Antibiotic transport kinetics in Gram-negative bacteria revealed via single-cell uptake analysis and mathematical modelling

: 1 The double-membrane cell envelope of Gram-negative bacteria is a formidable barrier to intracellular 3 antibiotic accumulation. A quantitative understanding of antibiotic transport in these cells is crucial for 4 drug development, but this has proved elusive due to the complexity of the problem and a dearth of 5 suitable investigative techniques. Here we combine microfluidics and time-lapse auto-fluorescence 6 microscopy to quantify antibiotic uptake label-free in hundreds of individual Escherichia coli cells. By 7 manipulating the microenvironment, we showed that drug (ofloxacin) accumulation is higher in growing 8 versus non-growing cells. Using genetic knockouts, we provide the first direct evidence that growth 9 phase is more important for drug accumulation than the presence or absence of individual transport 10 pathways. We use our experimental results to inform a mathematical model that predicts drug 11 accumulation kinetics in subcellular compartments. These novel experimental and theoretical results 12 pave the way for the rational design of new Gram-negative antibiotics.

these different pathways is often strongly regulated by the surrounding microenvironment 5 and can vary 23 from cell to cell 6 . Due to the many complexities of studying these transport problems, biophysical and 24 mathematical modelling has been used extensively to uncover detailed features of molecular transport in 25 synthetic model systems. For instance, a mathematical study of hydrodynamic entrance effects showed 26 that the hourglass shape of aquaporins might be a result of natural selection processes optimizing water 27 permeability 7 . One-dimensional diffusional models, both theoretical 8 and experimental 9 have been used 28 to shed light on the single-file motion of particles through narrow constrictions, simulating molecular 29 transport through biological nanopores. Colloidal model systems have been used to investigate Brownian 30 dynamics in biomimetic systems 10 , with recent reports showing the breakdown of transition-path-time 31 symmetry on molecular and meso-scales out of equilibrium 11 . 32 33 However, these molecular-scale modelling studies do not capture the kinetics of substrate uptake in living 34 cells and, from a biomedical perspective, a key transport challenge involves quantitatively understanding 35 the intracellular uptake of antibiotics in bacteria 12,13 . Antibiotic failure in the treatment of microbial 36 infections is predicted to cause 10 million deaths annually by 2050 14 . Gram-negative bacterial infections 37 are of particular concern, due to the protection against antibiotics provided by their complex double- 38 membrane cell envelopes ( Figure 1A). These structures include an asymmetric outer membrane that Figure S6. We quantify drug dosage precisely via its fluorescence (SI Note 1) in every experiment. 115 Further, we performed cellular autofluorescence controls in the absence of the drug and show that this 116 has a negligible effect on our results (SI Note 2). 117 118 We observe an increase in cellular drug fluorescence within seconds after the arrival of the drug in the 119 vicinity of the cells. Please note that previous population-level studies have shown biphasic ofloxacin 120 uptake in E. coli over longer timescales of up to an hour 33 , but here we focus our attention on the initial 121 stages of drug uptake, studying the immediate cellular response to drug dosage (t ≤ 400 s) at the single-122 cell level. 123 124 1. Growing bacteria accumulate more ofloxacin than non-growing bacteria: 125 126 Comparing growing versus non-growing PS cells (Figure 2A From Figure 2A and 2C, we also observe that the growing ompF mutant strain accumulates lower 139 amounts of ofloxacin than the PS (growing) over the timescales investigated. This is quantified in Figure   140 3 (ompF: norm. fluor. = 0.20 ± 0.11, mean ± s.d., N = 250; PS: norm. fluor. = 0.34 ± 0.11, N = 317, 141 mean ± s.d.; p<10 -10 ); knocking out the OmpF porin thus lowers the ability of ofloxacin to permeate into 142 the cell compared to the parental strain. Our result agrees with previous reports that show that OmpF 143 facilitates fluoroquinolone transport across Gram-negative outer membranes 3,24 .
