Metabolic Feedback Circuits Provide Rapid Control of Metabolite

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Letter

Metabolic Feedback Circuits Provide Rapid Control of Metabolite Dynamics Di Liu, and Fuzhong Zhang ACS Synth. Biol., Just Accepted Manuscript • DOI: 10.1021/acssynbio.7b00342 • Publication Date (Web): 03 Jan 2018 Downloaded from http://pubs.acs.org on January 3, 2018

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ACS Synthetic Biology

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Metabolic Feedback Circuits Provide Rapid Control of Metabolite Dynamics

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Authors: Di Liu1, Fuzhong Zhang1, 2, 3 *

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Department of Energy, Environmental & Chemical Engineering,

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Division of Biological & Biomedical Sciences,

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Institute of Materials Science & Engineering,

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Washington University in St. Louis, St. Louis, MO, 63130, USA

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*

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Dr. Fuzhong Zhang

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1 Brookings Drive

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St. Louis, MO, 63130, USA

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[email protected]

Correspondence:

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ACS Paragon Plus Environment

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Abstract

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Metabolism constitutes the basis of life, and the dynamics of metabolism dictate various cellular

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processes. However, exactly how metabolite dynamics are controlled remains poorly understood.

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By studying an engineered fatty acid-producing pathway as a model, we found that upon

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transcription activation a metabolic product from an unregulated pathway required seven cell

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cycles to reach to its steady state level, with the speed mostly limited by enzyme expression

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dynamics. To overcome this limit, we designed metabolic feedback circuits (MeFCs) with three

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different architectures, and experimentally measured and modeled their metabolite dynamics.

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Our engineered MeFCs could dramatically shorten the rise-time of metabolites, decreasing it by

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as much as 12-fold. The findings of this study provide a systematic understanding of metabolite

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dynamics in different architectures of MeFCs and have potentially immense applications in

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designing synthetic circuits to improve the productivities of engineered metabolic pathways.

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Key Words: metabolic control circuits / metabolite dynamics / metabolite overshoot / negative feedback / rise-time


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In nature, metabolism supports most cellular activities by providing building blocks, energy,

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cofactors and proper redox environments. Engineering microbial metabolic pathways, on the

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other hand, allows the production of chemicals, biofuels, and pharmaceuticals1–3. As a primary

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goal of systems biology, understanding the complex regulatory networks of metabolism not only

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informs us how nature allocates limited cellular resources to perform various cellular activities in

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changing environments4–7, but also provides design principles for synthetic biologists to better

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control metabolism for a variety of applications8–15.

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Microbial metabolism is mostly regulated via two types of controls: transcriptional

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regulation by controlling enzyme expression levels, which in turn affect metabolite

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concentration, and post-translational regulation by directly modifying enzyme activities via

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allosteric inhibition or activation. Post-translational metabolic regulation is common in central

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carbon metabolism, fatty acid biosynthetic pathway, and amino acid biosynthetic pathways, to

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rapidly adjust the cellular metabolite level within seconds16,17. On the other hand, transcriptional

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metabolic regulation is widely used in nutrient uptake, the tricarboxylic acid (TCA) cycle, amino

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acid biosynthesis, and energy production, with the primary goal to optimize protein expression

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levels and avoid overproduction of unnecessary proteins, which waste cellular resources18–20.

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Due to the involvement of transcription, translation, protein folding, and catalysis, transcriptional

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regulation changes the concentration of under-regulated metabolites much more slowly than

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post-translational regulation. Thus the change of a metabolite’s concentration (hereafter referred



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as metabolite dynamics) during the course of slow transcriptional regulation becomes important

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to cellular activities21, particularly for those metabolites involved in cell survival and growth,

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such as essential nutrients, building blocks for biosynthesis, and quorum sensing molecules.

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From a control systems standpoint, an ideal metabolic control would both optimize protein

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expression level and offer rapid and precise control over metabolite concentrations in response to

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various conditions. Transcriptional regulation is an attractive control strategy due to its capability

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of responding to various stimuli and controlling both protein and metabolite levels. Indeed,

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transcriptional regulation is regarded as the most common way for microbes to control their

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metabolism22. Previous studies have revealed that upon transcription induction in exponential

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growth phase, it takes five cell cycles (i.e., the number of cell divisions) for stable proteins to

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reach their steady state levels in an unregulated pathway23, and the speed can be accelerated to as

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short as two cell cycles with negative auto-regulation. However, negative auto-regulation is

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mostly found to control transcription factors in nature24 and the effect of synthetic negative

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auto-regulation to metabolite dynamics was not studied by previous work23. Due to the delay in

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enzyme catalysis, the dynamics of metabolite will be even slower (more than five cell cycles)

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than proteins in unregulated pathways, and thus postpone cellular response to environmental

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changes and could lead to sub-optimal cell growth. In addition, from an engineering perspective,

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the capability to accelerate metabolite dynamics is also preferred for rapid signal detection. For

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example, when using a pigmented metabolite (e.g. lycopene) as an easy-to-detect sensor output25,


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faster metabolite dynamics could potentially reduce the response time of biosensor. Thus, design

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of synthetic regulations to speed up metabolite dynamics is crucial to both 1) understand how the

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regulatory architectures and the associated biochemical parameters affect metabolism in natural

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regulatory networks and 2) provide guidelines to re-program metabolite dynamics for

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applications such as environmental bio-sensing, metabolite oscillators, and quorum sensing

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mediated population control26,27.

