Growth‐mediated negative feedback shapes quantitative antibiotic response
2022; Springer Nature; Volume: 18; Issue: 9 Linguagem: Inglês
10.15252/msb.202110490
ISSN1744-4292
AutoresS. Andreas Angermayr, Tin Yau Pang, Guillaume Chevereau, Karin Mitosch, Martin J. Lercher, Tobias Bollenbach,
Tópico(s)Evolution and Genetic Dynamics
ResumoArticle20 September 2022Open Access Source DataTransparent process Growth-mediated negative feedback shapes quantitative antibiotic response S Andreas Angermayr S Andreas Angermayr orcid.org/0000-0001-8619-2223 Institute for Biological Physics, University of Cologne, Cologne, Germany Institute of Science and Technology Austria, Klosterneuburg, Austria Contribution: Conceptualization, Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review & editing Search for more papers by this author Tin Yau Pang Tin Yau Pang orcid.org/0000-0003-4738-4032 Institute for Computer Science, Heinrich Heine University Düsseldorf, Düsseldorf, Germany Department of Biology, Heinrich Heine University Düsseldorf, Düsseldorf, Germany Contribution: Formal analysis, Investigation, Writing - review & editing Search for more papers by this author Guillaume Chevereau Guillaume Chevereau INSA de Strasbourg, Strasbourg, France Contribution: Data curation, Formal analysis, Writing - review & editing Search for more papers by this author Karin Mitosch Karin Mitosch Institute of Science and Technology Austria, Klosterneuburg, Austria Genome Biology Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany Contribution: Investigation, Methodology, Writing - review & editing Search for more papers by this author Martin J Lercher Martin J Lercher orcid.org/0000-0003-3940-1621 Institute for Computer Science, Heinrich Heine University Düsseldorf, Düsseldorf, Germany Department of Biology, Heinrich Heine University Düsseldorf, Düsseldorf, Germany Contribution: Formal analysis, Supervision, Writing - review & editing Search for more papers by this author Tobias Bollenbach Corresponding Author Tobias Bollenbach [email protected] orcid.org/0000-0003-4398-476X Institute for Biological Physics, University of Cologne, Cologne, Germany Center for Data and Simulation Science, University of Cologne, Cologne, Germany Contribution: Conceptualization, Resources, Data curation, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Writing - original draft, Project administration, Writing - review & editing Search for more papers by this author S Andreas Angermayr S Andreas Angermayr orcid.org/0000-0001-8619-2223 Institute for Biological Physics, University of Cologne, Cologne, Germany Institute of Science and Technology Austria, Klosterneuburg, Austria Contribution: Conceptualization, Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review & editing Search for more papers by this author Tin Yau Pang Tin Yau Pang orcid.org/0000-0003-4738-4032 Institute for Computer Science, Heinrich Heine University Düsseldorf, Düsseldorf, Germany Department of Biology, Heinrich Heine University Düsseldorf, Düsseldorf, Germany Contribution: Formal analysis, Investigation, Writing - review & editing Search for more papers by this author Guillaume Chevereau Guillaume Chevereau INSA de Strasbourg, Strasbourg, France Contribution: Data curation, Formal analysis, Writing - review & editing Search for more papers by this author Karin Mitosch Karin Mitosch Institute of Science and Technology Austria, Klosterneuburg, Austria Genome Biology Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany Contribution: Investigation, Methodology, Writing - review & editing Search for more papers by this author Martin J Lercher Martin J Lercher orcid.org/0000-0003-3940-1621 Institute for Computer Science, Heinrich Heine University Düsseldorf, Düsseldorf, Germany Department of Biology, Heinrich Heine University Düsseldorf, Düsseldorf, Germany Contribution: Formal analysis, Supervision, Writing - review & editing Search for more papers by this author Tobias Bollenbach Corresponding Author Tobias Bollenbach [email protected] orcid.org/0000-0003-4398-476X Institute for Biological Physics, University of Cologne, Cologne, Germany Center for Data and Simulation Science, University of Cologne, Cologne, Germany Contribution: Conceptualization, Resources, Data curation, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Writing - original draft, Project administration, Writing - review & editing Search for more papers by this author Author Information S Andreas Angermayr1,2,8, Tin Yau Pang3,4, Guillaume Chevereau5, Karin Mitosch2,6, Martin J Lercher3,4 and Tobias Bollenbach *,1,7 1Institute for Biological Physics, University of Cologne, Cologne, Germany 2Institute of Science and Technology Austria, Klosterneuburg, Austria 3Institute for Computer Science, Heinrich Heine University Düsseldorf, Düsseldorf, Germany 4Department of Biology, Heinrich Heine University Düsseldorf, Düsseldorf, Germany 5INSA de Strasbourg, Strasbourg, France 6Genome Biology Unit, European Molecular Biology Laboratory (EMBL), Heidelberg, Germany 7Center for Data and Simulation Science, University of Cologne, Cologne, Germany 8Present address: CeMM Research Center for Molecular Medicine of the Austrian Academy of Sciences, Vienna, Austria *Corresponding author. Tel: +49 221 470 1621; E-mail: [email protected] Molecular Systems Biology (2022)18:e10490https://doi.org/10.15252/msb.202110490 PDFDownload PDF of article text and main figures. Peer ReviewDownload a summary of the editorial decision process including editorial decision letters, reviewer comments and author responses to feedback. ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InMendeleyWechatReddit Figures & Info Abstract Dose–response relationships are a general concept for quantitatively describing biological systems across multiple scales, from the molecular to the whole-cell level. A clinically relevant example is the bacterial growth response to antibiotics, which is routinely characterized by dose–response curves. The shape of the dose–response curve varies drastically between antibiotics and plays a key role in treatment, drug interactions, and resistance evolution. However, the mechanisms shaping the dose–response curve remain largely unclear. Here, we show in Escherichia coli that the distinctively shallow dose–response curve of the antibiotic trimethoprim is caused by a negative growth-mediated feedback loop: Trimethoprim slows growth, which in turn weakens the effect of this antibiotic. At the molecular level, this feedback is caused by the upregulation of the drug target dihydrofolate reductase (FolA/DHFR). We show that this upregulation is not a specific response to trimethoprim but follows a universal trend line that depends primarily on the growth rate, irrespective of its cause. Rewiring the feedback loop alters the dose–response curve in a predictable manner, which we corroborate using a mathematical model of cellular resource allocation and growth. Our results indicate that growth-mediated feedback loops may shape drug responses more generally and could be exploited to design evolutionary traps that enable selection against drug resistance. Synopsis Growth-rate dependent sensitivity of E. coli to the antibiotic trimethoprim leads to a negative feedback loop that explains the extreme shallowness of the dose-response curve. This feedback loop is mediated by the regulation of the drug target dihydrofolate reductase (DHFR). Reducing the growth rate generally renders E. coli less sensitive to the antibiotic trimethoprim. This effect leads to a negative feedback loop, which causes the extreme shallowness of the trimethoprim dose-response curve. Growth-rate dependent regulation of the drug target dihydrofolate reductase (DHFR) mediates this feedback loop. A mathematical model of cellular resource allocation accurately captures these phenomena. Introduction Dose–response curves are a central concept in systems biology and essential for understanding emergent nonlinear phenomena at different scales. A prime example is bacterial gene regulation where cooperativity of transcription factor binding to promoter regions governs the steepness of dose–response curves that characterize gene expression as a function of transcription factor concentration (Bintu et al, 2005). Negative feedback can reduce the steepness of dose–response curves of gene expression, i.e., change their shape from sigmoidal to linear (Nevozhay et al, 2009). The steepness of transcription factor dose–response curves ultimately determines whether feedback loops in genetic circuits can produce biologically relevant functions such as bistability or oscillations (Elowitz & Leibler, 2000; Gardner et al, 2000). At the population level, the bacterial response to antibiotics is captured by similar dose–response curves that quantify the dependence of growth rate on drug concentration. Antibiotic dose–response curves are routinely measured to characterize antibiotic susceptibility via the minimal inhibitory concentration (MIC) or the concentration leading to 50% growth inhibition (IC50), two classic quantities to describe antibiotic efficacy. However, the quantitative shape of the antibiotic dose–response curve – especially its steepness – and its implications are underappreciated. The steepness of the dose–response curve varies drastically between antibiotics. For many antibiotics, the growth rate drops gradually from high to low as the drug concentration is increased (Fig 1A); in particular, this is the case for antibiotics targeting DNA replication at the gyrase (e.g. ciprofloxacin) or antibiotics targeting translation at the ribosome (e.g. tetracycline). Beta-lactams like mecillinam (an antibiotic targeting cell wall biosynthesis at a penicillin binding protein) have extremely steep dose–response curves where just a slight relative increase in drug concentration – by about two-fold – causes an abrupt