Detecting multistationarity in mass-action networks.

检测大规模行动网络中的多平稳性。

• 批准号: 284057449
• 负责人: Professor Dr.-Ing. Carsten Conradi
• 金额: --
• 依托单位: Institut für Algebra und Geometrie (IAG)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/284057449?language=en
• 关键词: Detecting; multistationarity; mass; action; networks.

Biochemical reaction networks with mass-action kinetics (mass-action networks) are widely used in systems biology. Every mass-action network defines a system of ordinary differential equations (ODEs) with polynomial right hand sides. Parameter values in these ODEs can only be specified within large intervals (due to high measurement uncertainty and difficult experimental conditions). Every mass-action network therefore defines a parametrized family of ODEs, where determining steady states numerically can be challenging already. Hence there is a growing interest of mathematicians in the underlying structures that determine dynamical or stationary behavior of a chemical reaction network.In this proposal we focus on structural conditions for the existence of multiple positive steady states (multistationarity), which is a desired property in many biological applications (e.g. modeling of cell division or programmed cell death). Deciding whether or not multistationarity is possible is mathematically equivalent to deciding whether or not a polynomial system with unknown coefficients has at least two positive solutions and hence a challenging question. Despite this being a question of real algebraic origin, most of the work in the area has been carried out in chemical engineering and mathematical biology. In this proposal we want to join our complementary experience in mathematical biology and algebraic geometry to make progress on understanding multistationarity in mass-action networks.Specific goals are (i) An understanding of when the steady state ideal is binomial. (ii) A description of boundary steady states and in particular their dependence on parameters and the network. (iii) An implementation of an automatic method for the detection of multistationarity..(iv) A better understanding of the geometry of parameter regions associated to multistationarity for selected classes of polynomial models from systems biology. Completion of these goals will be beneficial to mathematicians and biologists alike. This will open the field to scientists working in (real) algebraic geometry, providing many new and challenging problems and it will yield valuable tools for scientists working in systems biology.

具有质量作用动力学的生化反应网络（质量作用网络）在系统生物学中有着广泛的应用。每一个质量作用网络都定义了一个具有多项式右端的常微分方程（ODE）系统。这些常微分方程中的参数值只能在较大的区间内指定（由于高测量不确定性和困难的实验条件）。因此，每个质量作用网络都定义了一个参数化的常微分方程族，在这里用数值方法确定稳态已经是一个挑战。因此，数学家们对决定化学反应网络的动态或稳态行为的基础结构越来越感兴趣，在本提案中，我们专注于多个正稳态（多稳态性）存在的结构条件，这是许多生物学应用（例如细胞分裂或程序性细胞死亡的建模）中所期望的属性。 决定多平稳性是否可能在数学上等价于决定一个系数未知的多项式系统是否至少有两个正解，因此是一个具有挑战性的问题。尽管这是一个问题的真实的代数起源，大部分的工作在该地区已进行了化学工程和数学生物学。在这个提议中，我们希望加入我们在数学生物学和代数几何方面的互补经验，以在理解质量作用网络的多平稳性方面取得进展。具体目标是：（i）理解何时稳态理想是二项式。(ii)边界稳定状态的描述，特别是它们对参数和网络的依赖性。 (iii)一种多平稳性自动检测方法的实现(iv)更好地理解与系统生物学多项式模型的选定类别的多平稳性相关的参数区域的几何形状。这些目标的完成将有利于数学家和生物学家。 这将打开领域的科学家工作在（真实的）代数几何，提供了许多新的和具有挑战性的问题，它将产生宝贵的工具，科学家工作在系统生物学。