Natural Computing

, Volume 13, Issue 4, pp 583–595 | Cite as

Modeling scalable pattern generation in DNA reaction networks

  • Peter B. Allen
  • Xi Chen
  • Zack B. Simpson
  • Andrew D. Ellington


We have developed a theoretical framework for developing patterns in multiple dimensions using controllable diffusion and designed reactions implemented in DNA. This includes so-called strand displacement reactions in which one single-stranded DNA hybridizes to a hemi-duplex DNA and displaces another single-stranded DNA, reversibly or irreversibly. These reactions can be designed to proceed with designed rate and molecular specificity. By also controlling diffusion by partial complementarity to a stationary, cross-linked DNA, we can generate predictable patterns. We demonstrate this with several simulations showing deterministic, predictable shapes in space.


Reaction–diffusion Chemical reaction networks DNA circuits Strand displacement reactions 



We acknowledge the NIH fellowship GM095280. Additional support was provided by The Welch Foundation Grant F-1654, the NSSEFF (FA9550-10-1-0169), and NIH Eureka grant 5 R01 GM094933-01,02,03.

Supplementary material

11047_2013_9392_MOESM1_ESM.txt (53 kb)
Supporting Material: MATLAB program showing each simulation figure and its derivation is included online as allen_simulation_supplement.m. (TXT 52 kb)


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Peter B. Allen
    • 1
  • Xi Chen
    • 1
  • Zack B. Simpson
    • 1
  • Andrew D. Ellington
    • 1
  1. 1.University of Texas at AustinAustinUSA

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