An Exponentially Growing Nubot System Without State Changes

Self-assembly is the process in which simple units assemble into complex structures without explicit external control. The nubot model was proposed to describe self-assembly systems involving active components capable of changing internal states and moving relative to each other. A major difference between the nubot model and many previous self-assembly models is its ability to perform exponential growth. Several previous works focused on restricting the nubot model while preserving exponential growth. In this work, we construct a nubot system which performs exponential growth without any state changes. All nubots stay in fixed internal states throughout the growth process. This construction not only improves the previous optimal construction, but also demonstrates new trade-offs between different types of rules in the nubot system.

[1]  Erik Winfree,et al.  Active self-assembly of algorithmic shapes and patterns in polylogarithmic time , 2013, ITCS '13.

[2]  A. Turberfield,et al.  Coordinated chemomechanical cycles: a mechanism for autonomous molecular motion. , 2008, Physical review letters.

[3]  N. Seeman,et al.  Operation of a DNA Robot Arm Inserted into a 2D DNA Crystalline Substrate , 2006, Science.

[4]  William M. Shih,et al.  A 1.7-kilobase single-stranded DNA that folds into a nanoscale octahedron , 2004, Nature.

[5]  E. Klavins,et al.  An improved autonomous DNA nanomotor. , 2007, Nano letters.

[6]  Shawn M. Douglas,et al.  Folding DNA into Twisted and Curved Nanoscale Shapes , 2009, Science.

[7]  Michail G. Lagoudakis,et al.  2D DNA self-assembly for satisfiability , 1999, DNA Based Computers.

[8]  Jack H. Lutz,et al.  The Tile Assembly Model is Intrinsically Universal , 2011, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[9]  Ming-Yang Kao,et al.  Reducing tile complexity for self-assembly through temperature programming , 2006, SODA '06.

[10]  G. Seelig,et al.  Enzyme-Free Nucleic Acid Logic Circuits , 2022 .

[11]  Erik Winfree,et al.  Two computational primitives for algorithmic self-assembly: copying and counting. , 2005, Nano letters.

[12]  Ho-Lin Chen,et al.  A Minimal Requirement for Self-assembly of Lines in Polylogarithmic Time , 2017, DNA.

[13]  Ho-Lin Chen,et al.  Fast Algorithmic Self-assembly of Simple Shapes Using Random Agitation , 2014, DNA.

[14]  Sudheer Sahu,et al.  Autonomous Programmable Nanorobotic Devices Using DNAzymes , 2007, DNA.

[15]  M. Sahani,et al.  Algorithmic Self-Assembly of DNA , 2006 .

[16]  P. Yin,et al.  A DNAzyme that walks processively and autonomously along a one-dimensional track. , 2005, Angewandte Chemie.

[17]  Shawn M. Douglas,et al.  Self-assembly of DNA into nanoscale three-dimensional shapes , 2009, Nature.

[18]  Erik Winfree,et al.  Reducing facet nucleation during algorithmic self-assembly. , 2007, Nano letters.

[19]  Harry M. T. Choi,et al.  Programming biomolecular self-assembly pathways , 2008, Nature.

[20]  David Doty.  Randomized Self-Assembly for Exact Shapes , 2010, SIAM J. Comput..

[21]  Erik Winfree,et al.  The program-size complexity of self-assembled squares (extended abstract) , 2000, STOC '00.

[22]  N. Seeman,et al.  A precisely controlled DNA biped walking device , 2004 .

[23]  N. Seeman,et al.  Design and self-assembly of two-dimensional DNA crystals , 1998, Nature.

[24]  N. Pierce,et al.  A synthetic DNA walker for molecular transport. , 2004, Journal of the American Chemical Society.

[25]  A. Turberfield,et al.  A DNA-fuelled molecular machine made of DNA , 2022 .

[26]  Ashish Goel,et al.  Running time and program size for self-assembled squares , 2001, STOC '01.

[27]  M. Win,et al.  Higher-Order Cellular Information Processing with Synthetic RNA Devices , 2008, Science.

[28]  John H. Reif,et al.  Designs of Autonomous Unidirectional Walking DNA Devices , 2004, DNA.

[29]  D. Y. Zhang,et al.  Engineering Entropy-Driven Reactions and Networks Catalyzed by DNA , 2007, Science.

[30]  Robert M. Dirks,et al.  An autonomous polymerization motor powered by DNA hybridization , 2007, Nature Nanotechnology.

[31]  Erik Winfree,et al.  Complexity of Self-Assembled Shapes , 2004, SIAM J. Comput..

[32]  E. Winfree,et al.  Algorithmic Self-Assembly of DNA Sierpinski Triangles , 2004, PLoS biology.

[33]  Robert M. Dirks,et al.  Triggered amplification by hybridization chain reaction. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[34]  P. Rothemund.  Folding DNA to create nanoscale shapes and patterns , 2006, Nature.

[35]  N. Seeman,et al.  Construction of a DNA-Truncated Octahedron , 1994 .