Tunable diffusive lateral inhibition in chemical cells

  • Ning Li
  • Nathan Tompkins
  • Hector Gonzalez-Ochoa
  • Seth FradenEmail author
Regular Article


The Belousov-Zhabotinsky (BZ) reaction has become the prototype of nonlinear chemical dynamics. Microfluidic techniques provide a convenient method for emulsifying BZ solutions into monodispersed drops with diameters of tens to hundreds of microns, providing a unique system in which reaction-diffusion theory can be quantitatively tested. In this work, we investigate monolayers of microfluidically generated BZ drops confined in close-packed two-dimensional (2D) arrays through experiments and finite element simulations. We describe the transition from oscillatory to stationary chemical states with increasing coupling strength, controlled by independently varying the reaction chemistry within a drop and diffusive flux between drops. For stationary drops, we studied how the ratio of stationary oxidized to stationary reduced drops varies with coupling strength. In addition, using simulation, we quantified the chemical heterogeneity sufficient to induce mixed stationary and oscillatory patterns.

Graphical abstract


Soft Matter: Self-organisation and Supramolecular Assemblies 

Supplementary material

10189_2015_103_MOESM1_ESM.gif (33 kb)
Supplementary material, approximately 33.3 KB.
10189_2015_103_MOESM2_ESM.mpg (6.6 mb)
Supplementary material, approximately 6.59 MB.

Supplementary material, approximately 3.43 MB.

Supplementary material, approximately 3.43 MB.

10189_2015_103_MOESM5_ESM.mpg (300 kb)
Supplementary material, approximately 300 KB.

Supplementary material, approximately 1.65 MB.

10189_2015_103_MOESM7_ESM.mpg (4.4 mb)
Supplementary material, approximately 4.36 MB.
10189_2015_103_MOESM8_ESM.mph (1.5 mb)
Supplementary material, approximately 1.46 MB.


  1. 1.
    A.M. Turing, Philos. Trans. R. Soc. London 237, 37 (1952).CrossRefADSGoogle Scholar
  2. 2.
    K.U. Torii, Trends Cell Biol. 22, 438 (2012).CrossRefGoogle Scholar
  3. 3.
    M. Cohen, B. Baum, M. Miodownik, J. R. Soc. Interface 8, 787 (2011).CrossRefGoogle Scholar
  4. 4.
    P. Formosa-Jordan, M. Ibñaes, J. Stat. Mech. 2009, P03019 (2009).CrossRefGoogle Scholar
  5. 5.
    A.D. Economou, A. Ohazama, T. Porntaveetus, P.T. Sharpe, S. Kondo, M.A. Basson, A. Gritli-Linde, M.T. Cobourne, J.B.A. Green, Nat. Genet. 44, 348 (2012).CrossRefGoogle Scholar
  6. 6.
    R. Phillips, J. Kondev, J. Theriot, H. Garcia, Physical Biology of the Cell, 2nd edition (Garland Science, 2012).Google Scholar
  7. 7.
    F. Sagués, I.R. Epstein, Dalton Trans. 7, 1201 (2003).CrossRefGoogle Scholar
  8. 8.
    N. Tompkins, N. Li, C. Girabawe, M. Heymann, G.B. Ermentrout, I.R. Epstein, S. Fraden, Proc. Natl. Acad. Sci. U.S.A. 111, 4397 (2014).CrossRefADSGoogle Scholar
  9. 9.
    N. Li, J. Delgado, H.O. Gonzalez-Ochoa, I.R. Epstein, S. Fraden, Phys. Chem. Chem. Phys. 16, 10965 (2014).CrossRefGoogle Scholar
  10. 10.
    J. Delgado, N. Li, M. Leda, H.O. Gonzalez-Ochoa, S. Fraden, I.R. Epstein, Soft Matter 7, 3155 (2011).CrossRefADSGoogle Scholar
  11. 11.
    M. Toiya, V.K. Vanag, I.R. Epstein, Angew. Chem. Int. Ed. 47, 7753 (2008).CrossRefGoogle Scholar
  12. 12.
    M. Toiya, H.O. Gonzlez-Ochoa, V.K. Vanag, S. Fraden, I.R. Epstein, J. Phys. Chem. Lett. 1, 1241 (2010).CrossRefGoogle Scholar
  13. 13.
    C. Holtze, A.C. Rowat, J.J. Agresti, J.B. Hutchison, F.E. Angile, C.H.J. Schmitz, S. Koster, H. Duan, K.J. Humphry, R.A. Scanga et al., Lab Chip 8, 1632 (2008).CrossRefGoogle Scholar
  14. 14.
    R.M. Noyes, R. Field, E. Körös, J. Am. Chem. Soc. 94, 1394 (1972).CrossRefGoogle Scholar
  15. 15.
    R.J. Field, E. Körös, R.M. Noyes, J. Am. Chem. Soc. 94, 8649 (1972).CrossRefGoogle Scholar
  16. 16.
    V.K. Vanag, I.R. Epstein, J. Chem. Phys. 131, 104512 (2009).CrossRefADSGoogle Scholar
  17. 17.
    V.K. Vanag, I.R. Epstein, Phys. Rev. E 84, 066209:1 (2011).CrossRefADSGoogle Scholar
  18. 18.
    D.G. Aronson, G.B. Ermentrout, N. Kopell, Physica D 41, 403 (1990).CrossRefADSzbMATHMathSciNetGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Ning Li
    • 1
  • Nathan Tompkins
    • 1
  • Hector Gonzalez-Ochoa
    • 1
    • 2
  • Seth Fraden
    • 1
    Email author
  1. 1.Department of PhysicsBrandeis UniversityWalthamUSA
  2. 2.Department of Applied MathematicsIPICYTSan Luis PotosiMexico

Personalised recommendations