Gene networks that compensate for crosstalk with crosstalk

Crosstalk is a major challenge to engineering sophisticated synthetic gene networks. A common approach is to insulate signal-transduction pathways by minimizing molecular-level crosstalk between endogenous and synthetic genetic components, but this strategy can be difficult to apply in the context of complex, natural gene networks and unknown interactions. Here, we show that synthetic gene networks can be engineered to compensate for crosstalk by integrating pathway signals, rather than by pathway insulation. We demonstrate this principle using reactive oxygen species (ROS)-responsive gene circuits in Escherichia coli that exhibit concentration-dependent crosstalk with non-cognate ROS. We quantitatively map the degree of crosstalk and design gene circuits that introduce compensatory crosstalk at the gene network level. The resulting gene network exhibits reduced crosstalk in the sensing of the two different ROS. Our results suggest that simple network motifs that compensate for pathway crosstalk can be used by biological networks to accurately interpret environmental signals.

The red and green functions differ in their C and bmax values but have the same output fold-induction and same utility. The black function is shifted vertically relative to the red function, giving the same difference between bmax and C, but a lower output foldinduction and utility. The yellow function is shifted to lower Kd relative to the red function, and the purple function is shifted to a higher Kd relative to the red function, but all three functions have the same utility.

Supplementary Figure 2 | Sensitivities for different H2O2-sensing circuits. (A)
The sensitivity of the circuits in Fig. 1A was calculated from the Hill equations plotted in Fig. 1B. (B) The sensitivity of the circuits in Fig.  1D and 1E was calculated from the Hill equations plotted in Fig. 1F. The sensitivity was calculated as in (1):  Figure 2E. mCherry expression across a range of paraquat levels was normalized to mCherry expression at zero paraquat for the circuits and data in Figs. 2E and 2F. Lower IPTG concentrations increased the output fold-induction and input dynamic range.  Fig. 3B. The data shown is the mean of the relative error calculated from each experimental replicate and is thus different from that shown in Supplementary Note 2. The lowest concentrations of paraquat and H2O2 tested were zero, but are plotted as non-zero numbers so as to be shown on the logarithmic axes.  Fig. 3D. Crosstalk is reduced at high concentrations of paraquat, but is higher at low concentrations of paraquat compared to the initial dual-sensing strain ( Supplementary Fig. 7). The data shown are the mean of the relative error calculated from each experimental replicate. The lowest concentrations of paraquat and H2O2 tested were zero, but are plotted as non-zero numbers so as to be shown on the logarithmic axes. Relative mCherry Error

Supplementary Figure 9 | The dual-sensor circuit with the variable-analog compensation circuit without TEVp. (A)
The dual-sensor circuit with the variable-analog compensation circuit without pLsoxS-TEVp. mCherry expressed from oxySp is targeted for degradation due to the LAA degradation signal. (B) The mCherry output from the circuit in (A) in terms of fold-change relative to minimum fluorescence. Because oxySp-derived mCherry is rapidly degraded, the mCherry output looks similar to the first iteration of the dual-ROS sensing circuit (Fig. 3B). The data are derived from three biological replicates and flow cytometry experiments, each involving 30,000 events. The lowest concentrations of paraquat and H2O2 tested were zero, but are plotted as non-zero numbers so as to be shown on the logarithmic axes. Source data are provided as a Source Data file. Crosstalk is lower at high paraquat levels and is reduced at low paraquat compared to the initial dual-sensor circuit in Supplementary Fig. 7. The data shown is the mean of the relative error calculated from each experimental replicate. The lowest concentrations of paraquat and H2O2 tested were zero, but are plotted as non-zero numbers so as to be shown on the logarithmic axes. The sfGFP output is dependent upon H2O2 input concentration. The total mCherry output is the sum of mCherry resulting from the H2O2-sensing circuit and the paraquat-sensing circuit. (C) The dual-sensor circuit with the variable-analog compensation circuit. The sfGFP output is dependent upon H2O2 input concentration. The total mCherry output is the sum of mCherry resulting from the H2O2-sensing circuit and the paraquat-sensing circuit, where the paraquat-sensing circuit can adjust the amount of mCherry resulting from the H2O2-sensing circuit by adjusting the mCherry degradation rate. We describe this scenario as being conceptually analogous to a potentiometer whose output can be regulated by a paraquat circuit.    In the ideal scenario for the circuits from Fig. 3, mCherry expression should only be controlled by the input paraquat concentration. To determine the raw error in mCherry expression, we subtracted the mCherry level at every given concentration of paraquat and H2O2 from the mCherry level at the same concentration of paraquat but with zero H2O2. = s*9*tu*v U , w x y x X − s*9*tu*v U , w x y x ` In the figure above, mCherry expression across a range of paraquat concentrations and zero H2O2 is extrapolated and overlaid on top of mCherry expression across the entire range of paraquat and H2O2 concentrations. The difference between these two mCherry levels is the raw error. The raw error for a single experimental replicate for the circuit in Fig. 3A is shown below. The lowest concentrations of paraquat and H2O2 tested were zero, but are plotted as non-zero numbers so as to be shown on the logarithmic axes. The absolute error is calculated by taking the absolute value of the raw error. The absolute error for a single experimental replicate for the circuit in Fig. 3A is shown below. The lowest concentrations of paraquat and H2O2 tested were zero, but are plotted as non-zero numbers so as to be shown on the logarithmic axes.
= | s*9*tu*v U , w x y x X − s*9*tu*v U , w x y x ` | 3. Calculate the relative error: The relative error is calculated by normalizing the absolute error to the corresponding mCherry level at the same concentration of paraquat but with zero H2O2. The relative error for an experimental replicate for the circuit in Fig. 3A is shown below. The lowest concentrations of paraquat and H2O2 tested were zero, but are plotted as non-zero numbers so as to be shown on the logarithmic axes.
= | s*9*tu*v U , w x y x X − s*9*tu*v U , w x y x ` | s*9*tu*v U , w x y x ` Absolute Error mCherry 4. Sum the relative errors to get the total relative error: To calculate the total relative error, the relative error at every concentration of paraquat and H2O2 is summed.

=
• | s*9*tu*v U , w x y x X − s*9*tu*v U , w x y x ` | s*9*tu*v U , w x y x ` s*9*tu*v TUV , w x y x TUV s*9*tu*v`, w x y x ` This procedure for calculating errors has been illustrated for the mCherry output of a single experimental replicate of the circuit shown in Fig. 3A. The analogous procedure can be carried out for the sfGFP output of the circuits in Fig. 3, thus resulting in the calculations plotted in Fig. 3I. Relative Error mCherry