Biochemical reaction systems: multistationarity, persistence, and identifiability

生化反应网络是生命的基本引擎，产生从光合作用到消化的各种生物过程。这项研究的目的是分析这种具有质量作用动力学的网络。这些动力系统模拟不同的生物机制，将使用代数、几何和组合方法来研究它们。研究人员正在追求与反应网络直接相关的以下目标：(1)确定给定反应网络的组合几何如何影响所产生的动力系统的长期动态，(2)分类和分析多稳态反应网络，以及(3)使用实数根计数等实代数几何技术来参数化翻译后修饰系统(生物学中重要的信号基元)中的多平稳特性。在第四个研究方向中，研究人员正在分析某些消除理想的Grobner基，目的是制定可识别性标准，即参数是否可以从数据中唯一恢复的问题。这项研究将在化学反应系统中准稳态近似的背景下进行，也将在代数统计中的图形模型的设置中进行。这项研究试图为医学上相关的生化反应网络的动态行为提供新的见解。事实上，这项研究中研究的反应系统是生物分子活动的广泛使用的模型；例如药物相互作用的药理学模型、信号转导模型和酶机制。特别是，这项研究将深入了解反应系统的长期行为，并提供对多静态网络的更好理解。

Biochemical reaction networks are the fundamental engines of life, giving rise to biological processes ranging from photosynthesis to digestion. The objective of this research is to analyze such networks endowed with mass-action kinetics. These dynamical systems model various biological mechanisms, and they will be studied using algebraic, geometric, and combinatorial methods. The investigator is pursuing the following aims directly related to reaction networks: (1) determining how the combinatorial geometry of a given reaction network informs the long-term dynamics of the resulting dynamical system, (2) classifying and analyzing multistationary reaction networks, and (3) parametrizing multistationarity in post-translational modification systems (important signaling motifs in biology) using techniques from real algebraic geometry such as real root counting. In a fourth research direction, the investigator is analyzing Grobner bases of certain elimination ideals with the aim of developing criteria for identifiability, which is the question of whether parameters can be uniquely recovered from data. This investigation will occur both in the context of quasi-steady-state approximations in chemical reaction systems and in the setting of graphical models in algebraic statistics. This research seeks to provide new insights about the dynamical behavior of medically relevant biochemical reaction networks. Indeed, the reaction systems studied in this research are widely used models for biomolecular activities; examples include pharmacological models of drug interaction, signal transduction models, and enzymatic mechanisms. In particular, this research will yield insight into the long-term behavior of reaction systems and provide a better understanding of multistationary networks.