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Optimal Census by Quorum Sensing

Fig 5

Optimal MI and optimal MI increase.

Dependence of the optimal MI I^⋆ and the optimal MI increase ΔI^⋆ (in bits) on the burst size b and on the level of self-repression f_int,+ (in logarithmic scale) for both TF and sRNA regulations. The Xs indicate the values f_int,+ = 1/2 and b = 20 for which Table 1 was computed. In the top panels, the white curves are isoinformation curves separating regions where the optimal quorum-sensing channel can discriminate the indicated number of cell-density ranges. In the bottom panels, the white curves represent parameters for which feedbacks cannot improve information transfer (0 bits) or can double the number of distinguishable cell density ranges (1 bit). Note that, in both cases, a decrease in f_int,+ has to be matched by a larger bare MP output rate to ensure the boundary condition ${\tau }_m{f}_{\mathrm{\text{int}},+}{f}_m^{(1)}(a_{+})=m_{+}$. Parameter values: ρ₊/ρ₋ = 10⁴, a₋ = 0.1nM, a₊ = 1mM, m₋ = 100nM, m₊ = 600nM, f_int,− = 2, K = 15nM, h = 2 and v = 1μm³.

doi: https://doi.org/10.1371/journal.pcbi.1004238.g005