Propagating gene expression fronts in a one-dimensional coupled system of artificial cells

Article metrics


Living systems employ front propagation and spatiotemporal patterns encoded in biochemical reactions for communication, self-organization and computation1,2,3,4. Emulating such dynamics in minimal systems is important for understanding physical principles in living cells5,6,7,8 and in vitro9,10,11,12,13,14. Here, we report a one-dimensional array of DNA compartments in a silicon chip as a coupled system of artificial cells, offering the means to implement reaction–diffusion dynamics by integrated genetic circuits and chip geometry. Using a bistable circuit we programmed a front of protein synthesis propagating in the array as a cascade of signal amplification and short-range diffusion. The front velocity is maximal at a saddle-node bifurcation from a bistable regime with travelling fronts to a monostable regime that is spatially homogeneous. Near the bifurcation the system exhibits large variability between compartments, providing a possible mechanism for population diversity. This demonstrates that on-chip integrated gene circuits are dynamical systems driving spatiotemporal patterns, cellular variability and symmetry breaking.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Travelling gene expression front in an array of coupled DNA compartments.
Figure 2: Propagation dynamics regulated by gene circuit.
Figure 3: Emergent fluctuations in single compartments near the transition.


  1. 1

    Gregor, T., Fujimoto, K., Masaki, N. & Sawai, S. The onset of collective behavior in social amoebae. Science 328, 1021–1025 (2010).

  2. 2

    Bassler, B. L. & Losick, R. Bacterially speaking. Cell 125, 237–246 (2006).

  3. 3

    Hubaud, A. & Pourquié, O. Signalling dynamics in vertebrate segmentation. Nature Rev. Mol. Cell Biol. 15, 709–721 (2014).

  4. 4

    Kandel, E., Schwartz, J., Jessell, T. M., Seigelbaum, S. A. & Hudspeth, A. J. Principles of Neural Science (McGraw-Hill Professional, 2012).

  5. 5

    Bulter, T. et al. Design of artificial cell–cell communication using gene and metabolic networks. Proc. Natl Acad. Sci. USA 101, 2299–2304 (2004).

  6. 6

    Basu, S., Gerchman, Y., Collins, C. H., Arnold, F. H. & Weiss, R. A synthetic multicellular system for programmed pattern formation. Nature 434, 1130–1134 (2005).

  7. 7

    Matsuda, M., Koga, M., Nishida, E. & Ebisuya, M. Synthetic signal propagation through direct cell–cell interaction. Sci. Signal. 5, ra31 (2012).

  8. 8

    Danino, T., Mondragón-Palomino, O., Tsimring, L. & Hasty, J. A synchronized quorum of genetic clocks. Nature 463, 326–330 (2010).

  9. 9

    Isalan, M., Lemerle, C. & Serrano, L. Engineering gene networks to emulate Drosophila embryonic pattern formation. PLoS Biol. 3, e64 (2005).

  10. 10

    Loose, M., Fischer-Friedrich, E., Ries, J., Kruse, K. & Schwille, P. Spatial regulators for bacterial cell division self-organize into surface waves in vitro. Science 320, 789–792 (2008).

  11. 11

    Chang, J. B. & Ferrell, J. E. Mitotic trigger waves and the spatial coordination of the Xenopus cell cycle. Nature 500, 603–607 (2013).

  12. 12

    Keber, F. C. et al. Topology and dynamics of active nematic vesicles. Science 345, 1135–1139 (2014).

  13. 13

    Karzbrun, E., Tayar, A. M., Noireaux, V. & Bar-Ziv, R. H. Programmable on-chip DNA compartments as artificial cells. Science 345, 829–832 (2014).

  14. 14

    Zadorin, A. S., Rondelez, Y., Galas, J.-C. & Estevez-Torres, A. Synthesis of programmable reaction–diffusion fronts using DNA catalyzers. Phys. Rev. Lett. 114, 068301 (2015).

  15. 15

    Cross, M. & Hohenberg, P. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993).

  16. 16

    Tyson, J. J. & Keener, J. P. Singular perturbation theory of traveling waves in excitable media (a review). Physica D 32, 327–361 (1988).

  17. 17

    Fisher, R. A. The wave of advance of advantageous genes. Ann. Eugen. 7, 355–369 (1937).

  18. 18

    Keener, J. P. & Sneyd, J. Mathematical Physiology I (Springer, 1998).

  19. 19

    Winfree, A. T. Spiral waves of chemical activity. Science 175, 634–636 (1972).

  20. 20

    Bauer, G. J., McCaskill, J. S. & Otten, H. Traveling waves of in vitro evolving RNA. Proc. Natl Acad. Sci. USA 86, 7937–7941 (1989).

  21. 21

    Noireaux, V., Bar-Ziv, R. & Libchaber, A. Principles of cell-free genetic circuit assembly. Proc. Natl Acad. Sci. USA 100, 12672–12677 (2003).

  22. 22

    Noireaux, V. & Libchaber, A. A vesicle bioreactor as a step toward an artificial cell assembly. Proc. Natl Acad. Sci. USA 101, 17669–17674 (2004).