transition from full-speed growth to near-zero net growth (Fig 1A). At the other end of the spectrum, the folic acid synthesis inhibitor trimethoprim (TMP) has an extremely shallow dose–response curve (Palmer & Kishony, 2014; Chevereau et al, 2015; Rodrigues et al, 2016; Russ & Kishony, 2018): Reducing growth from full speed to zero with TMP requires a more than 100-fold increase in drug concentration (Fig 1A). In general, dose–response curves are well approximated by Hill functions and the Hill slope n ("dose-sensitivity") is a quantitative measure of their steepness (Chou & Talalay, 1983; Regoes et al, 2004; Chevereau et al, 2015): TMP has n ≈ 1.1 , while most antibiotics fall in the range 1.8 ≤ n ≤ 3.5 , and beta-lactams such as mecillinam have n > 6 (Fig 1A). Figure 1. Trimethoprim exhibits an extremely shallow dose response curve and its efficacy correlates strongly with growth rate compared to other antibiotics A. Dose–response curves (normalized growth rate as a function of drug concentration) for different antibiotics. Growth rate was measured via optical density measurements over time (Materials and Methods). Antibiotics used: Trimethoprim (TMP), tetracycline (TET), chloramphenicol (CHL), ciprofloxacin (CPR), lincomycin (LIN), nitrofurantoin (NIT), and mecillinam (MEC). The TMP dose–response curve (dark blue) is by far the shallowest. Lines are fits of the Hill function g c g 0 = 1 1 + c I C 50 n to the data. Drug concentrations were arbitrarily rescaled to better visualize dose–response curve steepness; for unscaled dose–response curves, see Appendix Fig S13. Error bars show standard deviation of 12 biological replicates. B. Schematic: Effect of growth-mediated feedback loops on dose–response curves. Negative feedback (blue) renders the dose–response curve shallower than in the absence of feedback (gray); positive feedback (red) steepens the dose–response curve. C. Density scatterplot showing growth response to TMP versus normalized drug-free growth rate for 3,913 gene deletion strains (Baba et al, 2006); these are essentially all viable gene deletion strains in E. coli, no selection of strains was made. These gene deletion strains exhibit diverse growth rates, offering an unbiased way to test the relation between the drug-free growth rate and the response to antibiotics. Response is defined as growth rate in the presence of TMP normalized to the drug-free growth rate of the respective deletion strain. TMP was used at a fixed concentration that inhibits wild type growth by about 30% (Chevereau et al, 2015). Spearman correlation coefficient ρ s is shown. D. Bar chart showing negative Spearman correlation coefficients − ρ s compared across antibiotics (Appendix Fig S1). Error bars show bootstrap standard error of ρ s . TMP (blue) exhibits by far the strongest negative correlation, indicating the existence of a particularly strong growth-mediated negative feedback loop for this antibiotic. Source data are available online for this figure. Source Data for Figure 1 [msb202110490-sup-0003-SdataFig1.zip] Download figure Download PowerPoint The steepness of the dose–response curve strongly affects the evolution of resistance by spontaneous mutations (Hermsen et al, 2012; Chevereau et al, 2015). Resistance mutations that slightly increase the MIC provide greater fitness benefits for drugs with a steep dose–response curve compared to drugs with a shallow curve, implying a greater chance to fix in the population. Thus, all else being equal, the rate of resistance evolution for a drug increases with the steepness of its dose–response curve – a trend that is observed in evolution experiments (Chevereau et al, 2015). This effect is strongest for drug concentrations near the IC50, occurring, for example, when populations of motile bacteria evolve resistance in spatial drug gradients where growth takes place primarily at a population front located in the region with drug concentrations that partially, but not completely, inhibit growth (Baym et al, 2016; Hol et al, 2016). Despite their fundamental relevance for resistance evolution and bacterial responses to antibiotics, the mechanisms that shape the dose–response curve are largely unknown. Feedback loops mediated by growth rate may play a key role in shaping the dose–response curve (Deris et al, 2013; Greulich et al, 2015). The action of antibiotics affects bacterial growth but the inverse is also true: Slower growing bacteria are less rapidly killed by antibiotics targeting cell wall biosynthesis (beta-lactams; Tuomanen et al, 1986; Lee et al, 2018) and non-growing (persister) cells are fully protected from many antibiotics (Balaban et al, 2004), offering a possibility to evade antibiotic treatments. However, it is not clear if there is a more general relation between the drug-free growth rate and common measures of antibiotic efficacy (such as MIC or IC50) that would generalize this trend across drug classes for both