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In this work, we employed an engineered fatty acid biosynthetic pathway that has defined

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interactions with other cellular processes to illustrate the interplay between individual

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transcriptional regulatory circuits and metabolite dynamics. Strikingly, we found that under

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exponential cell growth, free fatty acid (FFA), a metabolic product synthetized from an

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unregulated, one-step enzymatic pathway, requires seven cell doublings to reach its steady state

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level once enzyme expression is turned on. Our modeling showed that the slow FFA dynamics is

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not affected by enzymatic catalytic parameters in the unregulated pathway (see Results and

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Supporting Information for detail). We then constructed three metabolic feedback loops with

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different architectures to study metabolite dynamics under the control of each feedback

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regulation, using a combination of experimental and modelling methods. Our results show that

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negative feedback circuits can dramatically speed up metabolite rise-time (the time needed to

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reach half of the steady-state concentration). The findings of this study offer a quantitative and

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systematic guideline on choosing the genetic circuit architectures and biochemical parameters to

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control metabolite dynamics.



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Results and Discussion

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Long Rise-Times of Metabolite Levels in Unregulated Pathways

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To study the metabolite dynamics, a model pathway should satisfy the following criteria: 1)

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a sufficient supply of metabolic precursors, 2) defined transcriptional regulation, 3) minimal

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interactions with other metabolic pathways, and 4) controllable product consumption. Here we

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used an engineered FFA-producing pathway in Escherichia coli as a model. The engineered FFA

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pathway branches from the high-flux fatty acid biosynthetic pathway by expressing a cytosolic

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thioesterase (encoded by tesA) under the control of an inducible promoter, PLac. The thioesterase

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uses acyl-ACPs as metabolic precursors to produce FFAs. Acyl-ACPs are produced from the

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high-flux fatty acid biosynthetic pathway28, therefore ensuring a sufficient pool of metabolic

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precursors. There is little interaction between the natural regulatory networks and the activity of

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the thioesterase. In addition, although a small amount of FFA can be converted to fatty acyl-CoA,

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acyl-CoA cannot be metabolized in our engineered cell due to the deletion of fadE in

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β-oxidation8. If needed, FFAs can be converted to other metabolic products by introducing

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heterologous enzymes with controlled conversion rates. Thus, the FFA-producing pathway

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satisfies all the requirements of this study.

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To test the dynamics of a product in an unregulated pathway, the enzyme TesA was

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expressed from an IPTG-inducible promoter PLac to create an open loop pathway (OL, Figure


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1A). A red fluorescent protein (RFP, encoded by rfp) was placed 3’ of TesA in the same operon to

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monitor the dynamics of TesA expression level. Cells were cultivated in the exponential growth

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phase. After induction by IPTG, the changes in RFP fluorescence and FFA concentration over

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time were measured. Cell-density-normalized RFP fluorescence was used to indicate enzyme

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dynamics (hereafter refers to the change of enzyme concentrations), and the time course of

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cell-density-normalized FFA was measured as metabolite dynamics (Fig 1B&1C). Surprisingly,

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FFA takes as many as six to seven cell cycles to reach its steady state concentration after turning

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on the expression of TesA.

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To quantitatively understand the slow FFA accumulation, we constructed a general

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mathematical model to describe enzyme expression and metabolite dynamics in unregulated

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metabolic pathways. In the case of the single-step FFA-producing pathway, the enzyme is

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thioesterase and the metabolite is FFA. In the exponential growth phase with a constant supply of

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precursors and without feedback regulation, enzyme expression and metabolite concentration can

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be described by differential equations (1) and (2) in the Supporting Information M1. Solving

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these equations, we obtain

133 =

∙ 1 − exp −2 ∗ 1 134

=

∙ 1 − 2 ∗ + 1 ∙ exp −2 ∗ 2

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where N represents the number of cell cycles. [Enzyme]ss and [Metabolite]ss represent the steady

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state concentrations of the enzyme and the metabolite, respectively. Our experimental results

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matched well with the model prediction (R2=0.98): After a biosynthetic pathway is turned on, the

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settling time (defined as the time required for a response curve to reach and stay within 5% of the

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steady state level, Figure S1) for the protein and metabolite are five and seven cell cycles,

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respectively. Moreover, since equation (2) is independent of the catalytic parameters, the settling

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times are functions of cell cycles only, and not pathway specific. The long metabolite settling

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time was mostly caused by the slow rise of the enzyme concentration (a settling time of five cell

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cycles) and the slow metabolite consumption/dilution time. The slowly rising protein

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concentration has been observed previously for stable proteins under exponential cell growth23.

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Thus, we hypothesized that the metabolite dynamics (characterized as the rise-time) can be

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accelerated by a faster metabolite consumption/dilution rate and faster protein production

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dynamics.

