Two-Strain E. coli Consortium Control

• The two-strain E. coli consortium is a synthetic community composed of strains with distinct growth rates and metabolic capabilities, enabling complementary bioproduction processes.
• The system employs a dual-chamber bioreactor with precise flow control and real-time OD feedback to sustain stable, balanced strain composition under variable conditions.
• Advanced control strategies including switching controllers, MPC, and reinforcement learning ensure rapid setpoint tracking, disturbance rejection, and scalability for industrial applications.

A two-strain Escherichia coli consortium denotes a synthetic microbial community formed from two distinct E. coli strains, each exhibiting differential intrinsic growth rates or metabolic capabilities. Such consortia are engineered to exploit inter-strain complementarities and have significant application potential in bioproduction, bioprocessing, and synthetic ecology. Control over strain composition and total biomass is critical for ensuring functional robustness, stable coexistence, and optimal performance, especially in industrial settings where native interactions can cause population collapse or suboptimal yields. Recent technological developments have moved toward bioreactor-centered architectures and non-genetic control modalities to regulate these consortia, as exemplified by the dual-chamber system introduced by Brancato et al. (Brancato et al., 11 Nov 2025).

1. Bioreactor-Based Architectural Principles

The described control platform employs two continuously stirred bioreactor vessels (Chi.Bio units): a mixing chamber (MC) and a reservoir (R). The MC hosts both strains—designated as "fast" (strain 1, green) and "slow" (strain 2, pink)—allowing for co-cultivation under controlled conditions. The reservoir contains only strain 2 grown as a monoculture. Flows are precisely managed via microcontroller-regulated peristaltic pumps, maintaining volumetric stasis through coordinated waste removal and regulated inflow. Three independently actuated flow rates are implemented:

• $D_1$ (fresh medium to MC), $D_2$ (reservoir effluent to MC), and $D_R$ (fresh medium to reservoir), all bounded in $[0, 0.02]\,$mL/s.
• Optical density (OD) sensors sample each vessel every minute, generating feedback variables $y_1 = x_1 + x_2$ (MC) and $y_2 = x_2^R$ (R). This modular hardware allows dynamic redistribution of strain populations and sustains the slower-growing strain against competitive exclusion.

2. Mathematical Modeling of Population Dynamics

Mass-balance equations adapted for Monod-type microbial kinetics encapsulate the coupled system's dynamics. The reservoir obeys

$$\dot{x}_2^R = \mu_2(s_2)\,x_2^R - (D_R + D_2)\,x_2^R$$

with substrate consumption

$$\dot{s}_2 = -\mu_2(s_2)\,x_2^R + (D_R + D_2)(s_{in}-s_2).$$

The mixing chamber supports both strains: $$\begin{aligned} \dot{x}_1 &= \mu_1(s_1)\,x_1 - (D_1 + D_2)\,x_1 \ \dot{x}_2 &= \mu_2(s_1)\,x_2 - D_1\,x_2 + D_2(x_2^R-x_2) \ \dot{s}_1 &= -\mu_1(s_1)x_1 - \mu_2(s_1)x_2 + D_1(s_{in}-s_1)+D_2(s_2-s_1) \end{aligned}$$ Assuming substrate $\gg k_i$ (Monod constant for each strain), kinetics simplify: $\mu_i(s) \approx \mu_i^*$, yielding reduced models for control. Identified parameters are $\mu_1^* = 0.021$ min$^{-1}$ (fast), $\mu_2^* = 0.011$ min$^{-1}$ (slow), time-scale $\tau=0.215$.

3. Model-Based and Learning-Based Control Methodologies

Regulatory objectives in the MC are twofold:

• Drive total biomass to desired OD ($y_1 \rightarrow OD_d$).
• Shape composition ratio ($x_2 - r_d x_1 \rightarrow 0$), maintaining $x_i \geq x_{i,min} = 0.2$ to preclude strain extinction.

Two principal control strategies are employed: (A) Switching Controller: The state-space is segmented into four discrete regions ($R_1$–$R_4$) by switching surfaces $\sigma_1 = x_1 - x_{1,d}$, $\sigma_2 = x_2 - x_{2,d}$. Policy selects $(D_1, D_2)$ combinations guaranteeing closed-loop convergence to reference $(x_{1,d}, x_{2,d})$.

