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Optimal Census by Quorum Sensing

Fig 4

Optimal quorum-sensing response.

TF regulation is shown by dashed curves and sRNA regulation by solid curves. A. The bare MP expression rate $f_m^{(1)}(c)$, in the absence of self-regulation of the MP, obeys a Hill function with h = 2 (inset). Temporal dynamics of the optimal mean AI concentration and B. temporal dynamics of the optimal mean MP abundance. C. Optimal external feedback $f_{\mathrm{\text{ext}}}^{\star }$ with f₋ = a₋/(τ_a ρ₋) and D. optimal internal feedback $f_{\mathrm{\text{int}}}^{\star }$. E. Fano function with optimal feedback F^⋆ and without feedback F as functions of MP abundance m. The ratio of effective correlation times τ^⋆/τ = F^⋆/F is shown inset. In all panels, red curves indicate the optimal quorum-sensing response, black curves indicate the absence of all feedbacks $(f_{\mathrm{\text{ext}}}^{\prime }=0,f_{\mathrm{\text{int}}}=1)$. Parameter values: ρ₊/ρ₋ = 10⁴, a₋ = 0.1nM, a₊ = 1mM, m₋ = 100nM, m₊ = 600nM, f_int,− = 2, f_int,+ = 1/2, K = 15nM, h = 2, b = 20 and v = 1μm³.

doi: https://doi.org/10.1371/journal.pcbi.1004238.g004