Metabolite sequestration enables rapid recovery from nutrient depletion

Christopher Hartline, Ahmad A. Mannan, Fuzhong Zhang, Diego A. Oyarzún 1 Department of Energy, Environmental & Chemical Engineering, Washington University in St Louis, St. Louis, 63130, USA 2 Department of Mathematics, Imperial College London, London SW7 2AZ, UK 3 Current address: School of Engineering, University of Warwick, Coventry CV4 7AL, UK 4 School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, UK 5 School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3BF, UK † Equal contribution * Corresponding authors: F. Zhang (fzhang@seas.wustl.edu) and D. A. Oyarzún (d.oyarzun@ed.ac.uk).

Bacteria constantly adapt to changing environments by coordinating multiple levels of their intracellular machinery. The regulatory systems that enable rapid adaptations to nutritional changes require a complex interplay between metabolic genes and metabolites [3], which shapes cell fitness, bet hedging efficacy, population survival, as well as competition among microbiota.
Metabolite-gene interaction via metabolite-responsive transcription factors (MRTFs) is a common strategy that microbes employ to sense nutrient availability and to autonomously orchestrate changes in gene expression and metabolic flux [4]. Upon nutrient induction, cellular resources are invested in expressing enzymes dedicated to nutrient uptake. After nutrient depletion the uptake enzymes are no longer required, so control mechanisms down-regulate their expression to save cellular resources. While much of the literature has focused on the roles of MRTF control systems during nutrient induction [4,5], there is little understanding of how these systems regulate recovery dynamics after nutrient depletion.
The MRTF-regulated nutrient induction is a balanced process between response kinetics and resource economy.
Inducible expression systems are associated with a cost of having to synthesize the sensing component (e.g. MRTF). A rapid response to changing environments can achieve a higher cellular fitness, overcoming the invested cost of expressing the sensing component [6]. While typical inducible systems take a number of cell cycles for the expressed proteins to reach steady state [7], transcriptional regulation can affect the response time during induction. For instance, negative autoregulation has been shown to speed up gene expression [4], and metabolic feedback circuits can accelerate metabolite response [8]. However, how the control system exploits both regulatory architecture and parameters to shape the recovery dynamics is not well understood. Cells that rapidly shut down their metabolic pathways during depletion can avoid waste of limited resources and potentially gain growth benefits.
In this paper, we study a regulatory architecture commonly found in bacterial metabolic systems [9] ( Figure 1A and Table S1). In absence of nutrient, a MRTF represses expression of uptake and catabolic enzymes. When the nutrient becomes available, the internalized nutrient binds and sequesters the transcription factor, thus relieving the repression of metabolic enzymes and allowing nutrient import and utilization. In several instances of this control system, the transcription factor also represses its own expression (Table S1).
Using the Escherichia coli fatty acid catabolic pathway as a model system, we studied its dynamics in response to nutrient (oleic acid) shift between an ON-and OFF-state, defined as an environment with and without the presence of oleic acid ( Figure 1B). In the ON-state, oleic acid is imported as fatty acyl-CoA by small amounts of the transporter FadD. As intracellular acyl-CoA accumulates, it binds to the transcription factor FadR and sequesters it into a complex. The sequestering unbinds FadR from DNA [10], which relieves the repression of FadD and accelerates oleic acid import, forming positive feedback loop. This allows a rapid transition to the ON-state [11].
After switching to the OFF-state, release of free FadR from the complex recovers its inhibition on the expression of unnecessary catabolic enzymes.
We built a kinetic model based on four core components of the regulatory system: FadD (D), free FadR (R), acyl-CoA (A) and sequestered FadR (a-R), and parameterized it using experimentally measured time course data after induction with various concentrations of oleic acid (details in Methods). From model simulations, we defined two metrics to quantify the recovery after the switch from ON-to OFF-state ( Figure 1C). First, we define the recovery time (τ 50 ) as the time taken for FadD to decrease to half-way between its maximum and minimum steady state value after nutrient depletion ( Figure 1C). Second, we defined the metric η as the proportion of free FadR released from the sequestered complex after one doubling time:  Figure S4). Model simulations also reveal a strong inverse relation between τ 50 and η ( Figure 2B), indicating that the release of FadR from sequestration by acyl-CoA provides a mechanism to achieve rapid recovery during nutrient depletion. The sensitivity of this inverse relation increases when cells are exposed to a longer ON-state, because this leads to larger pools of sequestered FadR.