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Next, to speed up the metabolite dynamics by increasing its consumption rate, we studied

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the dynamics of an intermediate metabolite. A simple two-step metabolic pathway was simulated

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using ODE equations (See Supporting Information M2). Mathematical analysis revealed that an

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intermediate metabolite could reach to its steady state faster than that of a product, depending on

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its enzymatic consumption rate. The theoretical prediction was verified experimentally using an

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engineered two-step metabolic pathway, where a carboxylic acid reductase (CAR, encoded by


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car) was constantly expressed in the FFA-producing pathway (See Methods)29, converting FFA

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to fatty alcohols and making FFA a pathway intermediate (Fig 1D) (open loop intermediate,

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OLIM). As we increased the FFA consumption rate by tuning the expression level of CAR, FFA

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reached its steady state faster (Fig 1E). Further analysis also showed that as the intermediate’s

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consumption rate increased, its rise-time decreased until reaching a limit, where consumption of

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the intermediate was so rapid that metabolite dynamics overlapped with the dynamics of enzyme

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expression (Fig 1F).

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Overall, our results indicated that in the exponential growth phase, with a constant supply of

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precursors and without feedback regulation, the dynamics of a metabolite from an open loop,

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regardless of whether the metabolite is a pathway intermediate or an end product, are slow and

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are ultimately limited by the dynamics of enzyme expression. Under this condition, upon

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transcriptional activation of pathway enzymes, a metabolite takes at least five (for an

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intermediate) or seven (for a product) cell cycles to reach steady state if the pathway is not

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feedback regulated. Such slow responses greatly delay cell growth and adaptation if the

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metabolite is essential to cell growth, thus necessitating regulatory strategies to expedite

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metabolite dynamics.

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Genetic Negative Feedback Circuits Accelerate Metabolite Dynamics

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One of the most common transcriptional regulations of metabolism is negative feedback,

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where the product of a metabolic pathway inhibits the transcription of pathway enzymes. We



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hypothesized that such metabolic negative feedback circuits can speed up metabolite rise-time,

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just as negative gene circuits speed up the rise-time of under-controlled proteins23. To test this

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hypothesis, three different metabolic feedback systems were designed and constructed,

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representing three commonly found distinct regulation architectures in nature and engineered

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systems. The first feedback system contains a negative auto-regulated gene circuit, called a

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negative gene loop (NGL), where tesA is co-transcribed with a repressor, tetR, which feedback

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inhibits the expression of tesA-tetR via a hybrid promoter, PTL (Fig 2A). PTL was engineered by

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placing a TetR-binding site (TetO) between the -35 and -10 region of a strong promoter and a

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LacI-binding site (LacO) 3’ of the -10 region, thus allowing PTL to be repressed by both TetR and

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LacI. While the FFA-producing pathway can be transcriptionally activated by addition of IPTG,

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expression of TesA is negatively auto-regulated, thus affecting FFA dynamics (Fig 3A). This

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architecture is prevalent in nature for the regulation of ligand-independent transcription factors.

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The second feedback system, named a negative metabolic loop (NML, Fig 3B), contains a

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FFA-repressed transcription factor, FadR, which activates the expression of tesA through a

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hybrid promoter, PFL (Fig 2B). PFL was engineered based on a natural FA-activating promoter,

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PfabA. Specifically, PfabA contains a FadR-binding site (FadRO) 5’ of the -35 region, allowing the

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promoter to be activated by FadR by recruiting RNA polymerase. A LacO was placed 3’ of the

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-10 region of PfabA, allowing the resulting promoter PFL to be repressed by LacI, as

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experimentally verified (Fig 2B). Thus, upon transcriptional activation of FFA production via

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IPTG induction, FFA can be quickly synthesized. A proportion of the produced FFA is reversibly


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converted to acyl-CoA by an endogenous enzyme, acyl-CoA synthase. Acyl-CoA then binds to

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FadR and antagonizes FadR’s DNA-binding activity, decreasing the transcription rate from PFL,

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thus slowing FFA production. Overall, the NML forms a negative feedback loop that involves

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dynamic sensing of the metabolic product, FFA. NML mimics the prevalent natural regulation

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via ligand-dependent TFs, such as transcriptional inhibition of genes by the pathway end-product

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in a few E. coli amino acid biosynthetic pathways. The third feedback system, named a layered

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negative metabolic loop (LNML), contains three inhibition layers of regulation and requires two

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gene expression steps to feedback control the production of FFA. Specifically, an FA-activated

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promoter, PAR2, was engineered by inserting a FadRO between the -35 and -10 region of a phage

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promoter (previously shown to increase the dynamic range of the engineered promoters8,30), so

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that PAR2 can be repressed by FadR (Fig 2C). PAR2 was then used to control the expression of

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TetR, which represses the expression of the tesA-rfp from PTL. Thus, transcriptional activation of

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the pathway by IPTG induces tesA expression from PTL. The produced FFA antagonizes FadR’s

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DNA-binding activity via acyl-CoA, leading to activation of TetR expression from PAR2. TetR

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then decreases FFA production by down-regulating tesA expression (Fig 3C). To monitor enzyme

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expression, an rfp was cloned 3’ of TesA in all three feedback loops.

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Responses of the three engineered hybrid promoters to their corresponding effectors were

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first individually validated in expression tests. As expected, both PTL and PFL could be activated

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by 1 mM IPTG (Fig 2). PTL was then subjected to down-regulation by TetR, as tested by



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increasing the TetR expression level from a PBAD promoter using arabinose. PFL was subjected to

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downregulation by the addition of oleic acids in a dose-dependent manner (Fig 2A & 2B). PAR2

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could be activated by increasing the oleic acid concentration, per our design (Fig 2C). Next, three

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E. coli strains carrying engineered metabolic feedback systems were cultivated. Enzyme

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expression and metabolite dynamics after pathway activation were monitored by measuring

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cell-density-normalized fluorescence and FFA concentration. Both time course curves were then

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normalized by their steady state values.

