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A Multi-Functional Synthetic Gene Network: A Frequency Multiplier, Oscillator and Switch

Figure 5

1-dimensional sketch summarising the bifurcation structure.

The three main features are two simultaneous saddle-node bifurcations, a Hopf bifurcation and a pitchfork bifurcation. These occur at input concentrations of 0.4 nM, 7 nM and 9 nM respectively. The analysis covers the input concentration range 0–60 nM, and traces out three branches of equilibria, A, B and C. The structure can be divided into four dynamical regions corresponding to labels 1–4. The dynamics at each label are shown in the set of simulations above. At position 1 and 4 two stable equilibria exist simultaneously. In all simulation panels the horizontal axis is time (seconds) and the vertical axis is concentration. All simulations are for seconds. The concentration range on the vertical axis in panels 1 and 1, 2, 3 and 4 and 4, are 0–150 nM, 0–90 nM, 0–140 nM and 0–180 nM respectively. Simulation panels 4 and 4 used initial conditions nM, nM. All other panels used initial conditions nM, nM. Panels 1 and 1, 2, 3 and 4 and 4 use a constant input concentration nM, 5 nM, 7.5 nM and 10 nM (4 and 4) respectively. All simulations use table 1 parameters. Red dashed lines delineate the oscillatory region, which lies in between two stable regions in which trajectories decay to equilibrium levels. This diagram is intended to convey the qualitative aspects of the phase portrait. As such there is no scale on the vertical axis.

doi: https://doi.org/10.1371/journal.pone.0016140.g005