Gross Elizabeth, Harrington Heather A, Rosen Zvi, Sturmfels Bernd
San José State University, San José, CA, USA.
University of Oxford, Oxford, England.
Bull Math Biol. 2016 Jan;78(1):21-51. doi: 10.1007/s11538-015-0125-1. Epub 2015 Dec 8.
Steady-state analysis of dynamical systems for biological networks gives rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here, the variety is described by a polynomial system in 19 unknowns and 36 parameters. It has degree 9 over the parameter space. This case study explores multistationarity, model comparison, dynamics within regions of the state space, identifiability, and parameter estimation, from a geometric point of view. We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics.
生物网络动力学系统的稳态分析会在高维空间中产生代数簇，对其进行研究本身就很有意义。我们以Wnt信号通路的穿梭模型为例进行说明。在此，该簇由一个包含19个未知数和36个参数的多项式系统描述。它在参数空间上的次数为9。本案例研究从几何角度探讨了多稳态性、模型比较、状态空间区域内的动力学、可识别性和参数估计。我们采用了计算代数几何、多面体几何和组合学的现有方法。
