Figure 4.

The QSF secretion is under negative feedback. (a) Principle of the experiment: cell cultures are started at t = 0 in several dishes with a given cell density n₀. Then the medium is taken at various times t = T_i, so that it contains QSF at concentration c(T_i). (b(i)–b(iv)) For all media collected at different time points T_i, the activity was measured as a function of the dilution factor f. Same colours as in (c). The black lines represents the fit. (c) Then all the activity curves were collapsed onto the master curve (black line) to get the relative QSF concentrations, allowing to measure c(t)/c₀ for all T_i with the definition c(t)/c₀ = 1/f₀(t). (d) Computed QSF concentration in time, starting from n₀ = 3 × 10³ ml⁻¹ (blue circles), n₀ = 6 × 10⁴ ml⁻¹ (green triangles), n₀ = 3 × 10⁵ ml⁻¹ (red squares) and theoretical predictions from equation (3.6) (dashed lines, c_m = 8c₀ for n₀ = 3 × 10³ ml⁻¹, c_m = 12c₀ for n₀ = 6 × 10⁴ and 3 × 10⁵ ml⁻¹). The error bars represent the standard deviation (n = 3 independent experiments for each point). (e) Normalized secretion rate α/c₀ as a function of the concentration, computed from the c(t) obtained with n₀ = 3 × 10³ ml⁻¹. The grey lines show a linear fit (centre) and the bounding straight lines. (f) Theoretical concentration as a function of logn in populations starting from various initial densities n₀. The system exhibits a tendency to switch fast from 0 to 1 around n^* (dashed vertical line) with a weak sensitivity to n₀ (all the curves converge fast to the limit case of equation (3.6), black line).