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FFA displayed distinctly different dynamics in all three types of regulatory architectures.

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While NGL increased the speed of FFA dynamics only slightly compared to that of an

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unregulated pathway (Fig 3A), NML allowed FFA to reach steady state more rapidly, in three

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cell cycles (settling time), as compared to seven cell cycles for an unregulated pathway (Fig 3B).

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LNML, on the other hand, raised the FFA concentration quickly to a high level and gradually

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lowered it to its steady state, causing an overshoot of FFA concentration (Fig 3C). Compared to

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the rise-time for an unregulated pathway (2.48 cell cycles), the rise-times of FFA in three

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regulated pathways were 1.75, 1.33 and 0.21 cell cycles, decreased by 1.4-, 1.9-, and 11.8-fold,

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respectively. The dynamics of TesA concentration also changed, with patterns similar to that of

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FFA in each strain. The rise-times of TesA decreased from one cell cycle in the unregulated

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pathway to 0.41, 0.38, and 0.03 cell cycles in NGL, NML, and LNML, respectively, indicating

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that the rapid metabolite dynamics were results of transcriptional regulation of the enzyme


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expression level, consistent with our design (Fig 3A, 3B, &3C). Overall, our results

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demonstrated that the metabolic negative feedback loops could accelerate metabolite dynamics,

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decreasing metabolite rise-time by up to 11.8-fold.

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Model Analysis Elucidates Metabolite Dynamics for the Three Feedback Architectures To obtain a quantitative understanding of the regulated metabolite dynamics and to explore

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the limits of each regulatory architecture, general mathematical models were developed and

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fitted to our experimental data in each system (see Supporting Information and Fig 3). Circuit

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parameters that might be amenable to experimental tuning were varied in each model to explore

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the boundaries of metabolic control. In the case of the NGL, we varied the dissociation constant

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(Kd) between TetR and PTL and simulated FFA dynamics. As seen in Fig 4A and 4B, as Kd

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decreases (tighter repression of PTL by TetR), FFA reaches its steady state faster and its rise-time

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approaches a theoretical upper limit, the fastest metabolite dynamics under NGL control. Our

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experimental results lie close to this upper limit, consistent with the tight interaction between

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TetR and its operator site TetO in PTL (Kd = 30 nM). Under this theoretical upper limit condition,

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the protein’s rise-time was deceased by 5-fold (from one cell cycle to 0.21 cell cycle, Fig 4B),

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and the metabolite’s rise-time was decreased by only 1.57-fold (from 2.48 cell cycle in OL to

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1.58 cell cycle in the fastest NGL, Fig 4A). Thus, an NGL speeds up the response of protein

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expression upon transcriptional activation, but has mild effects on metabolite dynamics.

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Consistent with this observation, natural NGLs are mostly found to regulate transcription factors



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but rarely to regulate enzymes, possibly due to their inefficiency in controlling metabolite

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dynamics.

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Compared to NGL, NML exhibited a more dramatic acceleration in the metabolite dynamics,

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with a decrease in both the rise-time and the settling time. To further explore the effects of circuit

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parameters on metabolite dynamics, we varied the apparent enzyme expression rate ( "! , see

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Supporting Information M4) from 10-13 M/s to 10-8 M/s, and varied the apparent inhibition

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constant (#$ , see Supporting Information M4) from 10µM to 1 M to cover large biologically

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relevant ranges (Fig 4C). As the apparent inhibition constant increases, the repression from the

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negative feedback loop decreases, which increases the rise-time. On the other hand, the

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metabolite rise-time correlates non-monotonically with the enzyme expression rate. Because the

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steady state enzyme expression level is correlated with the enzyme expression rate, a very low

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TesA expression rate leads to a low TesA steady state level (close to its initial concentration),

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therefore resulting in a short rise-time. As the TesA expression rate increases, FFA accumulates

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to higher levels, which gradually cross the inhibition threshold (#$ ). When the FFA level is much

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lower than the threshold, TesA expression is barely inhibited, which causes an increase in

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rise-time. As the TesA expression rate further increases, FFA reaches a concentration much

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higher than the threshold, which leads to a strong repression that decreases the rise-time. In the

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parameter space we explored, the metabolite rise-time was decreased by more than two-fold in

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80% of the parameter space with small overshoot (percent overshoot < 50 in 86% of the


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parameter space). This suggests that NML is particularly effective in accelerating the metabolite

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dynamics without causing large overshoots.

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Comparing the three architectures, LNML had the shortest metabolite rise-time, but at the

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same time caused a large metabolic overshoot. Metabolite overshoot is an interesting

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phenomenon that can be potentially exploited for engineering purposes, including

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metabolite-triggered bistable switches31, transient metabolic signals32,33, and metabolic

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oscillators34,35. On the other hand, too large an overshoot may also adversely affect cell growth if

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the metabolite concentration is above the cellular tolerance level. Thus, it is essential to fine tune

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circuit parameters to balance the metabolite rise-time and the size of metabolic overshoot.

