Genetic controllers for enhancing the evolutionary longevity of synthetic gene circuits in bacteria

Abstract

Engineered gene circuits often degrade due to mutation and selection, limiting their long-term utility. Here we present designs for genetic controllers which maintain synthetic gene expression over time. Using a multi-scale “host-aware" computational framework, which captures interactions between host and circuit expression, mutation, and mutant competition, we evaluate several controller architectures based on three metrics for evolutionary stability: total protein output, duration of stable output, and half-life of production. We propose a number of designs with varying inputs (e.g., output per cell, growth rate) and actuation methods (transcriptional vs. post-transcriptional regulation). We find post-transcriptional controllers generally outperform transcriptional ones, but no single design optimizes all goals. Negative autoregulation prolongs short term performance, while growth-based feedback extends functional half-life. We propose three biologically feasible, multi-input controllers that improve circuit half-life over threefold without requiring coupling the process to an essential gene or a genetic kill switch.

Engineered gene circuits often degrade over time due to mutation and selection. Here the authors use a host-aware modelling framework to develop genetic controllers to sustain synthetic gene expression. They identify a range of design trade-offs in production, robustness and long-term performance.

Introduction

Synthetic biology seeks to engineer living organisms, often microbes, to perform desired functions, with a range of applications in healthcare, the chemicals industry and environmental science^1–3. However, loss or degradation of function over microbial generations shortens the lifespan of such systems and represents a fundamental roadblock to widespread adoption and application in industry^4,5.

Engineered synthetic gene networks, often referred to as “circuits”, utilise their host’s gene expression resources, such as ribosomes and amino acids, for their own expression. This disrupts the cell’s natural homeostasis as these resources are diverted away from host processes and towards circuit gene expression. This additional load imparted by the circuit often leads to a gross reduction in the cell growth rate, a phenomenon known as “burden” (reviewed extensively in refs. ^6–9). In microbes, such as E. coli, where growth rate is analogous to fitness, cells which contain gene circuits are at a selective disadvantage as they cannot produce new daughter cells as quickly as their faster-growing, unengineered counterparts.

DNA replication is an inherently error-prone process, so every cell division represents a possibility for such mutations to be introduced into a gene circuit. It is therefore inevitable that they will eventually arise within a large population¹⁰. Mutations to promoters, ribosome binding sites or transcription factor binding sites can result in significant changes to gene circuit dynamics. Where these mutations inhibit circuit function and correspondingly reduce cellular resource consumption, the aforementioned growth disparity enables the new mutant strains to outcompete the ancestral strain. As a result, synthetic gene circuit function is eventually eliminated from engineered populations⁴ (Fig. 1). In some cases, such evolutionary loss-of-function can occur so rapidly that a culture cannot be grown to a suitable size before its effects become significant¹¹.

Fig. 1. A schematic demonstrating how function is lost in an engineered population over evolutionary time.

Random mutations occur as a result of error-prone DNA replication, leading to mutants with reduced circuit function. These mutants have higher selective fitness, as the host cells can direct more resources towards growth. As a result, such mutants dominate the population and circuit function is eventually lost.

The evolutionary longevity of a gene circuit can be quantified by measuring the time taken for the population-level output to reach a pre-defined “breaking point”¹² (e.g., for a simple output-producing circuit, the “half-life” describes the time taken for the output to fall by 50%). A number of experimental approaches have been developed which aim to improve the evolutionary longevity of gene circuits (reviewed extensively in refs. ^13,14). These are divided into two broad approaches: (1) suppressing the emergence of circuit mutants and (2) reducing their selective advantage¹⁵. Examples of approach (1) include engineering host organisms with reduced mutation rate¹⁶ and reducing the use of repeated DNA sequences^4,10. Examples of approach (2) include systems where circuit function is artificially coupled to host survival^17–19. Such methods are often bespoke and may constrain the performance/function of a synthetic device. For example, in ref. ¹⁸, Yang et al. engineered a bidirectional promoter that simultaneously drives both GFP expression and antibiotic resistance with the view that mutations to the shared promoter ought to be selectively disadvantageous as antibiotic resistance is lost. Although the promoter sequence is maintained after serial passaging, the system remains prone to mutation in the ribosome binding site. In general, even when methods are implemented to extend the longevity of gene circuits, evolution is never entirely mitigated¹⁴ and some designs still lose expression within 24 h²⁰.

Maintenance of function in light of evolution is still an open challenge for engineering biology, with a need for design frameworks to predict and account for the mutation during the design process^5,21,22. Here, we tackle the problem from a systems perspective, aiming to identify feedback controller design paradigms that can improve evolutionary longevity. In this paper, we view the onset of mutation as a parametric uncertainty and the competition between mutant and ancestral strains as an environmental perturbation. Negative feedback is an attractive control strategy for minimising the impact of both perturbations and uncertainty because it enables a system to monitor its output and feed this information back into the system as an input, thereby adjusting its behaviour to maintain a known level. Negative feedback has been successfully implemented in synthetic biology for a variety of objectives^23,24, including optimising yields in metabolic engineering²⁵ and reducing the unexpected coupling between genetic parts (e.g.²⁶). It has been shown both theoretically and experimentally to reduce burden and improve the evolutionary longevity of synthetic circuits^27–30. However, existing work typically demonstrates that this reduction in burden is at least partly a result of reduced expression of the target genes (i.e., reduced circuit function), so the closed-loop systems are not compared against open-loop systems of equivalent function. Further, to date, little attention has been paid to how negative feedback controllers should be optimally designed to improve evolutionary longevity, both in terms of controller topology and design rules for part selection. By taking a systems engineering approach and developing mathematical models, we are able to investigate these considerations in silico.

Here, we use a host-aware design framework to analyse different design choices for the creation of genetic controllers which enhance the long-term performance of a simple genetic circuit. This model accounts for host-circuit interactions, dynamic growth and mutation, enabling us to evaluate the relationships between circuit expression, burden and evolutionary population dynamics^30–34. To evaluate evolutionary longevity, we consider both the maintenance of function in the short term (by measuring how long function is maintained within a narrow window around the designed level) and the persistence of the circuit in the long term (by measuring how long it takes for function to halve). We demonstrate the performance of a variety of controller architectures which differ in the quantity sensed by the system as the ‘control input’, and the mechanism through which control is enacted. In each case, we evaluate how to optimally design the controllers, the potential impact of additional controller resource consumption and their robustness to parametric variation to guide in vivo implementation.

We demonstrate three key factors which determine the effectiveness of genetic controllers for enhancing evolutionary longevity. Firstly, the choice of controller input: growth-based feedback significantly outperforms intra-circuit feedback and population-based feedback in the long term, while intra-circuit feedback can provide significant improvements in the short term. Secondly, the means of controller actuation: we show that post-transcriptional control, which exploits small RNAs (sRNA) to silence circuit RNA, outperforms transcriptional control via transcription factors, as this mechanism provides an amplification step which enables strong control with reduced controller burden. Thirdly, we show that systems with separate circuit and controller genes can exhibit significantly enhanced performance due to evolutionary trajectories where loss of controller function results in short-term increases in protein production. We also show that different controller architectures have different robustness to parametric uncertainty, which will complicate design selection for in vivo implementation. We propose a controller topology that combines control inputs and feedback mechanisms to improve both short- and long-term performance while maintaining enhanced robustness to parametric uncertainty.

Results

Modelling and quantifying gene circuit evolution

We develop an ordinary differential equation model of host-circuit interactions^31,33 and augment it with a model describing an evolving population of E.coli cells, taking a similar state-transition approach to ref. ³⁴ and ref. ³⁰. This multi-scale model comprises a set of competing populations sharing a single source of nutrients, with each population representing a different parameterisation (or “strain”) of an engineered E. coli cell. Mutation is implemented via transitions between these different strains, and selection emerges dynamically through differences in calculated growth rates. Simulations are performed in repeated batch conditions, where nutrients are replenished and population size is reset every 24 hours, mirroring previous experiments^4,10. Variables are given in molecules per cell (mc/cell). The complete model is defined in Supplementary Note 1. We perform simulations as defined in the Methods section entitled “Simulating an evolving population of engineered cells”.