To verify the model predictions, we sought to experimentally increase the fraction of released FadR (η) with two complementary strategies. We first decreased the rate of consumption of acyl-CoA by deleting the fadE gene, which encodes the second step of the fatty acid β-oxidation pathway. This prevents metabolization of acyl-CoA by β-oxidation, and leaves membrane incorporation (catalyzed by enzyme PlsB) as the only pathway for acyl-CoA consumption. We measured fadD expression dynamics after switching the strains from the ON-state (M9G + 1mM oleic acid media) to OFF-state (M9G media) using a red fluorescent protein (RFP) reporter fused downstream of the fadD promoter. In agreement with model predictions ( Figure 2C), the fadE knockout strain displayed a slower recovery than the wild type, with ~60% increase in recovery time ( Figure 2D). This entails an increased expenditure of biosynthetic resources to import a metabolite that is no longer present in the environment.
Next, we measured the fadD recovery dynamics after switching the cultures from growth in the ON-state for t 0 = 3, 6, and 9 hours ( Figure 1C). The resulting recovery times displayed a good qualitative agreement with model simulations ( Figures 2E,F). Recovery time did not show significant differences between 6 and 9 hours, possibly because slower recovery is counteracted by the delay of having to consume a higher level of accumulated acyl-CoA, or because the maximum level of sequestered FadR may already have been achieved at 6 hours.
Among the uptake systems in E. coli with the architecture of Figure 1A, we found that the majority have a transcriptional regulator that represses its own expression, few have constitutive expression of the regulator, and none display positive autoregulation (see Table S1). To better understand the salient features of each regulatory architecture and how they affect recovery dynamics, we built variants of our kinetic model with FadR under constitutive expression and positive or negative autoregulation (details in Methods). Simulations of the switch from the ON-to OFF-state suggest that these architectures behave similarly for short times spent in the ON-state, quickly sequestering all the free FadR ( Figure 3A). But for longer times in the ON-state, we found important differences in the dynamics of the level of sequestered FadR between the various modes of autoregulation.
Negative autoregulation leads to large accumulation of sequestered FadR, while positive autoregulation leads to an overall depletion of sequestered FadR. Constitutive expression, on the contrary, enabled the total level of FadR, primarily in the sequestered form, to be maintained at a constant level. Analysis of model equations reveals that these are structural properties of the model. We show mathematically (details in Supplementary Information S4) that after a long time in the ON-state, the steady state concentration of total FadR upon nutrient depletion follow the trends as we observed in Figure  Since release of sequestered FadR has a direct impact on recovery time, we sought to identify the benefits that make negative autoregulation favored over constitutive expression. Since production of FadR entails a biosynthetic cost, we compared both regulatory architectures in terms of the cost of FadR synthesis. From time-course simulations for varying fadR promoter strengths ( Figure 4B), we computed the total amount of synthesized FadR in the ON-and OFF-states. Results suggest that both architectures require identical biosynthetic costs in the ONstate, but negative autoregulation leads to significant savings in the OFF-state ( Figure 4C) as compared to constitutive expression. Therefore, although both architectures can in principle achieve the same recovery time, negative autoregulation achieves this with a lower cost on synthesis of the transcription factor.
Overall, we find that rapid release of free FadR from acyl-CoA sequestered a-R complex shortens the recovery time. Our simulations and experiments have shown that increasing the amount of stored FadR during induction and increasing consumption of the sequestering metabolite (acyl-CoA) expedites free FadR releasing, thus shortening the recovery time. Through our model simulations, we observed a delayed recovery driven by the need to reduced metabolite concentration to levels required to release free TF from stored complex. During the delay, wasteful expression of the uptake pathway was continued despite the absence of nutrient. Previous research has shown that upon induction, metabolite dynamics tend to lag behind slow production of metabolic enzymes [8].
Interestingly, here we find that after inducer depletion, the recovery of protein production can be limited by the metabolite dynamics. This has important implications for designing synthetic control circuits that utilize nonmetabolizable inducers, such as IPTG. With no consumption of the inducer, post-induction recovery response will be slow and cause a dramatic drain of cellular resources.
