Topology-dependent interference of synthetic gene circuit function by growth feedback

Abstract

Growth-mediated feedback between synthetic gene circuits and host organisms leads to diverse emerged behaviors, including growth bistability and enhanced ultrasensitivity. However, the range of possible impacts of growth feedback on gene circuits remains underexplored. Here we mathematically and experimentally demonstrated that growth feedback affects the functions of memory circuits in a network topology-dependent way. Specifically, the memory of the self-activation switch is quickly lost due to the growth-mediated dilution of the circuit products. Decoupling of growth feedback reveals its memory, manifested by its hysteresis property across a broad range of inducer concentration. On the contrary, the toggle switch is more refractory to growth-mediated dilution and can retrieve its memory after the fast-growth phase. The underlying principle lies in the different dependence of active and repressive regulations in these circuits on the growth-mediated dilution. Our results unveil the topology-dependent mechanism on how growth-mediated feedback influences the behaviors of gene circuits.

Figure 1.. Theoretical analysis reveals bistability, but experimental data shows no hysteresis.

a, Parameter fitting the dose-response curve of the prompter (P_BAD) shows ultrasensitivity. The results showed mean±s.d. (n=6). Unstable GFP variant (GFP-lva) is used as the reporter. b, Mathematical model predicts bistability from the SA circuit with P_BAD prompter. c, Steady-state distribution of GFP after 17 hours induction of various doses of L-ara with the initial state ‘OFF’ shows two distinct states (separated by the dash lines), ‘ON’ and ‘OFF’. d, The steady-state fraction of ‘ON’ cells after 17 hours induction of L-ara with the initial state ‘OFF’ (blue curve) or ‘ON’ (Red curve) shows no hysteresis. The ‘ON’ cells were pretreated with high-dose of L-ara (2.5×10⁻³%). Data displayed as mean±s.d. (n=3).

Figure 2.. Growth-mediated feedback disguises the bistability of the SA circuit.

a-b, Dynamics of growth (Optical Density, OD) (a) and GFP/OD (b) after 1:100 dilution of ‘ON’ cells into fresh medium with various doses of L-ara. Data indicate mean±s.d. (n=3). c, Diagram of coupling gene circuit with cell growth. The mathematical model is revised based on this diagram. d, Simulation with revised mathematical model shows AraC level as a function of time and L-ara dose. The system was set to ‘ON’ state initially. e, The process of memory loss of the SA circuit. Simulated trajectory (blue lines) of one cell is shown on the rate-balance plot of AraC. Two stable steady states (SSS, solid circles) and one unstable steady state (USS, open circle) are shown at the intersection of the production rate curve (green) and degradation curve (red). The system was set to the ‘ON’ state initially (solid green circle) and L-ara was set to 0. Four cell division events were considered in simulation (dashed line with yellow arrow). The separatrix (dash-dotted line) determines whether the system goes to ‘ON’ or ‘OFF’ states directed by the gray arrows. The rate-balance plot is based on the model without growth feedback. f, Simulation confirms that the bistable range of the SA circuit is significantly reduced when coupled with growth feedback.

Figure 3.. Decoupling of growth feedback reveals the bistability of the SA circuit.

a-b, Time-lapse imaging of GFP (and brightfield overlay) in the SA circuit showed that it switches off after several rounds of cell divisions with fast growth in fresh medium and then did not recover in the conditioned medium without inducer (a) but recovered with high-dose L-ara (b). Representative results from three replicates are shown. c-d, The dynamics of growth (c) and GFP (d) after 1:100 dilution of ‘ON’ cells into the conditioned medium without L-ara. Negative control (blue line) was the ‘OFF’ cells grown in conditioned medium with no L-ara. e, Hysteresis curves obtained using the new protocol by diluting ‘ON’ cells into the conditioned medium with various doses of L-ara. Data indicate mean±s.d. (n=3).

Figure 4.. The toggle switch is refractory to memory loss from the growth-mediated feedback.

a, Diagram of the toggle switch circuit coupled with growth feedback. Unstable GFP variant (GFP-laa) is used as the reporter. b-c, Dynamics of OD and GFP/OD after 1:100 dilution of ‘ON’ cells into fresh medium with high-dose or without inducer aTc. d, Hysteresis curves with conditioned medium (CM, green curve) and fresh medium (FM, red curve). GFP level was normalized to the level at the highest aTc. e, Simulated trajectory (blue lines) of one cell is shown in the direction field of LacI/TetR. Four cell division events were considered (indicated by dashed lines with yellow arrows in the enlarged box area). Two stable steady states (SSS, solid circles) and one unstable steady state (USS, open circle) are shown at the intersection of nullclines (green and red curves). The system was set to the ‘ON’ state initially (solid green circle) and aTc was set to 0. The separatrix (dash-dotted line) determines whether the system goes to the ‘ON’ or ‘OFF’ state directed by the gray arrows. The nullcline curves were based on the model without growth feedback. Data indicate mean±s.d. (n=3).