Here, we consider a simple synthetic process consisting of a single gene A, which could represent a fluorescent reporter protein such as GFP. Messenger RNA (mRNA) transcripts m_A are generated proportional to the maximal transcription rate ω_A. They combine with ribosomes R supplied by the host model to form “translation complexes” c_A, which yield protein p_A upon the completion of translation, having consumed cellular anabolites e. Through consumption of e and utilisation of R the host and circuit models become coupled and the phenomenon of burden is captured³². We define the total output of the system P to be the total number of molecules of p_A across the entire population composed of i strains:

$$P={\sum }_i\left(N_i{p_A}_i\right),$$ 1

where each strain i represents a different mutant, and N_i is the number of cells belonging to the ith strain (Fig. 2a). For this nominal open-loop system, we assume four distinct “mutation states” which differ in the value of the maximal transcription rate ω_A, corresponding to 100%, 67%, 33% and 0% of the nominal or designed level. Mutation occurs via transition rates between these populations such that only function-reducing mutations may occur, and such that more extreme mutations are less likely (Fig. 2b). (See Supplementary Note 1 and Supplementary Fig. S1 for a full description of the mutation scheme.)

Fig. 2. Simulating an open-loop process in repeated batch conditions.

a A schematic showing the function of the process. m_A is spawned and translated to create output p_A using host ribosomes. This process impacts host growth. The total output P comes from the output p_A across an entire population of engineered cells. b A visual depiction of the mutation scheme for this process. Coloured squares represent distinct ‘mutation states’ with different levels of function. Numbers in the squares show the percentage function of a given state relative to the designed level, implemented through differences in the maximal transcription rate ω_A: 100 represents a state functioning as designed, while 0 represents a completely non-functional state where no transcripts m_A are produced. Arrows signify possible transitions between mutation states, with lighter arrows representing mutations which occur less often. c‒f Time-series outputs using an open-loop process with maximal transcription rate ${\omega }_A=5\text{mc}{\min }^{-1}$. c Total population-wide circuit output P, plotted both in full (grey) and at the end of each simulation day (green). An ideal system would match an open-loop system in the absence of mutation, maintaining function indefinitely (blue). d Population size N, distributed according to mutation state. Dark green represents a fully-functional (100%) strain. Light green represents a non-functional (0%) strain. e Output per cell p_A according to mutation state over the first day. Dotted lines show maximum outputs. f Growth rate λ according to mutation state over the first day. Dotted lines show maximum growth rates. g For a wide range of processes (varying ω_A between 0.1 and 1000 mc min⁻¹), τ_±10 (black) and τ₅₀ (grey) against initial output P₀. Simulation results are provided as a Source Data file.

To measure the evolutionary longevity of this process, we define three metrics:

1. P₀, the initial output P from the ancestral population prior to any mutation.

2. τ_±10, the time taken for the output P to fall outside of the range P₀ ± 10%.

3. τ₅₀, the time taken for the output P to fall below P₀/2.

We define these metrics assuming that we wish to maximise production (P₀) and maintain performance near to the original state (τ_±10) for as long as possible. We propose τ₅₀ as a measure of long-term performance or “persistence” because the maintenance of “some function” may be sufficient for many applications, such as biosensing.

For the proposed nominal open-loop system, the total output P falls over the course of the simulation from its initial value P₀ to 0 molecules (Fig. 2c). This corresponds to a transition of the population makeup, which initially comprises entirely of fully functional cells but eventually is dominated by non-producing, faster growing mutants (Fig. 2d–f). For systems with increased process transcription (i.e., larger maximal transcription rates ω_A), the initial output P₀ increases as more protein is produced per cell. However, this increases the burden caused by the process and therefore reduces both τ₅₀ and τ_±10. Beyond a certain point, continuing to increase ω_A can overburden the cell, leading to a reduction in all metrics (Fig. 2g).

The objective of this paper is to evaluate the ability of different control strategies to improve the evolutionary longevity of this simple synthetic circuit. It is trivial to reduce the burden and improve both τ_±10 and τ₅₀ by reducing the production of p_A via the birth rate ω_A. However, this impedes circuit function (Supplementary Fig. S2a). We therefore define the performance of controllers in comparison to an open-loop system of equal initial output P₀. See Methods for Comparing controllers versus open-loop systems of equal output for full details as to how these metrics where determined. The ideal controller would extend τ_±10 and τ₅₀ at no loss in P₀.

Phenomenological models demonstrate the potential of negative feedback control to enhance evolutionary longevity

We consider three candidates for the choice of input for a control strategy designed to improve evolutionary longevity (Fig. 3a). We model all controllers phenomenologically by scaling the maximal transcription rate of the circuit gene ω_A by a regulatory function, so that protein production is inhibited when levels are already high:

$$w_A={\omega }_A\cdot \mathrm{\Theta }\left(u\right).$$ 2

Here, u is the control input of choice.

Fig. 3. Phenomenological modelling of different choices of control input.

a A simple schematic showing the three controller architectures: intra-circuit control (red), growth-based control (orange) and population-based control (lilac). Each output comes from a different layer of the combined multi-scale model (circuit model, host model and population model). See key in Fig. 2a for symbol meanings. b Time-series of population-wide output P over time for an open-loop system (black, dashed, w_A = 4.0 mc min⁻¹) and representative control systems of equivalent initial output P₀. (Intra-circuit: red, w_A = 10³ mc min⁻¹, k_A = 4.5 × 10² mc. Growth-based: orange, w_A = 87 mc min⁻¹, k_λ = 6.3 × 10⁻² min⁻¹. Population-based: lilac, w_A = 16 mc min⁻¹, k_P = 5.2 × 10⁸ mc.). c, d A large number of designs were generated by varying the maximal transcription rate ω_A and control parameters k_u. Against the initial output P₀, we plot the percentage change in (c) τ_±10 and (d) τ₅₀ vs an open-loop system of equal initial output. Points marked with an X correspond to the time-series plots in (b). These were selected as points on the Pareto fronts simultaneously optimising P₀, τ₅₀ and τ_±10, with initial output P₀ closest to 2 × 10⁹ molecules. e, f For circuits corresponding to trajectories in (b), (e) maximum protein production per cell p_A and (f) maximum growth rates λ across the first day (solid) and the day where τ₅₀ is reached (grey outline) for each mutation state. Lighter squares represent less functional strains. The horizontal line represents a non-functional strain. Simulation results are provided as a Source Data file.

Firstly, we consider product-based negative feedback where the protein per cell p_A is the control input (Fig. 3a, red). To maintain function close to a desired level, production is inhibited if there is an abundance of output and control is alleviated if production is low. We call this intra-circuit feedback. This is achieved via the regulatory function:

$$\mathrm{\Theta }\left(p_A\right)=\frac{{k_A}^2}{{k_A}^2+p_A^2}.$$ 3

Should a mutation occur which reduces the production of p_A, the strength of control will be eased, allowing the actual output levels to rise again. This means that mutations which reduce circuit output will have a lesser impact on burden, minimising the selective advantage of such mutations.

Secondly, we consider growth rate λ as the control input (Fig. 3a, orange). Since increased production of p_A corresponds to reduced growth, we employ feedback so that production is inhibited at low growth. We call this growth-based feedback, and use the regulatory function:

$$\mathrm{\Phi }\left(\mathrm{\lambda }\right)=\frac{{\mathrm{\lambda }}^2}{{k_{\mathrm{\lambda }}}^2+{\mathrm{\lambda }}^2}.$$ 4

If a burden-relieving mutation arises with reduced production of output p_A, control will be alleviated, enabling a resultant increase in output and a smaller selective advantage over the original designed strain.

Finally, since our objective is to maintain the performance of a synthetic circuit across an entire population, we consider using the total population-wide output P as an input for control (Fig. 3a, lilac). Such a system could be implemented physically using cell-to-cell communication systems such as quorum sensing. We employ feedback so that further production is inhibited when the population-wide output P is high. We call this population-based feedback, and use the regulatory function:

$$\mathrm{\Theta }\left(P\right)=\frac{{k_P}^2}{{k_P}^2+P^2}.$$ 5

Unlike with the other systems, individual cells do not directly respond to mutations in the circuits they carry by alleviating control, because such mutations do not significantly alter the population-level control input P. Instead, this system aims to maintain population-level output by steadily increasing the per-cell production of non-mutant cells to compensate for the increasing number of non-functional mutants.

