Antagonistic autoregulation speeds up a homogeneous response in Escherichia coli

By integrating positive and negative feedback loops, biological systems establish intricate gene expression patterns linked to multistability, pulsing, and oscillations. This depends on the specific characteristics of each interlinked feedback, and thus one would expect additional expression programs to be found. Here, we investigate one such program associated with an antagonistic positive and negative transcriptional autoregulatory motif derived from the multiple antibiotic resistance (mar) system of Escherichia coli. We studied the dynamics of the system by combining a predictive mathematical model with high-resolution experimental measures of the response both at the population and single-cell level. We show that in this motif the weak positive autoregulation does not slow down but rather enhances response speedup in combination with a strong negative feedback loop. This balance of feedback strengths anticipates a homogeneous population phenotype, which we corroborate experimentally. Theoretical analysis also emphasized the specific molecular properties that determine the dynamics of the mar phenotype. More broadly, response acceleration could provide a rationale for the presence of weak positive feedbacks in other biological scenarios exhibiting these interlinked regulatory architectures.


Strains construction
We engineered a two-color fluorescent reporter strain (Escherichia coli) to measure the activity of the marRAB promoter, following the work by Miyashiro & Goulian (2007) 1  This plasmid was integrated as single copy into the lambda phage attachment site of E. coli MG1655 using the helper plasmid pInt-TS (Weiss et al., 1999). The residual cat gene linked to the marRAB promoter was replaced by kan by electroporating a PCR product created from the template plasmid pKD4 into the appropriate strain carrying plasmid pKD46 to yield the strain JFP01 (this work). The two-color reporter strain JFP02 was created by moving the previous marker into strain TIM64 (a strain derived from a MG1655 that constitutively expresses CFP; TIM64 does not present any antibiotic resistance marker; Miyashiro & Goulian, 2007) by P1 transduction. 1 We thank Tim Miyashiro for strains, and Mark Goulian for strains and experimental advice.
Removal of the kan marker using plasmid pCP20 originated E. coli strain IE01. This was verified by PCR. In addition, E. coli strain IE02 was constructed by deletion of the rob gene in IE01 with the application of a Datsenko & Wanner (2000) knockout protocol followed by the removal of the kan marker using plasmid pCP20 (Datsenko & Wanner, 2000). The primers used were: 5'-ATATCCCAATGGCATCGTAAAGAACATTTTGAGGCATTTCAGTCAGTTGC GCTGGAGCTGCTTCGAA (forward), and 5'-ATGAACCTGAATCGCCAGCGGCATCAGCACCTTGTCGCCTTGCGTATAAT ATGAATATCCTCCTTAG (reverse). The sequence of the resulting strain was verified by PCR.
We also constructed two strains deleting the marA gene (named as TC01 and TC02) 2 . This was done from strains IE01 and IE02, respectively, using a variant of the Datsenko & Wanner (2000) knockout protocol, with the insert (kan marker with marA flanking regions) obtained by PCR from a KEIO collection strain (Baba et al., 2006). Strain IE01 (or IE02) containing the pKD46 plasmid was electroporated with this insert in presence of arabinose, allowing recombination in the marA locus. The primers used to obtain the insert were: 5'-CGAACCCGAATGACAAGC (forward), and 5'-GCTATTGCGGATGAAAGTGG (reverse). Correct substitution of the marA gene by kan marker was checked by PCR. We also used mineral oil for characterization. Cultures were grown as previously indicated, and then were used to load the multiwell plate (Thermo) with final volumes of 250 µL. Per well, we added directly 200 µL of culture (counting the volume of inducers), and 50 µL of mineral oil (Sigma). However, we found that the mar circuit does not respond to salicylate in partially anaerobic conditions. This may be explained, at least in part, by the fact that copper appears to shift intracellularly from Cu 2+ to Cu + in absence of oxygen (Rensing & Grass, 2003), but also because fluorescent proteins require oxygen to form the chromophores (Drepper et al., 2007). Note that previous experiments in partially anaerobic conditions like ours, but with another gene circuit, have shown expression with a GFP (Setty et al., 2003).

Culture media and reagents
program started first with OD 600 , then YFP, and finally CFP, followed by 30 s of shaking in orbital mode. Then it waited for 5 min, and it started again.

