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.

Background: Modeling molecules as undirected graphs and chemical reactions as graph rewriting operations is a natural and convenient approach to modeling chemistry. Graph grammar rules are most naturally employed to model elementary reactions like merging, splitting, and isomerisation of molecules. It is often convenient, in particular in the analysis of larger systems, to summarize several subsequent reactions into a single composite chemical reaction. Results: We introduce a generic approach for composing graph grammar rules to define a chemically useful rule compositions. We iteratively apply these rule compositions to elementary transformations in order to automatically infer complex transformation patterns. As an application we automatically derive the overall reaction pattern of the Formose cycle, namely two carbonyl groups that can react with a bound glycolaldehyde to a second glycolaldehyde. Rule composition also can be used to study polymerization reactions as well as more complicated iterative reaction schemes. Terpenes and the polyketides, for instance, form two naturally occurring classes of compounds of utmost pharmaceutical interest that can be understood as “generalized polymers” consisting of five-carbon (isoprene) and two-carbon units, respectively. Conclusion: The framework of graph transformations provides a valuable set of tools to generate and investigate large networks of chemical networks. Within this formalism, rule composition is a canonical technique to obtain coarse-grained representations that reflect, in a natural way, “effective” reactions that are obtained by lumping together specific combinations of elementary reactions.

A classical problem in metabolic design is to maximize the production of a desired compound in a given chemical reaction network by appropriately directing the mass flow through the network. Computationally, this problem is addressed as a linear optimization problem over the flux cone. The prior construction of the flux cone is computationally expensive and no polynomial-time algorithms are known.

The chemical universe of molecules reachable from a set of start compounds by iterative application of a finite number of reactions is usually so vast, that sophisticated and efficient exploration strategies are required to cope with the combinatorial complexity. A stringent analysis of (bio)chemical reaction networks, as approximations of these complex chemical spaces, forms the foundation for the understanding of functional relations in Chemistry and Biology. Graphs and graph rewriting are natural models for molecules and reactions. Borrowing the idea of partial evaluation from functional programming, we introduce partial applications of rewrite rules. A framework for the specification of exploration strategies in graph-rewriting systems is presented. Using key examples of complex reaction networks from carbohydrate chemistry we demonstrate the feasibility of this high-level strategy framework. While being designed for chemical applications, the framework can also be used to emulate higher-level transformation models such as illustrated in a small puzzle game.

Polymers of hydrogen cyanide and their hydrolysis products constitute a plausible, but still poorly understood proposal for early prebiotic chemistry on Earth. HCN polymers are generated by the interplay of more than a dozen distinctive reaction mechanisms and form a highly complex mixture. Here we use a computational model based on graph grammars as a means of exploring the chemical spaces of HCN polymerization and hydrolysis. A fundamental issue is to understand the combinatorial explosion inherent in large, complex chemical systems. We demonstrate that experimental data, here obtained by mass spectrometry, and computationally predicted free energies together can be used to guide the exploration of the chemical space and makes it feasible to investigate likely pathways and chemical motifs even in potentially open-ended chemical systems.