For all three systems, applying control to a given nominal process (here, ω_A = 10 mc min⁻¹) boosts longevity at the expense of initial output P₀, with stronger controllers (low k_A, high k_λ, low k_P) causing a more significant change (Supplementary Fig. S2b‒d). Representative dynamics from systems which initially produce the same population-wide output P are shown in Fig. 3b. This initial comparison suggests that intra-circuit control is capable of maintaining function at close to the designed level for longer (greater τ_±10), but that growth-based control is more effective at improving long-term persistence (greater τ₅₀). To assess the different strategies at the topological level, we generated many designs by varying both the process input ω_A and the controller strength (k_A, k_λ and k_P) while all other system parameters were fixed as defined in Supplementary Table 4. We observe that intra-circuit control excels in the short term while growth-based control excels in the long term across most parameter combinations, demonstrating that the result holds at the topological level (Fig. 3c, d). Except in cases of minimal output, population-based control is less effective and is the only strategy where some designs perform worse than open-loop. These differences in performance are a result of differences in the per-cell protein production and growth rates between mutant strains (Fig. 3e, f). For intra-circuit control, mutating into intermediate mutation states (where function is non-zero but less than the designed level) alleviates some of the control exerted by the controller, pushing production back up and providing a smaller growth advantage. However, this means that mutations which completely abolish function provide a greater growth advantage, allowing non-functional mutants to dominate quickly, accelerating loss-of-function. Growth-based control is capable of boosting the growth rate of the fully-functional state, thereby reducing the selective advantage of mutation into any other state. For population-based control, non-mutant cells become affected by a decline in population-wide output, so that control strength is eased over time. This allows them to produce more output, but leads to an even greater selective disadvantage, thereby accelerating loss-of-function.

Having established the theoretical differences in performance for different controller input strategies, we next consider how such systems could be implemented in living cells by deriving mechanistic models of biologically realisable topologies. We consider both transcription factor-based and RNA-based methods of control information processing and actuation. In the main text, we report the results for the intra-circuit and growth-based systems. Mechanistic modelling of a population-based controller which utilises quorum sensing confirms that such systems have poor performance (Supplementary Figs. S3‒S6). These results are described in Supplementary Note 2.

Intra-circuit feedback control improves short-term performance at the expense of longevity

The intra-circuit control strategy described in the above section and demonstrates the potential of negative feedback control to enhance evolutionary longevity (Fig. 3) is equivalent to an autoregulation motif where an inhibitory transcription factor inhibits itself. This limits its utility in practice, where one may want to stabilise the expression of an enzyme or signalling protein that performs a useful circuit-specific function. Here, we consider two biologically implementable control systems where feedback is enacted in proportion to the per-cell protein output p_A. The first is composed of an inhibitory transcription factor p_B, which is produced from the same promoter as circuit protein p_A, so that the functional identity of p_A is not constrained. p_B inhibits the production of both p_A and p_B (Fig. 4a). In this way, when production is high, increased inhibition reduces the production of new synthetic proteins, enabling the reduction of burden. This approach imitates previously implemented controllers (such as ref. ²⁶). We call this controller CLpATX ("Closed-loop, senses p_A, prevents transcription”). To implement this, we scale the birth rate of mRNAs by the regulatory function:

$${\mathrm{\Theta }}_A\left(p_B\right)=\frac{{k_B}^2}{{k_B}^2+{p_B}^2}.$$

Note that the controller protein here will exert an additional burden on top of the process gene.

Fig. 4. Protein-based control design and performance.

a A schematic describing the controller CLp_ATX. Controller protein p_B is produced from the same gene as output protein p_A and acts as an inhibitory transcription factor on the shared gene. b A schematic describing the controller CLp_ATL. See key in Fig. 2a for symbol meanings. A controller protein, p_B, is produced from the same gene as the output protein p_A, and acts as a transcription factor which activates the production of sRNA r_C. The feedback loop is completed through the combining of r_C with mRNA that codes for p_A and p_B, preventing it from being translated. c‒f Optimal performance for both CLp_ATX (blue) and CLp_ATL (red) for controller protein length n_B = 1, 300, 600 aa. c τ_±10 vs initial output P₀, (d) τ₅₀ vs initial output P₀, (e) %-change in τ_±10 over open-loop vs initial output P₀, (f) %-change in τ₅₀ over open-loop vs initial output P₀. g‒l Robustness analyses for (g‒i) CLp_ATX and (j‒l) CLp_ATL. For each of the 100 optimal controllers with n_B = 300 aa, 100 further controllers were generated by varying parameters by up to  ± 10% (dark grey) and  ± 25% (light grey). The percentage changes in three output metrics were calculated versus the original optimal systems: (g, j) P₀, (h, k) τ_±10 and (i, l) τ₅₀. Plots show the means (for  ± 10%) and standard deviations (for both  ± 10% and  ± 25%) of the percentage changes for each optimal controller. Percentages marked on the plots indicate the standard deviations across the entire Pareto front when parameters were varied by  ± 10%(± 25%). Simulation results are provided as a Source Data file.

The second negative feedback mechanism similarly makes use of a co-produced transcription factor p_B, but in this case it activates an sRNA r_C which then eliminates the mRNA m_A by sequestration (as in e.g.³⁵) (Fig. 4b). We call this controller CLpATL ("Closed-loop, senses p_A, prevents translation”). (For ease of reference, the names of the controllers, their inputs and mode of action are available in Supplementary Table S1). Note that there are now two genes which may be subject to mutation (the process and the sRNA) and so we update our mutation model to include 4² = 16 distinct mutation states, where each represents a unique pair [%_A, %_C], with %_A, %_C ∈ {100%, 67%, 33%, 0%}. We assume that mutations only affect a single promoter at a time (Supplementary Fig. S1). (See Supplementary Note 1 for a full description of both models for a full description of the mutation scheme.)

We first consider the transcriptional controller architecture: CLp_ATX. To determine its performance across a range of processes, we performed multi-objective optimisations to simultaneously maximise P₀, τ_±10 and τ₅₀, varying the control strength k_B, the control protein ribosome binding rate b_B and the circuit maximal transcription rate ω_A (see Methods section “Multi-objective optimisation”). To evaluate performance, we then compared these outputs with corresponding open-loop systems of equal initial output P₀. (See Methods section “Comparing controllers versus open-loop systems of equal output”).

For controller protein lengths typical of bacterial regulators (i.e., n_B = 300 amino acids (aa)), improvements in τ₅₀ are minimal, but τ_±10 can be improved by up to 60% versus open-loop (Fig. 4c–f, blue). Our optimisations show that, where improvements are possible, control strength should be maximised (i.e., low k_B) across the Pareto front (Supplementary Fig. S7, blue). This is because stronger inhibitors do not need to be as abundant to achieve the same strength of feedback, and so controller burden can be minimised. At low outputs P₀, where performance increases are minimal or non-existent, controller binding strength b_B is very small, so there is less pressure to minimise k_B as controller proteins are less abundant. Systems which produce less output (and have increased longevity) tend to have less synthetic transcription (low ω_A) and less controller translation (low b_B) (Supplementary Fig. S7, blue).

We tested the robustness of the optimal designs to parametric uncertainty by varying the optimal parameters randomly by up to  ± 10% to generate 10,000 alternate designs. We repeated the analysis for  ± 25%. To quantify robustness, we tracked the percentage change in each metric (P₀, τ_±10 and τ₅₀) versus its corresponding optimal system. A robust architecture would have small standard deviations in these values when the designs across the Pareto front are subjected to variation (See Methods section “Robustness analysis”). Here, optimal controllers are very robust to parametric variation, with changes in P₀, τ_±10 and τ₅₀ having standard deviations of 5.6% (13.9%), 3.3% (6.8%), and 2.9% (7.0%) respectively, compared with the original optimal systems when parameters were varied by  ± 10% (± 25%) (Fig. 4g–i). (See Supplementary Note 3 for our comprehensive robustness analysis (Supplementary Fig. S8a‒d and Supplementary Table S2).)

