Causality and independence in perfectly adapted dynamical systems
This work addresses the challenge of accurately modeling causal relationships in biological systems for researchers in systems biology and causal inference.
The paper tackled the problem of identifying perfect adaptation in dynamical systems from differential equations and equilibrium data, and demonstrated that perfect adaptation can mislead causal discovery algorithms, as shown with a protein signaling pathway model using both simulations and real-world data.
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.