Mapping global sensitivity of cellular network dynamics: sensitivity heat maps and a global summation law
Mapping global sensitivity of cellular network dynamics: sensitivity heat maps and a global summation law
复制标题
DOI：
10.1098/rsif.2008.0084.focus
复制
发表时间：
2008-08-06
影响因子：
3.9
通讯作者：
Rand, D. A.
中科院分区：
文献类型：
--
作者：
Rand, D. A.
由基因调控、信号传导和代谢网络产生的动力学系统是强非线性的，具有高维状态空间并且依赖于大量的参数。理解这种系统的结构和功能之间的关系是一个相当大的挑战。我们需要工具来确定监管的关键点，阐明鲁棒性和控制等问题，并帮助设计实验。在这里，我通过开发敏感性分析的新技术来解决这个问题。特别是，我展示了如何通过两个新的图形对象：灵敏度热图和参数灵敏度谱来全局分析复杂系统的灵敏度。敏感性分析的方法是全局的，因为它研究整个模型解的变化，而不是像经典敏感性分析那样一次只关注一个输出变量。这种观点依赖于发现局部几何刚性的系统，数学的洞察力，使一个切实可行的方法，这样的问题可行的高度复杂的系统。此外，我们证明了一个新的求和定理，大大推广了以前的结果振荡和其他动力学现象。这个定理可以被解释为一个数学定律，说明在这种系统中需要在脆弱性和鲁棒性之间取得平衡。
The dynamical systems arising from gene regulatory, signalling and metabolic networks are strongly nonlinear, have high-dimensional state spaces and depend on large numbers of parameters. Understanding the relation between the structure and the function for such systems is a considerable challenge. We need tools to identify key points of regulation, illuminate such issues as robustness and control and aid in the design of experiments. Here, I tackle this by developing new techniques for sensitivity analysis. In particular, I show how to globally analyse the sensitivity of a complex system by means of two new graphical objects: the sensitivity heat map and the parameter sensitivity spectrum. The approach to sensitivity analysis is global in the sense that it studies the variation in the whole of the model's solution rather than focusing on output variables one at a time, as in classical sensitivity analysis. This viewpoint relies on the discovery of local geometric rigidity for such systems, the mathematical insight that makes a practicable approach to such problems feasible for highly complex systems. In addition, we demonstrate a new summation theorem that substantially generalizes previous results for oscillatory and other dynamical phenomena. This theorem can be interpreted as a mathematical law stating the need for a balance between fragility and robustness in such systems.