DNA Computing and Molecular Programming

In this paper, we investigate the computational power of two variants of Winfree’s abstract Tile Assembly Model [14] at temperature 1: the Stage Tile Assembly Model and the Step-wise Tile Assembly Model. In the Stage Tile Assembly Model, the intermediate assemblies are assembled in several “bins” and they can be mixed in prescribed order and attach together to form more complex structures. The Step-wise Tile Assembly Model is a simplified model of stage assembly in which only one bin is used and assembly happens by attaching tiles one by one to the growing structure. An interesting and still open question is whether the abstract Tile Assembly Model at temperature 1 is Turing Universal, i.e., it can simulate a Turing machine. It is known that various slight modifications of the model are indeed Turing Universal. Namely, deterministic self-assembly in 3D and probabilistic self-assembly in 2D at temperature 1 [3] and self-assembly model at temperature 1 with a single negative glue [10] are known to be able to simulate a Turing machine. In this paper we show that the Step-wise Tile Assembly Model and the Stage Tile Assembly Model are also Turing Universal at temperature 1.

[1]  E. Sambriski,et al.  Sequence effects in the melting and renaturation of short DNA oligonucleotides: structure and mechanistic pathways , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[2]  Bernard Yurke,et al.  Using DNA to Power Nanostructures , 2003, Genetic Programming and Evolvable Machines.

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

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

[5]  David Yu Zhang,et al.  Cooperative hybridization of oligonucleotides. , 2011, Journal of the American Chemical Society.

[6]  Carsten Svaneborg,et al.  LAMMPS framework for dynamic bonding and an application modeling DNA , 2011, Comput. Phys. Commun..

[7]  J. SantaLucia,et al.  A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

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

[9]  G. Papoian,et al.  Supporting Information : Chemically Accurate Coarse-Graining of Double-Stranded DNA , 2010 .

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

[11]  David Soloveichik,et al.  Robust Stochastic Chemical Reaction Networks and Bounded Tau-Leaping , 2008, J. Comput. Biol..

[12]  J. SantaLucia,et al.  The thermodynamics of DNA structural motifs. , 2004, Annual review of biophysics and biomolecular structure.

[13]  Matthew Cook,et al.  Computation with finite stochastic chemical reaction networks , 2008, Natural Computing.

[14]  Edward H. Shortliffe,et al.  A model of inexact reasoning in medicine , 1990 .

[15]  Masami Hagiya,et al.  Chain Reaction Systems Based on Loop Dissociation of DNA , 2005, DNA.

[16]  Jean Sturm,et al.  Persistence Length of Single-Stranded DNA , 1997 .

[17]  G. Seelig,et al.  DNA as a universal substrate for chemical kinetics , 2010, Proceedings of the National Academy of Sciences.

[18]  Luca Cardelli.  Two-domain DNA strand displacement , 2013, Math. Struct. Comput. Sci..

[19]  N. Seeman.  DNA in a material world , 2003, Nature.

[20]  Lloyd M. Smith,et al.  Thermodynamically based DNA strand design , 2005, Nucleic acids research.

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

[22]  Lulu Qian,et al.  Supporting Online Material Materials and Methods Figs. S1 to S6 Tables S1 to S4 References and Notes Scaling up Digital Circuit Computation with Dna Strand Displacement Cascades , 2022 .

[23]  N. Seeman.  Nucleic acid junctions and lattices. , 1982, Journal of theoretical biology.

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

[25]  Lulu Qian,et al.  Efficient Turing-Universal Computation with DNA Polymers , 2010, DNA.

[26]  A. Condon,et al.  Less haste, less waste: on recycling and its limits in strand displacement systems , 2011, Interface Focus.

[27]  Byoung-Tak Zhang,et al.  A Bayesian Algorithm for In Vitro Molecular Evolution of Pattern Classifiers , 2004, DNA.

[28]  Jehoshua Bruck,et al.  Neural network computation with DNA strand displacement cascades , 2011, Nature.

[29]  J J de Pablo,et al.  A mesoscale model of DNA and its renaturation. , 2009, Biophysical journal.