Figure 1.
A Sketch of the Instantaneous Growth Rate λ of a Single Cell as a Function of the Concentration X of Component X.
If the average expression level Xs is close to the optimal expression level Xopt, biochemical noise will always decrease the growth rate. If, however, the average expression level deviates sufficiently from the optimal expression level (i.e. if ax>bx2 in Equation 11), then fluctuations can enhance the growth rate of the population, even when the growth rate λ of a single cell is linear in X, i.e. if b = 0. The reason is that fast growing cells dominate the population.
Figure 2.
Relative Change in the Growth Rate as a Function of the Average Repressor Concentration.
The growth rate is averaged over different lactose concentrations in the environment (see Equation 17), for two different lactose concentration distributions in the environment.
Figure 3.
Different Regulatory Networks Can Yield the Same Optimal Enzyme Expression Level as a Function of Inducer Concentration.
This is illustrated for two regulatory networks of the lac system, which differ in the dissociation constants of lactose-repressor binding and repressor-operator binding. Panels (A) and (B) show the response functions at two different stages of the lac regulatory network, while panel (C) shows the resulting optimal enzyme expression level as a function of lactose concentration. (A) The fraction of repressor that is not bound by lactose, Xfree/X, as a function of lactose concentration for two different lactose-repressor binding constants. (B) The corresponding response curves of the enzyme expression level as a function of the fraction of free repressor. The total expression level of repressor is chosen to correspond to the optimal growth rate (see Figure 2). (C) The resulting optimal enzyme expression level as a function of the lactose concentration, as predicted by Equation 20 [12].
Figure 4.
The Optimal Design of the lac Regulatory Network Is Determined by the lac Repressor Copy Number and the Repressor–Lactose Binding Constant.
Contour plot of the growth rate as a function of the repressor copy number X and repressor-lactose binding constant KD. The weighting of the lactose levels is nonuniform. Lower binding constants allow for higher optimal growth rates at lower optimal expression levels for the repressor.