Modelling biomolecules through atomistic graphs: theory, implementation, and applications

Describing biological molecules through computational models enjoys ever-growing popularity. Never before has access to computational resources been easier for scientists across the natural sciences. The need for accurate, efficient, and robust modelling tools is therefore irrefutable. This, in turn, calls for highly interdisciplinary research, which the thesis presented here is a product of. Through the successful marriage of techniques from mathematical graph theory, theoretical insights from chemistry and biology, and the tools of modern computer science, we are able to computationally construct accurate depictions of biomolecules as atomistic graphs, in which individual atoms become nodes and chemical bonds/interactions are represented by weighted edges. When combined with methods from graph theory and network science, this approach has previously been shown to successfully reveal various properties of proteins, such as dynamics, rigidity, multi-scale organisation, allostery, and protein-protein interactions, and is well poised to set new standards in terms of computational feasibility, multi-scale resolution (from atoms to domains) and time-scales (from nanoseconds to milliseconds). Therefore, building on previous work in our research group spanning over 15 years and to further encourage and facilitate research into this growing field, this thesis's main contribution is to provide a formalised foundation for the construction of atomistic graphs. The most crucial aspect of constructing atomistic graphs of large biomolecules compared to small molecules is the necessity to include a variety of different types of bonds and interactions, because larger biomolecules attain their unique structural layout mainly through weaker interactions, e.g. hydrogen bonds, the hydrophobic effect or π-π interactions. Whilst most interaction types are well-studied and have readily available methodology which can be used to construct atomistic graphs, this is not the case for hydrophobic interactions. To fill this gap, the work presented herein includes novel methodology for encoding the hydrophobic effect in atomistic graphs, that accounts for the many-body effect and non-additivity. Then, a standalone software package for constructing atomistic graphs from structural data is presented. Herein lies the heart of this thesis: the combination of a variety of methodologies for a range of bond/interaction types, as well as an implementation that is deterministic, easy-to-use and efficient. Finally, some promising avenues for utilising atomistic graphs in combination with graph theoretical tools such as Markov Stability as well as other approaches such as Multilayer Networks to study various properties of biomolecules are presented