3. Knocking out tolC does not increase ofloxacin accumulation compared to the PS: 146 147 Interestingly, we were unable to detect an increase in ofloxacin accumulation in growing tolC mutant 148 cells compared to the PS at the 400 s time-point ( Figure 3). In fact, as reported above, we measured a 149 small decrease in the drug fluorescence in growing tolC cells compared to the growing PS cells (tolC: 150 norm. fluor. = 0.31 ± 0.08, N = 211, mean ± s.d.; PS: norm. fluor. = 0.34 ± 0.11, N = 317, mean ± s.d.; 151 p=2.7×10 -4 ). This finding is addressed in detail in the Discussion. 152 153 4. Direct comparison reveals that growth phase plays a more significant role in ofloxacin accumulation 154 than knocking out ompF: 155 156 Our ability to directly compare drug accumulation in different metabolic states revealed that the growing 157 ompF mutant strain accumulates more ofloxacin than the non-growing PS (growing ompF: norm. 158 fluor. = 0.20 ± 0.11, mean ± s.d., N = 250; non-growing PS: norm. fluor. = 0.10 ± 0.03, N = 405, mean 159 ± s.d.; p<10 -10 ), suggesting that the growth phase plays an even bigger role than the removal of OmpF in 160 drug uptake. We believe this is the first time such a direct comparison has been performed. These results 161 emphasize the importance of studying the role of the cellular metabolic state in drug uptake. 162 163 5. Ofloxacin uptake is homogeneous across a clonal population: 164 165 A major advantage of single-cell approaches is their ability to quantify heterogeneity (or the lack thereof) 166 in the cellular response to treatment within the individual cells in a population 34 . In order to estimate 167 heterogeneity in drug uptake across the bacteria, we first estimated the variation in cellular fluorescence 168 in the absence of the drug and found a mean coefficient of variation (CV) of approximately 10% (see 169 Methods). We found a similar CV when quantifying the heterogeneity in the cellular fluorescence 170 corresponding to drug uptake. As seen in Figure S6, such variation is representative across the biological 171 repeats. We thus conclude that ofloxacin uptake is homogeneous across the clonal populations that we 172 studied, which is remarkable considering the recent reports on cellular heterogeneity within microbial The quantitative comparisons above provide a static picture regarding the impact of porins, pumps and 179 growth stages on ofloxacin accumulation in Gram-negative bacteria at the whole-cell level. However, the 180 most desirable information concerns the dynamics governed by the kinetics of drug accumulation in 181 different subcellular compartments. It is crucial to understand how much of a drug actually reaches its 182 target which, in the case of ofloxacin, lies in the cytoplasm 36 . However, there are currently no 183 experimental techniques capable of quantifying subcellular drug accumulation at the single-cell level. 184 We therefore turn to theoretical modelling to investigate this process. We rationalize our experimental 185 single-cell drug uptake data via a mathematical model (see Methods), where parameters governing porins 186 ( 0 ) and efflux pumps ( ) are allowed to vary between cells in the population according to a log-normal 187 distribution 37 . The inferred parameter distributions for growing bacteria from the three investigated 188 strains are presented in Figure 4A profiles of the non-growing cells, we chose not to infer model parameters from those experiments.   194  195   Once model parameters were inferred from all the individual experiments (using the corresponding drug   196 dosage profiles for each experiment), we used these parameters in the model to predict drug accumulation 197 in the various subcellular compartments for cells belonging to the three strains ( Figure 4C). In this 198 estimation for Figure 4C, we used an average experimental drug dosage profile (dashed black line, top 199 panel, Figure 4C) as the input. The overlap (or lack thereof) between the [20,80] posterior predictive 200 intervals (shaded regions in Figure 4C) allows us to predict the probability of PS cells having a 201 higher/lower ofloxacin concentration than each of the mutants, at the subcellular level. The pairwise 202 comparisons (at t = 400 s) for the different strains/compartments are presented in Table S4. 203 204 The model predicts that the drug saturates all the binding sites in the outer membrane within 205 approximately 175 s in all three strains. The PS strain has the highest outer membrane drug concentration, 206 with the ompF mutant having an approximately 2.25-fold lower concentration, which corresponds to 207 the fewer binding sites available in the mutant ( Figure 4A). At the end of the experiment, the probability 208 that the PS strain has a higher drug concentration than the ompF mutant in the outer membrane is 0.924; 209 in contrast, between the PS and the tolC mutant, the probability that the PS has more drug in the outer 210 membrane is 0.525, suggesting no appreciable difference (Table S4).

