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1. Space colonization by branching trachea explains the morphospace of a simple respiratory organ

   https://doi.org/10.1016/j.ydbio.2020.02.005  

   Ruiz-Sobrino, A.; Martín-Blanco, C.A.; Navarro, T.; Almudí, I.; Masiero, G.; Jiménez-Caballero, M.; Buchwalter, D.B.; Funk, D.H.; Gattolliat, J.L.; Lemos, M.C.; et al (June 2020, Developmental Biology)

   n/a (Ed.)

   Branching morphogenesis helps increase the efficiency of gas and liquid transport in many animal organs. Studies in several model organisms have highlighted the molecular and cellular complexity behind branching morphogenesis. To understand this complexity, computational models have been developed with the goal of identifying the “major rules” that globally explain the branching patterns. These models also guide further experimental exploration of the biological processes that execute and maintain these rules. In this paper we introduce the tracheal gills of mayfly (Ephemeroptera) larvae as a model system to study the generation of branched respiratory patterns. First, we describe the gills of the mayfly Cloeon dipterum, and quantitatively characterize the geometry of its branching trachea. We next extend this characterization to those of related species to generate the morphospace of branching patterns. Then, we show how an algorithm based on the “space colonization” concept (SCA) can generate this branching morphospace via growth towards a hypothetical attractor molecule (M). SCA differs from other branch-generating algorithms in that the geometry generated depends to a great extent on its perception of the “external” space available for branching, uses few rules and, importantly, can be easily translated into a realistic “biological patterning algorithm”. We identified a gene in the C. dipterum genome (Cd-bnl) that is orthologous to the fibroblast growth factor branchless (bnl), which stimulates growth and branching of embryonic trachea in Drosophila. In C. dipterum, this gene is expressed in the gill margins and areas of finer tracheolar branching from thicker trachea. Thus, Cd-bnl may perform the function of M in our model. Finally, we discuss this general mechanism in the context of other branching pattern-generating algorithms. 

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2. Self-assembly of shapes at constant scale using repulsive forces

   https://doi.org/https://doi.org/10.1007/s11047-018-9707-9  

   Luchsinger, Austin; Schweller, Robert; Wylie, Tim (March 2019, Natural computing)

   The algorithmic self-assembly of shapes has been considered in several models of self-assembly. For the problem of shape construction, we consider an extended version of the two-handed tile assembly model, which contains positive (attractive) and negative (repulsive) interactions. As a result, portions of an assembly can become unstable and detach. In this model, we utilize fuel-efficient computation to perform Turing machine simulations for the construction of the shape. In this paper, we show how an arbitrary shape can be constructed using an asymptotically optimal number of distinct tile types (based on the shape’s Kolmogorov complexity). We achieve this at O(1) scale factor in this straightforward model, whereas all previous results with sublinear scale factors utilize powerful self-assembly models containing features such as staging, tile deletion, chemical reaction networks, and tile activation/deactivation. Furthermore, the computation and construction in our result only creates constant-size garbage assemblies as a byproduct of assembling the shape. 

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3. DNA conformational equilibrium enables continuous changing of curvatures

   https://doi.org/10.1039/D2NR05404C  

   Mao, Dake; Paluzzi, Victoria E.; Zhang, Cuizheng; Mao, Chengde (January 2023, Nanoscale)

   Assembly of complex structures from a small set of tiles is a common theme in biology. For example, many copies of identical proteins make up polyhedron-shaped, viral capsids and tubulin can make long microtubules. This inspired the development of tile-based DNA self-assembly for nanoconstruction, particularly for structures with high symmetries. In the final structure, each type of motif will adopt the same conformation, either rigid or with defined flexibility. For structures that have no symmetry, their assembly remains a challenge from a small set of tiles. To meet this challenge, algorithmic self-assembly has been explored driven by computational science, but it is not clear how to implement this approach to one-dimensional (1D) structures. Here, we have demonstrated that a constant shift of a conformational equilibrium could allow 1D structures to evolve. As shown by atomic force microscopy imaging, one type of DNA tile successfully assembled into DNA spirals and concentric circles, which became less and less curved from the structure's center outward. This work points to a new direction for tile-based DNA assembly. 

