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Revisiting Hybridization Kinetics with Improved Elementary Step Simulation

Authors Jordan Lovrod, Boyan Beronov, Chenwei Zhang, Erik Winfree, Anne Condon

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Jordan Lovrod
  • University of British Columbia, Vancouver, Canada
Boyan Beronov
  • University of British Columbia, Vancouver, Canada
Chenwei Zhang
  • University of British Columbia, Vancouver, Canada
Erik Winfree
  • California Institute of Technology, Pasadena, CA, USA
Anne Condon
  • University of British Columbia, Vancouver, Canada

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Jordan Lovrod, Boyan Beronov, Chenwei Zhang, Erik Winfree, and Anne Condon. Revisiting Hybridization Kinetics with Improved Elementary Step Simulation. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 5:1-5:24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


Nucleic acid strands, which react by forming and breaking Watson-Crick base pairs, can be designed to form complex nanoscale structures or devices. Controlling such systems requires accurate predictions of the reaction rate and of the folding pathways of interacting strands. Simulators such as Multistrand model these kinetic properties using continuous-time Markov chains (CTMCs), whose states and transitions correspond to secondary structures and elementary base pair changes, respectively. The transient dynamics of a CTMC are determined by a kinetic model, which assigns transition rates to pairs of states, and the rate of a reaction can be estimated using the mean first passage time (MFPT) of its CTMC. However, use of Multistrand is limited by its slow runtime, particularly on rare events, and the quality of its rate predictions is compromised by a poorly-calibrated and simplistic kinetic model. The former limitation can be addressed by constructing truncated CTMCs, which only include a small subset of states and transitions, selected either manually or through simulation. As a first step to address the latter limitation, Bayesian posterior inference in an Arrhenius-type kinetic model was performed in earlier work, using a small experimental dataset of DNA reaction rates and a fixed set of manually truncated CTMCs, which we refer to as Assumed Pathway (AP) state spaces. In this work we extend this approach, by introducing a new prior model that is directly motivated by the physical meaning of the parameters and that is compatible with experimental measurements of elementary rates, and by using a larger dataset of 1105 reactions as well as larger truncated state spaces obtained from the recently introduced stochastic Pathway Elaboration (PE) method. We assess the quality of the resulting posterior distribution over kinetic parameters, as well as the quality of the posterior reaction rates predicted using AP and PE state spaces. Finally, we use the newly parameterised PE state spaces and Multistrand simulations to investigate the strong variation of helix hybridization reaction rates in a dataset of Hata et al. While we find strong evidence for the nucleation-zippering model of hybridization, in the classical sense that the rate-limiting phase is composed of elementary steps reaching a small "nucleus" of critical stability, the strongly sequence-dependent structure of the trajectory ensemble up to nucleation appears to be much richer than assumed in the model by Hata et al. In particular, rather than being dominated by the collision probability of nucleation sites, the trajectory segment between first binding and nucleation tends to visit numerous secondary structures involving misnucleation and hairpins, and has a sizeable effect on the probability of overcoming the nucleation barrier.

Subject Classification

ACM Subject Classification
  • Applied computing → Chemistry
  • DNA reaction kinetics
  • kinetic model calibration
  • simulation-based Bayesian inference
  • continuous-time Markov chains


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  1. Victor a Bloomfield, Donald M. Crothers, and Ignacio Tinoco. Nucleic Acids: Structures, Properties and Functions. University Science Books, Sausalito, Calif, 2000. Google Scholar
