Robustness and the cycle of phosphorylation and dephosphorylation in a two-component regulatory system

Abstract

The EnvZ/OmpR system in Escherichia coli, which regulates the expression of the porins OmpF and OmpC, is one of the simplest and best-characterized examples of two-component signaling. Like many other histidine kinases, EnvZ is bifunctional; it phosphorylates and dephosphorylates the response regulator OmpR. We have analyzed a mathematical model of the EnvZ-mediated cycle of OmpR phosphorylation and dephosphorylation. The model predicts that when EnvZ is much less abundant than OmpR, as is the case in E. coli, the steady-state level of phosphorylated OmpR (OmpR-P) is insensitive to variations in the concentration of EnvZ. The model also predicts that the level of OmpR-P is insensitive to variations in the concentration of OmpR when the OmpR concentration is sufficiently high. To test these predictions, we have perturbed the porin regulatory circuit in E. coli by varying the expression levels of EnvZ and OmpR. We have constructed two-color fluorescent reporter strains in which ompF and ompC transcription can be easily measured in the same culture. Using these strains we have shown that, consistent with the predictions of our model, the transcription of ompC and ompF is indeed robust or insensitive to a wide range of expression levels of both EnvZ and OmpR.

Figure 1

A model of the EnvZ/OmpR two-component circuit. The kinetics are described by four differential equations together with the constraints that the total amount of EnvZ and OmpR are constant. The concentration of ATP is assumed constant and is absorbed into the rate constant k_k. The explicit form of the equations is given in Supporting Text.

Figure 2

Coomassie-stained gels of cell envelope fractions showing that porin osmoregulation in MDG131 (lanes b and d) and MC4100 (lanes a and c) are comparable. Low osmolarity cultures (lanes a and b) were grown in medium A, and high osmolarity cultures (lanes c and d) were grown in medium A supplemented with 15% sucrose.

Figure 3

Fluorescence measurements of ompF (YFP) and ompC (CFP) osmo-regulation in MDG131. Cultures were grown in minimal media with varying concentrations of sucrose. (a) YFP (⧫) and CFP (□) fluorescence (arbitrary units) normalized by culture optical density. (b) CFP/YFP fluorescence ratio (▵). Each error bar denotes the SD of three independent cultures.

Figure 4

(a) CFP/YFP fluorescence ratios versus EnvZ levels for cultures of MDG135/pEnvZ at low osmolarity (minimal medium) with varying amounts of IPTG. Fluorescence and EnvZ levels were normalized by WT values, which were determined from MDG131/pEB5. (b) Similar measurements for growth at high osmolarity (minimal medium with 15% sucrose). Fluorescence and EnvZ levels were normalized by the low osmolarity WT values (WT 0%) as in a. For reference, the low osmolarity data are also shown in b. ▴, MDG135/pEnvZ 0% sucrose; ▵, MDG131/pEB5 0% sucrose; ⧫, MDG135/pEnvZ 15% sucrose; ◊, MDG131/pEB5 15% sucrose. The WT level of EnvZ at high osmolarity is ≈2.1 times higher than the level at low osmolarity. Each error bar denotes the SD of three independent cultures.

Figure 5

(a) CFP/YFP fluorescence ratios versus OmpR levels for cultures of MDG133/pEB15 at low osmolarity (minimal medium) with varying amounts of IPTG. Fluorescence and OmpR levels were normalized by WT values, which were determined from MDG131/pEB16. (b) Similar measurements for growth at high osmolarity (minimal medium with 15% sucrose). Fluorescence and OmpR levels were normalized by the low osmolarity WT values (WT 0%) as in a. For reference, the low osmolarity data are also shown in b. ▴, MDG133/pEB15 0% sucrose; ▵, MDG131/pEB16 0% sucrose; ⧫, MDG133/pEB15 15% sucrose; ◊, MDG131/pEB16 15% sucrose. The WT level of OmpR at high osmolarity is ≈1.7 times higher than the level at low osmolarity. Each error bar denotes the SD of three independent cultures.