A Design Principle of Group-level Decision Making in Cell Populations
Figure 3
Conditions for group-level transitions in quorum sensing.
(A) A phase diagram showing the bistable regions in parameter space (ε, λ) of the simple autoinduction circuit (Eq, 1). The black lines indicate phase boundaries between GB (Group-level Bistability), AB (Autonomous-Bistability), and M (Mono-stability) (Eqs. S2-14 and S2-6 in Text S1). CO (Constitutively ON) means the cells are always in the ON state; i.e., xi∼1, regardless of cell density in the case of M (white region). Log10 CVρ/CVk<0 (blue and cyan region) and log10 CVρ/CVk>0 (red and pink region) indicate regions where cell-cell heterogeneity in the threshold value is reduced or not reduced, respectively. The yellow line indicates log10 CVρ/CVk = 0, determined numerically with spline interpolation. The × and + correspond to Figs. 2A and 2B, respectively. (B) A phase diagram for the simple autoinduction circuit (Eq. 1; Fig. 1C) and the dual positive-feedback circuit (Eq. 3; Fig. 1D). The m and n are cooperativity coefficients (Eq. 3). As in (A), solid and dashed lines denote the phase boundaries between PB/CB and CB/M, respectively (Eqs. S2-15 and S2-23 in Text S1). λ = 20 (grey) and 100 (black). The bottom row shows the parameter ε for the bacterial QS operons, las, rhl, lux, and car estimated from the literature (Table S6). For the las, rhl, and lux systems, estimates for two independent data sets are plotted.