This model considers that the dynamics between biomass X(t) and fluorescence R(t) can be approximately described by an integral time constant τ_p, a derivative time constant τ_z, and a gain K: τpdRtdt=−Rt+KXt−τzdXtdt

The transfer function between the input and the output expressed through the Laplace transform notation is: RsXs=K1−τzs1+τps

In this model, we consider an additional integral time constant τ_p2 between the input X(t) and the output R(t), represented in the following equation through an auxiliary state variable X₁(t): τp1dX1tdt=−X1t+KXt−τzdXtdtτp2dRtdt=−Rt+X1t

In Laplace transform notation: RsXs=K1−τzs1+τp1s1+τp2s

In this model, we consider an additional integral time constant τ_p3 between the input X(t) and the output R(t), represented in the following equation through an additional state variable X₂(t): τp1dX1tdt=−X1t+KXt−τzdXtdtτp2dX2tdt=−X2t+X1tτp3dRtdt=−Rt+X2t

In Laplace transform notation: RsXs=K1−τzs1+τp1s1+τp2s1+τp3s

In order to identify the model from the samples, we used an approximate discrete model based on the bilinear transform (Oppenheim and Schafer, 2010): s←2Tsz−1z+1 where z⁻¹ corresponds to a pure delay in the sample and T_s is the sampling frequency. Parameters of the discrete model were fitted by linear regression using the R package with the dynlm package (Zeileis, 2014), which was also employed to perform the simulations.

The core of the malonyl-CoA sensor is an RFP gene driven by the synthetic pFR1 promoter (Liu et al., 2015). pFR1 is a combination of P_A1 promoter from phage T7 (Deuschle et al., 1986) and two FapR-binding segments flanking the −10 region. The FapR protein, originating from Bacillus subtilis, dissociates from the DNA upon the binding of malonyl-CoA (Schujman et al., 2003), thereby allowing the E. coli RNA polymerase to transcribe the downstream sequences. The transcription of FapR is driven by a pAra promoter (controlled by the AraC protein), pFR1 is therefore increasingly repressible by elevating the l-arabinose levels. The AraC and FapR transcription factors, as well as RFP are all encoded on pBFR1k_RFP_8FapR, a kanamycin-resistant plasmid constructed by the workgroup of Fuzhong Zhang (Liu et al., 2015). The authors validated the quantitative nature of malonyl-CoA sensing by generating a calibration curve that correlated the fluorescence levels to LC-MS measurements of intracellular malonyl-CoA. In order to use this sensor to compare the malonyl-CoA productivity of our construct collection available on the kanamycin-resistant pRSF vector, we generated a chloramphenicol-resistant version of the plasmid, which we call pCFR (plasmids used in this study are listed in Table S1 in Supplementary Material). The functionality of pCFR, as well as that of the original sensor plasmid was benchmarked with the help of cerulenin. This is an inhibitor of 3-ketoacyl-ACP synthase I and II (D’Agnolo et al., 1973), which participate in the committing step of free fatty acid biosynthesis. The inhibition of these enzymes results in a substantial intracellular accumulation of malonyl-CoA (Davis et al., 2000), and should therefore cause an increase in RFP fluorescence. Indeed, E. coli cells carrying either pBFR1k_RFP_8FapR or pCFR responded to cerulenin with a sharp increase in OD-normalized fluorescence (Figures 1A,B). As a matter of fact, a small scale screening of four pCFR-carrying clones allowed the identification of the most effectively functioning plasmid, which was chosen for all downstream experiments (Figure 1B). As expected, the ratio of RFP/OD values of cerulenin-treated to control cultures was higher in minimal medium than in LB broth (Figure 1C), due to the relatively high background-fluorescence of LB medium (Xu et al., 1999). For this reason, all further measurements were carried out in minimal medium.

