Fig. 4.

Design principles of multistable switches. a Using the Lu model with added positive autoregulation we uncover the design principles dictating if a switch will be bistable, tristable, or quadristable. b An initial bifurcation analysis of the LU-DP switch uncovers the stabilities it is capable when varying the parameter for gene expression (while keeping all other parameters fixed). c–e By considering the bivariate distributions of the parameters we can uncover the differences in the parameters of a bistable switch compared to a tristable switch, compared to a quadristable switch. The posterior distribution of the bistable switch is shown in purple, the tristable switch in red and the quadristable switch in green, all plotted on the prior ranges. The bivariate distributions for which a difference is observed between the stabilities are in black boxes. An example of the phenotype (phase plot) from each switch is shown next to the corresponding posterior distribution. Parameter legend key: g _x production rates; k _x degradation rates; n _xy Hill coefficients; x _xy Hill threshold concentrations; l _xy transcription rate fold change; n _xx autoregulation Hill coefficients; x _xx autoregulation Hill threshold concentrations; l _xx autoregulation transcription rate fold change