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Supplementary material from "A Biomimetic Branching Signal-Passing Tile Assembly Model with Dynamic Growth and Disassembly"

Posted on 2024-05-14 - 09:46
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 behavior can emerge from the appropriate parameterization 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 behaviors that are not possible in the Y-STAM; these additional behaviors include refinement of network assemblies, obstacle avoidance, and programmable growth patterns. We make extensive simulations of our Y-STAM and Y-STAM+ models. For example, our 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.

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