Reachability Bounds for Chemical Reaction Networks and Strand Displacement Systems

Chemical reaction networks (CRNs) and DNA strand displacement systems (DSDs) are widely-studied and useful models of molecular programming. However, in order for some DSDs in the literature to behave in an expected manner, the initial number of copies of some reagents is required to be fixed. In this paper we show that, when multiple copies of all initial molecules are present, general types of CRNs and DSDs fail to work correctly if the length of the shortest sequence of reactions needed to produce any given molecule exceeds a threshold that grows polynomially with attributes of the system.

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

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

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

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

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

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

[7]  Luca Cardelli,et al.  Two-domain DNA strand displacement , 2010, Mathematical Structures in Computer Science.

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

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

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

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

[12]  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 .

[13]  G. Seelig,et al.  Dynamic DNA nanotechnology using strand-displacement reactions. , 2011, Nature chemistry.

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