bacteriostatic and bactericidal antibiotics. Recent findings further suggest that antibiotic lethality depends on bacterial metabolic state rather than growth rate alone (Lopatkin et al, 2019). Slower growth caused by nutrient limitation affects the bacterial susceptibility to ribosome-targeting antibiotics but the IC50 changes in opposite ways with increasing drug-free growth rate for different ribosome inhibitors: it decreases for tetracycline and chloramphenicol but increases for streptomycin and kanamycin (Greulich et al, 2015). In engineered strains expressing a constitutive resistance gene, a positive feedback loop leads to high dose-sensitivity and even bistability (i.e. co-existence of growing and non-growing cells) in the presence of the ribosome-targeting antibiotic chloramphenicol (Deris et al, 2013). Positive feedback occurs as faster growth leads to the upregulation of the resistance enzyme, which in turn enables even faster growth. Growth-mediated feedback loops could more generally explain the drastic differences in dose-sensitivity between antibiotics (Fig 1A) with positive feedback producing higher (Deris et al, 2013) and negative feedback lower dose-sensitivity. However, such feedback loops shaping the dose–response curve of sensitive wild-type bacteria have not yet been characterized. Here, we establish that negative growth-mediated feedback produces an extremely shallow drug dose–response curve. Focusing on TMP, we vary bacterial growth rates by diverse environmental and genetic perturbations and show that, in contrast to most other antibiotics we investigated, slower growth generally lowers the susceptibility of Escherichia coli to this antibiotic. The molecular origin of this phenomenon lies in the expression of the drug target, which is upregulated in response to TMP but also when the growth rate is lowered by other means: TMP lowers growth, which in turn reduces susceptibility to TMP. We show that synthetically reversing this feedback loop can drastically steepen the dose–response curve. The negative feedback loop leads to a seemingly paradoxical situation where adding the antibiotic can even enhance growth under extreme nutrient limitations. It can be envisioned that such growth-mediated feedback loops in drug responses could be used to design evolutionary traps that invert selection for resistance. Results Growth-mediated feedback loops can affect the dose–sensitivity of drugs We hypothesized that a growth-mediated negative feedback loop could explain the shallowness of the dose–response curve of TMP. We focused on TMP because it had by far the shallowest dose–response of all antibiotics we investigated (Fig 1A). As an antibiotic, TMP lowers bacterial growth (by inhibiting dihydrofolate reductase, DHFR, encoded by folA). If a lower growth rate in turn protects bacteria from TMP, the resulting growth-mediated negative feedback loop could lead to a shallow dose–response curve (Fig 1B). In contrast, for antibiotics where faster growth protects bacteria, positive growth-mediated feedback leads to ultrasensitivity (Fig 1B) and can even produce bistability as previously reported (Elf et al, 2006; Deris et al, 2013). These results show that growth-mediated feedback loops can affect the dose-sensitivity of drugs in general. Slower growth generally lowers susceptibility to TMP and steepens its dose–response curve To test experimentally whether negative growth-mediated feedback underlies the shallow TMP dose–response curve, we varied the growth rate in several independent ways and investigated its effect on TMP susceptibility compared with susceptibility to other antibiotics. We first made use of a purely genetic way of varying growth. Specifically, we exploited the growth rate variability resulting from genome-wide gene deletions to expose global trends that are independent of the specific effects of individual gene deletions. Non-essential gene deletions often reduce the drug-free growth rate – some by up to ∼50% (Chevereau et al, 2015). We re-analyzed a dataset of growth rates of ∼4,000 E. coli gene deletion mutants under different antibiotics representing common modes of action (Chevereau & Bollenbach, 2015); this analysis was genome-wide and not restricted to a smaller sample of gene deletion mutants, minimizing potential bias. Growth rates were measured at concentrations that inhibit the reference strain by ∼30% to ensure that (i) most gene deletion strains exhibit significantly reduced growth compared to no drug and (ii) most gene deletion strains that are more sensitive to the antibiotic than the wild type still grow exponentially, allowing quantitative analysis. While each gene can have specific effects for each antibiotic (Nichols et al, 2011; Chevereau et al, 2015), most genes should be unrelated to the drug's mode of action. The global trend of drug susceptibility across all gene deletion strains can thus reveal general consequences of