  2. Daniel P. Aalberts, John M. Parman, and Noel L. Goddard. Single-strand stacking free energy from DNA beacon kinetics. Biophysical Journal, 84(5):3212-3217, 2003. URL:
  3. Grégoire Altan-Bonnet, Albert J. Libchaber, and Oleg Krichevsky. Bubble dynamics in double-stranded DNA. Physical Review Letters, 90(13):138101, 2003. URL:
  4. Yaniv Amir, Eldad Ben-Ishay, Daniel Levner, Shmulik Ittah, Almogit Abu-Horowitz, and Ido Bachelet. Universal computing by DNA origami robots in a living animal. Nature Nanotechnology, 9(5):353-357, 2014. URL:
  5. Jonathan Bath, Simon J. Green, and Andrew J. Turberfield. A free-running DNA motor powered by a nicking enzyme. Angewandte Chemie International Edition, 44(28):4358-4361, 2005. URL:
  6. Jonathan Bath and Andrew J. Turberfield. DNA nanomachines. Nature Nanotechnology, 2(5):275-284, 2007. URL:
  7. Michael Betancourt. A short review of ergodicity and convergence of Markov chain Monte Carlo estimators. arXiv e-prints, 2021. URL:
  8. Grégoire Bonnet. Dynamics of DNA Breathing and Folding for Molecular Recognition and Computation. PhD Thesis, Rockefeller University, 2000. Google Scholar
  9. Grégoire Bonnet, Oleg Krichevsky, and Albert Libchaber. Kinetics of conformational fluctuations in DNA hairpin-loops. Proceedings of the National Academy of Sciences, 95(15):8602-8606, 1998. URL:
  10. George E. P. Box. Sampling and Bayes' inference in scientific modelling and robustness. Journal of the Royal Statistical Society: Series A (General), 143(4):383-404, 1980. URL:
  11. Ronald R. Breaker and Gerald F. Joyce. The expanding view of RNA and DNA function. Chemistry & Biology, 21(9):1059-1065, 2014. URL:
  12. Thomas R. Cech and Joan A. Steitz. The noncoding RNA revolution: Trashing old rules to forge new ones. Cell, 157(1):77-94, 2014. URL:
  13. Arkadiusz Chworos, Isil Severcan, Alexey Y. Koyfman, Patrick Weinkam, Emin Oroudjev, Helen G. Hansma, and Luc Jaeger. Building programmable jigsaw puzzles with RNA. Science, 306(5704):2068-2072, 2004. URL:
  14. Ibrahim I. Cisse, Hajin Kim, and Taekjip Ha. A rule of seven in Watson-Crick base-pairing of mismatched sequences. Nature Structural & Moleuclar Biology, 19(6):623, 2012. URL:
  15. Nadine L. Dabby. Synthetic Molecular Machines for Active Self-Assembly: Prototype Algorithms, Designs, and Experimental Study. PhD Thesis, California Institute of Technology, 2013. URL:
  16. Timothy A. Davis. Algorithm 832: UMFPACK v4.3: An unsymmetric-pattern multifrontal method. ACM Transactions on Mathematical Software, 30(2):196-199, 2004. URL:
  17. Aesara Developers. Aesara. Accessed: 2023-04-10.
  18. P. Diaconis and L. Saloff-Coste. What do we know about the Metropolis algorithm? Journal of Computer and System Sciences, 57(1):20-36, 1998. URL:
  19. Hendrik Dietz, Shawn M. Douglas, and William M. Shih. Folding DNA into twisted and curved nanoscale shapes. Science, 325(5941):725-730, 2009. URL:
  20. Shawn M. Douglas, Ido Bachelet, and George M. Church. A logic-gated nanorobot for targeted transport of molecular payloads. Science, 335(6070):831-834, 2012. URL:
  21. Shawn M. Douglas, Hendrik Dietz, Tim Liedl, Bjorn Hogberg, Franziska Graf, and William M. Shih. Self-assembly of DNA into nanoscale three-dimensional shapes. Nature, 459(7245):414-418, 2009. URL:
  22. Eric C Dykeman. An implementation of the Gillespie algorithm for RNA kinetics with logarithmic time update. Nucleic Acids Research, 43(12):5708-5715, 2015. URL:
  23. Christoph Flamm, Walter Fontana, Ivo L. Hofacker, and Peter Schuster. RNA folding at elementary step resolution. RNA, 6(03):325-338, 2000. URL:
  24. Daniel Foreman-Mackey, David W. Hogg, Dustin Lang, and Jonathan Goodman. emcee: The MCMC hammer. Publications of the Astronomical Society of the Pacific, 125(925):306, 2013. URL:
  25. Mark E. Fornace. Computational Methods for Simulating and Parameterizing Nucleic Acid Secondary Structure Thermodynamics and Kinetics. PhD Thesis, California Institute of Technology, 2022. URL:
