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The Kinetic Space of Multistationarity in Dual Phosphorylation
Journal of Dynamics and Differential Equations ( IF 1.3 ) Pub Date : 2020-09-04 , DOI: 10.1007/s10884-020-09889-6
Elisenda Feliu , Nidhi Kaihnsa , Timo de Wolff , Oğuzhan Yürük

Multistationarity in molecular systems underlies switch-like responses in cellular decision making. Determining whether and when a system displays multistationarity is in general a difficult problem. In this work we completely determine the set of kinetic parameters that enable multistationarity in a ubiquitous motif involved in cell signaling, namely a dual phosphorylation cycle. In addition we show that the regions of multistationarity and monostationarity are both path connected. We model the dynamics of the concentrations of the proteins over time by means of a parametrized polynomial ordinary differential equation (ODE) system arising from the mass-action assumption. Since this system has three linear first integrals defined by the total amounts of the substrate and the two enzymes, we study for what parameter values the ODE system has at least two positive steady states after suitably choosing the total amounts. We employ a suite of techniques from (real) algebraic geometry, which in particular concern the study of the signs of a multivariate polynomial over the positive orthant and sums of nonnegative circuit polynomials.



中文翻译:

双磷酸化中多平稳性的动力学空间

分子系统中的多平稳性是细胞决策中类似开关的反应的基础。通常,确定系统是否以及何时显示多平稳性是一个难题。在这项工作中,我们将完全确定一组动力学参数,以使参与细胞信号传导的普遍存在基序(即双重磷酸化周期)具有多平稳性。另外,我们证明了多平稳性和单平稳性区域都是路径连接的。我们通过参数化多项式常微分方程(ODE)系统模拟了蛋白质浓度随时间变化的动力学,该系统由质量作用假设产生。由于该系统具有由底物和两种酶的总量定义的三个线性第一积分,我们研究什么参数值ODE系统后,选择适当的总量至少有两个积极的稳定状态。我们采用(实数)代数几何的一组技术,这些技术特别关注对正正态和非负电路多项式之和的多元多项式符号的研究。

更新日期:2020-09-05
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