Identifying the parametric occurrence of multiple steady states for some biological networks
Identifying the parametric occurrence of multiple steady states for some biological networks
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DOI：
10.1016/j.jsc.2019.07.008
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发表时间：
2020-05-01
影响因子：
0.7
通讯作者：
Weber, Andreas
中科院分区：
文献类型：
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作者：
Bradford, Russell;Davenport, James H.;Weber, Andreas
我们考虑一个问题，从生物网络分析确定区域的参数空间中，有多个稳定状态的积极真实的值的变量和参数。我们描述了多种方法来解决这个问题，使用符号计算的工具。我们描述了如何取得进展，以实现半代数描述的参数空间的多平稳区域，并比较符号和数值方法。生物网络研究的模型的丝裂原活化蛋白激酶（MAPK）网络已经消耗了相当大的努力，使用特殊的见解，其结构相应的模型。我们的主要例子是一个包含11个变量和19个参数的11个方程的模型，其中3个是符号处理的兴趣。该模型还施加积极性条件的所有变量和parameters.We组合的符号计算方法设计的混合等式/不等式系统，特别是虚拟替代，懒惰的真实的三角化和圆柱代数分解，以及简化技术适应高斯消元和图论。我们能够确定我们的主要例子在2维参数空间的多平稳性的半代数条件。我们还研究了第二个MAPK模型和一个符号网格采样技术，可以定位这样的区域在三维参数空间。(C)2019爱思唯尔有限公司版权所有。
We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address the problem using tools from Symbolic Computation. We describe how progress was made to achieve semi-algebraic descriptions of the multistationarity regions of parameter space, and compare symbolic and numerical methods.The biological networks studied are models of the mitogen-activated protein kinases (MAPK) network which has already consumed considerable effort using special insights into its structure of corresponding models. Our main example is a model with 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment. The model also imposes positivity conditions on all variables and parameters.We apply combinations of symbolic computation methods designed for mixed equality / inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition, as well as a simplification technique adapted from Gaussian elimination and graph theory. We are able to determine semi-algebraic conditions for multistationarity of our main example over a 2-dimensional parameter space. We also study a second MAPK model and a symbolic grid sampling technique which can locate such regions in 3-dimensional parameter space. (C) 2019 Elsevier Ltd. All rights reserved.