Understanding how information is encoded and transferred by biochemical networks is of fundamental importance in cellular and systems biology. This requires analysis of the relationships between the stochastic trajectories of the constituent molecular (or submolecular) species that comprise the network. We describe how to identify conditional independences between the trajectories or time courses of groups of species. These are robust network properties that provide important insight into how information is processed. An entire network can then be decomposed exactly into modules on informational grounds. In the context of signalling networks with multiple inputs, the approach identifies the routes and species involved in sequential information processing between input and output modules. An algorithm is developed which allows automated identification of decompositions for large networks and visualization using a tree that encodes the conditional independences. Only stoichiometric information is used and neither simulations nor knowledge of rate parameters are required. A bespoke version of the algorithm for signalling networks identifies the routes of sequential encoding between inputs and outputs, visualized as paths in the tree. Application to the toll-like receptor signalling network reveals that inputs can be informative in ways unanticipated by steady-state analyses, that the information processing structure is not well described as a bow tie, and that encoding for the interferon response is unusually sparse compared with other outputs of this innate immune system.
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