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Because LNML consists of multiple layers of interactions, there is a large set of

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experimental tunable parameters. These include the protein production rate (such as TesA and

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TetR), and the dissociation constants between TFs and their cognate promoters (such as

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FadR-PAR2 and TetR-PTL). We systematically varied the experimentally-tunable parameters in our

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model and studied how they affected the metabolite rise-time and the size of the overshoot. The

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maximum protein production rates of TesA and TetR were varied from 10-13 M/s to 10-8 M/s, and

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the dissociation constants of FadR-PAR2 and TetR-PTL were scanned from 0.1 nM to 10 µM, both

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covering broad ranges of biologically relevant values. As the maximum TetR production rate

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increases, FFA exhibits a shorter rise-time and a higher percent overshoot (defined as the ratio of



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the amount of overshoot to the steady-state) (Fig 4D). Interestingly, the rise-time and the percent

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overshoot correlates non-monotonically with the maximum TesA expression rate (Fig 4D). A

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slow TesA production rate leads to minimal TetR expression, causing a long delay in TetR

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accumulation to repress the circuit, which generates a large percent overshoot and results in a

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short rise-time. Contrariwise, a high enzyme expression rate leads to strong activation, and a

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delay of repression follows because high levels of repressors are accumulated to bring down the

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enzyme expression rate, which generates overshoot and a short rise-time (Figure S2). In addition,

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as we increase the dissociation constant between TetR and PTL, the repression strength of the

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circuit becomes weaker and thus approaches the dynamic behavior of an OL (Fig 4D). However,

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as the binding affinity between FadR and PAR2 decreases, the FFA rise-time decreases and

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reaches a valley before it increases. At low Kd (FadR-PAR2), high FFA concentrations are required

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to turn on PAR2, which causes a delay in repression and a long rise-time. As Kd (FadR-PAR2)

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increases, less FFA is needed to turn on PAR2, and thus rise-time decreases. When Kd (FadR-PAR2)

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further increases beyond a certain level, TetR expression becomes insensitive to FFA

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concentration, leading to a longer rise-time (Figure S2). Interestingly, the Kd (FadR-PAR2) of the

311

rise-time valley shifts right as the Kd (TetR-PTL) decreases. This was because as Kd (TetR-PTL)

312

decreases, TesA expression becomes more sensitive to TetR levels, thus increasing the threshold

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of Kd (FadR-PAR2) that can produce varying PTL-sensitive TetR concentrations at different FFA

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levels. Overall, our model results suggest that a decrease in rise-time is always coupled with an

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increase in the size of overshoot. To shorten the rise-time, a high inverter (TetR) maximum


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expression rate and low Kd (TetR-PTL) should be used. In addition, fine tuning of the maximum

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enzyme (TesA) expression rate and Kd (FadR-PAR2) are also crucial to obtain a short rise-time for

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the LNML circuit.

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Comparing different negative feedback topologies, metabolic overshoot is often seen in

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LNML, indicating that metabolic overshoot is more tightly associated with the regulatory

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architecture rather than the circuit parameters. The addition of an inverter in LNML (the TetR

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layer) creates an additional step of gene expression, increasing the delay time from metabolite

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sensing to its repression. Indeed, when the TetR degradation rate is increased (we denote this

325

architecture as LNML-Deg), the overshoot region shrinks and the overshoot size decreases

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dramatically, while rise-times remain short (See Supporting Information, Figure S3). This

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finding suggests that using an inverter with a short life time, such as fusing a degradation tag to

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the repressor or using RNA-based repression mechanisms, can potentially shorten the settling

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time.

330 331 332

Discussion While previous work mostly focused on the effects of transcriptional regulatory networks on

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protein concentration changes23 and steady state metabolite levels, this work provided a

334

systematic and quantitative view of how transcriptional feedback circuits affect metabolite

335

dynamics. Three types of commonly observed architectures of metabolic feedback loops were



336

constructed and analyzed both experimentally and mathematically. Under these feedback

337

controls, metabolite rise-time can be dramatically increased, by up to 11.8-fold over that of

338

unregulated metabolic pathways. The effects of several regulatory parameters on metabolite

339

dynamics were also systematically studied, allowing a deeper understanding of metabolic

340

regulation in both natural and engineered systems.

341

Overall, our results suggest that NML is the most effective architecture to accelerate

342

metabolite dynamics, with dramatically decreased rise-time and little overshoot. In NML, since

343

low and high #$ may lead to large metabolic overshoots and long rise-times, respectively, these

344

parameter values should be avoided when constructing metabolic circuits. By comparison,

345

LNML is also effective in shortening the rise-time but mostly at the cost of generating large

346

overshoots. Since a high enzyme expression rate is often preferred in engineering applications to

347

increase metabolite concentrations, a medium expression level of the inverter is preferred to

348

speed up the response while maintaining a relatively small percent overshoot. In addition,

349

because the rise-time and percent overshoot correlate non-monotonically with Kd (FadR-PAR2),

350

fining tuning of Kd (FadR-PAR2) allows further precise control of the metabolite dynamics.

351

Compared to NML and LNML, NGL is inefficient in accelerating metabolite dynamics when

352

employed in a metabolic pathway. This is mostly caused by the relative small delay in

353

feedback-regulated TesA synthesis compared to NML and LNML. Delay in TesA synthesis

354

resulted in FFA overshoot, which allowed FFA concentration to quickly reach its half steady state

355

concentration, leading to a short FFA rise-time. Nevertheless, NGL may be considered when a


Page 18 of 38

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356

metabolite biosensor is not available. These design guidelines can be used to choose a proper

357

regulatory architecture and parameters to achieve desirable metabolite dynamics.

