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Graph Transformation (also graph rewriting) is a rewriting system on graphs. Unsurprisingly, graph transformation constitutes a universal model of computation and has numerous applications in software engineering. Formally, graph transformation is an algebraic method, based on category theory. Nonetheless, graph transformation applications are often very intuitive, owning largely to the visual nature of graphs.

Within my work, the focus was on application of graph transformation to chemistry. "Drawing" molecules as graphs is very intuitive, and graphs have been a visual tool of chemists since the mid-19th century. Graph transformation rules then capture the chemical reactions, transforming the input molecules into output molecules. More precisely, each graph transformation rule specifies a class of reactions that perform the same chemical transformation, characterised by the graph pattern being rewritten. A graph transformation rule thus models a physico-chemical mechanism of a class of chemical reactions.

My focus has specifically been enzymatic reactions in biochemistry. Enzymatic reactions are specific in that the performed transformations are often very indirect and can be thought of as proceeding through a sequence of elementary reaction steps with a net energetically favourable effect. I worked on a technique to exploit the knowledge of such elementary steps, or enzymatic mechanisms, for some enzymatic reactions, to extrapolate and propose detailed mechanisms for other reactions as well [2021].

The individual steps of the enzymatic mechanisms often "undo" the effects of the previous ones, achieving the desired bond rearrangement by shifting charges between electron donor and acceptor groups of the molecules involved. Such transient changes to the molecular structure are invisible at the level of the overall enzymatic reaction. I have therefore worked to develop a fully formal method for classification of enzymatic reactions, and a clear visualisation of any transient transformations, which delimit crucial components of the molecules that allow the reaction to proceed [2022].

Last but not least, while staying true to the motivation in chemical application, I have worked on a method to automatically extract a set of graph transformation rules from empirical data, such as chemical reaction networks. The method is very general and can likely be adapted to other rewriting systems without much modification. It also ties directly into computing fundamentals via the notion of Kolmogorov complexity [TBD].