  We present an elaborate framework for formally modelling pathways in chemical
reaction networks on a mechanistic level. Networks are modelled mathematically
as directed multi-hypergraphs, with vertices corresponding to molecules and
hyperedges to reactions. Pathways are modelled as integer hyperflows and we
expand the network model by detailed routing constraints. In contrast to the
more traditional approaches like Flux Balance Analysis or Elementary Mode
analysis we insist on integer-valued flows. While this choice makes it
necessary to solve possibly hard integer linear programs, it has the advantage
that more detailed mechanistic questions can be formulated. It is thus possible
to query networks for general transformation motifs, and to automatically
enumerate optimal and near-optimal pathways. Similarities and differences
between our work and traditional approaches in metabolic network analysis are
discussed in detail. 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 manually designed
pathways can be further optimised. We then use a model of sugar chemistry to
investigate pathways in the autocatalytic formose process. A graph
transformation-based approach is used to automatically generate the reaction
networks of interest.