358 359

It is suggested that natural enzymes are usually expressed at abundant levels at steady state,

360

and thus serve as a buffer to maintain a steady cell metabolism under small environmental

361

perturbations22,36. However, under drastic environmental changes, such as the depletion of amino

362

acids, transcriptional regulation turns on the expression of an entire biosynthetic pathway,

363

causing large metabolic changes. During such a transition, the ability to rapidly adjust enzyme

364

expression and catalysis to produce a desirable level of the target metabolite increases the rate of

365

adaptation. Thus, negative metabolic feedback loops provide rapid response to large

366

environmental changes by quickly optimizing both enzyme and metabolite levels. On the other

367

hand, the vast majority of engineered pathways in the field of metabolic engineering and

368

synthetic biology are unregulated and could be slow to respond to large metabolic changes.

369

Therefore, this study also provides guidelines to design synthetic regulatory circuits to speed up

370

metabolite dynamics in engineered systems.

371 372

The benefit of a faster metabolite rise-time is, however, also accompanied with a possible

373

metabolic overshoot. Metabolic overshoot may be undesired in most natural systems, due to the

374

overproduction of unnecessary proteins and metabolites. Although overshoot can be mitigated to

375

some degree by fine-tuning the regulatory parameters of the metabolic feedback circuits, our



376

study found that it is more tightly associated with regulatory architectures. Compared to LNML,

377

NML has a greater parameter space where a shorter rise-time is achieved without overshoot,

378

strongly suggesting why NML is the most commonly found transcription metabolic regulation in

379

prokaryotes. For synthetic biology applications where metabolite overshoot is needed, LNML

380

provides a large parameter space to generate overshoot with tunable size.

381 382

Gene regulation lies at the center of systems biology, and its functional role has inspired

383

researchers to build synthetic regulation for various engineering applications. In this work, we

384

exploited genetic circuits to speed up metabolite dynamics. Our study filled the gap that links

385

gene regulation with metabolite dynamics and indicated that, beyond optimizing cellular

386

resources for enzyme production, transcriptional regulation also plays a critical role in quickly

387

adapting metabolite levels to large environmental shifts. Our work also provides a systematic

388

design principle that illustrates how regulation architectures and parameter fine-tuning affect

389

metabolite productivity, which can be used to engineer synthetic feedback circuits to better

390

control metabolite dynamics.

391 392

Methods

393

Materials Phusion DNA polymerase, restriction enzymes, and T4 ligase were purchased from

394

Thermo Fisher Scientific (Waltham, Massachusetts, U.S.A.). Gel purification and plasmid

395

miniprep kits were purchased from iNtRON Biotechnology (Lynnwood, WA, U.S.A.). All


Page 20 of 38

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396

primers were synthesized by Integrated DNA Technologies (Coralville, IA, U.S.A). All reagents

397

were purchased from Sigma Aldrich (St. Louis, MO, U.S.A.). E. coli DH10B was used for

398

cloning purposes, and E. coli DH1 (∆fadE) was used to construct negative feedback circuits.

399 400

Plasmids and strains Plasmid pB5k-tesA-RFP was constructed by cloning a cytosolic

401

thioesterase gene tesA (‘tesA: leader sequence deleted) to the 5’ of RFP in a Biobrick vector

402

pBbB5k-RFP between the restriction sites EcoRI and BglII (see full plasmid sequence in

403

Supporting Information)37. To create pB5k-tesA and pB8k-tesA, tesA was amplified and cloned

404

3’ of the PBAD promoter in Biobrick plasmids pBbB5k-RFP and pBbB8k-RFP between restriction

405

sites EcoRI and XhoI, respectively. Plasmid pA5c-CAR was constructed by cloning a carboxylic

406

acid reductase29 3’ of a PLacUV5 promoter in a Biobrick plasmid pBbA5c-RFP between restriction

407

sites EcoRI and XhoI. Plasmid pETLa-RFP was created by inserting one TetO site in between the

408

-35 and -10 region of the PlacUV5 promoter (Supplementary Table S3) in a Biobrick plasmid

409

pBbE5a-RFP, using a one-step Golden-Gate DNA assembly method. To create pETLa-tesA-RFP,

410

tesA was cloned 5’ of rfp in the pETLa-RFP plasmid between restriction sites EcoRI and BglII.

411

The gene tetR was amplified from a BioBrick plasmid, pBbA2c-RFP, and cloned 3’ of the PBAD

412

promoter in a Biobrick plasmid pB8k-RFP between restriction sites EcoRI and XhoI, yielding

413

pB8k-tetR. Plasmid pBAR2k-RFP was constructed from phage PA1 promoter by placing one

414

FadRO site between the -35 and -10 regions of the promoter to control the expression of RFP in

415

a Biobrick vector, pBbB5k-RFP. Plasmid pETLa-tesA-tetR-RFP was constructed by cloning tetR



416

3’ of tesA and 5’ of rfp in the pETLa-tesA-RFP plasmid. To create pEFLa-tesA-RFP, promoter

417

PFL was engineered by placing one LacO site 3’ of the -10 region of PfabA (Supplementary Table

418

S3) to replace the PTL promoter in plasmid pETLa-tesA-RFP. Plasmid pBAR2k-tetR and

419

pA8c-fadR were constructed by replacing rfp in pBAR2k-RFP and pBbA8c-RFP with tetR and

420

fadR, respectively. Strains were created by transforming the corresponding plasmids into DH1

421

(∆fadE) competent cells. Plasmids (Table S1), strains (Table S2), and promoter sequences (Table

422

S3) are summarized in the Supporting Information.

