A domain-level DNA strand displacement reaction enumerator allowing arbitrary non-pseudoknotted secondary structures

Information technologies enable programmers and engineers to design and synthesize systems of startling complexity that nonetheless behave as intended. This mastery of complexity is made possible by a hierarchy of formal abstractions that span from high-level programming languages down to low-level implementation specifications, with rigorous connections between the levels. DNA nanotechnology presents us with a new molecular information technology whose potential has not yet been fully unlocked in this way. Developing an effective hierarchy of abstractions may be critical for increasing the complexity of programmable DNA systems. Here, we build on prior practice to provide a new formalization of ‘domain-level’ representations of DNA strand displacement systems that has a natural connection to nucleic acid biophysics while still being suitable for formal analysis. Enumeration of unimolecular and bimolecular reactions provides a semantics for programmable molecular interactions, with kinetics given by an approximate biophysical model. Reaction condensation provides a tractable simplification of the detailed reactions that respects overall kinetic properties. The applicability and accuracy of the model is evaluated across a wide range of engineered DNA strand displacement systems. Thus, our work can serve as an interface between lower-level DNA models that operate at the nucleotide sequence level, and high-level chemical reaction network models that operate at the level of interactions between abstract species.

[1]  Eric Jones,et al.  SciPy: Open Source Scientific Tools for Python , 2001 .

[2]  Miran Liber,et al.  Detailed study of DNA hairpin dynamics using single-molecule fluorescence assisted by DNA origami. , 2013, The journal of physical chemistry. B.

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

[4]  Hiroaki Kitano,et al.  The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models , 2003, Bioinform..

[5]  Peng Yin,et al.  Optimizing the specificity of nucleic acid hybridization. , 2012, Nature chemistry.

[6]  Matthew R. Lakin,et al.  Bioinformatics Applications Note Systems Biology Visual Dsd: a Design and Analysis Tool for Dna Strand Displacement Systems , 2022 .

[7]  Masami Hagiya,et al.  DNA computation simulator based on abstract bases , 2001, Soft Comput..

[8]  David H Mathews,et al.  RNA Secondary Structure Analysis Using RNAstructure , 2006, Current protocols in bioinformatics.

[9]  J. Wetmur Hybridization and renaturation kinetics of nucleic acids. , 1976, Annual review of biophysics and bioengineering.

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

[11]  Luca Cardelli,et al.  Abstractions for DNA circuit design , 2011, Journal of The Royal Society Interface.

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

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

[14]  Conrad Steenberg,et al.  NUPACK: Analysis and design of nucleic acid systems , 2011, J. Comput. Chem..

[15]  David H Mathews,et al.  RNA pseudoknots: folding and finding , 2010, F1000 biology reports.

[16]  P. Hsieh,et al.  The kinetics of spontaneous DNA branch migration. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[17]  E. Andersen Prediction and design of DNA and RNA structures. , 2010, New biotechnology.

[18]  Hamidreza Chitsaz,et al.  A partition function algorithm for interacting nucleic acid strands , 2009, Bioinform..

[19]  W. Hughes,et al.  Multi-Arm Junctions for Dynamic DNA Nanotechnology. , 2017, Journal of the American Chemical Society.

[20]  Grégoire Altan-Bonnet,et al.  Bubble dynamics in double-stranded DNA. , 2003, Physical review letters.

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

[22]  Hagiya Masami,et al.  Abstraction of DNA Graph Structures for Efficient Enumeration and Simulation , 2011 .

[23]  Matthew R. Lakin,et al.  Modelling, Simulating and Verifying Turing-Powerful Strand Displacement Systems , 2011, DNA.

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

[25]  Erik Winfree,et al.  Stochastic Simulation of the Kinetics of Multiple Interacting Nucleic Acid Strands , 2015, DNA.

[26]  Jonathan Bath,et al.  Remote toehold: a mechanism for flexible control of DNA hybridization kinetics. , 2011, Journal of the American Chemical Society.

[27]  D. Porschke A direct measurement of the unzippering rate of a nucleic acid double helix. , 1974 .

[28]  Vincent Danos,et al.  Internal coarse-graining of molecular systems , 2009, Proceedings of the National Academy of Sciences.

[29]  Jehoshua Bruck,et al.  Programmability of Chemical Reaction Networks , 2009, Algorithmic Bioprocesses.

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

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

[32]  Niles A. Pierce,et al.  An algorithm for computing nucleic acid base‐pairing probabilities including pseudoknots , 2004, J. Comput. Chem..

[33]  F. Simmel,et al.  Principles and Applications of Nucleic Acid Strand Displacement Reactions. , 2019, Chemical reviews.