  23. 23

    Weitz, M. et al. Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator. Nature Chem. 6, 295–302 (2014).

  24. 24

    Niederholtmeyer, H., Stepanova, V. & Maerkl, S. J. Implementation of cell-free biological networks at steady state. Proc. Natl Acad. Sci. USA 110, 15985–15990 (2013).

  25. 25

    Kim, J., White, K. S. & Winfree, E. Construction of an in vitro bistable circuit from synthetic transcriptional switches. Mol. Syst. Biol. 2, 68 (2006).

  26. 26

    Bajard, L. et al. Wnt-regulated dynamics of positional information in zebrafish somitogenesis. Development 141, 1381–1391 (2014).

  27. 27

    Kessler, D. & Levine, H. Pattern formation in dictyostelium via the dynamics of cooperative biological entities. Phys. Rev. E 48, 4801–4804 (1993).

  28. 28

    Meyer, T. Cell signalling by second messenger waves. Cell 64, 675–678 (1991).

  29. 29

    Rondelez, Y. Competition for catalytic resources alters biological network dynamics. Phys. Rev. Lett. 108, 018102 (2012).

  30. 30

    Strogatz, S. H. International Edition Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemestry and Engeneering (Westview Press, 2001).

  31. 31

    Artavanis-Tsakonas, S., Rand, M. D. & Lake, R. J. Notch signaling: Cell fate control and signal integration in development. Science 284, 770–776 (1999).

  32. 32

    Wang, X., Zeng, W., Lu, G., Russo, O. L. & Eisenbraun, E. High aspect ratio Bosch etching of sub-0.25 μm trenches for hyperintegration applications. J. Vac. Sci. Technol. B 25, 1376–1381 (2007).

  33. 33

    Buxboim, A. et al. A single-step photolithographic interface for cell-free gene expression and active biochips. Small 3, 500–510 (2007).

  34. 34

    Bracha, D., Karzbrun, E., Shemer, G., Pincus, P. A. & Bar-Ziv, R. H. Entropy-driven collective interactions in DNA brushes on a biochip. Proc. Natl Acad. Sci. USA 110, 4534–4538 (2013).

  35. 35

    Daube, S. S., Bracha, D., Buxboim, A. & Bar-Ziv, R. H. Compartmentalization by directional gene expression. Proc. Natl Acad. Sci. USA 107, 2836–2841 (2010).

  36. 36

    Shin, J. & Noireaux, V. Efficient cell-free expression with the endogenous E. coli RNA polymerase and sigma factor 70. J. Biol. Eng. 4, 8 (2010).

  37. 37

    Shin, J. & Noireaux, V. An E. coli cell-free expression toolbox: Application to synthetic gene circuits and artificial cells. ACS Synth. Biol. 1, 29–41 (2012).

  38. 38

    Caschera, F. & Noireaux, V. Synthesis of 2.3 mg/ml of protein with an all Escherichia coli cell-free transcription–translation system. Biochimie 99, 162–168 (2014).

  39. 39

    Karzbrun, E., Shin, J., Bar-Ziv, R. H. & Noireaux, V. Coarse-grained dynamics of protein synthesis in a cell-free system. Phys. Rev. Lett. 106, 048104 (2011).

  40. 40

    Karu, A. E., Sakaki, Y., Echols, H. & Linn, S. The γ protein specified by bacteriophage γ. Structure and inhibitory activity for the recBC enzyme of Escherichia coli. J. Biol. Chem. 250, 7377–7387 (1975).

  41. 41

    Ferrell, J. E. Tripping the switch fantastic: How a protein kinase cascade can convert graded inputs into switch-like outputs. Trends Biochem. Sci. 21, 460–466 (1996).

  42. 42

    Gardner, T. S., Cantor, C. R. & Collins, J. J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000).

  43. 43

    Chang, D.-E. et al. Building biological memory by linking positive feedback loops. Proc. Natl Acad. Sci. USA 107, 175–180 (2010).

  44. 44

    Huang, D., Holtz, W. J. & Maharbiz, M. M. A genetic bistable switch utilizing nonlinear protein degradation. J. Biol. Eng. 6, 9 (2012).

  45. 45

    Hughes, K. T. & Mathee, K. The anti-sigma factors. Annu. Rev. Microbiol. 52, 231–286 (1998).

Download references


We thank S. S. Daube for helpful discussions. V.N. thanks J. Garamella, R. Marshall and M. Rustad for technical help. This work was supported by: the Israel Science Foundation, the Minerva Foundation, and the Volkswagen Foundation (R.H.B.-Z.); the US–Israel Binational Science Foundation (R.H.B.-Z. and V.N.).

Author information

All authors contributed to all aspects of this work.

Correspondence to Roy H. Bar-Ziv.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 6785 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tayar, A., Karzbrun, E., Noireaux, V. et al. Propagating gene expression fronts in a one-dimensional coupled system of artificial cells. Nature Phys 11, 1037–1041 (2015) doi:10.1038/nphys3469

Download citation

Further reading