Chemical Transformation Motifs - Modelling Pathways as Integer Hyperflows

We model chemical reaction networks as directed hypergraphs that are generated in rule-based manner, using graph grammars as models of given sets of reaction mechanisms. Graphs serve as abstractions of molecules. This provide a level of chemical realism sufficient to ensure conservation of mass, atom type, and charge. Atom maps, for instance, are thus consistently defined within the model. The generative approach pursued here goes beyond the necessarily static network models that need to be specified a priori and allows, in particular, application to network design problems. Chemical pathways are represented by integer hyperflows. In contrast to more traditional approaches of flux balance analysis or elementary mode analysis we insist on integer-valued flows. Although this choice makes it necessary to solve possibly hard integer linear programs it conveys the advantage that more detailed mechanistic questions can be formulated and computed directly. Similarities and differences between our work and traditional approaches in metabolic network analysis are discussed in detail. Three topics are used to demonstrate the applicability of the mathematical framework to real-life problems. We first explore the design space of possible non-oxidative glycolysis pathways and show that recent manual pathways can be further optimised. We then use a very general model of sugar chemistry to investigate the flows in the autocatalytic formose reaction and its relatives. Finally, we turn to the problem of recognizing complex autocatalytic cycles in large reaction networks, where we demonstrate how the TCA cycle and glyoxylate cycle as well as its combinations can be identified as autocatalytic.