Skip to main content
SpringerLink
Log in

Modeling scalable pattern generation in DNA reaction networks

  • Published:
Natural Computing Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Allen P, Chen X, Ellington AD (2012) Spatial control of DNA reaction networks by DNA sequence. Molecules 17(12):13390–13402

    Article  Google Scholar 

  • Aristotle (2004) On the generation of animals. Kessinger Publishing, Whitefish

    Google Scholar 

  • Breslauer KJ, Frank R, Blacker H, Marky LA (1986) Predicting DNA duplex stability from the base sequence. Proc Natl Acad Sci USA 83(11):3746–3750

    Article  Google Scholar 

  • Castets V, Dulos E, Boissonade J, De Kepper P (1990) Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern. Phys Rev Lett 64(24):2953

    Article  Google Scholar 

  • Chen Q, Whitmer JK, Jiang S, Bae SC, Luijten E, Granick S (2011) Supracolloidal reaction kinetics of Janus spheres. Science 331(6014):199–202

    Article  Google Scholar 

  • Fan JA, He Y, Bao K, Wu C, Bao J, Schade NB, Manoharan VN, Shvets G, Nordlander P, Liu DR, Capasso F (2011) DNA-enabled self-assembly of plasmonic nanoclusters. Nano Lett 11(11):4859–4864

    Article  Google Scholar 

  • Fernandez JG, Khademhosseini A (2010) Micro-masonry: construction of 3D structures by microscale self-assembly. Adv Mater 22(23):2538–2541

    Article  Google Scholar 

  • Field RJ, Noyes RM (1974) Oscillations in chemical systems. V. Quantitative explanation of band migration in the Belousov-Zhabotinskii reaction. J Am Chem Soc 96(7):2001–2006

    Article  Google Scholar 

  • Fujii T, Rondelez Y (2013) Predator–prey molecular ecosystems. ACS Nano 7(1):27–34

    Article  Google Scholar 

  • Gregor T, Tank DW, Wieschaus EF, Bialek W (2007) Probing the limits to positional information. Cell 130(1):153–164

    Article  Google Scholar 

  • Kleiner RE, Dumelin CE, Tiu GC, Sakurai K, Liu DR (2010) In vitro selection of a DNA-templated small-molecule library reveals a class of macrocyclic kinase inhibitors. J Am Chem Soc 132(33):11779–11791

    Article  Google Scholar 

  • Koch AJ, Meinhardt H (1994) Biological pattern formation: from basic mechanisms to complex structures. Rev Mod Phys 66(4):1481–1507

    Article  Google Scholar 

  • Lander AD (2007) Morpheus unbound: reimagining the morphogen gradient. Cell 128(2):245–256

    Article  Google Scholar 

  • Li X, Liu DR (2004) DNA-templated organic synthesis: nature’s strategy for controlling chemical reactivity applied to synthetic molecules. Angew Chem Int Ed Engl 43(37):4848–4870

    Article  Google Scholar 

  • Macfarlane RJ, Lee B, Jones MR, Harris N, Schatz GC, Mirkin CA (2011) Nanoparticle superlattice engineering with DNA. Science 334(6053):204–208

    Article  Google Scholar 

  • Maini PK, Othmer HG (2001) Mathematical models for biological pattern formation. Springer, Berlin

    Book  Google Scholar 

  • Murnen HK, Rosales AM, Jaworski JN, Segalman RA, Zuckermann RN (2010) Hierarchical self-assembly of a biomimetic diblock copolypeptoid into homochiral superhelices. J Am Chem Soc 132(45):16112–16119

    Article  Google Scholar 

  • Nakamasu A, Takahashi G, Kanbe A, Kondo S (2009) Interactions between zebrafish pigment cells responsible for the generation of Turing patterns. Proc Natl Acad Sci USA 106(21):8429–8434

    Article  Google Scholar 

  • Nakano S, Fujimoto M, Hara H, Sugimoto N (1999) Nucleic acid duplex stability: influence of base composition on cation effects. Nucleic Acids Res 27(14):2957–2965

