A biomimetic branching signal-passing tile assembly model with dynamic growth and disassembly

Natural biological branching processes can form tree-like structures at all scales and, moreover, can perform various functions to achieve specific goals; these include receiving stimuli, performing two-way communication along their branches, and dynamically reforming (extending or retracting branches). They underlie many biological systems with considerable diversity, frequency, and geometric complexity; these include networks of neurons, organ tissue, mycorrhizal fungal networks, plant growth, foraging networks, etc. This paper presents a biomimetic DNA tile assembly model (Y-STAM) to implement dynamic branching processes. The Y-STAM is a relatively compact mathematical model providing a design space where complex, biomimetic branch-like growth and behaviour can emerge from the appropriate parametrization of the model. We also introduce a class of augmented models (Y-STAM