Joanna A Ellis-Monaghan, University of Amsterdam
2022 AWM Research Symposium
Discrete and Topological Models for Biological Structures

Applications of immediate concern have driven some of the most interesting questions in the field of graph theory and networks, for example graph drawing and computer chip layout problems, random networks and modeling the internet, graph connectivity measures and ecological systems, etc. Currently, scientists are engineering self-assembling DNA molecules to serve emergent applications in biomolecular computing, nanoelectronics, biosensors, drug delivery systems, and organic synthesis. Often, the self-assembled objects, e.g. lattices or polyhedral skeletons, may be modeled as graphs. Thus, these new technologies in self-assembly are now generating challenging new design problems for which graph theory and networks are natural tools. We will present some new applications in DNA self-assembly and describe some of the graph-theoretical design strategy problems arising from them. We will see how finding optimal design strategies leads to new computational complexity questions, and from thence to the need for simulation models. We adapt a network configuration model to this application, giving a structural-scale simulation for experimental output.

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