Analysis of fluorescence data
We collected time-course data of fluorescence (YFP and CFP) and absorbance.
Background values of absorbance and fluorescence, which corresponded to M9 minimal medium, were subtracted to correct the signals. The normalized fluorescence (for both YFP and CFP) was calculated as the ratio of fluorescence and absorbance.
Similar values of normalized fluorescence were reported for MG1655 cells and for M9 minimal medium, which indicated that the auto-fluorescence of cells was negligible in this case. The growth rate of cells was calculated as the slope of the linear regression between the log of corrected absorbance and time in exponential phase. Time-dependent promoter activity, defined as the instantaneous production rate of normalized YFP fluorescence (magnitude per cell), was calculated for each time point using the derivative of the normalized fluorescence. Promoter activity in steady state, defined as the stationary production rate of normalized YFP fluorescence (magnitude per cell) in exponential phase, was calculated as the average over time (for t > 2 h) of normalized fluorescence times growth rate. The error associated to that measure was obtained by calculating the standard deviation over replicates in all time points, then squaring all these deviations to average them, and finally getting the root square. Data were analyzed with Matlab (MathWorks).

Quantification of fluorescence in single cells
Experiments of induction were carried out to study the heterogeneity of the dynamic response. Culture (volume of 2 mL) inoculated from a single colony was grown overnight in LB medium supplemented with glucose 0.4% at temperature of 37 ºC and shaking of 170 rpm. Culture was then diluted 1:200 in M9 minimal medium (10 µL of culture into a final volume of 2 mL) and was grown for 4 h at temperature of 37 ºC and shaking of 170 rpm. The different cultures diluted 1:10 were then used to load the agarose pads.
Agarose pads were prepared with a volume of 5 mL of M9 minimal medium and 0.075 g of agarose. It was dissolved by vortexing and microwaving. The pads were then allowed to solidify for about 1 h at room temperature before seeding bacteria. 2 µL of each culture were then used to load the pads. They were kept for about 15 min at room temperature so that cells can be absorbed into the agarose. Just before characterization with the microscope, 2.5 µL salicylate from a solution 0.1 M was used to induce cells in solid medium, having estimated the volume of the agarose pad in 50 µL (resulting concentration of salicylate about 5 mM).
In each pad, fields with an adequate initial density of cells were chosen, the first photo was taken, and salicylate was added. Photos were taken for each field every 12 minutes.

Analysis of single cell images
Microscopy photos were segmented and analyzed using the EBImage package for R from Bioconductor. Segmentation allowed us to identify sets of pixels belonging to individual cells, and measure the average apparent YFP and CFP intensities for each of these sets. YFP or the ratio YFP/CFP was used as proxy for system activity. It was normalized by subtracting the initial value, and then dividing by the final value, obtaining a dynamics that goes from 0 to 1.

Bottom-up mathematical model
We constructed a system of ordinary differential equations (ODEs) by knowing the topology of the circuit. MarR, MarA and MarB form an operon controlled by promoter P mar (Alekshun & Levy, 1997;Chubiz et al., 2012). MarR represses P mar , which can be modulated by salicylate (Cohen et al., 1993). MarB also represses P mar (Vinué et al., 2013), whereas MarA activates it (Martin et al., 1996). On the other hand, Rob is controlled by promoter P rob , and it activates P mar (Alekshun & Levy, 1997). MarA and Rob repress P rob (Schneiders & Levy, 2006). Finally, in our system YFP models a downstream gene controlled by promoter P mar . Although MarR, MarA and MarB are transcribed from the same promoter, the corresponding protein expressions may be different each other due to distinct translation rates. By analyzing the 5' untranslated regions of MarR, MarA and MarB with RBS calculator (Salis et al., 2009), considering the 30 nucleotides upstream and the 7 nucleotides downstream of the start codon, we found that translation rates of MarA and MarB are about 30fold and 20-fold, respectively, higher than the translation rate of MarR. This is in tune with previous experimental observations (Martin & Rosner, 2004). In addition, promoter P mar is regulated by CRP-cAMP. Here, we do not consider the moderate activation of Rob by salicylate (Chubiz et al., 2012), because this protein is highly expressed and then a moderate increase in it will not significantly impact the results.
Therefore, we could write where µ is the cell growth rate, d the degradation rate of MarA (d >> µ), noting that MarA is quickly degraded by protease Lon (Griffith et al., 2004), b (and b * ) the fold increase of MarA (MarB) translation rate, and P mar and P rob the activity of promoters P mar and P rob , respectively.
In this work, we considered a ∆rob scenario to precisely study the antagonistic autoregulatory motif implemented by MarR and MarA. Also, we neglected the effect of MarB 4 . The equation for P mar , knowing that MarA acts as a monomer whereas MarR as a dimer (Martin et al., 1996), could be approached by a Hill function (Bintu et al., 2005). Therefore, it turned out where K A , and K R are the effective dissociation constants for transcription regulation, and r the activation fold change. P 0 is the basal protein synthesis rate.
In addition, we have where q S is the effective dissociation constant between salicylate (Sal) and MaR, n S the Hill coefficient, and a the minimal fraction of free MarR.

