才能正常运作。这些网络由基因、信使RNA、蛋白质、代谢物和其他内部和外部化学物质组成。这些网络的任何改变都可能导致发育、细胞增殖和其他功能的病理改变。对网络如何随时间(动态)变化的研究是数学生物界持续研究的重点。然而，许多根本性的问题仍然悬而未决。这项研究的中心目标是促进我们的理解，并为细胞内网络的全局动力学性质的结构分析建立一个理论和计算框架。该项目将涉及来自数学、工程和物理科学的本科生、研究生和博士后。这项数学工作的结果将具有远远超出分子领域的科学意义，因为同样的形式主义可以用来对生物和生态组织的不同层面上的现象进行建模，从细胞到组织，从生物体到生态系统和流行病。该项目旨在开发新的分析和计算方法来表征高度非线性生物系统的行为。在广泛应用的推动下，它将研究控制基本细胞过程的更大网络的核心元素，如转录和翻译、细胞生长和分裂、迁移和分化。这些过程包括基因调控、蛋白质通过磷酸化或甲基化的翻译后修饰、T细胞受体激活的动力学校对、核糖体翻译延伸过程以及其他调节和信号通路。诸如集合不变性(动力学何时保持“安全”集合而不违反生理约束？)、稳定性(系统在扰动之后，甚至在持续期间何时返回到同态值？)，以及在参数变化下定性行为的稳健性等问题，可以通过通用的数学语言来框架和分析。具体地说，这项工作将提供计算上明确的“证书”，以生物相互作用网络(BINS)的形式表示，保证不变性、稳定性或健壮性，允许仅从化学计量结构验证系统属性，即使面对关于参数甚至反应动力学的确切形式的大量不确定性。该项目将扩展可以用该技术分析的网络类别，证明新的定理，找到更有效的证书构造，引入额外的工具，并分析输入的影响，如受体系统中的配体。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Living cells depend on delicate intracellular networks for their correct functioning. These networks are composed of genes, messenger RNA, proteins, metabolites, and other internal and external chemicals. Any alteration of these networks can lead to pathologies in development, cell proliferation, and other functions. The study of how networks change in time (dynamics) is the focus of a sustained research effort by the mathematical biology community. Yet, many fundamental questions remain open. The central goal of this research is to advance our understanding and develop a theoretical and computational framework for the structural analysis of global dynamical properties of intracellular networks. The project will involve the participation of undergraduate, graduate, and postdoctoral students from the mathematical, engineering, and physical sciences. The results of this mathematical work will have scientific relevance much beyond the molecular realm, because the same formalism can be used to model phenomena at different levels of biological and ecological organization, from cells to tissues to organisms to ecological systems and epidemics. This project aims to develop novel analytical and computational approaches to characterize the behavior of highly nonlinear biological systems. Motivated by a wide variety of applications, it will study core elements of the larger networks that control fundamental cellular processes such as transcription and translation, cell growth and division, migration, and differentiation. These include processes such as gene regulation, protein post-translational modifications by phosphorylation or methylation, kinetic proofreading in T cell receptor activation, ribosome translation elongation processes, and other regulatory and signaling pathways. Questions such as set invariance (when do the dynamics preserve a "safe" set, not violating physiological constraints?), stability (when does the system return to homoeostasis values after, or even during persistent, perturbations?), and robustness of qualitative behavior under parameter changes can be framed and analyzed through a common mathematical language. Specifically, the work will provide computationally explicit "certificates" that guarantee invariance, stability, or robustness, expressed in the formalism of Biological Interaction Networks (BINs), that allow for the verification of system properties just from the stoichiometric structure, even in the face of substantial uncertainty regarding parameters and even the exact form of the reaction kinetics. This project will expand the class of networks that can be analyzed with the technique, proving new theorems, finding more efficient constructions of certificates, introducing additional tools, and analyzing the effect of inputs, such as ligands in receptor systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.