growth inhibition, independent of the specific cellular limitation causing the growth rate reduction. Non-specific growth rate changes caused by gene deletions indicate that slower growth protects E. coli from TMP but less so from other antibiotics. By correlating the drug-free growth rate of deletion strains with their growth rate in the presence of drugs, we revealed the dependencies of drug susceptibility on the drug-free growth rate. The clearest trend emerged for TMP: Its relative effect on growth was weaker in gene deletion strains that had lower growth rates in the absence of drugs (Spearman correlation ρ s = − 0.6 ; Fig 1C). Compared to other antibiotics, this effect was most pronounced for TMP (Fig 1D and Appendix Fig S1). Slower-growing mutants can grow at increased TMP concentrations: While it was technically not feasible to study this genome-wide, full dose–response curve measurements for a smaller set of 78 arbitrarily selected gene deletion mutants showed that the IC50 is weakly negatively correlated with the growth rate in the absence of drug for TMP ( ρ s = − 0.27 , p = 0.019 ) but this correlation is not significantly different from zero for other antibiotics (Appendix Fig S2). Thus, TMP represents an extreme case, both in terms of dose-sensitivity and in terms of susceptibility-dependence on growth rate. Overall, these results suggest that slower growth generally lowers the susceptibility to TMP. Slow growth can also protect E. coli from other antibiotics but to a far lesser extent. For the prodrug nitrofurantoin (NIT) and the translation inhibitors tetracycline (TET) and chloramphenicol (CHL), there was a weak negative correlation between the drug-free growth rate and that in the presence of the drug ( ρ s = − 0.31 for NIT, ρ s = − 0.26 for TET, ρ s = − 0.22 for CHL; Fig 1D; Appendix Fig S1). For the beta-lactam mecillinam (MEC), this trend was even weaker ( ρ s = − 0.14 ) and for ciprofloxacin (CPR) almost entirely absent ( ρ s = − 0.05 ). There appears to be a tendency for the magnitude of this negative correlation to decrease with increasing dose-sensitivity when compared among drugs (Fig 1A and D), although this trend is not significant due to the limited number of different drugs and the outliers NIT and CPR deviate from this trend. Although other factors certainly contribute to the shape of dose–response curves, this observation supports the notion that growth-mediated feedbacks are an important contributor to the shape of the dose–response curve for TMP (Fig 1B) and possibly for other antibiotics as well. Reducing growth rate by other means like a nutrient limitation or imposing a protein burden also protects E. coli from TMP but less so from other antibiotics. To systematically determine how the efficacy of different antibiotics changes with drug-free growth rate, we used several independent approaches to change the growth rate. First, we used glucose limitation in batch culture by adding a non-metabolizable structural analog of glucose, α-methyl glucoside, in varying concentrations to the growth medium. This analog competes with glucose for uptake into the cell, but unlike glucose it cannot be utilized for growth (Hansen et al, 1975). Second, we used different carbon sources (glucose, fructose, mannose, glycerol, and galactose) in the growth medium, which is a classic strategy to test for growth-dependent effects (Bremer & Dennis, 2008). Third, we overexpressed a gratuitous protein from an inducible promoter to burden the cells (Dong et al, 1995; Scott et al, 2010). These approaches have different physiological consequences, but they all reduce the growth rate in a gradual and controlled manner, while the maximal growth rate and the accessible dynamic range of relative growth inhibition vary between them (Fig 2). Although TMP can kill bacteria under certain nutrient conditions by causing thymineless death, it can only stop the growth and cause cell stasis in minimal media (Kwon et al, 2010). In our experiments, the relevant TMP concentrations are below the MIC and very few cells die, as confirmed by time-lapse imaging of individual cells in a microfluidic chamber (Appendix Fig S16). This facilitates the interpretation of the data, as the growth rate and the death rate no longer need to be measured separately. Collectively, the three different approaches we used enable us to vary growth rate over a wide range and identify general effects of growth rate, which occur independently of the exact cause of the growth rate reduction. Figure 2. Slower growth generally lowers the efficacy of trimethoprim but not other antibiotics A. Growth rate under glucose limitation achieved by adding the non-metabolizable structural glucose analog α-methyl glucoside (αMG) at different ratios to glucose in a minimal medium (Materials and Methods). B. Normalized growth rate (gray scale) from a checkerboard assay in a two-dimensional concentration gradient of TMP and