Fig. 3

The three variants of the deterministic Lu models. a The classic switch with no autoregulation is bistable as shown in the stream plot and the phase plot. In the stream plot, the colours indicate the magnitude of the vectors, with yellow indicating high and red low values. The blue points represent stable steady states and the grey points represent unstable steady states. The phase plot shows the steady state values for 100 particles at the final population. Each particle is represented by a different shade of blue. The most restricted parameters for this behaviour are the degradation rates (k _x and k _y ), which both have to be high while the net protein production for X and Y must be balanced. b The extended Lu model with a single positive autoregulation on X. This model is bistable when the production rate of X, g _x , is small. c The Lu model with double positive autoregulation is tristable as shown in the stream plot and the phase plot. We find two types of tristable behaviour, one where the third steady state is zero-zero and one where the third state is high