423 424

Cell growth and fluorescence assay Cell growth curves and cell culture fluorescence were

425

recorded on an Infinite F200PRO (TECAN) plate reader. Strains were first cultivated overnight

426

in Luria−Bertani (LB) medium (220 rpm, 37 °C) supplemented with appropriate antibiotics (50

427

mg/L ampicillin, 50 mg/L kanamycin, and 30 mg/L chloramphenicol). To test PTL promoter

428

behavior, the overnight LB cultures were inoculated 2% v/v into fresh minimal medium9 with

429

2% glucose, and the overnight minimal medium culture was then inoculated into fresh minimal

430

medium. To test PFL promoter behavior, the overnight LB cultures were inoculated into fresh

431

minimal medium with 1% glycerol as a carbon source (supplemented with 0.5% tergitol NP-40),

432

and the overnight minimal medium culture was then inoculated into fresh minimal medium. The

433

PAR2 promoter was tested using a method modified from previous publication8. Specifically, cells

434

were induced with the corresponding inducer concentrations at OD=0.6, and then were incubated

435

in a 96-well plate inside the plate reader with shaking (218.3 rpm, 37 °C). The cell density


Page 22 of 38

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436

(OD600) and red fluorescence (excitation, 535 ± 9 nm; emission, 620 ± 20 nm) were recorded

437

every 1000 s until the cell culture reached the stationary phase. Fluorescence from a wild-type E.

438

coli DH1 (∆fadE) cell culture was used as the background, and was subtracted from all

439

fluorescence measurements. The background-corrected fluorescence was later normalized by cell

440

density as measured at OD600.

441 442

Protein and metabolite production dynamics The OL, OLIM, NGL, NML, and LNML strains

443

were inoculated into LB medium with appropriate antibiotics (50 mg/L ampicillin, 50 mg/L

444

kanamycin, and 30 mg/L chloramphenicol). For adaptation, overnight LB cultures of OL, NGL,

445

and LNML strains were inoculated 2% v/v into M9 medium supplemented with 1% glycerol and

446

amino acids, the same composition as EZ-rich medium. The overnight culture of OLIM was

447

inoculated 2% v/v into M9 medium supplemented with 2% glucose and 0.5% yeast extract. This

448

medium was used to maintain a constant growth rate throughout the two subsequent induction

449

processes. For adaptation, the overnight LB culture of NML was inoculated 2% v/v into minimal

450

medium, supplemented with 1% glycerol. The overnight cultures in minimal medium were used

451

to inoculate 25 mL of the corresponding fresh minimal medium with an initial OD600 of 0.08 and

452

then induced when the OD600 reached 0.6. Strains NGL and LNML were supplemented with 50

453

nM of aTc to remove leaky expressed TetR. Strain OLIM was first induced with 4 µM or 40 µM

454

IPTG and maintained under steady state for five cell cycles before 0.4% arabinose was added to

455

induce CAR. Cell cultures were diluted under the same induction conditions periodically to



456

maintain the cells in the exponential growth phase. OD600 and fluorescence were measured every

457

1-2 cell cycles, and cell cultures were collected at each sampling point and stored at -20 °C for

458

FFA quantification. FFA were quantified using a previously published method9. Fluorescence and

459

FFA concentration were normalized by cell density as measured by OD600, and the data were

460

then normalized by the steady state to obtain the protein and metabolite dynamic curves.

461 462

Mathematical model and fitting to experimental data Fitting the model to the experimental

463

data was performed by implementing least-squares non-linear optimization, using the MATLAB

464

Global Optimization Toolbox function MultiStart. All model parameters were left free to be

465

fitted, and the optimization was initiated from thousands of random guesses of the set of

466

parameter values to ensure convergence onto a global solution. Kinetic models, coefficient of

467

determination (R2), and the fitted parameters of OL, OLIM, NGL, NML, and LNML are in the

468

Supporting Information. The fitted parameters and R2 are summarized in the Supporting

469

Information Table S4. In Fig 4C, the parameter value, ktesA=77.75 s-1, is used for tuning the

470

apparent expression rate of TesA and apparent inhibition constant. Parameters used in Fig 4D for

471

tuning the maximum expression rates of TesA and TetR are ktesA=230.90 s-1, kd,tetR=3.85e-8 M,

472

kfadR, FFA=0.001 M, and k2=138.50. Parameters used in Fig 4D for tuning Kd (TetR-PTL) and Kd

473

(FadR-PAR2) are rTL=1e-10 M/s, rAR2=1e-10 M/s, ktesA=230.90 s-1, and kfadR, FFA=0.001 M. All data

474

points in Fig 4C, 4D, and S3 are logarithmically spaced. Protein (TetR) degradation was


Page 24 of 38

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475

considered as first-order kinetics and a degradation rate constant of kdeg=0.0004 s-1 was used in

476

Fig S3.

477 478

Supporting Information

479

Supplementary tables, figures, mathematical models of negative feedback circuits and DNA

480

sequences of selected plasmids and genes

481 482

Author Information

483

Corresponding author

484

*E-mail: [email protected]

485 486

Author contribution

487

F.Z. and D.L. conceived the project and designed the experiments. D.L. performed the

488

experiments and modeling, and analyzed the data. F.Z. and D.L. wrote the paper.