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The periplasm is also predicted to contain approximately 30-fold lower ofloxacin concentrations than the 213 cytoplasm for all three strains at t = 400 sthis is likely due to the binding of the ofloxacin molecules to 214 their targets within the cytoplasm. The model also predicts a lag time of approximately 100 s between 215 drug accumulation in the outer membrane versus drug uptake in the cytoplasm. In the cytoplasm, the 216 difference between the PS and the mutant strains is less obvious. The model predicts that, at the end of 217 the experiment, the PS strain has a probability of 0.719 of having a higher drug concentration in the 218 cytoplasm than the ompF mutant (Table S4). Comparing the PS and the tolC mutant, the 219 corresponding probability is 0.549. Drug uptake in Gram-negative bacteria is an extremely complex biophysical phenomenon because of the 224 different physicochemical pathways and combination of active and passive transport processes involved. 225 However, it is essential to understand the roles of these pathways in a quantitative manner to rationally 226 design drugs that can accumulate in the vicinity of their targets, which will crucially contribute to 227 overcoming the void in Gram-negative drug discovery.

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We have developed a novel combination of experiment and theoretical modelling to tackle the challenge 230 of quantifying antibiotic uptake in single Gram-negative bacteria. Unlike the majority of techniques, 231 which involve complex washing steps after drug delivery, or are limited to certain specific media 232 conditions 12,13 , our microfluidic platform facilitates the study of drug uptake in different 233 microenvironments and cellular metabolic states. We quantify drug dosage in every experiment, which 234 allows us to correct for any variations in fluorescence intensities/flow conditions between experiments. 235 Since we use microfluidics, we quantify drug uptake from the moment the drug arrives in the vicinity of 236 the cells, facilitating the real-time measurement of the transport process.

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It is worth noting that we can measure over a hundred cells in an experiment; by reducing the time 239 resolution it is also possible to correspondingly increase the number of cells measured, since typically 240 . CC-BY 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/645507 doi: bioRxiv preprint thousands of cells are confined in the microfluidic device. This ability will be used in future studies, 241 especially for drugs whose uptake timescales are longer than fluoroquinolones. Since our excitation 242 wavelength is 365 nm, in contrast to previous studies using deep UV illumination to study antibiotic 243 uptake in single cells 20,38 , we can work with standard optics and light sources, rather than needing quartz 244 objectives and cover slips, and deep UV light sources which may not be easily accessible. Although 245 cellular metabolites may also fluoresce at similar wavelengths, we have corrected this by subtracting the 246 baseline cellular fluorescence as described in the Methods (and in SI Note 2). Note that metabolite 247 concentrations are known to fluctuate in response to fluoroquinolone treatment, but this is typically less 248 than a two-fold change within the timescales of our experiment and includes both increases and 249 decreases 39 . The baseline cellular autofluorescence (growing PS cells, Figure S1B) shows typical 250 intensities of approximately 1700 (arb. units), while the fluorescence increases in the cells due to drug 251 accumulation are approximately 5200 (arb. units, Figure S1C). Therefore, we estimate that the maximum  Figure S7 in the SI. This strongly suggests that 275 the differences in ofloxacin uptake that we observe between growing and non-growing cells are due to 276 phenotypic modifications of the cell envelope transport pathways, rather than phenotypic modifications 277 at the drug target level. 278 279 In growing cells, knocking out the ompF gene led to a decrease in drug accumulation compared to the 280 parental strain, in line with previous results 3 , confirming that fluoroquinolones utilize porins to enter E. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/645507 doi: bioRxiv preprint As described in the Results, we did not measure any increase in drug accumulation in the tolC strain. The use of mathematical modelling and Bayesian inference to rationalize our data enabled us to maximize 305 the information embedded in our time-lapse single-cell measurements, leading to predictions of the 306 kinetics of the uptake process. We extracted kinetic parameters corresponding to the single-cell drug 307 uptake profiles and quantified changes in these parameters in the different strains ( Figure 4A-B). To 308 validate our inference procedure, we used data simulated by the model and showed that we can indeed 309 recover the parameter values which were used for generating these (Fig. S8). Importantly, the model 310 allowed us to predict drug accumulation in the different subcellular compartments, which is a major 311 milestone for the entire research community working on this problem. It is important to note that these The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/645507 doi: bioRxiv preprint pathways disabled. Our experimental results showed that the growth phase of the cells, as determined by 337 the nutrient microenvironment, plays