[34]  D. Turner,et al.  Incorporating chemical modification constraints into a dynamic programming algorithm for prediction of RNA secondary structure. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Erik Winfree,et al.  Verifying Chemical Reaction Network Implementations: A Bisimulation Approach , 2016, DNA.

[36]  D. Turner,et al.  RNA structure prediction. , 1988, Annual review of biophysics and biophysical chemistry.

[37]  P. Schuster,et al.  RNA folding at elementary step resolution. , 1999, RNA.

[38]  N. Destainville,et al.  Physics of base-pairing dynamics in DNA , 2015, 1510.05574.

[39]  E. Siggia,et al.  Modeling RNA folding paths with pseudoknots: application to hepatitis delta virus ribozyme. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[40]  A. Ansari,et al.  A kinetic zipper model with intrachain interactions applied to nucleic acid hairpin folding kinetics. , 2012, Biophysical journal.

[41]  Hieu Bui,et al.  Modeling DNA Nanodevices Using Graph Rewrite Systems , 2017 .

[42]  K. Hall,et al.  Millisecond time-scale folding and unfolding of DNA hairpins using rapid-mixing stopped-flow kinetics. , 2012, Journal of the American Chemical Society.

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

[44]  James R Faeder,et al.  Rule-based modeling of biochemical systems with BioNetGen. , 2009, Methods in molecular biology.

[45]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[46]  J. Doye,et al.  DNA hybridization kinetics: zippering, internal displacement and sequence dependence , 2013, Nucleic acids research.

[47]  Erik Winfree,et al.  Automated sequence-level analysis of kinetics and thermodynamics for domain-level DNA strand-displacement systems , 2018, Journal of the Royal Society Interface.

[48]  Lulu Qian,et al.  Scaling up molecular pattern recognition with DNA-based winner-take-all neural networks , 2018, Nature.

[49]  Erik Winfree,et al.  Thermodynamic Analysis of Interacting Nucleic Acid Strands , 2007, SIAM Rev..

[50]  J. Wetmur DNA probes: applications of the principles of nucleic acid hybridization. , 1991, Critical reviews in biochemistry and molecular biology.

[51]  Masami Hagiya,et al.  Abstraction of Graph-Based Models of Bio-molecular Reaction Systems for Efficient Simulation , 2012, CMSB.

[52]  Daniel Merkle,et al.  A Software Package for Chemically Inspired Graph Transformation , 2016, ICGT.

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

[54]  Erik Winfree,et al.  Leakless DNA Strand Displacement Systems , 2015, DNA.

[55]  Erik Winfree,et al.  A General-Purpose CRN-to-DSD Compiler with Formal Verification, Optimization, and Simulation Capabilities , 2017, DNA.

[56]  David Yu Zhang,et al.  Towards Domain-Based Sequence Design for DNA Strand Displacement Reactions , 2010, DNA.

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

[58]  E Rivas,et al.  A dynamic programming algorithm for RNA structure prediction including pseudoknots. , 1998, Journal of molecular biology.

[59]  P. Yin,et al.  Complex shapes self-assembled from single-stranded DNA tiles , 2012, Nature.

[60]  N. Gates,et al.  Kinetics of Renaturation of DNA , 2003 .

[61]  P. Stadler,et al.  RNA structures with pseudo-knots: Graph-theoretical, combinatorial, and statistical properties , 1999, Bulletin of mathematical biology.

[62]  A Libchaber,et al.  Kinetics of conformational fluctuations in DNA hairpin-loops. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[65]  E. Winfree,et al.  Synthetic in vitro transcriptional oscillators , 2011, Molecular systems biology.

[66]  Niles A Pierce,et al.  Sequence Design for a Test Tube of Interacting Nucleic Acid Strands. , 2015, ACS synthetic biology.

[67]  Xi Chen,et al.  Shaping up nucleic acid computation. , 2010, Current opinion in biotechnology.

[68]  Lorenzo Rovigatti,et al.  Coarse-graining DNA for simulations of DNA nanotechnology. , 2013, Physical chemistry chemical physics : PCCP.

[69]  D. W. Staple,et al.  Open access, freely available online Primer Pseudoknots: RNA Structures with Diverse Functions , 2022 .

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

[71]  Le A. Trinh,et al.  Programmable in situ amplification for multiplexed imaging of mRNA expression , 2010, Nature Biotechnology.

[72]  Erik Winfree,et al.  Enzyme-free nucleic acid dynamical systems , 2017, Science.

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

[74]  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.

[75]  Nicholas J Porubsky,et al.  Constrained Multistate Sequence Design for Nucleic Acid Reaction Pathway Engineering. , 2017, Journal of the American Chemical Society.

