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Tile Blockers as a Simple Motif to Control Self-Assembly: Kinetics and Thermodynamics

Authors Constantine G. Evans , Angel Cervera Roldan , Trent Rogers , Damien Woods

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ACM Subject Classification
  • Applied computing → Chemistry
  • Applied computing → Physics
  • Theory of computation → Models of computation
Keywords
  • Self-assembly
  • kinetic model
  • kinetic simulation
  • thermodynamic prediction

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Abstract

A fundamental problem in crystallisation, and in molecular tile-based self-assembly in particular, is how to simultaneously control its two main constituent processes: seeded growth and spontaneous nucleation. Often, we desire out-of-equilibrium growth without spontaneous nucleation, which can be achieved through careful calibration of temperature, concentration and experimental time-scale a laborious and overly-sensitive approach. Another technique is to find alternative nucleation-resistant tile designs [Minev et al, 2001]. Rogers, Evans and Woods [In prep] propose blockers: short DNA strands designed to dynamically block DNA tile sides, altering self-assembly dynamics. Experiments showed independent and tunable control on nucleation and growth rates.
Here, we provide a theoretical explanation for these surprising results. We formally define the kBlock model where blockers bind to tiles at thermodynamic equilibrium in solution and stochastic kinetics allow self-assembly of a tiled structure. In an intentionally simplified mathematical setting we show that blockers permit reasonable seeded growth rates, akin to a non-blocked tile system at lower tile concentration, crucially giving nucleation rates that are exponentially suppressed. We then implement the kBlock model in a stochastic simulator, with results showing remarkable alignment with oversimplified theory. We provide evidence of blocker-induced tile buffering, where a large reservoir of blocked tiles slowly feeds a small unblocked tile subpopulation which acts like a regular, non-blocked, low tile concentration system, yet is capable of long-term buffered assembly. Finally, and perhaps most satisfyingly, theory and simulations align remarkably well with DNA self-assembly experiments over a wide range of concentrations and temperatures, matching the size of growth temperature windows to within 12%. Blockers are a straightforward solution to the challenging problem of simultaneously and independently controlling growth and nucleation, using a motif compatible with many DNA tile systems.

Cite As Get BibTex

Constantine G. Evans, Angel Cervera Roldan, Trent Rogers, and Damien Woods. Tile Blockers as a Simple Motif to Control Self-Assembly: Kinetics and Thermodynamics. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DNA.31.7

Author Details

Constantine G. Evans
  • Hamilton Institute and Department of Computer Science, Maynooth University, Ireland
Angel Cervera Roldan
  • Hamilton Institute and Department of Computer Science, Maynooth University, Ireland
Trent Rogers
  • Hamilton Institute and Department of Computer Science, Maynooth University, Ireland
  • Computer Science & Computer Engineering, University of Arkansas, Fayetteville, AR, USA
Damien Woods
  • Hamilton Institute and Department of Computer Science, Maynooth University, Ireland

Funding

Supported by Science Foundation Ireland (SFI) under grants numbers 20/FFP-P/8843 and 18/ERCS/5746, European Research Council (ERC) under the European Union’s (EU) Horizon 2020 research and innovation programme (grant No 772766, Active-DNA project), and European Innovation Council and SMEs Executive Agency (EISMEA), No 101115422, DISCO project. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the EU, ERC, EISMEA or SFI. Neither the EU nor the granting authority can be held responsible for them.

Acknowledgements

We thank Erik Winfree for questions seeking a theoretical explanation of our experimental results at DNA28, as well as David Doty for suggesting, and Rebecca Schulman for discussions on, tile-buffering [Schaffter et al., 2020].

Supplementary Materials

References

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