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4. Simulation of the Abstract Tile Assembly Model Using Crisscross Slats

   https://doi.org/10.4230/LIPIcs.DNA.30.3  

   Drake, Phillip; Hader, Daniel; Patitz, Matthew J (September 2024, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Seki, Shinnosuke; Stewart, Jaimie Marie (Ed.)

   The abstract Tile Assembly Model (aTAM) provides an excellent foundation for the mathematical study of DNA-tile-based self-assembling systems, especially those wherein logic is embedded within the designs of the tiles so that they follow prescribed algorithms. While such algorithmic self-assembling systems are theoretically powerful, being computationally universal and capable of building complex shapes using information-theoretically optimal numbers of tiles, physical DNA-based implementations of these systems still encounter formidable error rates and undesired nucleation that hinder this theoretical potential. Slat-based self-assembly is a recent development wherein DNA forms long slats that combine together in 2 layers, rather than square tiles in a plane. In this approach, the length of the slats is key; while tiles typically only bind to 2 neighboring tiles at a time, slats may bind to dozens of other slats. This increased coordination between slats means that several mismatched slats must coincidentally meet in just the right way for errors to persist, unlike tiles where only a few are required. Consequently, while still a novel technology, large slat-based DNA constructions have been successfully implemented in the lab with resilience to many tile-based construction problems. These improved error characteristics come at a cost however, as slat-based systems are often more difficult to design and simulate than tile-based ones. Moreover, it has not been clear whether slats, with their larger sizes and different geometries, have the same theoretical capabilities as tiles. In this paper, we show that slats are capable of doing anything that tiles can, at least at scale. We demonstrate that any aTAM system may be converted to and simulated by an effectively equivalent system of slats. Furthermore, we show that these simulating slat systems can be made more efficiently, using shorter slats and a smaller scale factor, if the simulated tile system avoids certain uncommon growth patterns. Specifically, we consider 5 classes of aTAM systems with increasing complexity, from zig-zag systems which grow in a rigid pattern to the full class of all aTAM systems, and show how they may be converted to equivalent slat systems. We show that the simplest class may be simulated by slats at only a 2c × 2c scale, where c is the freely chosen coordination number of the slats, and further show that the full class of aTAM systems can be simulated at only a 5c × 5c scale. These results prove that slats have the full theoretical power of aTAM tiles while also providing constructions that are compact enough for potential DNA-based implementations of slat systems that are both capable of powerful algorithmic self-assembly and possessing of the strong error resilience of slats. 

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5. Freezing Simulates Non-freezing Tile Automata

   https://doi.org/https://doi.org/10.1007/978-3-030-00030-1_10  

   Chalk, C.; Luchsinger, A.; Martinez, E.; Schweller, R.; Winslow, A.; Wylie, T. (October 2018, DNA Computing and Molecular Programming)

   Self-assembly is the process by which a system of particles randomly agitate and combine, through local interactions, to form larger complex structures. In this work, we fuse a particular well-studied generalization of tile assembly (the 2-Handed or Hierarchical Tile Assembly Model) with concepts from cellular automata such as states and state transitions characterized by neighboring states. This allows for a simplification of the concepts from active self-assembly, and gives us machinery to relate the disparate existing models. We show that this model, coined Tile Automata, is invariant with respect to freezing and non-freezing transition rules via a simulation theorem showing that any non-freezing tile automata system can be simulated by a freezing one. Freezing tile automata systems restrict state transitions such that each tile may visit a state only once, i.e., a tile may undergo only a finite number of transitions. We conjecture that this result can be used to show that the Signal-passing Tile Assembly Model is also invariant to this constraint via a series of simulation results between that model and the Tile Automata model. Further, we conjecture that this model can be used to consolidate the several oft-studied models of self-assembly wherein assemblies may break apart, such as the Signal-passing Tile Assembly Model, the negative-glue 2-Handed Tile Assembly Model, and the Size-Dependent Tile Assembly Model. Lastly, the Tile Automata model may prove useful in combining results in cellular automata with self-assembly. 

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