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⁺) that provide time- and space-dependent modulations of tile glue strengths, which enable further diverse behaviours that are not possible in the Y-STAM; these additional behaviours include refinement of network assemblies, obstacle avoidance, and programmable growth patterns. We perform and discuss extensive simulations of the Y-STAM and the Y-STAM⁺. We envision that these models could be applied at the mesoscale and the molecular scale to dynamically assemble branching DNA nanostructures and offer insights into complex biological self-assembly processes.