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Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions


Networks of organic chemical reactions are important in life and probably played a central part in its origin1,2,3. Network dynamics regulate cell division4,5,6, circadian rhythms7, nerve impulses8 and chemotaxis9, and guide the development of organisms10. Although out-of-equilibrium networks of chemical reactions have the potential to display emergent network dynamics11 such as spontaneous pattern formation, bistability and periodic oscillations12,13,14, the principles that enable networks of organic reactions to develop complex behaviours are incompletely understood. Here we describe a network of biologically relevant organic reactions (amide formation, thiolate–thioester exchange, thiolate–disulfide interchange and conjugate addition) that displays bistability and oscillations in the concentrations of organic thiols and amides. Oscillations arise from the interaction between three subcomponents of the network: an autocatalytic cycle that generates thiols and amides from thioesters and dialkyl disulfides; a trigger that controls autocatalytic growth; and inhibitory processes that remove activating thiol species that are produced during the autocatalytic cycle. In contrast to previous studies that have demonstrated oscillations and bistability using highly evolved biomolecules (enzymes15 and DNA16,17) or inorganic molecules of questionable biochemical relevance (for example, those used in Belousov–Zhabotinskii-type reactions)18,19, the organic molecules we use are relevant to metabolism and similar to those that might have existed on the early Earth. By using small organic molecules to build a network of organic reactions with autocatalytic, bistable and oscillatory behaviour, we identify principles that explain the ways in which dynamic networks relevant to life could have developed. Modifications of this network will clarify the influence of molecular structure on the dynamics of reaction networks, and may enable the design of biomimetic networks and of synthetic self-regulating and evolving chemical systems.

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Figure 1: Overview of the network of organic reactions.
Figure 2: Summary of the batch kinetic studies of the organic reaction network.
Figure 3: Schematic representation of the CSTR experimental set-up.
Figure 4: The network of organic reactions displays bistability and sustained oscillations under flow.

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This work was funded in part by the Simons Foundation under award 290364 and by the Templeton Foundation under award 48423. A.A. was supported by the Swedish Research Council (VR).

Author information

Authors and Affiliations



S.N.S. and G.M.W. conceived the research and designed the experiments. S.N.S., L.J.K., A.A., M.Z., V.E.C., M.B. and K.K. performed the experiments and analysed the data. S.N.S., L.J.K., A.A. and J.M.F. performed the computational simulations. S.N.S., L.J.K., J.M.F., V.E.C. and G.M.W. wrote the manuscript.

Corresponding author

Correspondence to George M. Whitesides.

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The authors declare no competing financial interests.

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Reviewer Information

Nature thanks A. Bissette, S. Fletcher and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Figure 1 1H NMR kinetic experiments showing the mechanism for autocatalysis in AlaSEt with CSSC reaction.

a, Scheme for the reaction between AlaSEt and CSH. b, Scheme for the reaction between AlaSEt and hexamethylendiamine. c, Kinetic plot for the reaction between AlaSEt and CSH. Reaction conditions: D2O, pH 7.5, 500 mM phosphate buffer, 25 °C, AlaSEt (58 mM), CSH (88 mM). d, Kinetic plot for the reaction between AlaSEt and hexamethylendiamine. Reaction conditions: D2O, pH 7.5, 500 mM phosphate buffer, 25 °C, AlaSEt (58 mM), hexamethylendiamine (88 mM). e, Kinetic plot for our autocatalytic thiol network. Reaction conditions: 500 mM phosphate buffer pH 7.5, 25 °C, D2O. Points represent experimental data and solid lines represent the predictions of numerical simulations of the system. We assume the following: all disulfide–thiol interchange reactions proceed with the same rate constant kSS = 0.65 s−1 M−1; Kent ligation proceeds with rate constant kL = 0.41 s−1 M−1; and hydrolysis proceeds with rate constant kw = 7.00 × 10−6 s−1). The poor fit of the experiment with [CSSC] = 23 mM is a result of a simplifying assumption that all thiolate–disulfide interchanges in the model occur with equal rate constants in the forward and reverse directions. f, Time profiles for selected individual compounds in the autocatalytic thiol network. Reaction conditions: 500 mM phosphate buffer pH 7.5, 25 °C, D2O, [AlaSEt] = 46 mM, [CSSC] = 46 mM.

Extended Data Figure 2 Schematic representation of the thiol–disulfide interchange reactions and thiol–thioester exchange reactions.

The thiol–thioester exchange reactions are those that we omitted from Fig. 1b because they do not significantly alter the dynamics of the system.

Extended Data Figure 3 Batch kinetic experiments.

ac, Kinetics plots for the reaction of AlaSEt with CSSC and maleimide. Reaction conditions: 500 mM phosphate buffer pH 7.5, 25 °C, D2O, [AlaSEt] = 46 mM, CSSC = 46 mM, [maleimide] = 1.16 mM (a), 2.31 mM (b) or 3.47 mM (c). d, e, Kinetics plots for batch reaction between AlaSEt, CSSC, maleimide and acrylamide. Reaction conditions: 1 M phosphate buffer pH 8, 25 °C, H2O, [AlaSEt] = 46 mM, [CSSC] = 92 mM, [maleimide] = 10 mM, [acrylamide] = 160 mM (d) or 320 mM (e).

