Different Regulatory Networks Can Yield the Same Optimal Enzyme Expression Level as a Function of Inducer Concentration.

<p>This is illustrated for two regulatory networks of the <i>lac</i> 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 <i>lac</i> 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, <i>X</i>_free/<i>X</i>, 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 <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000125#pcbi-1000125-g002" target="_blank">Figure 2</a>). (C) The resulting optimal enzyme expression level as a function of the lactose concentration, as predicted by Equation 20 <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000125#pcbi.1000125-Dekel1" target="_blank">[12]</a>.