Determining interaction directionality in complex biochemical networks from stationary measurements

Revealing interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Some methods may reveal undirected network topology, e.g., using node-node correlation. Yet, the direction of the interaction, thus a causal inference, remains to be determined - especially in steady-state observations. We introduce a method to infer the directionality within this network only from a "snapshot" of the abundances of the relevant molecules. We examine the validity of the approach for different properties of the system and the data recorded, such as the molecule's level variability, the effect of sampling and measurement errors. Simulations suggest that the given approach successfully infer the reaction rates in various cases.