In an ideal case where the repressor causes minimal burden (i.e., n_B → 0 aa), performance can be significantly boosted to the levels suggested by the phenomenological models. The binding rate b_B can be increased without significantly increasing burden (Supplementary Fig. S7, blue). However, increasing the repressor size n_B to 600 aa, and therefore increasing controller burden, performance deteriorates to worse than open-loop and any benefits of control are lost entirely. As repressor size increases from 300 aa to 600 aa, the parametric design rules do not qualitatively change (Supplementary Fig. S7, blue).

To better understand how design choices impact this controller architecture, we tested the performance of this controller for a nominal process of maximal transcription rate ω_A = 50 mc min⁻¹ and controller protein length n_B = 300 aa by varying the controller ribosome binding rate b_B and the controller strength k_B. We show that τ_±10 can be improved by a more significant margin than τ₅₀, and across a wider portion of the design space, suggesting that it is easier to boost short-term performance than long-term performance (Supplementary Fig. S9). (See Supplementary Note 4.)

Post-transcriptional control outperforms transcriptional control for intra-circuit feedback

Unlike CLp_ATX, which only enhances performance when controller size (and therefore burden) is minimal, CLp_ATL is capable of significantly improving both τ_±10 and τ₅₀, even in the presence of large controller sizes (n_B = 600 aa) (Figs. 4c–h, 5a, red). For typical regulator lengths (n_B = 300 aa), τ₅₀ can be more than doubled, with τ_±10 showing an even more extreme improvement at low initial outputs of up to  + 400% versus open-loop. Although this system significantly outperforms CLp_ATX, the optimal control designs are less robust, with random parameter variation of up to  ± 10% (± 25%) causing larger variations in output metrics: changes in P₀, τ_±10 and τ₅₀ have standard deviations of 7.3% (18.7%), 4.5% (11.6%) and 4.3% (10.7%) respectively (Fig. 4j–l). (See Supplementary Note 3 for a comprehensive robustness analysis (Supplementary Fig. S8e–h and Supplementary Table S2).) As with CLp_ATX, maximising controller strength (i.e., minimising k_B) is crucial to achieve the most control for the least burden for n_B = 300 aa and n_B = 600 aa. For n_B = 1 aa, controller burden is much less significant, so pushing k_B to its absolute minimum is less important. Producing sRNA r_C does not result in an additional burden, and so maximising its production allows for the strongest control (Supplementary Fig. S7, red). The demonstrated improvements in longevity of CLp_ATL over CLp_ATX are a result of two key mechanisms: (i) reduced controller burden (at equivalent control strength) and (ii) the emergence of mutations to the controller itself (enabling the short-term growth of high-producing strains).

Fig. 5. Understanding the improved performance of CLp_ATL.

a–c Comparing CLp_ATX (blue) and CLp_ATL (red). a Population-wide process outputs P over time for two representative controllers. b Initial output P₀ against the maximal transcription rate of the process gene ω_A across all optimal controllers. c Controller protein per cell p_B vs process output protein per cell p_A across all optimal controllers. d–f The effect of controller mutation on CLp_ATL with n_B = 300 aa. d Population-wide output P over time according to mutation state. e Population size according to mutation state. f Bar charts for CLp_ATL with n_B = 300 aa showing (i) growth rate λ (min⁻¹), (ii) process protein output per cell p_A (molecules/cell) and (iii) sRNA per cell r_C (molecules/cell). Each subplot represents a unique mutation state. Moving rightwards signifies mutation of the process, and moving downwards signifies mutation of the controller. Simulation results are provided as a Source Data file.

Firstly, we see that optimal controllers utilise larger maximal transcription rates ω_A (Fig. 5b) and require much less controller protein p_B than CLp_ATX (Fig. 5c). This is a result of the p_B-mediated activation of r_C, which amplifies the “impact” that each burdensome controller protein can achieve. This enables CLp_ATL to provide “more control for less burden” and significantly enhance performance in the long term.

Secondly, this process-controller system has two promoters (A driving the gene expression and C driving the controller). When the process promoter mutates (affecting the process transcription rate ω_A), synthetic protein production falls, causing an increase in growth rate. However, when the sRNA promoter mutates (affecting the sRNA transcription rate ω_C), the strength of control falls, so synthetic protein production rises, leading to a decrease in growth rate. Over time, the emergence of both types of mutation leads to a heterogeneous population of mutant strains, some of which produce more protein p_A than the ancestral strain (Fig. 5d–f). It is important to note that there are two sources of mutant spread: (1) the emergence of new mutants via random mutation and (2) the competition between mutant strains as a result of their relative growth rates. In the long term, growth rate differences are the predominant cause of mutant domination; the higher-producing strains are outcompeted by faster-growing strains. However, early in the time course, when the majority of the population is still fully functional, the dynamics is primarily affected by the emergence of new mutations. Mutations to the controller can therefore initially balance out with mutations to the process, enabling function to be maintained close to the designed level for much longer, until out-competition becomes the dominant source of mutant spread. This effect also explains why the improvement in τ_±10 is so high for smaller initial outputs P₀: the differences in growth rate between mutants become much smaller, so the emergence of new mutants makes up a bigger proportion of the mutant spread, so cells with mutated controllers (and increased output) make up a larger fraction of the combined population, balancing out the cells with reduced process output. This results in a linear relationship between τ_±10 and τ₅₀ for optimal systems as the initial output P₀ varies. This contrasts with CLp_ATX, where increases in τ_±10 are more restricted than increases in τ₅₀ at low outputs P₀ (Supplementary Fig. S10a, e).

These higher-producing mutants are only prevalent in the short term but contribute significantly to the excellent short-term performance (τ_±10) of CLp_ATL. The improvement in long-term performance over CLp_ATX is primarily a result of the reduced burden. To verify this claim, we separately considered a system with two dimensions of mutation but no additional burden. We observe improvements in short-term performance when we include a second controller-specific mutation site whose mutation leads to an increase in process output. However, long-term performance, optimal parameter choices and robustness are not significantly impacted (Supplementary Figs. S11 and S12). (See full details in Supplementary Note 5).

As with CLp_ATX, we explored how design choices influence performance for a nominal process (ω_A = 50 mc min⁻¹). As before, we see that τ_±10 improves over a larger portion of the design space than τ₅₀, demonstrating that short-term maintenance of function is easier to improve than long-term persistence (Supplementary Figs. S13 and S14). See Supplementary Note 4 for a full description.

We have shown that CLp_ATL outperforms CLp_ATX partly as a result of the low burden of transcription compared with translation. We extended our cell model to capture energy consumption, and therefore burden, by transcription. We found that CLp_ATX is insensitive to this additional burden and that CLp_ATL outperforms it except at the highest transcriptional burden (Supplementary Fig. S15). See Supplementary Note 6 for a comprehensive discussion. Given this observation, we proceed with the assumption that transcriptional burden remains negligible and that translational demands (in terms of both energy consumption and cellular resource competition) dominate bacterial growth and host-circuit interactions, in accordance with established models and experimental data^{19,31,36–38}.