αMG. Dashed black line shows contour line of 90% growth inhibition (IC90 line). Red arrow shows increase in IC90 as growth is lowered. Inset: Normalized growth rate as a function of TMP concentration along the column marked in blue. C. Fold-change in IC90 at αMG/glucose ratio 2.5 in assays as in (B) for different antibiotics (Appendix Fig S5). Lowering growth rate increases IC90 for TMP but not for other antibiotics. D. Growth rate in rich medium (LB) under different levels of overexpression of a gratuitous protein from a T5-lac promoter; overexpression burden is controlled by IPTG concentration (Materials and Methods). E. As (B) but for growth rate reduction by protein overexpression in a two-dimensional concentration gradient of TMP and IPTG. F. Fold-change in IC90 at 1.25 mM IPTG in assays as in (E) for different antibiotics (Appendix Fig S6). Overexpression of unnecessary protein increases IC90 for TMP by almost five-fold; no comparable increase occurs for other antibiotics. G. Growth rate in minimal medium containing different carbon sources (Materials and Methods): Glucose (GLU), fructose (FRU), mannose (MAN), galactose (GAL), and glycerol (GLY). H. Normalized growth rates (gray scale) on different carbon sources (x-axis) at different TMP concentrations (y-axis). I. Fold-change in IC90 in assays as in (H) for different antibiotics (Appendix Fig S7). Data information: Error bars in (A, D and G) show standard deviation from 6, 12, and 18 biological replicates, respectively; day-to-day reproducibility of growth rate measurements is high (Appendix Fig S3). Error bars in (C and F) show standard deviation from three neighboring αMG/glucose ratios and IPTG concentrations centered at 2.5 and 1.25 mM, respectively. IPTG alone has no detectable effect on growth at these concentrations (Appendix Fig S4). Error bars in (I) show standard deviation from three biological replicates. Antibiotic abbreviations are as in Fig 1. CHL was not used in the protein overexpression assay in (F) since the plasmid used for overexpression has a CHL-resistance marker (Materials and Methods). Sample growth curves are in Appendix Fig S11. The same analysis for the IC50 instead of IC90 and a different normalization of the dose–response curves is shown in Appendix Fig S15. Source data are available online for this figure. Source Data for Figure 2 [msb202110490-sup-0004-SdataFig2.zip] Download figure Download PowerPoint TMP inhibits growth less under glucose limitation: Lowering the growth rate by glucose limitation enabled bacteria to grow at slightly increased TMP concentrations (Fig 2B and C). This trend was reflected in an increase in IC90 and IC50, whether these concentrations were defined in terms of the highest drug-free growth rate (Fig 2) or in terms of the drug-free growth rate at each level of glucose depletion (Appendix Fig S15). The observed increases were even more pronounced when growth was lowered by overexpressing a gratuitous protein – a truncated and inactive version of tufB (Dong et al, 1995) expressed from a synthetic promoter PLlacO-1 (Lutz & Bujard, 1997) induced by addition of isopropyl β-D-1-thiogalactopyranoside (IPTG; Fig 2D–F and Appendix Fig S15). Reducing growth by using different carbon sources in a minimal medium could also slightly protect bacteria from TMP, in particular for glycerol (Fig 2G–I and Appendix Fig S15). Changing carbon sources had modest effects, presumably because even the highest growth rate (achieved with glucose only) is relatively low and the fold-change in growth is considerably smaller than for glucose limitation (Fig 2A, D and G). These effects did not occur to a comparable extent for other antibiotics representing common modes of action (Fig 2C, F and I); however, gratuitous protein overexpression also lowered the susceptibility to mecillinam (MEC), albeit to a lesser extent (Fig 2F and Appendix Fig S6), consistent with the established effect of growth rate on beta-lactam efficacy (Tuomanen et al, 1986; Lee et al, 2018). The effects of growth rate changes were clearly drug-specific and strongest for TMP. Under severe glucose limitation (high ratios of α-methyl glucoside over glucose), which does not support growth, the addition of TMP even rescued bacteria and enabled them to grow again (Fig 2B). As a result, the TMP dose–response curve in this regime has a very unusual non-monotonic shape (inset in Fig 2B) that is hard to interpret in comparison with conventional dose–response curves of Hill-function shape. Therefore, we restricted further analysis of the effects of drug-free growth rate on the quantitative shape of the TMP dose–response curve to lower ratios of α-methyl glucoside over glucose. The non-monotonic dose–response curve indicates that, under extreme nutrient limitation, the antibiotic TMP can paradoxically promote bacterial growth (inset in Fig 2B) – perhaps the most drastic il
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