Decomposing the Parameter Space of Biological Networks via a Numerical Discriminant Approach
Decomposing the Parameter Space of Biological Networks via a Numerical Discriminant Approach
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DOI：
10.1007/978-3-030-41258-6_9
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发表时间：
2016-04
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影响因子：
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通讯作者：
H. Harrington;D. Mehta;H. Byrne;J. Hauenstein
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文献类型：
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作者：
H. Harrington;D. Mehta;H. Byrne;J. Hauenstein
生物学中的许多系统（以及其他物理和工程系统）可以用包含大量参数的常微分方程系统来描述。在研究这些大型非线性系统的动态行为时，识别和表征模型参数变化时的稳态解非常有用，这是高维参数环境中的技术难题。我们不是简单地确定参数空间中不同点处稳态的数量和稳定性，而是将参数空间分解为有限多个区域，稳态解的数量和结构在每个不同区域内是一致的。从计算代数的角度来看，这些区域的边界包含在判别轨迹中。我们开发了全局和局部数值算法来构建判别轨迹并对参数景观进行分类。我们通过将数值方法应用于分子和细胞网络模型来展示它们。
Many systems in biology (as well as other physical and engineering systems) can be described by systems of ordinary differential equation containing large numbers of parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and characterize the steady-state solutions as the model parameters vary, a technically challenging problem in a high-dimensional parameter landscape. Rather than simply determining the number and stability of steady-states at distinct points in parameter space, we decompose the parameter space into finitely many regions, the number and structure of the steady-state solutions being consistent within each distinct region. From a computational algebraic viewpoint, the boundary of these regions is contained in the discriminant locus. We develop global and local numerical algorithms for constructing the discriminant locus and classifying the parameter landscape. We showcase our numerical approaches by applying them to molecular and cell-network models.