Growth-based feedback enhances evolutionary longevity

Synthetic circuit burden elicits the upregulation of specific natural promoters, which can be considered to be burden sensors. These promoters can be exploited to design control systems that are sensitive to burden³⁹. When burden is high and growth is low, greater restriction on the process can alleviate burden and reduce the selective benefit of mutations to the process gene. As with intra-circuit control, we considered two growth-based controller designs: CLλTX ("Closed-loop, senses λ, prevents transcription”) (where control is exerted by an inhibitory transcription factor) and CLλTL ("Closed-loop, senses λ, prevents translation”) (which exploits sRNA-mediated mRNA sequestration). Both CLλTX and CLλTL improve evolutionary performance, with CLλTL outperforming CLλTX in both the short term (greater τ_±10) and long term (greater τ₅₀ except at very high initial outputs P₀) (Supplementary Fig. S16). Here, we focus our analysis on CLλTL, with the discussion of CLλTX presented in Supplementary Note 7 (Supplementary Figs. S16 and S17). This controller exploits growth-sensitive promoters to drive transcription of an sRNA r_C (Fig. 6a). When the cell undergoes stress (i.e., low growth rate), a controller protein p_B is produced, which activates sRNA expression (r_C). This sRNA combines with and eliminates the mRNA for the process gene m_A, preventing it from being translated. There are three promoters in this system, so we employ a mutation scheme consisting of 4³ = 64 distinct strains corresponding to unique triplets {%_A, %_B, %_C} with {%_A, %_B,%_C} ∈ {100, 67, 33, 0} (Supplementary Fig. S1). (See Supplementary Note 1 and Supplementary Fig. S1 for a full description of the mutation scheme.)

Fig. 6. Optimal outputs for CLλTL.

a A schematic describing the controller. Controller protein p_B is produced from a growth-sensitive promoter and activates the production of sRNA r_C. r_C combines with and deactivates process mRNA m_A. See key in Fig. 2a for symbol meanings. b–e Optimal performance for both CLλTL (orange) and CLp_ATL (red) for controller protein length n_B = 1, 300, 600 aa. b τ_±10 vs initial output P₀, (c) τ₅₀ vs initial output P₀, (d) %-change in τ_±10 over open-loop vs initial output P₀, (e) %-change in τ₅₀ over open-loop vs initial output P₀. f–h Robustness analysis. For each of the 100 optimal controllers with n_B = 300 aa, 100 further controllers were generated by varying parameters by up to  ± 10% (dark grey) and  ± 25% (light grey). The percentage changes in three output metrics were calculated versus the original optimal systems: (f) P₀, (g) τ_±10 and (h) τ₅₀. Plots show the means (for  ± 10%) and standard deviations (for both  ± 10% and  ± 25%) of the percentage changes for each optimal controller. Percentages marked on the plots indicate the standard deviations across the entire Pareto front when parameters were varied by  ± 10%(± 25%). Only original optimal controllers where τ_±10 = τ₉₀ are considered. Simulation results are provided as a Source Data file.

For typical regulator protein sizes (n_B = 300 aa), CLλTL slightly outperforms CLp_ATL in the short term, but significantly outperforms it in the long term, with possible improvements of more than 200% versus open-loop (Figs. 6b–e, 7a). The difference in performance in systems with minimal burden (n_B = 1 aa) and high burden (n_B = 600 aa) is very small, suggesting that this controller topology is less sensitive to controller burden than intra-circuit controllers. Observing the population dynamics, we see that when mutations affect the process gene, there is less variation in protein production and a minimal loss in growth rate, so mutant strains with reduced function have less of a selective advantage (Fig. 7b, d). Similarly, when mutations affect the controller, the new mutant strains with increased function have less of a selective disadvantage (Fig. 7c, e).

Fig. 7. Why does CLλTL outperform CLp_ATL?

a Time-series output for representative optimal controllers with n_B = 300 aa. (Open-loop black dotted line). b Protein output per cell p_A over time for the first day of simulation according to mutation state, considering only states with a mutated process and a fully functional controller. c Protein output per cell p_A over time for the first day of simulation, considering only states with a mutated controller and fully functional process (solid line mutation in ω_B, dotted line mutation in ω_C). d, e Growth rates λ according to mutation state. Main plots show time series over the first day. Horizontal lines indicate differences in the maximum growth rates of each state over the first day. d Only states with mutated process. e Only states with mutated controllers (solid line/square is mutation in ω_B, dotted line/triangle is mutation in ω_C). Simulation results are provided as a Source Data file.

Investigating the optimal controller designs shows only ω_A has significant variation across the Pareto front. All other parameters demonstrate clear optimal choices across the performance space (Supplementary Fig. S17, orange). The strength of control from the transcription factor should be maximised (k_B minimised). This becomes more crucial as protein length increases, corresponding also to a reduction in ribosome utilisation (reduced b_B) but increased transcription of controller genes (increased ω_B and ω_C). k_λ controls the sensitivity of the controller to changes in growth rate. Our optimisations show that controllers should have k_λ in the region of 0.002 to 0.005 min⁻¹, suggesting a high sensitivity to growth rate.

We note that some optimal systems with low initial outputs have τ_±10 worse than open-loop. Investigating the system dynamics shows that these “fail” because their output increases significantly in the early stages of the simulation as a result of controller mutation (Supplementary Fig. S18a–c). These are systems for which the 90%-life τ₉₀ (defined as the time taken for output to fall below 90% of its original value) is not equal to τ_±10. These systems have low output and very strong controllers, so when the controller mutates, they produce a comparatively very large amount of output protein. Despite these strains with mutant controllers having very low growth rates and only arising in small numbers, their contribution to the population-wide output is significant (Supplementary Fig. S18e). The effect is enhanced by the existence of two separate controller genes, both of which can be mutated to yield this increase in output. This effect can be exploited to generate systems with excellent τ₅₀ but poor τ_±10 because of an initial increase in output before an eventual fall. This effect is more pronounced in systems with very low initial outputs P₀, because the functional systems are less burdensome and therefore have less of a growth disadvantage (Supplementary Fig. S18f, g). This means that a greater proportion of mutant spread initially comes from the emergence of new mutants rather than competition between strains.

This phenomenon also makes this topology much less robust to parametric variation. In some cases, small variations in parameters can significantly and discretely alter the value of τ_±10 as systems which previously remained below  + 10% of the original value may now exceed it. Considering only the original designs where τ_±10 = τ₉₀, 21.6% (28.2%) of designs fail to maintain τ_±10 = τ₉₀ after parameters are randomly varied by up to  ± 10% (± 25%). Standard deviations in the percentage change of P₀, τ_±10 and τ₅₀ are 15.3% (37.3%), 30.8% (38.7%) and 9.2% (24.0%), demonstrating that, despite the improvements in long-term performance, this controller topology is much less robust than intra-circuit topologies (Fig. 6f–h). As with the intra-circuit systems, the post-transcriptional feedback mechanism (CLλTL) enables much greater optimal performance than the transcriptional feedback mechanism (CLλTX), but this comes at the expense of a reduction in robustness: for CLλTX, standard deviations in the percentage change of P₀, τ_±10 and τ₅₀ are 9.1% (22.6%), 22.7% (35.9%) and 9.2% (17.4%) (Supplementary Fig. S16h–j). (See Supplementary Note 3 for a detailed robustness analysis of both controllers (Supplementary Fig. S19).) For systems where τ_±10 = τ₉₀, τ_±10 and τ₅₀ maintain a linear relationship (Fig. S10b, e).

To understand how design choices influence the performance of growth-based feedback systems, we considered how varying the controller parameters would influence the performance of CLλTX for a nominal process of ω_A = 50 mc min⁻¹. This is described in Supplementary Note 4. Unlike intra-circuit feedback, where it is easier to improve τ_±10, growth-based feedback improves τ₅₀ across a wider portion of the design space, suggesting that growth-based controllers could have greater potential for in vivo implementation in applications where circuit persistence is more important for maintenance of function close to the designed level (Supplementary Fig. S20).

We extended our analysis of growth-based control by considering a protein-free implementation where the growth-sensitive promoters drive the sRNA expression directly (rather than via a regulator protein). This system can improve performance versus open-loop but does not outperform CLλTL (Supplementary Figs. S21 and S22). See Supplementary Note 8.

Combining control schemes enhances robustness of growth-based feedback

We have shown intra-circuit control excels at maintaining short-term performance because it reduces the selective advantage of intermediate mutation states, whereas growth-based control excels at enhancing long-term performance because it boosts the growth rate of the fully functional state. Further, we have shown that sRNA-mediated controllers have enhanced optimal performance but poorer robustness than controllers which actuate directly via transcription factors. We therefore considered whether combining multiple inputs and mechanisms of feedback could combine the benefits of the individual systems and enable greater improvements in both longevity and robustness. We first considered a phenomenological model of a control strategy which utilises both product-based and growth-based control in conjunction. This system is described in Supplementary Note 9 and is capable of combining the benefits of both intra-circuit feedback and growth-based feedback to significantly enhance both short-term and long-term performance by up to 50% compared with the best performing single-input systems (Supplementary Fig. S23).