[76]  L. Stols,et al.  Sensitive fluorescence-based thermodynamic and kinetic measurements of DNA hybridization in solution. , 1993, Biochemistry.

[77]  Vincent Danos,et al.  Rule-Based Modelling of Cellular Signalling , 2007, CONCUR.

[78]  Erik Winfree,et al.  Effective design principles for leakless strand displacement systems , 2018, Proceedings of the National Academy of Sciences.

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

[80]  Mark W. Schmidt,et al.  Inferring Parameters for an Elementary Step Model of DNA Structure Kinetics with Locally Context-Dependent Arrhenius Rates , 2017, DNA.

[81]  Luca Cardelli,et al.  A programming language for composable DNA circuits , 2009, Journal of The Royal Society Interface.

[82]  David H. Mathews,et al.  NNDB: the nearest neighbor parameter database for predicting stability of nucleic acid secondary structure , 2009, Nucleic Acids Res..

[83]  Daniel T Gillespie,et al.  Stochastic simulation of chemical kinetics. , 2007, Annual review of physical chemistry.

[84]  Michael S. Samoilov,et al.  Automated Abstraction Methodology for Genetic Regulatory Networks , 2006, Trans. Comp. Sys. Biology.

[85]  A. Turberfield,et al.  DNA fuel for free-running nanomachines. , 2003, Physical review letters.

[86]  Matthew R. Lakin,et al.  A Logic Programming Language for Computational Nucleic Acid Devices. , 2018, ACS synthetic biology.

[87]  M. Guéron,et al.  Studies of base pair kinetics by NMR measurement of proton exchange. , 1995, Methods in enzymology.

[88]  Justin Werfel,et al.  DyNAMiC Workbench: an integrated development environment for dynamic DNA nanotechnology , 2015, Journal of The Royal Society Interface.

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

[90]  Matthew R. Lakin,et al.  A strand graph semantics for DNA-based computation , 2016, Theor. Comput. Sci..

[91]  D. Crothers,et al.  THE KINETICS OF DNA DENATURATION. , 1964, Journal of molecular biology.

[92]  Friedrich C Simmel,et al.  Nucleic acid based molecular devices. , 2011, Angewandte Chemie.

[93]  Brian Munsky,et al.  Reduction and solution of the chemical master equation using time scale separation and finite state projection. , 2006, The Journal of chemical physics.

[94]  Joachim Niehren,et al.  Structural Simplification of Chemical Reaction Networks Preserving Deterministic Semantics , 2015, CMSB.

[95]  Christian M. Reidys,et al.  Topology and prediction of RNA pseudoknots , 2011, Bioinform..

[96]  Erik Winfree,et al.  Robustness and modularity properties of a non-covalent DNA catalytic reaction , 2010, Nucleic acids research.

[97]  P J Goss,et al.  Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[98]  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 .

[99]  T. Pollard,et al.  Annual review of biophysics and biophysical chemistry , 1985 .

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

[101]  S. Woodson,et al.  Loop dependence of the stability and dynamics of nucleic acid hairpins , 2007, Nucleic acids research.

[102]  Luca Cardelli,et al.  Programmable chemical controllers made from DNA. , 2013, Nature nanotechnology.

[103]  Nadine L. Dabby,et al.  Synthetic Molecular Machines for Active Self-Assembly: Prototype Algorithms, Designs, and Experimental Study , 2013 .

[104]  N. Seeman Nanomaterials based on DNA. , 2010, Annual review of biochemistry.

[105]  Matthew R. Lakin,et al.  Modular Verification of DNA Strand Displacement Networks via Serializability Analysis , 2013, DNA.

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

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

[108]  Joseph M. Schaeffer,et al.  On the biophysics and kinetics of toehold-mediated DNA strand displacement , 2013, Nucleic acids research.

[109]  Peter F. Stadler,et al.  ViennaRNA Package 2.0 , 2011, Algorithms for Molecular Biology.

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

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

[112]  Lulu Qian,et al.  Compiler-aided systematic construction of large-scale DNA strand displacement circuits using unpurified components , 2017, Nature Communications.

[113]  P. Hsieh,et al.  Formation of a single base mismatch impedes spontaneous DNA branch migration. , 1993, Journal of molecular biology.

[114]  Xi Chen,et al.  Probing spatial organization of DNA strands using enzyme-free hairpin assembly circuits. , 2012, Journal of the American Chemical Society.

[115]  Erik Winfree,et al.  Verifying Chemical Reaction Network Implementations: A Pathway Decomposition Approach , 2014, Theor. Comput. Sci..