Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to equilibrium. With the help of the causal ordering algorithm, one can construct graphical representations of dynamical systems that represent the causal relations between the variables and the conditional independences in the equilibrium distribution. We apply these tools to formulate sufficient graphical conditions for identifying perfect adaptation from a set of first-order differential equations. Furthermore, we give sufficient conditions to test for the presence of perfect adaptation in experimental equilibrium data. We apply this method to a simple model for a protein signalling pathway and test its predictions both in simulations and using real-world protein expression data. We demonstrate that perfect adaptation can lead to misleading orientation of edges in the output of causal discovery algorithms.
翻译:动态系统中的完美适应性是一种现象,即一个或多个变量对外部刺激的持续变化具有初步的瞬态反应,但随着系统趋同到平衡时又恢复到原来的价值。在因果订购算法的帮助下,我们可以构建动态系统的图形表达方式,代表变量与均衡分布中有条件的独立的因果关系。我们运用这些工具来设计足够的图形条件,从一组一阶差异方程式中确定完美的适应性。此外,我们为测试实验平衡数据是否存在完全的适应性提供了充分的条件。我们将这种方法应用到一个蛋白质信号路径的简单模型中,并在模拟和使用真实世界蛋白表达数据中测试其预测。我们证明,完美适应可导致因果发现算法产出的边缘的误导方向。