To assess the impact of biochemical constraints and controller burden on this strategy, we developed five multi-input mechanistic models which exploit both transcriptional and translational mechanisms of introducing feedback control: (i) CLp_ATLλTL uses protein-based feedback to inhibit transcription of the process gene and growth-based feedback to prevent translation of the process gene by activating sRNA (Fig. 8a), (ii) CLp_ATLλTX uses protein-based feedback to prevent translation of the process gene by activating sRNA and growth-based feedback to inhibit transcription of the process gene (Fig. 8b), (iii) CLp_ATLλTL uses both protein-based feedback and growth-based feedback to co-operatively activate sRNA production and prevent translation of the process gene (Fig. 8c), (iv) CLp_ATXλTX uses both protein-based feedback and growth-based feedback to co-operatively inhibit transcription of the process gene (Supplementary Fig. S24a) and (v) CLp_ATLλPF (PF := protein-free) uses both protein-based feedback and growth-based feedback to co-operatively prevent translation of the process gene by putting the sRNA gene directly on a growth-sensitive promoter (Supplementary Fig. S24b). Models for all five multi-input controllers are detailed in Supplementary Note 1.

Fig. 8. Designing multi-input controllers.

a–c Schematics of mechanistic multi-input controllers: (a) CLp_ATXλTL (protein-based inhibition of transcription, growth-based inhibition of translation, teal), (b) CLp_ATLλTX (protein-based inhibition of translation, growth-based inhibition of transcription, crimson), (c) CLp_ATLλTL (protein-based inhibition of translation, growth-based inhibition of translation, purple). See key in Fig. 2a for symbol meanings. d–i Optimised outputs for three multi-input controllers compared with CLλTL. (d) τ_±10 vs initial output P₀, (e) τ₅₀ vs initial output P₀, (f) %-change in τ_±10 over open-loop vs initial output P₀, (g) %-change in τ₅₀ over open-loop vs initial output P₀. h–j Robustness analysis for CLp_ATLλTX. For each of the 100 optimal controllers with n_B = 300 aa, 100 further controllers were generated by varying parameters by up to  ± 10% (dark grey) and  ± 25% (light grey). The percentage changes in three output metrics were calculated versus the original optimal systems: (h) P₀, (i) τ_±10 and (j) τ₅₀. Plots show the means (for  ± 10%) and standard deviations (for both  ± 10% and  ± 25%) of the percentage changes for each optimal controller. Percentages marked on the plots indicate the standard deviations across the entire Pareto front when parameters were varied by  ± 10%(± 25%). Only original optimal controllers where τ_±10 = τ₉₀ are considered. Simulation results are provided as a Source Data file.

Here, we present a discussion of systems (i–iii). We solved a multi-objective optimisation problem to identify Pareto optimal designs and found that the potential improvements gained from combining the control inputs are counteracted by additional controller burden, leading to only marginal improvements in performance versus CLλTL (Fig. 8d–g). The three multi-input controllers perform very similarly and obey similar primary qualitative design principles: maximise the production of sRNA (large w_C), minimise the ribosome binding rate of the growth-sensitive protein ${p_B}_2$ (small ${b_B}_2$), and maximise the strength of transcriptional control (small ${k_B}_1$ and ${k_B}_2$) (Supplementary Fig. S25). The relationship between τ_±10 and τ₅₀ is the same as that for CLλTL (Supplementary Fig. S10c, f). CLp_ATLλTX showed the best robustness overall, with changes in P₀, τ_±10 and τ₅₀ having the standard deviations: 8.1% (20.0%), 16.9% (24.6%) and 6.8% (14.3%) (compared with 15.3% (37.3%), 30.8% (38.7%) and 9.2% (24.0%) for CLλTL) when parameters were randomly varied by up to  ± 10% (± 25%) (Fig. 8h–j). Further, only 8.8% (13.4%) of controllers failed to maintain τ_±10 = τ₉₀ (compared with 21.5% (28.2%) for CLλTL). Both CLp_ATXλTL and CLp_ATLλTL also show significantly improved robustness compared with CLλTL (Fig. S26).

Although CLp_ATXλTX enhances performance versus open-loop, it performs worse than systems (i–iii) without providing a notable improvement in robustness: changes in P₀, τ_±10 and τ₅₀ have the standard deviations 11.1% (28.1%), 19.1% (28.6%) and 4.2% (10.1%) (Supplementary Fig. S24, navy). 80.6% of controllers retain τ_±10 = τ₉₀. At the same initial output P₀, this controller is more highly expressed (larger ω_A) with weaker control in the intra-circuit component and stronger control in the growth-based component (larger k_λ, larger ${k_B}_1$) (Supplementary Fig. S27, navy). CLp_ATLλPF similarly enhances performance versus open-loop, but not to the extent of systems (i–iii). However, it does offer an improvement in robustness, with changes in P₀, τ_±10 and τ₅₀ having the standard deviations 6.6% (16.7%), 3.4% (8.6%) and 3.4% (8.6%), with 100% of designs retaining τ_±10 = τ₉₀ (Supplementary Fig. S24, lime). However, this system requires a very high growth-based control strength (large k_λ) that may be difficult to achieve in practice (Supplementsry Fig. S27, lime). A comprehensive analysis of the robustness of all multi-input controllers is described in Supplementary Note 3 (Supplementary Figs. S28 and S29 and Supplementary Table S2).

Negative feedback control increases bioproduction

The design of our negative feedback controllers focused on the maximisation of three primary metrics: P₀, τ_±10 and τ₅₀, with superior systems providing improvements in longevity compared with open-loop systems of the same initial output P₀. Such improvements are crucial for applications where reliable performance over time is required, such as logic gates or systems which sense and respond to environmental changes. For bioproduction applications, maximising total production is the primary objective. Noting that some of our controllers exhibit a production/longevity trade-off, we set out to evaluate the ability of the controllers to enhance bioproduction. We proposed two new performance metrics which focus on quantify total protein production from our simulations: Q, the cumulative output of protein p_A across the entire evolutionary simulation of repeated batch culture, and Q_max, the maximum value of Q across all optimal designs. The calculation of these metrics are defined in the Methods section “Cumulative production”.

For every system, an increase in initial output P₀ corresponds to an increase in cumulative output Q, except at very high initial outputs, where the burden is significant enough to reduce total output even where initial output increases (Fig. 9a–b). All controllers, bar CLp_ATX, show improvements in production over open loop implementations. This demonstrates that the despite the potential loss in initial output that negative feedback control can create, the enhanced evolutionary stability that control confers enables higher total output over time. In some cases, CLp_ATX performs worse than open loop (Fig. 9c, blue). CLp_ATL outperforms CLp_ATX with the potential to improve on the open-loop cumulative output by up to twofold (Fig. 9c, red). CLλTL shows an even greater improvement of up to threefold (Fig. 9c, orange). This suggests that the sRNA-based controllers outperform those based on transcription factors, and that growth-based control outperforms intra-circuit control for this objective. The cumulative outputs of the three multi-input controllers are very similar to each other and very similar to CLλTL, suggesting that combining control inputs neither harms nor enhances the total cumulative production of a system (Fig. 9b, d).

Fig. 9. Investigating the cumulative output Q.

We consider an open-loop system (black) and six controllers: (a, c) CLp_ATX (blue), CLp_ATL (red), CLλTX (orange). b, d CLp_ATXλTL (teal), CLp_ATLλTX (crimson) and CLp_ATXλTL (purple). a, b Cumulative output Q against initial output P₀. c,d Percentage-change in Q versus an open-loop system of equal initial output against initial output P₀. Each marker represents a controller design from the multi-objective optimisation of P₀, τ_±10 and τ₅₀. Simulation results are provided as a Source Data file.