489 490

Acknowledgement

491

The authors would like to thank Ahmad Mannan for his help in data fitting. This work was

492

supported by the National Science Foundation (MCB1453147) and the Human Frontier Science

493

Program (RGY0076/2015).

494



495

References

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589


Figures

590 591 592

Figure 1. Enzyme and metabolite concentration changes in unregulated metabolic

593

pathways.

594

A. An engineered free fatty acid (FFA) pathway was chosen as the model pathway to study the

595

dynamics of a pathway product. FFAs were produced by expressing a thioesterase (encoded by

596

tesA) under the control of a PLac promoter. RFP was expressed in the same operon to monitor the

597

expression dynamics of the thioesterase.

598

B, C. Expression dynamics of the (B) thioesterase and (C) FFA. TesA and FFA dynamics (dots)

599

were fitted to equations (1) and (2), respectively (solid line).

600

D. A fatty alcohol pathway was used as a model pathway to study the dynamics of a pathway

601

intermediate. The fatty alcohol pathway was constructed by expressing a thioesterase under the



602

control of a PBAD promoter and a carboxylic acid reductase (encoded by car) under the control of

603

a PLac promoter.

604

E.

605

FFA consumption rates were measured and fitted to a model. Data are plotted together with the

606

production dynamics of a pathway product for comparison.

607

F.

608

rates. As the consumption rate of the intermediate increases (from light gray to dark gray lines),

609

the intermediate dynamics further speed up and hit an upper limit.

FFA production dynamics with high (labelled as OLIM_hc) and low (labelled as OLIM_lc).

Simulation results of the intermediate dynamics with different intermediate consumption

610 611 612


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613 614

Figure 2. Design of synthetic promoters to create negative feedback circuits.

615

A. Design and characterization of the PTL promoter. A hybrid promoter, PTL, was created by

616

incorporating TetO and LacO into the promoter. The promoter was activated by IPTG and

617

repressed by TetR in a dose-dependent manner.

618

B. Design and characterization of the PFL promoter. A hybrid promoter, PFL, was created by

619

introducing LacO into the promoter region of the FabA promoter. The promoter was activated by

620

IPTG and repressed by fatty acids in a dose-dependent manner.

621

C.

622

was engineered by introducing FadRO into the promoter region of a phage promoter. The

623

promoter was activated by oleic acids.

Design and characterization of the PAR2 promoter. A fatty acid responsive promoter, PAR2,



624 625

Figure 3. Negative feedback circuits with three different architectures and their metabolite

626

and enzyme dynamics.

627

A. Design and dynamics of metabolite and enzyme in a negative gene loop (NGL). In the NGL,

628

PTL promoter is used to control the expression of the tesA-tetR-rfp operon. Induction of the

629

operon initiates the synthesis of TetR, which feeds back to inhibit the operon.

630

B. Design and dynamics of metabolite and enzyme in a negative metabolic loop (NML). In the

631

NML, PFL is used to control the expression of the tesA-rfp operon. Upon induction of PFL, FFA

632

synthesis is initiated, and its accumulation turns down the expression of the operon.

633

C. Design and dynamics of metabolite and enzyme in a layered negative metabolic loop


Page 34 of 38

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634

(LNML). In the LNML, PTL is used to control the expression of the tesA-rfp operon. The inverter

635

TetR is placed under the control of PAR2. Production of free fatty acids is turned on by inducing

636

TesA synthesis, and the accumulation of free fatty acids induces TetR expression. The

637

accumulation of TetR turns down TesA synthesis by inhibiting PTL.

638

Fluorescence and FFA concentration were normalized by cell density as measured by OD600, and

639

the data were then normalized by the steady state to obtain the enzyme and metabolite dynamic

640

curves. Normalized free fatty acid and enzyme accumulation dynamics were all fitted with

641

kinetic models (solid black lines) and are plotted with those of a non-regulated pathway (solid

642

gray lines) for comparison.

643 644 645



646

647


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648

Figure 4. Tuning of circuit parameters to control enzyme and metabolite dynamics.

649

A, B.

650

between TetR and PTL. Kd decreases from light gray to dark gray lines. Upper limits of

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achievable metabolite and enzyme dynamics were observed.

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C. Rise-time and percent overshoot of NML under varied tunable circuit parameters. Parameter

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value used is ktesA=77.75 s-1.

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D. Rise-time and percent overshoot of LNML under varied tunable circuit parameters. Parameter

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values used for tuning the maximum expression rates of TesA and TetR are ktesA=230.90 s-1,

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kd,tetR=3.85e-8 M, kfadR, FFA=0.001 M, and k2=138.50. Parameters used for tuning Kd (TetR-PTL)

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and Kd (FadR-PAR2) are rTL=1e-10 M/s, rAR2=1e-10 M/s, ktesA=230.90 s-1, and kfadR, FFA=0.001 M.

Dynamics of (A) metabolite and (B) enzyme in NGL with varying dissociation constants

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For Table of Contents /Abstract Graphic Use Only

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Title: Metabolic Feedback Circuits Provide Rapid Control of Metabolite Dynamics

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Authors: Di Liu1, Fuzhong Zhang1, 2, 3 *

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Metabolic Feedback Circuits Provide Rapid Control of Metabolite

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