Simplification of the mathematical model
Our bottom-up mathematical model can be simplified for a better analysis of the dynamic response. By noting we could write a simplified system of ODEs. Thus, we obtained where MarA could be approached to a quasi-steady state ( € x ∝ π mar , a function of time). And also we had In case of maximal induction of the system with salicylate, a modulates the regulatory role of MarR. To obtain dimensional parameters, see Table S1 for values of K R and K A .

An extended model including mRNA
Our bottom-up mathematical model can be extended to account for the mRNA (r), the same molecule for MarA and MarR. Thus, we wrote having assumed a degradation rate of the mRNA of 4d. Note that if we consider dr / dt = 0, we recover the previous model.

Stochastic modeling
Using a Langevin approach 5 , our ODE-based mathematical model can be extended to account for the inherent stochasticity of biological systems. Because in bacteria noise has two components (intrinsic and extrinsic) and is predominantly generated at the transcription level (Swain et al., 2002), we considered a stochastic process x s (where s is the inverse of the correlation time) with statistics ξ s (t) = 0 and we have the stochastic process that describes intrinsic noise (very rapid fluctuations), while with s = µ, we have the one that describes extrinsic noise (slow fluctuations). Thus, and having assumed similar mRNA degradation and MarR translation rates [note that x d is a stochastic process associated to intrinsic noise at the mRNA level, which is translated to generate intrinsic noise at the protein level; see Rodrigo et al. (2013)], we can write where q is the extrinsic noise magnitude. This system can be solved numerically by following the method described by Rodrigo et al. (2011). 5 The Langevin approach is based on the construction of an Itô stochastic differential equation (Gillespie, 2000).
The master equation that is useful to represent the stochasticity of biochemical systems is indeed equivalent to the Langevin equation for an appropriate random force (Bedeaux, 1977). The Langevin approach, however, allows maintaining the ODE formalism and even introducing easily noises with particular correlation times. Promoter activity is highest in the wild-type system, then higher in the ∆rob system   Table S1, except for p 0 because here we considered p 0 r = 1 (constant) to maintain the same expression level in all cases.

Supplementary Figures and Figure Legends
This plot shows, on the one hand, that when a approaches to 0 the response time increases because of the lack of active repressor. On the other hand, it shows that when r increases the response time also does because the dynamics is delayed.  Table S1.   Table S1. Note that whilst competition between regulators can lead to pulsatile dynamics with different periods and amplitudes, the noncompetitive scenario, provided some nonlinearity, mainly shows a characteristic period and a limited amplitude (Munteanu et al., 2010). In green, we represent noise in gene expression (coefficient of variation). In blue, we show the dynamics in the deterministic regime (which approximates very well to the average).  (Table S1). Dynamic response of the system upon induction with different concentrations of salicylate (top, ∆rob system; bottom, ∆rob∆marA system). We represent the normalized fluorescence (YFP) with time. Error bars represent standard deviations. Figure S11: Experimental results of control to assess the dynamic behavior of the system.
(A) Growth curves for different levels of salicylate (∆rob system). Cells are in exponential growth phase up to 3 h (then they start entering in saturation), with R 2 > 0.94 in all cases by fitting Absorbance to exp(µt). For 5 mM salicylate, we obtained µ = 0.43 h -1 and R 2 = 0.98. These curves also show that salicylate (especially those levels higher than 1 mM) produces a cost.
(B) Normalized CFP fluorescence with time (∆rob system). CFP is expressed from a constitutive promoter, then its expression should be constant with time and 26 independent of salicylate. These curves show that there is a slight dependence with time and salicylate, perhaps influenced by evaporation or by the growth rate (Klumpp et al., 2009). However, this has not a significant impact on the dynamics of the mar circuit.  Knowing that q = h ex p mar (2/µ) 1/2 Swain et al., 2002