a more significant role in ofloxacin uptake than either the porin 338 OmpF or the efflux protein TolC. More generally, this suggests that the metabolic state of the cell is a 339 crucial determinant of cellular drug uptake, which deserves detailed, quantitative investigation in well-340 controlled microenvironments. Combining our data with mathematical modelling and Bayesian inference 341 enabled us to predict the kinetic parameters underlying ofloxacin accumulation in the different 342 subcellular compartments of E. coli cells. This has previously proved extremely challenging primarily 343 due to the small size of typical bacterial cells and the need for complicated washing steps before 344 measuring drug uptake 12,13 , which may bias the results. We used the parameters extracted from fitting 345 the model to our experimental data to predict drug accumulation in the outer membrane, the periplasm 346 and the cytoplasm in parental, ompF and tolC E. coli. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/645507 doi: bioRxiv preprint remained uniform during drug exposure across all experiments and metabolic conditions; it is well known 433 that pH regulates the charge state of fluoroquinolones, which affects their membrane permeabilities 25,50 . 434 The LED was triggered by the camera to ensure that the cells were only exposed to the excitation light 435 during image acquisition. It must be noted that to reduce the background auto-fluorescence at 365 nm, 436 prior to the ofloxacin flush the imaging area was bleached with the excitation light for 5 s. As detailed 437 below, we performed controls (see Figure S2) with propidium iodide staining after UV and ofloxacin 438 exposure to confirm that the UV light used did not compromise the cells' membrane integrity. The centroids of the regions in the binary image resulting from applying this threshold are used to 459 determine the axis of the side channels by using Principal Component Analysis. The axis of the side 460 channels is then used to determine the upper and lower extents of the side-channel-region, which are then 461 used to generate a side-channel-region mask, in addition to two candidate main-channel-region masks. 462 The side-channel-region mask is then used to select bacterial regions from the binary image. The correct 463 channel is identified from the two candidate regions by analysing the fluorescence for the region whose 464 mean signal exhibits the most variation.  Finally, since the cellular auto-fluorescence profiles were flat ( Figure S1B,D), we did not need to correct 501 for this effect when analysing the drug uptake experimental data; we simply subtracted the initial cellular 502 fluorescence (at t = 0) from the cell fluorescence at all the time-points, as detailed above. We should also 503 mention that the automated tracking works better for growing cells than for non-growing cells, which 504 were smaller in size and therefore more difficult to detect. However, this does not significantly affect the We compare this variability in cellular auto-fluorescence with the apparent heterogeneity in drug uptake 521 in the cells in Figure S1A. To estimate this value, we measured the intensity of the cells at the end of the  (Table S2). The parameter 3 was calculated on the basis of passive diffusion measurements 556 of ofloxacin permeability across lipid vesicle bilayers ( Figure S3). To account for any potential binding 557 of the drug to targets within the cytoplasm, we do not assume any equivalence between 3 and 5 , an 558 approach similar to that applied by Westfall et al. 31 ; we only make the assumption that 5 ≤ 3 . 559 Crucially, the parameters ( 1 , 2 , 5 , 0 , , ) were inferred from the experimental data obtained with 560 the PS, ompF and tolC E. coli strains ( Figure S6). The total drug concentration was calculated as: We obtained maximum likelihood estimates (MLEs) of the free model parameters (Table S2) using the 575 medians of the drug uptake profiles for all the cells in an experiment. Please note that for convenience 576 we use the term "population-averaged" throughout the text to refer to these median values of the drug 577 uptake profiles. Since our data was normalized based on the fluorescence of the drug dose (see Methods; 578 image analysis), estimates of parameters 1 , 0 , , incorporate a constant factor related to the 579 concentration of the drug dose (see Table S2). We denote the scaled version of these parameters using    Figures S1-S8   786   Tables S1-S4   787   . CC-BY 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/645507 doi: bioRxiv preprint

Fig. 1. Quantifying and modelling ofloxacin uptake label-free in individual E. coli cells. A)
Schematic of the main processes involved in drug translocation across Gram-negative cell envelopes. Drug molecules penetrate the outer membrane (M) primarily through protein porins, with association and dissociation rates 1 and 2 , respectively. 