    Article  Google Scholar 

  • Nichol JW, Khademhosseini A (2009) Modular tissue engineering: engineering biological tissues from the bottom up. Soft Matter 5(7):1312–1319

    Article  Google Scholar 

  • Okabe-Oho Y, Murakami H, Oho S, Sasai M (2009) Stable, precise, and reproducible patterning of bicoid and hunchback molecules in the early drosophila embryo. PLoS Comput Biol 5(8):e1000486

    Article  Google Scholar 

  • Ouchterlony O (1958) Diffusion-in-gel methods for immunological analysis. Prog Allergy 5:1–78

    Google Scholar 

  • Peter IS, Davidson EH (2009) Modularity and design principles in the sea urchin embryo gene regulatory network. FEBS Lett 583(24):3948–3958

    Article  Google Scholar 

  • Phillips A, Cardelli L (2009) A programming language for composable DNA circuits. J R Soc Interface 6(Suppl 4):S419–S436

    Article  Google Scholar 

  • Qian L, Winfree E (2011) Scaling up digital circuit computation with DNA strand displacement cascades. Science 332(6034):1196–1201

    Google Scholar 

  • Reeves GT, Muratov CB, Schupbach T, Shvartsman SY (2006) Quantitative models of developmental pattern formation. Dev Cell 11(3):289–300

    Article  Google Scholar 

  • Robelek R, Stefani FD, Knoll W (2006) Oligonucleotide hybridization monitored by surface plasmon enhanced fluorescence spectroscopy with bio-conjugated core/shell quantum dots. Influence of luminescence blinking. Phys Status Solidi 203(14):3468–3475

    Article  Google Scholar 

  • Rothemund PWK (2006) Folding DNA to create nanoscale shapes and patterns. Nature 440(7082):297–302

    Article  Google Scholar 

  • Soloveichik D, Seelig G, Winfree E (2010) DNA as a universal substrate for chemical kinetics. Proc Natl Acad Sci USA 107(12):5393–5398

    Article  Google Scholar 

  • Turing AM (1952) The chemical basis of morphogenesis. Philos Trans R Soc B 237(641):37–72

    Article  Google Scholar 

  • Umulis DM (2009) Analysis of dynamic morphogen scale invariance. J R Soc Interface 6(41):1179–1191

    Article  Google Scholar 

  • Vanag VK, Epstein IR (2001) Pattern formation in a tunable medium: the Belousov-Zhabotinsky reaction in an aerosol OT microemulsion. Phys Rev 87(22):228301

    Google Scholar 

  • Yan D, Lin XH (2009) Shaping morphogen gradients by proteoglycans. Cold Spring Harb Perspect Biol 1(3):a002493

    Article  Google Scholar 

  • Yin P, Choi HMT, Calvert CR, Pierce NA (2008) Programming biomolecular self-assembly pathways. Nature 451(7176):318–322

    Article  Google Scholar 

  • Yurke B (2007) Using DNA to power the nanoworld. Control Nanoscale Motion 711:331–347

    Article  Google Scholar 

  • Zhang DY, Winfree E (2009) Control of DNA strand kinetics using toehold exchange. J Am Chem Soc 131:17303–17314

    Article  Google Scholar 

  • Zhu Z, Wu C, Liu H, Zou Y, Zhang X, Kang H, Yang CJ, Tan W (2010) An aptamer cross-linked hydrogel as a colorimetric platform for visual detection. Angew Chem Int Ed 49(6):1052–1056

    Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. University of Texas at Austin, Austin, Tx, USA

    Peter B. Allen, Xi Chen, Zack B. Simpson & Andrew D. Ellington

Authors
  1. Peter B. Allen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zack B. Simpson
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andrew D. Ellington
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrew D. Ellington.

Electronic supplementary material

Below is the link to the electronic supplementary material.

11047_2013_9392_MOESM1_ESM.txt

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

Rights and permissions

Reprints and permissions

About this article

Cite this article

Allen, P.B., Chen, X., Simpson, Z.B. et al. Modeling scalable pattern generation in DNA reaction networks. Nat Comput 13, 583–595 (2014). https://doi.org/10.1007/s11047-013-9392-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-013-9392-7

Keywords

Search

Navigation