The maximum cumulative protein production, Q_max, for each system is as follows: Open-loop, 1.42 × 10¹¹ mc; CLp_ATX, 1.54 × 10¹¹ mc; CLp_ATL, 1.59 × 10¹¹ mc; CLλTL, 2.47 × 10¹¹ mc; CLp_ATXλTL, 3.13 × 10¹¹ mc; CLp_ATLλTX, 2.46 × 10¹¹ mc; CLp_ATLλTL, 2.44 × 10¹¹ mc. Every controller is capable of enhancing the maximum possible cumulative output, even when Q has not been explicitly optimised for, with the best performing controllers having more than double the maximum cumulative open-loop output. All together these results suggest that the use of evolutionary stabilising negative feedback controllers has the potential to improve yields in industrial bioproduction settings.

Discussion

Here, we presented designs for feedback controllers which act to stabilise synthetic gene expression over evolutionary time. We developed a ‘host-aware’ and ‘mutation-aware’ multi-scale model of microbial gene expression, growth and population dynamics, which mechanistically captures both the interplay between circuits and their host (successfully predicting the growth defect imparted by circuit burden) and the interplay between ancestral cells and their low/non-functional mutants (successfully capturing natural selection)^30–34. Within this model, we embedded mechanistic models of feedback controllers, implementable as synthetic gene regulatory networks (‘circuits’) and coupled these host-circuit-controller models with multi-objective optimisations to identify designs which maximise circuit production (P₀), maintain the circuit performance close to its ancestral level (τ_±10) and maintain its presence in the population in the long-term (τ₅₀).

We showed that product-based ‘intra-circuit’ transcriptional feedback, where a transcription factor is co-transcribed with the circuit gene and inhibits the expression of both proteins, can effectively increase both short-term and long-term performance by increasing τ_±10 and τ₅₀ compared with an open-loop system of equivalent output P₀. Our sensitivity analysis shows a larger design space for increasing τ_±10 than τ₅₀, suggesting that maintaining performance in the short term is likely easier to achieve in vivo. Our evolutionary simulations show that this strategy acts to maintain protein production at the cellular level in light of mutations in protein production rates. That is, mutant strains with weaker promoters don’t have significantly impeded protein outputs. We showed that implementing negative feedback by a transcription factor is effective at nearly doubling τ_±10 and τ₅₀, but that the additional burden of the controller can abolish any benefit of control; when the regulating protein’s length is greater than the E. coli average of 300 amino acids, the control scheme can perform worse than open loop in many cases. We then proposed an alternative mechanism for implementing negative feedback, where the process is instead co-transcribed with an activatory transcription factor. This regulator protein activates the expression of an sRNA which sequesters and silences the mRNA, completing the negative feedback loop. This controller outperforms the transcriptional controller in both the long and short term, with a more than twofold improvement in τ_±10. Further, this control strategy is less sensitive to controller size, as larger controllers remain capable of enhancing performance versus open-loop. We propose two contributing factors towards this improvement. First, the strong gain of the controller, which enables a smaller quantity of regulator proteins to give rise to a stronger inhibitory action. This is a result of the amplification step created by the transcription of the sRNA, and is the more significant factor in the long term. Second, the potential for mutations to affect the controller gene and yield a small number of slower-growing mutant strains which produce more than the ancestral strain. This factor more significantly affects short-term performance, as the emergence of new mutants makes up a more significant portion of ‘mutant spread’ early in the time course, before out-competition becomes the predominant factor as a result of growth rate differences. We find that, although designs based on transcriptional feedback have worse optimal performance, they are more robust to parametric uncertainty than those based on sRNA-mediated post-transcriptional feedback, implying that such designs will be easier to engineer in vivo. Our analysis demonstrates that, while sRNA-mediated feedback gives superior performance, this can only be achieved if the parameters can be precisely tuned experimentally. In bacteria, such as E. coli, where metabolic and gene expression resource consumption is dominated by translation, sRNA can be created with little additional cost to the host, enabling a significant negative feedback action for low cost. However, this advantage may not translate to other organisms, such as mammalian cell lines, where recent evidence suggests transcriptional limitations may be significant⁴⁰.

Given that growth rate is central in governing the evolutionary longevity of a circuit, and is the key physiological metric impacted by circuit expression, we proposed growth-based feedback as an alternative control strategy for enhancing evolutionary longevity. These controllers inhibit circuit output at low growth. Our evolutionary simulations show that this strategy acts to maintain growth rates in light of mutation, and so mutants do not get the same selective advantage as in the open-loop system. Biologically, these controllers can be implemented using stress-sensitive promoters to drive expression of a transcription factor³⁹. We tested both transcriptional control (where the transcription factor inhibits circuit expression) and post-transcriptional control (where the transcription factor activates an sRNA which silences the circuit mRNA). Both implementations are capable of increasing τ_±10 and τ₅₀, but, as in the intra-circuit case, the sRNA-mediated feedback mechanism enables greater performance. Further, varying the size of the regulator protein shows that the transcriptional mechanism is much more sensitive to regulator size (i.e., controller burden) than the sRNA-based scheme. The growth-based controllers based on sRNA-mediated feedback achieve similar optimal performance to the intra-circuit feedback in the short term (i.e., similar maximal increases in τ_±10), but significantly exceed it in the long term, increasing τ₅₀ by 50%. This suggests that growth-based control could be the best strategy for engineering evolutionary longevity, particularly if circuit persistence is of more importance than maintenance of function within a narrow bound. However, our robustness analysis finds that these controllers are much less robust, with some designs falling significantly off the Pareto front. Since population-wide output was the quantity we wanted to maintain over time, we also considered controllers which sense production at the population level, which can be implemented using quorum-sensing. However, these controllers were unable to compete with intra-circuit and growth-based feedback strategies.

To overcome the drawbacks of poor robustness of the growth-based post-transcriptional feedback controller, we developed a number of multi-input controllers which take both protein production and growth as inputs. Whilst our initial resource-free phenomenological models shows such controllers should yield significant improvements in longevity (when compared to single-input topologies), mechanistic models showed that these are sensitive to resource consumption, with additional controller burden abolishing most performance benefits. However, incorporating the additional feedback reduced the sensitivity of a system’s output to parametric uncertainty, allowing for enhanced robustness and more reliable performance, without diminishing longevity. These multi-input controllers are therefore the most promising options for in vivo implementation, as they combine the high performance of the growth-based system with the increased robustness that will simplify the selection of biological parts without perfectly tuned parameter values.

Extending our analysis to evaluate the cumulative (total) protein production of our systems over time, we showed that systems with controllers always produce more protein that than open loop (uncontrolled) systems. As we previously found, the best controllers where those based on translational control and those which utilised a growth-based input. Despite not optimising the controller designs to maximise production, we showed that negative feedback could improve total yield despite an initial loss in production per cell. Our results show that increasing evolutionary stability via negative feedback is an attractive strategy for improving yields in industrial bioproduction.

Here, we have conducted a comprehensive analysis of feedback controllers when applied to a process consisting of a single gene over repeated batch cultures. This approach replicates previous experimental investigations of synthetic gene circuit evolution^4,10,20. Controlling the evolutionary stability of more complex gene circuits represents a more significant challenge, as the dynamics of our negative feedback controllers and the complex processes may interact. It is common practice in control engineering to design a bespoke controller for each individual process. Our controllers can be scaled to stabilise gene expression in systems where gene expression levels are desired to be approximately binary (such as logic gates, activation cascades or induction systems), provided there are sufficient experimental choices of inhibitory regulator (e.g., orthogonal transcription factor proteins or sRNAs) - albeit with controller kinetics adjusted to suit the new process. Whilst controller designs will need to be optimised for the new processes, we expect our general design rules to hold: that negative feedback will stabilise expression over evolutionary time scales, that translation-based systems will offer superior performance over transcription-based systems (and that the latter may in fact reduce evolutionary stability) and that systems which seek to control function at the population level will be less effective. The choice of intra-circuit or growth-based feedback (and associated differences in design robustness) remains an area for future work. Engineering controllers to stabilise the evolutionary stability of circuits with time-varying dynamics (such as oscillators) represents an additional challenge, given that the introduction of the new controller dynamics may abolish the desired circuit behaviour⁴¹. Engineering control systems to make such systems more robust and reduce the interactions between host and circuit remains an open question.

