DNA walker circuits: computational potential, design, and verification

Unlike their traditional, silicon counterparts, DNA computers have natural interfaces with both chemical and biological systems. These can be used for a number of applications, including the precise arrangement of matter at the nanoscale and the creation of smart biosensors. Like silicon circuits, DNA strand displacement systems (DSD) can evaluate non-trivial functions. However, these systems can be slow and are susceptible to errors. It has been suggested that localised hybridization reactions could overcome some of these challenges. Localised reactions occur in DNA ‘walker’ systems which were recently shown to be capable of navigating a programmable track tethered to an origami tile. We investigate the computational potential of these systems for evaluating Boolean functions and forming composable circuits. We find that systems of multiple walkers have severely limited potential for parallel circuit evaluation. DNA walkers, like DSDs, are also susceptible to errors. We develop a discrete stochastic model of DNA walker ‘circuits’ based on experimental data, and demonstrate the merit of using probabilistic model checking techniques to analyse their reliability, performance and correctness. This analysis aids in the design of reliable and efficient DNA walker circuits.

[1]  David J Scott,et al.  Cleavage of individual DNA strands by the different subunits of the heterodimeric restriction endonuclease BbvCI. , 2005, Journal of molecular biology.

[2]  Richard A. Muscat,et al.  A programmable molecular robot. , 2011, Nano letters.

[3]  Jonathan Bath,et al.  Small molecule signals that direct the route of a molecular cargo. , 2012, Small.

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

[5]  Marta Z. Kwiatkowska,et al.  Computing Cumulative Rewards Using Fast Adaptive Uniformisation , 2013, Computational Methods in Systems Biology.

[6]  A. Turberfield,et al.  Direct observation of stepwise movement of a synthetic molecular transporter. , 2011, Nature nanotechnology.

[7]  Jing Pan,et al.  A synthetic DNA motor that transports nanoparticles along carbon nanotubes. , 2014, Nature nanotechnology.

[8]  Darko Stefanovic,et al.  Mechanism of diffusive transport in molecular spider models. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Ruojie Sha,et al.  A Bipedal DNA Brownian Motor with Coordinated Legs , 2009, Science.

[10]  Andrew Phillips,et al.  Localized Hybridization Circuits , 2011, DNA.

[11]  Jonathan Bath,et al.  A DNA-based molecular motor that can navigate a network of tracks. , 2012, Nature nanotechnology.

[12]  Thomas Hérault,et al.  Approximate Probabilistic Model Checking , 2004, VMCAI.

[13]  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 .

[14]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[15]  Robert K. Brayton,et al.  Verifying Continuous Time Markov Chains , 1996, CAV.

[16]  Marta Z. Kwiatkowska,et al.  Stochastic Model Checking , 2007, SFM.

[17]  Marta Z. Kwiatkowska,et al.  Computing Cumulative Rewards Using Fast Adaptive Uniformization , 2015, ACM Trans. Model. Comput. Simul..

[18]  J. von Neumann,et al.  Probabilistic Logic and the Synthesis of Reliable Organisms from Unreliable Components , 1956 .

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

[20]  Marta Z. Kwiatkowska,et al.  PRISM 4.0: Verification of Probabilistic Real-Time Systems , 2011, CAV.

[21]  K. Wagner Über eine Eigenschaft der ebenen Komplexe , 1937 .

[22]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.

[23]  J. Reif,et al.  A unidirectional DNA walker that moves autonomously along a track. , 2004, Angewandte Chemie.

[24]  D. Y. Zhang,et al.  Control of DNA strand displacement kinetics using toehold exchange. , 2009, Journal of the American Chemical Society.

[25]  J. Neumann Probabilistic Logic and the Synthesis of Reliable Organisms from Unreliable Components , 1956 .

[26]  Christel Baier,et al.  Model-Checking Algorithms for Continuous-Time Markov Chains , 2002, IEEE Trans. Software Eng..

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

[28]  Allan Clark,et al.  Formal Methods for Performance Evaluation , 2007 .

[29]  A. Turberfield,et al.  A free-running DNA motor powered by a nicking enzyme. , 2005, Angewandte Chemie.

[30]  A. Turberfield,et al.  Mechanism for a directional, processive, and reversible DNA motor. , 2009, Small.

[31]  Marta Kwiatkowska,et al.  Probabilistic model checking for systems biology , 2011 .