  26. Jinglin Fu, Yuhe Renee Yang, Alexander Johnson-Buck, Minghui Liu, Yan Liu, Nils G. Walter, Neal W. Woodbury, and Hao Yan. Multi-enzyme complexes on DNA scaffolds capable of substrate channelling with an artificial swinging arm. Nature Nanotechnology, 9(7):531-536, 2014. URL:
  27. Yang Gao, Lauren K. Wolf, and Rosina M. Georgiadis. Secondary structure effects on DNA hybridization kinetics: a solution versus surface comparison. Nucleic Acids Research, 34(11):3370-3377, 2006. URL:
  28. Andrew Gelman, Aki Vehtari, Daniel Simpson, Charles C. Margossian, Bob Carpenter, Yuling Yao, Lauren Kennedy, Jonah Gabry, Paul-Christian Bürkner, and Martin Modrák. Bayesian workflow. arXiv e-prints, 2020. URL:
  29. Charles Geyer. Introduction to Markov chain Monte Carlo. In Steve Brooks, Andrew Gelman, Galin Jones, and Xiao-Li Meng, editors, Handbook of Markov Chain Monte Carlo, volume 20116022. Chapman and Hall/CRC, 2011. URL:
  30. Charles J. Geyer. Practical Markov chain Monte Carlo. Statistical Science, 7(4):473-483, 1992. URL:
  31. Daniel T. Gillespie. Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81(25):2340-2361, 1977. URL:
  32. Noel L. Goddard, Grégoire Bonnet, Oleg Krichevsky, and Albert Libchaber. Sequence dependent rigidity of single stranded DNA. Physical Review Letters, 85(11):2400, 2000. URL:
  33. Hiroaki Hata, Tetsuro Kitajima, and Akira Suyama. Influence of thermodynamically unfavorable secondary structures on DNA hybridization kinetics. Nucleic Acids Research, 46(2):782-791, 2018. URL:
  34. Ivo L. Hofacker. Vienna RNA secondary structure server. Nucleic Acids Research, 31(13):3429-3431, 2003. URL:
  35. Stephan Hoyer and Joe Hamman. Xarray: N-D labeled Arrays and Datasets in Python. Journal of Open Research Software, 5(1):10, 2017. URL:
  36. Yonggang Ke, Luvena L. Ong, William M. Shih, and Peng Yin. Three-dimensional structures self-assembled from DNA bricks. Science, 338(6111):1177-1183, 2012. URL:
  37. Jiho Kim, Sören Doose, Hannes Neuweiler, and Markus Sauer. The initial step of DNA hairpin folding: a kinetic analysis using fluorescence correlation spectroscopy. Nucleic Acids Research, 34(9):2516-2527, 2006. URL:
  38. Ravin Kumar, Colin Carroll, Ari Hartikainen, and Osvaldo Martin. ArviZ a unified library for exploratory analysis of Bayesian models in Python. Journal of Open Source Software, 4(33):1143, 2019. URL:
  39. Gregory M. Kurtzer, Vanessa Sochat, and Michael W. Bauer. Singularity: Scientific containers for mobility of compute. PLOS ONE, 12(5):e0177459, 2017. URL:
  40. Martin Langecker, Vera Arnaut, Thomas G. Martin, Jonathan List, Stephan Renner, Michael Mayer, Hendrik Dietz, and Friedrich C. Simmel. Synthetic lipid membrane channels formed by designed DNA nanostructures. Science, 338(6109):932-936, 2012. URL:
  41. Tim Liedl, Björn Högberg, Jessica Tytell, Donald E. Ingber, and William M. Shih. Self-assembly of three-dimensional prestressed tensegrity structures from DNA. Nature Nanotechnology, 5(7):520-524, 2010. URL:
  42. Pavel Loskot, Komlan Atitey, and Lyudmila Mihaylova. Comprehensive review of models and methods for inferences in bio-chemical reaction networks. Frontiers in Genetics, 10, 2019. URL:
  43. Jordan Lovrod. Bayesian modelling of DNA secondary structure kinetics: revisiting path space approximations and posterior inference in exponentially large state spaces. MSc Thesis, University of British Columbia, 2023. URL:
  44. Robert R. F. Machinek, Thomas E. Ouldridge, Natalie E. C. Haley, Jonathan Bath, and Andrew J. Turberfield. Programmable energy landscapes for kinetic control of DNA strand displacement. Nature Communications, 5(1):5324, 2014. URL:
  45. Chengde Mao, Weiqiong Sun, Zhiyong Shen, and Nadrian C. Seeman. A nanomechanical device based on the B–Z transition of DNA. Nature, 397(6715):144-146, 1999. URL:
  46. David H. Mathews, Jeffrey Sabina, Michael Zuker, and Douglas H. Turner. Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. Journal of Molecular Biology, 288(5):911-940, 1999. URL:
  47. Sean A. McKinney, Alasdair D. J. Freeman, David M. J. Lilley, and Taekjip Ha. Observing spontaneous branch migration of Holliday junctions one step at a time. Proceedings of the National Academy of Sciences, 102(16):5715-5720, 2005. URL:
  48. Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller. Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6):1087-1092, 1953. URL:
  49. Larry E. Morrison and Lucy M. Stols. Sensitive fluorescence-based thermodynamic and kinetic measurements of DNA hybridization in solution. Biochemistry, 32(12):3095-3104, 1993. URL:
  50. G. Eric Plum, Kenneth J. Breslauer, and Richard W. Roberts. 7.02 - Thermodynamics and kinetics of nucleic acid association/dissociation and folding processes. In Comprehensive Natural Products Chemistry, pages 15-53. Pergamon, Oxford, 1999. URL:
  51. Brittany Rauzan, Elizabeth McMichael, Rachel Cave, Lesley R. Sevcik, Kara Ostrosky, Elisabeth Whitman, Rachel Stegemann, Audra L. Sinclair, Martin J. Serra, and Alice A. Deckert. Kinetics and thermodynamics of DNA, RNA, and hybrid duplex formation. Biochemistry, 52(5):765-772, 2013. URL:
  52. Luis P. Reynaldo, Alexander V. Vologodskii, Bruce P. Neri, and Victor I. Lyamichev. The kinetics of oligonucleotide replacements. Journal of Moleuclar Biology, 297(2):511-520, 2000. URL:
  53. Christian P. Robert and George Casella. Monte Carlo statistical methods, volume 2. Springer, 1999. URL:
  54. Paul W. K. Rothemund. Folding DNA to create nanoscale shapes and patterns. Nature, 440(7082):297-302, 2006. URL:
  55. Vivekananda Roy. Convergence diagnostics for Markov chain Monte Carlo. Annual Review of Statistics and Its Application, 7:387-412, 2020. URL:
  56. John Salvatier, Thomas V. Wiecki, and Christopher Fonnesbeck. Probabilistic programming in Python using PyMC3. PeerJ Computer Science, 2:e55, 2016. URL:
  57. John SantaLucia. A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics. Proceedings of the National Academy of Sciences, 95(4):1460-1465, 1998. URL:
  58. John SantaLucia Jr. and Donald Hicks. The thermodynamics of DNA structural motifs. Annu. Rev. Biophys. Biomol. Struct., 33:415-440, 2004. URL:
  59. Joseph M. Schaeffer. Stochastic Simulation of the Kinetics of Multiple Interacting Nucleic Acid Strands. PhD Thesis, California Institute of Technology, 2013. URL:
  60. Joseph M. Schaeffer, Chris Thachuk, and Erik Winfree. Stochastic simulation of the kinetics of multiple interacting nucleic acid strands. In DNA Computing and Molecular Programming, volume 9211 of Lecture Notes in Computer Science, pages 194-211, 2015. URL:
  61. John S. Schreck, Thomas E. Ouldridge, Flavio Romano, Petr Šulc, Liam P. Shaw, Ard A. Louis, and Jonathan P.K. Doye. DNA hairpins destabilize duplexes primarily by promoting melting rather than by inhibiting hybridization. Nucleic Acids Research, 43(13):6181-6190, 2015. URL:
  62. Verena J. Schüller, Simon Heidegger, Nadja Sandholzer, Philipp C. Nickels, Nina A. Suhartha, Stefan Endres, Carole Bourquin, and Tim Liedl. Cellular immunostimulation by CpG-sequence-coated DNA origami structures. ACS Nano, 5(12):9696-9702, 2011. URL:
  63. Georg Seelig, David Soloveichik, David Yu Zhang, and Erik Winfree. Enzyme-free nucleic acid logic circuits. Science, 314(5805):1585-1588, 2006. URL:
  64. Nadrian C. Seeman. Nucleic acid junctions and lattices. Journal of Theoretical Biology, 99(2):237-247, 1982. URL:
  65. Alexander Serganov and Evgeny Nudler. A decade of riboswitches. Cell, 152(1-2):17-24, 2013. URL:
  66. Daniel J. Sharpe and David J. Wales. Efficient and exact sampling of transition path ensembles on Markovian networks. The Journal of Chemical Physics, 153(2):024121, 2020. URL:
  67. Daniel J. Sharpe and David J. Wales. Nearly reducible finite Markov chains: Theory and algorithms. The Journal of Chemical Physics, 155(14):140901, 2021. URL:
  68. Niranjan Srinivas, Thomas E. Ouldridge, Petr Šulc, Joseph M. Schaeffer, Bernard Yurke, Ard A. Louis, Jonathan P. K. Doye, and Erik Winfree. On the biophysics and kinetics of toehold-mediated DNA strand displacement. Nucleic Acids Research, 41(22):10641-10658, 2013. URL:
  69. Yuri Suhov and Mark Kelbert. Markov Chains: A Primer in Random Processes and Their Applications, volume 2. Cambridge University Press, 2008. Google Scholar
  70. Theano Development Team. Theano: A Python framework for fast computation of mathematical expressions. arXiv e-prints, 2016. URL:
