Turning machines: a simple algorithmic model for molecular robotics

Abstract

Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model, also easily generalisable to 2D to 3D folding. A Turning Machine starts out as a line of connected monomers in the discrete plane, each with an associated turning number. A monomer turns relative to its neighbours, executing a unit-distance translation that drags other monomers along with it, and through collective motion the initial set of monomers eventually folds into a programmed shape. We provide a suite of tools for reasoning about Turning Machines by fully characterising their ability to execute line rotations: executing an almost-full line rotation of $$5\pi /3$$ 5 π / 3 radians is possible, yet a full $$2\pi$$ 2 π rotation is impossible. Furthermore, line rotations up to $$5\pi /3$$ 5 π / 3 are executed efficiently, in $$O(\log n)$$ O ( log n ) expected time in our continuous time Markov chain time model. We then show that such line-rotations represent a fundamental primitive in the model, by using them to efficiently and asynchronously fold shapes. In particular, arbitrarily large zig-zag-rastered squares and zig-zag paths are foldable, as are y-monotone shapes albeit with error (bounded by perimeter length). Finally, we give shapes that despite having paths that traverse all their points, are in fact impossible to fold, as well as techniques for folding certain classes of (scaled) shapes without error. Our approach relies on careful geometric-based analyses of the feats possible and impossible by a very simple robotic system, and pushes conceptional hardness towards mathematical analysis and away from molecular implementation.

Reconfigurable multi-component nanostructures built from DNA origami voxels

“…Increasing the poly-T hinge predicted reduced twist but increased angular spread in oxDNA simulations, which would likely result in less rigid monomers (Supplementary Fig. [13][14][15][16][17]. Instead, alternating patterns of inward and outward pointing hinges were tested experimentally.…”

“…14,15 Similarly, recent theoretical models predict that local-to-global folding of linear chains could provide an effective strategy for molecular robotics. 16 Here, we develop a system of modular DNA nanoscale 'voxels' to explore these approaches to increase yield and reconfiguration efficiency of multi-component nanostructures.DNA is an excellent material for self-assembly of nanostructures due to its sequence-specific binding and ease of both synthesis and chemical modification. Diverse self-assembly principles have been demonstrated with DNA, including: algorithmic self-assembly, 17,18 hierarchical assembly, [19][20][21][22] controlled nucleation of shapes, 23 pathways, 24 and micron-scale structures, 25 allosteric shape change propagated across structures, 26 paper-folding, 27 molecular transport, 12 self-limiting growth, 28,29 and crystal growth to macroscale structures with nanoscale features.…”

“…14, 15 Similarly, recent theoretical models predict that local-to-global folding of linear chains could provide an effective strategy for molecular robotics. 16 Here, we develop a system of modular DNA nanoscale ‘voxels’ to explore these approaches to increase yield and reconfiguration efficiency of multi-component nanostructures.…”

From Molecular Robotics to Molecular Cybernetics: The First Step Toward Chemical Artificial Intelligence

“…The researchers not only study various topics of molecular robotics [8], but also propose an evolutionary scenarios in molecular robot development in terms of structural and functional complexity (Fig. 1) [2,3].…”