Causality and independence in perfectly adapted dynamical systems

TL;DR

This paper explores the causal structure of perfectly adapted dynamical systems, providing graphical conditions for identifying adaptation and demonstrating potential pitfalls in causal discovery from equilibrium data.

Contribution

It introduces graphical criteria for detecting perfect adaptation in dynamical systems and tests these criteria on biological data, highlighting challenges in causal inference.

Findings

Graphical conditions can identify perfect adaptation from differential equations.

Perfect adaptation can mislead causal discovery algorithms.

Method validated on protein signaling pathway data.

Abstract

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.