Isocost Lines Describe the Cellular Economy of Genetic Circuits

Abstract

Genetic circuits in living cells share transcriptional and translational resources that are available in limited amounts. This leads to unexpected couplings among seemingly unconnected modules, which result in poorly predictable circuit behavior. In this study, we determine these interdependencies between products of different genes by characterizing the economy of how transcriptional and translational resources are allocated to the production of proteins in genetic circuits. We discover that, when expressed from the same plasmid, the combinations of attainable protein concentrations are constrained by a linear relationship, which can be interpreted as an isocost line, a concept used in microeconomics. We created a library of circuits with two reporter genes, one constitutive and the other inducible in the same plasmid, without a regulatory path between them. In agreement with the model predictions, experiments reveal that the isocost line rotates when changing the ribosome binding site strength of the inducible gene and shifts when modifying the plasmid copy number. These results demonstrate that isocost lines can be employed to predict how genetic circuits become coupled when sharing resources and provide design guidelines for minimizing the effects of such couplings.

Figure 1

Rationale of the circuit. (A) On the left, schematic representation of the construct used to study the cellular economy of genetic circuits. GFP is constitutively expressed and RFP is under the control of activator LuxR and input AHL. Curved arrows and hairpins represent promoters and terminators, respectively (for details, see Fig. S1). On the right, the mean fluorescence levels at the steady state are presented for the indicated concentrations of AHL (nM), normalized to the values with no AHL (for details, see Fig. S15). (B) On the left, schematic representation of the construct used to study the separation of the pool of resources used by the plasmid and by the chromosomal genes. On the right, the mean fluorescence levels at the steady state are presented for the indicated concentrations of AHL (nM), normalized to the values with no AHL (for details, see Figs. S2–S5). We also constructed MBP-tetR with the chromosomally integrated GFP together with constitutively expressed TetR on a plasmid (for details, see Section A2 in the Supporting Material) to demonstrate that possible reductions to the chromosomal GFP expression are detectable (for details, see Figs. S6–S8). (C) In the control circuit MBP-gapA, the RFP gene of MBP-1.0 has been replaced by the glyceraldehyde dehydrogenase encoding gene (gapA) from E. coli. MBP-dRFP does not contain RFP. On the right, GFP dose response plots for the circuit MBP-1.0 and the controls MBP-gapA and MBP-dRFP (for details, see Fig. S15). All data plots represent mean values and standard deviations of populations in the steady state analyzed by flow cytometry in three independent experiments.

Figure 2

Isocost lines predicted by the model. (A) Decreasing the RBS strength of RFP $\left({\text{p}}_1\right)$, that is, increasing the dissociation constant $k_1$, rotates the isocost line clockwise. (B) Decreasing the plasmid copy number n shifts the isocost line down.

Figure 3

Influence of the RBS strength of RFP on the isocost line. (A) AHL dose response plots of GFP (upper) and RFP (lower) when RFP RBS strength is changed. The numbers indicate the relative strength of the RBS for RFP compared with MBP-1.0. (B) Linear relationships between GFP and RFP production. The steady-state values of GFP are represented as a function of the values of RFP in the same experiment. For numerical simulation results, see Section B4 in the Supporting Material. All plots represent mean values and standard deviations of populations in the steady state analyzed by flow cytometry in three independent experiments (for details, see Fig. S18).

Figure 4

Influence of the plasmid copy number on the isocost line. (A) AHL dose response plots of GFP (upper) and RFP (lower) when plasmid copy number is changed. The plasmid MBP-1.0 was tested in the DIAL hosts JTK60 J (64 $\pm$ 2 copies), H (18 $\pm$ 4 copies), and E (4 $\pm$ 1 copies). These copy numbers lead to 60%, 48%, and 29% change in GFP, respectively. (B) Linear relationships between GFP and RFP production. The steady-state values of GFP are represented as a function of the values of RFP in the same experiment. For numerical simulation results, see Section B4 in the Supporting Material. All plots represent mean values and standard deviations of populations in the steady state analyzed by flow cytometry in three independent experiments (for details, see Fig. S23).

Figure 5

Realizable region of protein concentration. The theoretically predicted realizable region $\mathcal{R}$ is denoted by the gray triangle, which is defined by the origin and the isocost line corresponding to $\left(N,K\right)$, depicted in blue. Experimental data points are also shown in the figure. The isocost line starts on the $p_2$ -axis but never reaches the $p_1$ -axis, because some small amount of RNAP and thus ribosomes will still be allocated for $p_2$. To see this figure in color, go online.