Extended Data Figure 4 Calibration curves for the determination of the total concentration of free thiols.

a, Calibration curve for the batch experiments; [RSH] = A × 28.71 mM, where A stands for absorbance. b, Calibration curve for the detection system in which a microfluidic chip was coupled to the fibre optic spectrophotometer; [RSH] = (A − 0.01496) × 21.32 mM. c, Trace of the absorbance from the calibration experiment for the detection system in which a glass flow cell was coupled to the Cary 60 ultraviolet–visual spectrophotometer; [RSH] = (A – 0.03848) × 7.16 mM. The concentrations above the lines show β-mercaptoethanol (ME) concentrations used for getting responses in absorbance under the line. The inset shows a separate experiment where 5 mM of ME were used. d, Calibration curve that was obtained from the data in c. The inset demonstrates loss of linearity of the calibration curve above approximately 8 mM of ME. Error bars in a, b and d correspond to 95% confidence intervals calculated using Student’s t-test (three independent experiments for each point).

Extended Data Figure 5 Bistability in the maleimide delayed autocatalytic thiol network.

ac, Modelling of the hysteresis in the maleimide delayed autocatalytic thiol network in a CSTR with the following parameters: kSS = 0.65 s−1 M−1, kL = 0.41 s−1 M−1, kw = 9.26 × 10−6 s−1, kmal = 150 s−1 M−1, [CSSC]0 = 100 mM, [AlaSEt]0 = 50 mM, [mal]0 = 1.16 mM (a), 2.31 mM (b) or 3.47 mM (c). df, Hysteresis curves for bistability experiments with different maleimide concentrations. Reaction conditions: 0.5 M phosphate buffer pH 7.5, 25 °C, [AlaSEt] = 47 mM, [CSSC] = 92 mM, [maleimide] = 1.16 mM (d), 2.31 mM (e) or 3.47 mM (f). In all panels, arrows indicate the direction of change. Error bars in d, e and f correspond to standard deviations that were calculated from data points (n > 100) in the time intervals that were used to determine the steady-state values of [RSH] for each space velocity.

Extended Data Figure 6 Identification of space velocities resulting in sustained oscillations.

a, Numerical simulations predicting sustained oscillations based on the following parameters: kSS = 0.444 s−1 M−1, kL = 0.46 s−1 M−1, kw = 6.64 × 10−5 s−1, kmal = 150 s−1 M−1, kAAm = 0.014 s−1 M−1, [CSSC]0 = 100 mM, [AlaSEt]0 = 50 mM, [mal]0 = 10 mM, [acrylamide]0 ≡ [AAm]0 = 290 mM (see Methods), space velocity SV = 0.0002 s−1. b, Adjustment of the flow rate in the oscillatory experiments. Reaction conditions: 1 M phosphate buffer pH 8, [AlaSEt] = 47 mM, [CSSC] = 92 mM, [maleimide] = 10.3 mM, [acrylamide] = 321 mM.

Extended Data Figure 7 Summary of all oscillatory experiments.

Reaction conditions: 1 M phosphate buffer pH 8, [AlaSEt] = 47 mM, [CSSC] = 92 mM, [maleimide] = 10.3 mM, [acrylamide] = 321 mM. The qualitatively different behaviour of the system at space velocity SV = 2.8 × 10−4 s−1 (bottom row) is an indication of the bifurcation point. The apparent thiol concentration of 0.5–1 mM in experiments 2 and 3 at this space velocity is the result of a background reaction of AlaSEt with Ellman’s reagent that occurs with a rate constant that is about 4 × 104 times slower than the reported apparent second-order rate constant of the reaction between Ellman’s reagent and β-mercaptoethanol at pH 7 (ref. 36).

Extended Data Figure 8 Analysis of for the three-component model.

a, Results of the linear stability analysis of the three-component model. The graphs show steady states, which were calculated from the model (equation (1); with S0 = 0.05 M, I0 = 0.01 M, k1 = 0.25 s−1 M−1, k2 = 300 s−1 M−1, k3 = 0.0035 s−1 and k4 = 7 × 10−5 s−1), and their stability. In this model, k0 is the space velocity (SV). The right panel shows detailed analyses of the region indicated by the dashed square in the left panel. Details of the linear stability analysis is provided in Supplementary Information. b, A phase plot computed from the three-component model. c, Experimental hysteresis plot demonstrating the transition from oscillations to bistability with lowering of the feeding concentration of maleimide; arrows indicate the direction of change. Error bars correspond to standard deviations calculated from data points (n > 100) in the time intervals that were used to determine the steady-state values of [RSH] for each space velocity. Reaction conditions: 1 M phosphate buffer pH 8, 25 °C, [AlaSEt] = 47 mM, [CSSC] = 92 mM, [maleimide] = 4 mM, [acrylamide] = 321 mM. Dashed line shows correspondence between the maleimide concentration and the range space velocities on the phase plot and in the experiment.

Extended Data Figure 9 Details of the full numerical model and an illustration of bistability and hysteresis.

a, Schematic representation of the reactions that were considered in the full models of the bistable network and the oscillatory network. b, An example of a fold bifurcation. As the control parameter is increased, the system transitions from having two stable states (A and A′) to having just one (B). The transition from A to B is often called a critical transition. After the transition, lowering the control parameter will not return the system to A. This phenomenon is called hysteresis. When the control parameter is lowered sufficiently, the system will again transition from having two stable states (C and C′) to having just one (D).

Extended Data Table 1 pKa values for the most important thiol and amino derivatives, and estimated populations of different species at equilibrium

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Semenov, S., Kraft, L., Ainla, A. et al. Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions. Nature 537, 656–660 (2016).

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