  71. Gael Varoquaux and Olivier Grisel. Joblib: Running Python functions as pipeline jobs., 2009. Accessed: 2023-04-15.
  72. Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, C J Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods, 17:261-272, 2020. URL:
  73. Mark I. Wallace, Liming Ying, Shankar Balasubramanian, and David Klenerman. Non-Arrhenius kinetics for the loop closure of a DNA hairpin. Proceedings of the National Academy of Sciences, 98(10):5584-5589, 2001. URL:
  74. Anthony S. Walsh, HaiFang Yin, Christoph M. Erben, Matthew J. A. Wood, and Andrew J. Turberfield. DNA cage delivery to mammalian cells. ACS Nano, 5(7):5427-5432, 2011. URL:
  75. Erik Winfree. Algorithmic Self-Assembly of DNA. PhD Thesis, California Institute of Technology, 1998. URL:
  76. Joseph N. Zadeh, Conrad D. Steenberg, Justin S. Bois, Brian R. Wolfe, Marshall B. Pierce, Asif R. Khan, Robert M. Dirks, and Niles A. Pierce. NUPACK: Analysis and design of nucleic acid systems. Journal of Computational Chemistry, 32(1):170-173, 2011. URL:
  77. David Yu Zhang and Erik Winfree. Control of DNA strand displacement kinetics using toehold exchange. Journal of the American Chemical Society, 131(47):17303-17314, 2009. URL:
  78. Jinny X. Zhang, John Z. Fang, Wei Duan, Lucia R. Wu, Angela W. Zhang, Neil Dalchau, Boyan Yordanov, Rasmus Petersen, Andrew Phillips, and David Yu Zhang. Predicting DNA hybridization kinetics from sequence. Nature Chemistry, 10(1):91-98, 2018. URL:
  79. Jinny X. Zhang, Boyan Yordanov, Alexander Gaunt, Michael X. Wang, Peng Dai, Yuan-Jyue Chen, Kerou Zhang, John Z. Fang, Neil Dalchau, Jiaming Li, Andrew Phillips, and David Yu Zhang. A deep learning model for predicting next-generation sequencing depth from DNA sequence. Nature Communications, 12(1):4387, 2021. URL:
  80. Yong-Xing Zhao, Alan Shaw, Xianghui Zeng, Erik Benson, Andreas M. Nyström, and Björn Högberg. DNA origami delivery system for cancer therapy with tunable release properties. ACS Nano, 6(10):8684-8691, 2012. URL:
  81. Sedigheh Zolaktaf. Efficiently estimating kinetics of interacting nucleic acid strands modeled as continuous-time Markov chains. PhD Thesis, University of British Columbia, 2020. URL:
  82. Sedigheh Zolaktaf, Frits Dannenberg, Xander Rudelis, Anne Condon, Joseph M. Schaeffer, Mark Schmidt, Chris Thachuk, and Erik Winfree. Inferring parameters for an elementary step model of DNA structure kinetics with locally context-dependent Arrhenius rates. In DNA Computing and Molecular Programming, volume 10467 of Lecture Notes in Computer Science, pages 172-187, 2017. URL:
  83. Sedigheh Zolaktaf, Frits Dannenberg, Mark Schmidt, Anne Condon, and Erik Winfree. Predicting DNA kinetics with a truncated continuous-time Markov chain method. Computational Biology and Chemistry, 104:107837, 2023. URL:
  84. Sedigheh Zolaktaf, Frits Dannenberg, Erik Winfree, Alexandre Bouchard-Côté, Mark Schmidt, and Anne Condon. Efficient parameter estimation for DNA kinetics modeled as continuous-time Markov chains. In DNA Computing and Molecular Programming, volume 11648 of Lecture Notes in Computer Science, pages 80-99, 2019. URL:
  85. Michael Zuker. Mfold web server for nucleic acid folding and hybridization prediction. Nucleic Acids Research, 31(13):3406-3415, 2003. URL:
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