0 refers to the concentration of functional porin binding sites in the outer membrane. Any residual (non-porin) transport across the outer membrane LPS barrier is modelled with 4 . Drug transport through the inner membrane is modelled with kinetic parameters 3 and 5 . Drug molecules are subject to removal from the cell via active efflux mechanisms which follow Michaelis-Menten kinetics ( , ). B) Schematic of the microfluidic chip used for the ofloxacin uptake experiment. A main channel of height 25 m and width 100 m is used for continuously exchanging the microenvironment with nutrient, drug or dye delivery; cells are confined single-file in a network of side channels whose height and width are both 1.4 m, with length 25 m. C) Section of epifluorescence images showing the delivery of ofloxacin (100×MIC, 12.5 g/ml in PBS) and its corresponding uptake by the cells in the side channels. The ofloxacin molecules within and around the bacteria are tracked using their auto-fluorescence at ex= 365 nm. Scale bar = 5 m. D) Quantitative estimation of the temporal profile of ofloxacin delivery in the chip, and the corresponding ofloxacin uptake profile of 90 individual E. coli cells; the thick red line represents the mean and the grey shaded area the standard deviation of the ofloxacin uptake profiles of the 90 cells investigated. The fluorescence values are reported after correcting for the background and normalizing to the fluorescence of the drug as detailed in the Methods. The complete datasets prior to normalization for the three different E. coli strains investigated are presented in the SI in Figure S6. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/645507 doi: bioRxiv preprint All values are reported after subtracting the background and the initial cellular fluorescence (before drug arrival) as explained in the Methods. For reference, the complete datasets for all strains/conditions including all the biological repeats are provided in Figure S6 in the SI. Dashed lines represent the drug dosage profiles (right Y-axes) in the main channel. These individual drug dosage profiles are provided as inputs when modelling the drug uptake in the corresponding cells in an experiment. The cell fluorescence profiles are shown in red (left Y-axes), along with the mean (thick red line) and standard deviation (grey shading) for all the cells in an experiment. Comparing growing versus non-growing PS bacteria (panels A and B) directly shows that the growing cells accumulate more drug than non-growing cells. This is apparent in the tolC strain as well ( Figure  S6). Comparing the cell fluorescence profiles of growing PS (A), ompF (C) and tolC (D) also clearly shows that the ompF mutant accumulates less ofloxacin than the other two strains. A quantitative analysis of the amount of drug accumulated at the end of the experiments for each strain/condition is provided in Figure 3.
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Fig. 3. Final level of normalized whole cell fluorescence for the different strains and nutritional conditions. (A)
Fluorescence distributions across the different strains and conditions. In the insets, n refers to number of experimental repeats, N reports the total number of bacteria and CV refers to the coefficient of variation of the data. All comparisons are made at t = 400 s. (B) Comparison of data pooled from the different experiments shows that non-growing PS E. coli show significantly lower ofloxacin uptake than growing PS E. coli (p<10 -10 ). This was also true in the tolC strain, where non-growing cells showed significantly lower uptake (p<10 -10 ) than growing cells, suggesting ofloxacin uptake critically depends on the growth phase of the cells within the timescales of our experiment. Growing ompF E. coli showed lower whole cell drug accumulation than growing PS (p<10 -10 ) and tolC (p<10 -10 ) cells, in line with expectations. However, growing ompF E. coli accumulated more ofloxacin than non-growing PS cells (p<10 -10 ), suggesting that the growth phase of the cells as set by the nutrient environment plays an even more important role than the deletion of ompF in drug uptake. The horizontal lines in the interior of the boxes report the medians of the respective distributions. Statistical significance tested using a 2-sample ttest incorporating Welch's correction; the complete set of p-values is reported in the SI (Table S1).
. CC-BY 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/645507 doi: bioRxiv preprint  Figures S4 and S5 respectively. C) Predicted ofloxacin uptake in the different bacterial compartments. Temporal dependence of the normalized drug concentration in the cytoplasm, periplasm and outer membrane for PS (red), ompF (blue) and tolC (green) bacteria in response to the drug dosage input (dashed black line, top panel). These drug uptake profiles were obtained by using the kinetic parameter values in (A) and (B) and the theoretical model (equations (i)-(iii)). The concentrations reported are normalized to the drug dosage concentration (12.5 g/ml ofloxacin). The solid lines correspond to median accumulation in the respective compartments and the shaded area represents the [20,80] posterior predictive interval of the accumulation. The results shown were generated by running the model using 500 independent samples of parameters 0 ′ and ′ from their joint posterior distributions. All other parameters were fixed to the values given in Table S2. The model predicts the saturation of binding sites in the outer membrane. The median saturation concentration in the outer membrane is approximately 2.25-fold higher in the PS compared with the ompF strain. The periplasmic drug concentrations are approximately 30-fold lower than the cytoplasmic concentrations, which is likely due to the drug binding to its targets within the cytoplasm. Using the [20,80] posterior predictive intervals, we have calculated the probabilities of cells from the different strains showing higher/lower accumulation in the different compartments in a pairwise manner. These results are provided in Table S4.
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