The potential impact of synthetic biology is vast, with applications expected to transform the fields of healthcare, chemical production, agriculture and more over the next decade⁴². However, the utility of complex gene circuit designs will be severely limited if they cannot be employed predictably and stably over the timescales required for industrial bioprocesses. It is therefore crucial for circuits to be designed with evolution in mind. While various approaches have been developed to date which improve the longevity of synthetic circuits and pathways, these are often bespoke, rely on selectable markers, or require complex redesign based on the specific process of interest. Here, we have demonstrated that feedback control can be employed effectively to improve evolutionary longevity, both in the short term (i.e., maintaining function close to the designed level) and the long term (i.e., persisting within a population over time). Our designs do not rely on selectable markers (reducing the need for antibiotics at scale) or on conferring a selective disadvantage to mutants (a promising approach, but one which is vulnerable to loss of the toxic module or loss of control of such a module). In this work, we account for controller mutation during our analysis, and therefore our proposed designs are themselves robust to evolutionary change. The proposed approaches can be easily applied to different systems without the need for significant redesign, and can be incorporated alongside existing approaches, contributing towards the ultimate goal of synthetic biology applications that perform reliably in the long term.

Methods

Simulating an evolving population of engineered cells

Throughout this paper, we make use of an ODE model capturing the dynamics of an evolving population of engineered cells. This model is similar to one recently developed by Ingram and Stan³⁴. The complete circuit-host-population model is described in detail in Supplementary Note 1, alongside complete models of all the control systems considered throughout the paper. Tables of variables and parameters are given in Supplementary Tables S3‒S5. Mutation schemes are shown in Supplementary Tables S6 and S7. Simulations are performed which replicate repeated batch conditions. Every 24 h, a representative sample of 1000 cells is selected from the combined population, and the external substrate is reset to s_X = 10¹² molecules. Over the course of each day, the substrate is consumed and the population grows until the supply is exhausted and the population levels out. This aims to replicate a typical laboratory-based study¹⁰. This is preferable to chemostat conditions because growth rates are not determined by the chemostat dilution rate, which can cause additional problems if the cells are overburdened and cannot achieve growth fast enough to match it. The model is encoded in MATLAB and we used the inbuilt ode15s function to perform the simulations.

Comparing controllers versus open-loop systems of equal output

To evaluate the performance of a given controller parameterisation X with initial output $P_{0_X}$, we compared its long-term performance (${\tau }_{{\pm 10}_X}$ and ${\tau }_{{50}_X}$) against an open-loop system of equal initial output. To achieve this, we first generated a large set of 5000 open-loop designs by varying ω_A over a wide range between 0.1 and 1000 mc min⁻¹ (Fig. 2g). This yielded multi-valued relationships between output (P₀) and longevity (τ_±10 and τ₅₀), due to the existence of overburdened systems; when ω_A is pushed above a certain threshold, both output and longevity fall. To create a set with a single-valued relationship between output and longevity, we removed the overburdened systems. We then used linear interpolation to find the open-loop relationship between output and longevity for a system with an initial output $P_{0_X}$. For figures where we explicitly show the time-series outputs of different systems with comparable initial outputs P₀ (e.g., Fig. 3b), we first found the Pareto fronts from a large set of designs which simultaneously maximised P₀, τ_±10 and τ₅₀, then selected points from the fronts with P₀ as close as possible to a set value.

Multi-objective optimisation

Here we outline how we generated optimal designs for the considered controller topologies. For each topology, we first generated a large number of samples using the efast algorithm⁴³, by varying a large number of parameters over wide biologically feasible ranges. By examining the outputs from the sampling, we identified those parameters u which were most significant in determining P₀, τ_±10 and τ₅₀ and used these to perform a multi-objective optimisation to simultaneously maximise these three objectives:

$$\begin{array}{c}{\mathrm{maximise}}_{\mathbf{u}}\left(P_0,{\tau }_{\pm 10},{\tau }_{50}\right)\hfill \\ \text{subject to}\mathbf{L}\le \mathbf{u}\le \mathbf{U}.\hfill \end{array}$$ 6

Here, L and U represent the lower and upper bounds of the parameters u. Separate optimisations were performed for each of the considered control topologies, with each being repeated for different controller protein lengths n_B = 1, 300, 600 aa (where applicable). The parameters optimised for each controller, and their biologically feasible upper/lower bounds, are defined in Supplementary Table S8. A detailed discussion of the choices of boundary values is given in Supplementary Note 1. To perform the optimisations, we used Matlab’s gamultiobj genetic algorithm function, with population size 250, Pareto fraction 0.4 and tolerance 10⁻⁴, yielding Pareto fronts consisting of 100 individuals. The fixed and optimised controller parameters are reported in Supplementary Table S8.

Robustness analysis

Outputs from optimisations yielded Pareto fronts of 100 individuals and a set of optimal parameters u. From this set of individuals, we removed any parameterisations with exceedingly poor short-term performance (i.e., where τ_±10 ≠ τ₉₀). For the remaining individuals, we generated 100 alternative parameterisations by randomly varying each parameter by up to  ± X%, for X = 10, 25. For example, in the case where X = 10, each parameter varied in the optimisation u_i was selected from a uniform distribution with lower bound 0.9u_i and upper bound 1.1u_i, yielding a window of  ± 10% around the original values. In instances where this would push a parameter beyond the upper or lower bounds defined in the multi-objective optimisations, we set the value of the parameter to be exactly the boundary value, to avoid searching a portion of the design space that wasn’t available in the optimisations. To evaluate the robustness of individual controllers, we compared these random parameterisations against their original designs, considering the percentage change of five metrics:

1. P₀, the initial population-wide output.

2. τ₅₀, the time taken for population-wide output P to halve.

3. τ_±10, the time taken for population-wide output P to fall outside a window of  ± 10% of its original value.

4. τ₉₀, the time taken for population-wide output P to fall to 90% of its original value.

5. P_max, the maximum population-wide output P over the course of the simulation.

Standard deviations of these percentages indicate the level of variability in the function of a system at the topological level. In addition, we evaluated the percentage of random designs which showed a discrete change in the value of τ_±10 due to it no longer being equal to τ₉₀. Throughout the main text, we focus our analysis primarily on P₀, τ_±10 and τ₅₀. A more detailed analysis covering τ₉₀ and P_max is provided in Supplementary Note 3. All means and standard deviations for all controllers are presented in Supplementary Table S2.

Cumulative production

The translation rate $T_{L_A}$ of protein p_A gives the rate of production of output protein p_A per cell. Integrating $T_{L_A}$ over the time course of the simulation, therefore, gives the total production of p_A per cell. We define the cumulative output Q of a system to be the total production of p_A across an entire culture over the course of a simulation. For a system composed of n mutation states, with population sizes N_i and translation rates $T_{L_{A_i}}$, Q is defined as follows:

$$Q={\sum }_{i=1}^n{\int }_{t=0}^{t_{\mathrm{end}}}{T}_{L_{A_i}}{N}_{i}dt.$$

We define t_end to be the point where output falls below 1% of its initial value P₀. We calculated the value of Q for each controller design given by the multi-objective optimisations. Across those optimal designs, we designate the maximum value of Q as Q_max. To assess the ability of a given controller architecture to improve total bioproduction, we compared Q_max against the maximum cumulative production for an open-loop system. Note that Q_max and $Q_{{max}_{\mathrm{OL}}}$ don’t necessarily correspond to the same initial output P₀.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

A.P.S.D. conceived and designed the research. D.P.B. developed the models, conducted all computations, and plotted the results. D.P.B. and A.P.S.D. discussed the results and wrote the paper.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

Optimisation results generated from this study and are available in the Source Data file. Source data are provided in this paper.

Code availability

The code used to develop the model, perform the analyses and generate results in this study is publicly available and has been dpositite on Github at https://github.com/apsduk/byrom-nat-commun-2025 under a CC-BY 4.0 license. The specific version of the code associated with this publication is archived in Zenodo and citable with 10.5281/zenodo.16094166⁴⁴.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-025-63627-4.