(B) Model Predictive Control (MPC): Applied to the reservoir, optimizing cost

$J(t) = \sum_{k=0}^{N-1}[c(t+k) + V_F(x(t+N))]$

over horizon $N=5$ min, penalizing deviation from $x_{2,d}^R$ with quadratic cost, including constraints on actuation.

Additionally, a PI controller is implemented for the reservoir, embedded in the Chi.Bio platform.

Reinforcement learning via Deep Q-Networks (DQN) is leveraged in both chambers, trained in simulation with randomized growth rates and sensor noise. The MC agent processes ten-dimensional recent error history and acts in a discretized control space. Reward structures enforce rapid convergence, extinction avoidance, and reference tracking. DQN training (200 episodes, 180 steps each) achieves inference latency $<$1 ms.

4. Experimental Validation and Protocols

Experimental identification involved monoculture OD-tracking in MC ($D_2=0$) with randomized $D_1$ steps; least-squares regression provided parameter values and performance metrics (RMSE for $x_1$: 3.83 OD units, $x_2$: 0.48). EKF observer validation used flow cytometry (GFP gating for strain discrimination) compared to filter estimates; MSEs were 0.001 ($x_1$) and 0.004 ($x_2$).

Control performance was evaluated under multiple scenarios:

• Fixed setpoints: $x_1(0)=x_2(0)=0.4$, $OD_d=0.7$, $r_d=0.6$ ($90$ min runs).
• Composition tracking: $r_d$ step over $120$ min.
• Biomass tracking: $OD_d$ step over $120$ min.
• Disturbance rejection: 3 mL LB injected at $t=100$ min; resilience to sharp dilution tested.

Reservoir controllers underwent reference steps at $x_2^R(0)=0.8 \rightarrow 0.65 \rightarrow 0.50$, with a $37^{\circ}$C to $30^{\circ}$C temperature shift for dynamic robustness assessment.

5. Quantitative Results and Comparative Analysis

Reservoir controllers (PI, MPC, DQN) settled to references in $\leq 7$ min, with normalized RMSE $\leq 5\%$. Under a $\sim10\%$ growth-rate shift (temperature perturbation), NRMSE altered by $<0.01$, evidencing robustness.

Mixing chamber regulation delivered:

• Fixed-point operation: Ratio settling times $\sim43$ min (Switch), $53$ min (DQN); OD settling $4$ min/$16$ min; NRMSE $9\%/7\%$ (ratio), $5\%/7\%$ (OD).
• Time-varying references: Ratio $t_s \sim10$ min (Switch)/$31$ min (DQN); NRMSE $11\%/14\%$.
• Disturbance rejection: Post-perturbation recovery within $20\%$ band; pre-/post-dilution NRMSE ratios $6\%/8\%$ (ratio), $7\%/8\%$ (OD).

Paired two-tailed t-tests found $p>0.1$ for settling times and NRMSEs across triplicates, indicating no statistically significant difference between Switch and DQN controllers within experimental variability.

6. Limitations and Robustness Characteristics

Only aggregate OD is measurable in real time, demanding EKF state estimation with residual error affecting ratio-tracking. Peristaltic pump limitations at low flow rates (backflow, coarse granularity at $\{0, 0.01, 0.02\}$ mL/s) restrict control action resolution. Substrate dynamics are neglected under $s \gg k$, valid only for $OD < 1.0$.

Sim-to-real augmentation (randomized growth parameters, injected sensor noise) confers robustness to controllers, demonstrated to tolerate $\pm10\%$ shifts in $\mu_i^*$ and rapid dilution shocks without population extinction or loss of setpoint tracking.

7. Scalability and Future Directions

The dual-chamber architecture is inherently modular. Scalability to multi-strain consortia is achievable by introducing additional reservoirs or hierarchical control layers. The framework abstains from genetic modifications or drastic environmental shifts, facilitating deployment in applications where metabolic burden or compositional flexibility are limiting. A plausible implication is increased relevance for process-scale bioproduction and complex synthetic ecologies.

By integrating a hardware architecture (dual-vessel bioreactors) with interchangeable model-based (Switch, MPC, PI) and learning-based (DQN) controllers, precise in vivo regulation of two-strain E. coli consortia is attainable, enabling dynamic setpoint tracking, compositional maintenance, and resilience to environmental perturbations (Brancato et al., 11 Nov 2025).