In its original publication by Liu et al. (2015), the malonyl-CoA sensor was characterized in a split form: the FapR and RFP genes were carried by two separate plasmids. Therefore, we re-characterized pBFR1k_RFP_8FapR in order to find the optimal conditions of comparing various malonyl-CoA producer enzymes using the single-plasmid sensor construct. The expression level of the FapR repressor was varied by administering a dilution series of arabinose, while the expression level of the malonate transporter (matC) and the matB from plasmid pACYCmatCmatB was controlled by altering the IPTG concentration. A 4 × 4 concentration matrix was thus applied to cells carrying either both plasmids or just the sensor plasmid. As apparent from the OD-normalized fluorescence values shown on Figure 2, an arabinose concentration of 0.01% proved to be optimal, taking both specificity and sensitivity into account, similarly to the originally published sensor system. At lower arabinose concentrations, specificity deteriorated, since the sensor plasmid produced slight increases in fluorescence in response to IPTG even in the absence of the malonyl-CoA producer plasmid. This could indicate the promoter’s non-specific binding to LacI, which is competitively inhibited by sufficient quantities of the FapR protein. Increasing arabinose levels to 0.1% strongly reduced fluorescence levels of the sample, leading to a decrease of sensitivity and of the signal to noise ratio, possibly resulting from an over-repression by FapR. The initial decrease in fluorescence/OD values, seen on all graphs is likely due to the delay of RFP expression compared to culture growth.

To compare the malonyl-CoA production efficiencies of alternative malonyl-CoA-producing pathways, at least one representative enzyme for each pathway was cloned, as described earlier (Fehér et al., 2014). Briefly, the matB, atoDA, mmsA, and cagg1256 genes, as well as the accABCD gene complex were expressed from the high-copy plasmid pRSFduet. To provide sufficient amounts of substrate, a MatC was co-expressed with matB and atoDA, and the medium was supplemented with Na-malonate. To elevate the substrate levels for mmsA and cagg1256, cultures were supplemented with β-alanine, which is converted to 3-oxopropanoate (malonate semialdehyde) by the cell’s endogenous 4-aminobutyrate aminotransferase. In every case, the fluorescence/OD values were monitored over time after growing the cells in various IPTG concentrations. Cells carrying the empty pRSFduet plasmid (besides the sensor plasmid) were used as a negative control. Based on their response, the strains carrying the various constructs fell into either one of the two following categories: (i) the cells exhibited growth and a dose-dependent fluorescence/OD response to IPTG (pRSFmmsA and pRSFcagg) (Figure 3) or (ii) the cells exhibited absolutely no growth upon IPTG induction in minimal medium (pRSFMaccABCD and pRSFatoDA) (Figures 4A,B). It is important to note that certain cells of the latter category also gave a seemingly dose-dependent response to IPTG (such as pRSFatoDA), but their fluorescence and OD values were practically unchanged during the course of the experiment, most probably indicating that the trend in their ratio is an artifact (Figure S1 in Supplementary Material). Interestingly, both types of responses were seen with pRSFmatCmatB-carrying cells, in a quite irreproducible manner (see Discussion and Figures 4C,D and Figure S2 in Supplementary Material). The growth curves obtained by inducing strains carrying various producer plasmids are summarized on Figure S3 in Supplementary Material.

Since the overexpression of certain members of the accABCD complex (Davis et al., 2000), as well as protein overproduction in general (Flores et al., 2004) have been described to have a toxic effect on the cells, the overexpression of certain constructs was repeated using lower-copy vectors. For the accABCD complex, pMSD8, an ultra-low-copy variant was available expressing the four genes as a T7-driven operon. In addition, two medium-copy alternatives, pETM6-PaccABCD and pETM6-MaccABCD, carrying the genes as a pseudo-operon (separate promoters) and in monocistronic form (separate promoters and terminators), respectively, were also obtained and tested (Xu et al., 2012, 2013). All three plasmids displayed a clear dose-dependent fluorescence/OD pattern, well above the levels of the negative control (Figures 5A–C). For matCmatB, pACYCmatCmatB was readily available as a low-copy alternative that functioned in a quite well-reproducible fashion (Figure 2), when tested with the pBFR1k_RFP_8FapR sensor plasmid.