Further theoretical analysis revealed principles that explain how autoregulation shapes the recovery time. We found that negative autoregulation of the transcription factor provides a resource-saving strategy for the recovery dynamics. We found that MRTFs in 13 out of 18 nutrient uptake systems (see Table SF1) have negative autoregulation, suggesting an evolutionary pressure for a resource-saving control strategy. Past studies in the literature have found that expression under negative autoregulation can decrease response times in gene expression [7], linearize dose-response in responsive systems [12], and even speed up metabolic dynamics [8]. In addition to these properties, we find that negative autoregulation enables faster and more resource-saving metabolic recovery to nutrient depletion.
Recent efforts in synthetic biology focus on engineering gene control circuits to manipulate microbial metabolism.
In large fermentations, microbial hosts face highly heterogeneous and dynamic environments. Our results provide core design principles for synthetic gene circuits. These design rules can help to achieve rapid recovery and to mitigate against deleterious nutrient fluctuations, and are useful in applications at the interface of synthetic biology and metabolic engineering.  (Tables S4 and S5). E. coli DH10β was used for plasmid construction.

Materials
The plasmid pSfadDk-rfp was constructed by cloning the fadD promoter (500 bp upstream of its translation start site) into the 5' of a rfp gene in a BglBrick vector, pBbSk-rfp [13] using Golden Gate DNA Assembly [14]. The positively autoregulated fadR strain was engineered by replacing fadR's native promoter with a FadR-activated promoter P fadRpo via CRISPR-Cas9 genome editing [15]. Detailed engineering methods and the characterization of the P fadRpo promoter are described in Supplementary Information S8.
Three reporter strains were created to measure expression kinetics from the fadD promoter. These strains were created by transforming plasmid pSfadDk-rfp into either the wild-type DH1 strain, DH1(ΔfadE), or an engineered strain with positively autoregulated fadR, resulting in WT-reporter, ΔfadE-reporter, and PA-reporter, respectively.

Media conditions.
where F is the background-corrected, cell-density-normalized fluorescence. The recovery time was calculated as For switches after defined times in the ON-state, cultures were first grown in exponential growth phase for 24-28 hours in M9G. Samples from these cultures were then centrifuged (5500 rcf, 2 minutes) and suspended in M9G+OA with an initial OD 600 of 0.08 and cultivated in 96-well plates for various amount of time as indicated.
Kinetic model of fatty acid uptake. To study the system dynamic response to induction (ON-state) and its postinduction recovery (OFF-state) (Fig. 1C), we built a kinetic model for fatty acid uptake. We define the kinetic model as a system of ODEs describing the rate of change of each system component: , , where R, D, A and aR represent the concentrations of transcription factor FadR, uptake enzyme FadD, internalized fatty acid acyl-CoA, and sequestered complex acyl-CoA-FadR, respectively (Fig.1B). The reversible sequestering of one FadR dimer by two acyl-CoA molecules (stoichiometry as defined in [17]) is modeled as mass-action kinetics in the term . The term represents the expression and autoregulation of the fadR promoter.
To model FadR negative autoregulation for the wild-type strain, we use . (10) Further details of the model are given in Supplementary Information S2, and descriptions of parameters in Table   S2. We parameterized the model with time course data of RFP expressed from a fadD promoter induced at different oleic acid concentrations, and fitted values can be found in Table S3. Details of the experimental strain, the data used and the fitting process are given in Supplementary Information S2. For the models with constitutive expression and positive autoregulation of FadR, we use , . (3) Model simulations. The kinetic model of the fatty acid uptake control system (Fig. 1A) was solved in MATLAB R2018a, using the ODE solver suite. To simulate the ON-state, simulations were initialized using the steady state values achieved from running simulations in absence of oleic acid (OA = 0 µM). A constant level of oleic acid was set at t = 0, with OA = 1000 µM in Eq. (8), and simulations were run to steady state, or a defined time (to emulate time spent in ON-state). To simulate the OFF-state, the system was initialized using either the steady state or endpoint values achieved in the ON-state, but now with OA = 0 µM in Eq. (8). Simulations of the OFF-state were run to steady state, and recovery times were calculated from a measure of the time from the start of the OFF-state till when FadD reached half-way between its initial (max) value and minimum steady state value.
In Figure 3, for fair comparison model parameters are set such that the steady state concentration of FadR is the same for all three architectures prior to switching to the ON-state. Likewise, in Figure 4B-C for fair comparison, fadR promoter strengths for both architectures were set to achieve same concentration of sequestered FadR in the ON-state (and thus equal recovery times).