Figure 4.

(a) Schematic illustration of the surface regulation model in a cell-sized compartment. (b) Theoretical analysis of anomalous scaling of produced protein 〈cV〉 in confined cell-free systems. Three types of regulation regime show different size-dependent scaling. Repression (blue, $\alpha \gg {\alpha }^{⁎}$), no regulation (black, k_on = 0), and activation (red, $\alpha \ll {\alpha }^{⁎}$) correspond to β = 4.0, β = 3.0, and β = 2.0 for 〈cV〉 ∝ R^β respectively (broken lines are guide for the eyes). (c) Total produced protein number 〈cV〉 is plotted along radius of droplet R. The data shown are the same as CFGE in Fig. 3(b) (blue circles), and Eq. (6) is fitted to them with a least-square regression (blue solid curve). Black broken lines are fitted to the data points R < R_c and R > R_c, and the corresponding slopes are shown as the texts R^4.2 and R^3.1 respectively.