These results prompted us to subclone our pathway collection into a pACYC backbone, thereby reducing the copy-number of all constructs to ~15. When expressed this way, all five constructs (matCmatB, mmsA, cagg1256, M.accABCD, and matCatoDA) allowed cell growth and displayed a scalable, IPTG-dependent fluorescence (Figures 2 and 6). As it turned out, the concise nature of the dataset obtained with the pACYC-collection allowed us to fit various models describing the response of the sensor to malonyl-CoA production (see below).

Since E. coli strain BL21DE3, the host used in our experiments is not deleted for the genes of arabinose catabolism, it breaks down arabinose when the medium is depleted for glucose. This likely causes a decrease in FapR expression, and a consequent derepression of RFP at the end of growth. As a result, a second, sudden increase in fluorescence was seen in many samples upon the transition to stationary phase, as apparent from juxtaposing the temporal evolution of fluorescence and OD (Figure S4 in Supplementary Material). To avoid this effect, we analyzed fluorescence levels corresponding to the log-phase (OD = 0.6), a physiological state when arabinose catabolism is still inhibited by the catabolite repression of E. coli. Figure S5 in Supplementary Material shows some of the fluorescence vs. OD plots generated to obtain such readings.

Prior to comparing the performance of various malonyl-CoA-producing constructs, we investigated the reproducibility of our measurements at three different levels. First, we compared the fluorescence values of parallel clones, resulting from the transformation of a given producer construct. These displayed a strong variation in their response to IPTG, which was not unexpected taking into account their heterologous colony morphologies (Figure 7A). Second, we re-tested the best performing clones after their storage in the form of glycerol stocks. Reproducibility was substantially better, being the best for the lowest copy-number pMSD8 plasmid (Figure 7A). For other constructs, the performance seemed to fall into two distinct clusters: it either matched that of earlier measurements, or deteriorated to a lower, near-zero value, as demonstrated by the dose–response curves of pETM6-MaccABCD (Figure 7B). This phenomenon was reminiscent of a burden-relieving mutation that swept through the population early after induction. The third level of reproducibility corresponds to comparing the performance of a given strain in the same microtiter plate in the same measurement-run, starting from the same overnight seed-culture (Figure 7C). The high reproducibility of such measurements was sufficient to draw conclusions on the effect of providing the substrates for malonyl-CoA production (see below).

To test whether providing the substrates of malonyl-CoA synthesis in the growth medium offers a measurable advantage in the product levels, we repeated the experiment for, pACYCmatCmatB and pACYCmatCatoDA with and without Na-malonate as well as for pRSFmmsA and pRSFcagg with and without β-alanine. For pACYCmatCmatB, we observed significantly boosted production at 0.3 and 0.6 mM IPTG (Figure 8A). However, the presence of Na-malonate significantly hindered the performance of pACYCmatCatoDA at IPTG concentrations of 0.3 mM and above (Figure 8B). Similarly, supplementing β-alanine to pRSFmmsA seemed to have a negative effect at 0.6 mM IPTG induction (Figure 8C). No significant effect was seen for adding the substrate to pRSFcagg (not shown).

The four alternative pathways for malonyl-CoA production, as well as the top-scoring enzymes that catalyze the required steps were sought for by RetroPath, our retrosynthetic biology tool developed for metabolic engineering (Carbonell et al., 2011). As opposed to our initial plans, the growth-inhibitory effect of certain pRSF-based constructs prohibited us to validate the ranking of the alternative pathways by direct comparison of their measured fluorescence values. Indeed, the toxicity of overproducing malonyl-CoA by overexpression of acetyl-CoA carboxylase has been described before (Davis et al., 2000). The performance of the readily available low-copy variants of accABCD, however (pMSD8, pETM6-PaccABCD, and pETM6-MaccABCD), indicated the importance of using lower-copy expression vectors. After recloning our gene-set into pACYC-derived plasmids, matCatoDA, MaccABCD, mmsA, cagg1256, and matCmatB all permitted growth when expressed. Importantly, based on their fluorescence values, these constructs all produced significantly more malonyl-CoA when induced with 1 mM of IPTG, than the control cell harboring no production (see below). Ranking the alternative malonyl-CoA-producing pathways was not feasible due to the high variation of the data. Important practical conclusions could be nevertheless made, listed in the Section “Discussion.”

