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Complex dynamics in a two-enzyme reaction network with substrate competition


Enzymatic reaction networks capable of generating complex spatiotemporal dynamics are not only the basis of essential biological processes, but also the basic units of synthetic systems with autonomous, adaptive and programmable behaviours. Activation and inhibition have been usually considered as indispensable interactions for the construction of such networks. Here we present an enzymatic reaction network that consists of a flavin adenine dinucleotide-dependent oxidoreductase and a peroxidase that can generate tunable complex dynamics. These include charging/discharging, rectangular and parabolic pulses in a closed system, which are based on delayed and self-adapting substrate competition, rather than on activation or inhibition. Additionally, this system can spontaneously form visible spatiotemporal patterns that arise from reaction-driven Rayleigh–Bénard convection. This work demonstrates that substrate competition could be an alternative path towards constructing biochemical networks with complex dynamics.

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Fig. 1: Examples of complex dynamic behaviour generated by enzymatic networks under batch conditions.
Fig. 2: Tuning the network output to create various pulse waveforms.
Fig. 3: Pulse response can be reactivated by controlling the oxygen flux.
Fig. 4: The formation and evolution of spatiotemporal patterns.


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This work was supported by the Defense Threat Reduction Agency under award no. HDTRA 1-14-1-0051.

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Authors and Affiliations



Y.Z. and H.H. conceived and designed the research and wrote the manuscript. Y.Z. performed the experiments. S.T. performed the statistical analysis and modelling. All the authors discussed the results and commented on the manuscript.

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Correspondence to Henry Hess.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Methods, Figures 1–13, Table 1, Notes 1 and 2, and References

Supplementary Video 1

Demonstration of green bottle experiment (20× speed).

Supplementary Video 2

Evolution of spatiotemporal patterns in the solution with a depth of 2.6 mm (20× speed).

Supplementary Video 3

Evolution of spatiotemporal patterns in the solution with a depth of 7.0 mm (20× speed).

Supplementary Video 4

Evolution of spatiotemporal patterns in the solution with a depth of 8.8 mm (20× speed).

Supplementary Video 5

Visualization of the convective flows by adding tracer particles (real-time movie).

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Zhang, Y., Tsitkov, S. & Hess, H. Complex dynamics in a two-enzyme reaction network with substrate competition. Nat Catal 1, 276–281 (2018).

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