Towards a robust approach to infer causality in molecular systems satisfying detailed balance

Abstract: The ability to distinguish between correlation and causation of variables in molecular systems remains an interesting and open area of investigation. In this work, we probe causality in a molecular system using two independent computational methods that infer the causal direction through the language of information transfer. Specifically, we demonstrate that a molecular dynamics simulation involving a single Tryptophan in liquid water displays asymmetric information transfer between specific collective variables, such as solute and solvent coordinates. Analyzing a discrete Markov-state and Langevin dynamics on a 2D free energy surface, we show that the same kind of asymmetries can emerge even in extremely simple systems, undergoing equilibrium and time-reversible dynamics. We use these model systems to rationalize the unidirectional information transfer in the molecular system in terms of asymmetries in the underlying free energy landscape and/or relaxation dynamics of the relevant coordinates. Finally, we propose a computational experiment that allows one to decide if an asymmetric information transfer between two variables corresponds to a genuine causal link.