In order to characterize the sensor, we modeled the sensor response to the production of malonyl-CoA, its measured signal. Ideally, the sensor once calibrated should display a good reproducibility as well as a stable sensitivity for its use in applications such as screening or feedback regulation. For that purpose, it is desirable to keep the dynamic response of the sensor uncoupled from any parameter variation so that the relationship with the measured signal and its output corresponds basically to a linear one. The time of response of such linear sensor, on the other hand, should be kept below some reasonable limit in order to avoid large lags introducing potential instability into the system. Here, as we are basing our model on the observations of OD and RFP, we need to consider in our model the relation between these variables with respect to the malonyl-CoA concentration, the signal that is measured by the sensor. In this study, the model necessarily will be kept simple, as our purpose is to provide a set of parameters that can be easily measured in order to calibrate the sensor.

Similarly to other proposed models (Anesiadis et al., 2008), we consider that the signal undergoes several transformation stages in cascade-mode going from the biomass to the fluorescence levels:

We assume that the variation on concentration of malonyl-CoA M(t) depends on its instant production, given by the rate v_m, which is specific to each selected malonyl-CoA-producing construct or pathway, multiplied by the biomass X(t) minus the malonyl-CoA that is consumed for growth defined as a constant rate v_g that multiplies the variation in time of biomass and another term for degradation, defined by a rate constant γ_m: (1)dMtdt=vmXt−vgdXtdt−γmMt

During the exponential growth phase, this previous equation is simplified as: (2)dMtdt=vm−μvgXt−γmMt where μ is the specific growth rate.

In our sensor model, we are assuming that under same inducer and regulatory conditions on a strain population, malonyl-CoA levels should change basically because of the change in the rate of production of this metabolite by the strain (v_m in Eq. 1), which would correspond to a different gain of the sensor, i.e., a different measured RFP and biomass X in steady state.

Such gain according to the sensor model in Eqs 1–4, the gain or relationship in steady state between RFP and X is given by the following relationship between model parameters: (5)RX=Kdvmγmκγr

Regarding model dynamics, we considered three simplified models for the response dynamics depending on the time constants that are considered (see Materials and Methods): (1) a first-order with integral and derivative terms; (2) a second-order model consisting of a first-order model with integral and derivative terms and an additional first-order integral term; and (3) a third-order model with the integral and derivative terms and two additional first-order integral terms.

As shown in Figure 10, measured responses were in general fitted with an increasing level of accuracy to each of the three approximate sensor models. For some constructs, however, measurements could not be successfully fitted to model 3 (see Figure S4 in Supplementary Material). Therefore, we decided to use model 2 (the one considering one derivative and two integral terms) as the reference model in order to characterize the dynamics of the sensor. Table 1 provides a list of estimated parameters for different constructs. Time constants ranged between approximately 1 and 10 h.

According to our simplified model of the sensor consisting on a second-order transfer function, gain between biomass and RFP should depend on the level of induction of the malonyl-CoA-producing enzyme. Time constants, on the contrary, should not depend on the level of induction, but should be constitutive parameters of the sensor that can be calibrated for each construct. As shown in Figure 11, we found effectively a good correlation between IPTG levels and sensor gain (r = 0.72, p-value = 8.1 × 10⁻⁶), indicating that the sensor is responsive to changes in induction of the enzyme. Time constants, as expected, were not significantly affected by changes in the IPTG concentration. These time constants, on the other hand, appear as distinctively clustered for each construct, showing the robustness of the sensor (Figure 12).