论文标题
稳定状态的本地和全球鲁棒性
Local and global robustness at steady state
论文作者
论文摘要
我们研究了一类自主普通微分方程（ODES）系统的稳态，这是由（BIO）化学反应网络产生的核心示例。更确切地说，我们研究系统的稳态在什么条件下包含在坐标超平面的平行翻译中。 为此，我们主要关注由广义多项式组成的ODE，并利用代数和几何工具来关联稳态集的局部和全局结构。具体来说，我们考虑以坐标为$ x_i $的本地属性称为零灵敏度，这意味着切线空间包含在$ x_i = c $的超平面中，并提供标准以识别它。我们认为全局属性称为绝对浓度鲁棒性（ACR），这意味着所有稳态都包含在$ x_i = c $的形式的超平面中。 我们澄清并形式化了两种方法之间的关系。特别是，我们表明ACR意味着零灵敏度，并通过中间属性确定两个属性何时不同意，我们将局部ACR称为局部ACR。对于建模生化反应网络引起的系统家族，我们获得了第一个实用和自动化标准来决定（局部）ACR。
We study the robustness of the steady states of a class of systems of autonomous ordinary differential equations (ODEs), having as a central example those arising from (bio)chemical reaction networks. More precisely, we study under what conditions the steady states of the system are contained in a parallel translate of a coordinate hyperplane. To this end, we focus mainly on ODEs consisting of generalized polynomials, and make use of algebraic and geometric tools to relate the local and global structure of the set of steady states. Specifically, we consider the local property termed zero sensitivity at a coordinate $x_i$, which means that the tangent space is contained in a hyperplane of the form $x_i=c$, and provide a criterion to identify it. We consider the global property termed absolute concentration robustness (ACR), meaning that all steady states are contained in a hyperplane of the form $x_i=c$. We clarify and formalise the relation between the two approaches. In particular, we show that ACR implies zero sensitivity, and identify when the two properties do not agree, via an intermediate property we term local ACR. For families of systems arising from modelling biochemical reaction networks, we obtain the first practical and automated criterion to decide upon (local) ACR.
