Bifunctional enzyme action as a source of robustness in biochemical reaction networks: a novel hypergraph approach

Substrate modification networks are ubiquitous in living, biochemical systems. A higher-level hypergraph 'skeleton' captures key information about which substrates are transformed in the presence of modification-specific enzymes. Many different detailed models can be associated with the same skeleton; however, uncertainty related to model fitting increases with the level of detail. We show that essential dynamical properties such as existence of positive steady states and concentration robustness can be extracted directly from the skeleton independent of the detailed model. The novel formalism of directed hypergraphs is used to prove that bifunctional enzyme action plays a key role in generating robustness. Moreover, we use another novel concept of 'current' on a directed hypergraph to establish a link between potentially remote network components. Current is an essential notion required for existence of positive steady states, and furthermore, current-matching combined with bifunctionality generates concentration robustness.