domain: sdv chim

text:
Estelle Dumont

Julia Vergalli

Laurence Conraux

Carine Taillier

Aurelie Vassort

Jelena Pajovic

Matthieu Réfrégiers

Michael Mourez

Aurélie Vassort

Jelena Pajović

Jean- Marie Pagès
email: jean-marie.pages@univ-amu.fr

UMR_MD1 J.-M Pagès

Antibiotic and efflux: Combined spectrofluorimetry and mass spectrometry to evaluate the involvement of concentration and efflux activity in antibiotic intracellular accumulation

Introduction

A main challenge in bacterial chemotherapy is to determine and carefully use the in situ parameters that modulate the activity of drugs in order to improve antibacterial efficacy. [START_REF] Brown | Trends and exceptions of physical properties on antibacterial activity for Gram-positive and Gram-negative pathogens[END_REF][START_REF] Payne | Drugs for bad bugs: confronting the challenges of antibacterial discovery[END_REF] This is particularly important with the continuing emergence and the spread of MDR bacteria that contribute to therapeutic failure. [START_REF] Watkins | Overview: Global and local impact of antibiotic resistance[END_REF][START_REF] Laxminarayan | Access to effective antimicrobials: a worldwide challenge[END_REF][START_REF] Boucher | 10 x '20 Progress--development of new drugs active against gram-negative bacilli: an update from the Infectious Diseases Society of America[END_REF][START_REF] Page | Discovery and development of new antibacterial agents targeting Gramnegative bacteria in the era of pandrug resistance: is the future promising?[END_REF] Several papers illustrate the intensity and relevance of the concern and it is absolutely required to understand membrane permeation and intracellular concentration of antibiotics in clinical isolates: crossing the double membrane barrier to reach a threshold concentration is a pivotal step of antibacterial action. [START_REF] Nikaido | Molecular basis of bacterial outer membrane permeability revisited[END_REF][START_REF] Pagès | The porin and the permeating antibiotic: a selective diffusion barrier in Gram-negative bacteria[END_REF][START_REF] Blair | Molecular mechanisms of antibiotic resistance[END_REF][START_REF] Masi | Mechanisms of envelope permeability and antibiotic influx and efflux in Gram-negative bacteria[END_REF][START_REF] Nikaido | Prevention of drug access to bacterial targets: permeability barriers and active efflux. -Semantic Scholar[END_REF][START_REF] Li | The challenge of efflux-mediated antibiotic resistance in Gram-negative bacteria[END_REF][START_REF] Bolla | Membrane permeability and regulation of drug 'influx and efflux' in Enterobacterial pathogens[END_REF][START_REF] Zgurskaya | Permeability barrier of Gram-negative cell envelopes and approaches to bypass it[END_REF][START_REF] Krishnamoorthy | Synergy between active efflux and outer membrane diffusion defines rules of antibiotic permeation into Gram-negative bacteria[END_REF] This key point has not been strongly addressed until now or only in few specific cases with characterized bacterial strains. [START_REF] Masi | Mechanisms of envelope permeability and antibiotic influx and efflux in Gram-negative bacteria[END_REF][START_REF] Bolla | Membrane permeability and regulation of drug 'influx and efflux' in Enterobacterial pathogens[END_REF][START_REF] Bolla | Strategies for bypassing the membrane barrier in multidrug resistant Gram-negative bacteria[END_REF][START_REF] Stavenger | TRANSLOCATION Project: How to get good drugs into bad bugs[END_REF] As recently reported [START_REF] Masi | Mechanisms of envelope permeability and antibiotic influx and efflux in Gram-negative bacteria[END_REF][START_REF] Blair | How to measure export via bacterial multidrug resistance efflux pumps[END_REF][START_REF] Masi | Fluorescence enlightens RND pump activity and the intrabacterial concentration of antibiotics[END_REF] , there is a large collection of methods available to measure efflux activity, but their sensitivity and validity must be clearly demonstrated under different conditions. Thus, the lack of appropriate assays containing well-defined internal controls that allow standardization of signals obtained with various strains under various conditions is a serious bottleneck for medicinal chemistry efforts aiming for the optimization of an antibiotic intracellular accumulation. Mass spectrometry appears as a promising technique to determine the intracellular accumulation of label-free compounds. [START_REF] Zhou | Thinking outside the 'Bug': A unique assay to measure intracellular drug penetration in Gram-negative bacteria[END_REF][START_REF] Pu | Enhanced efflux activity facilitates drug tolerance in dormant bacterial cells[END_REF][START_REF] Brown | A mass spectrometry-based assay for improved quantitative measurements of efflux pump inhibition[END_REF][START_REF] Richter | Predictive compound accumulation rules yield a broad-spectrum antibiotic[END_REF][START_REF] Davis | General platform for systematic quantitative evaluation of small-molecule permeability in bacteria[END_REF] Ultimately, this approach might help to characterize the membrane permeation of any potential drugs, quantify antibiotic accumulation kinetics with appropriate internal controls and meet the throughput requirements of optimization programs based on structure-activity relationship. In the case of fluorescent drugs, intracellular accumulation can be monitored using a synchrotron light source and use the intrinsic fluorescence of bacterial amino acids as a powerful internal standard to correct for biological variations associated with bacterial samples. [START_REF] Kaščáková | Antibiotic transport in resistant bacteria: Synchrotron UV fluorescence microscopy to determine antibiotic accumulation with single cell resolution[END_REF] For example, the fluoroquinolone antibiotic, fleroxacin, exhibits sufficient changes in fluorescence intensity to monitor its accumulation in single bacterial cells. [START_REF] Kaščáková | Antibiotic transport in resistant bacteria: Synchrotron UV fluorescence microscopy to determine antibiotic accumulation with single cell resolution[END_REF][START_REF] Pagès | New peptide-based antimicrobials for tackling drug resistance in bacteria: Single-cell fluorescence imaging[END_REF] Recent results allowed us to validate this method with a multidrug resistant clinical strain of Enterobacter aerogenes and an efflux pump deficient (tolC) derivative of this strain, demonstrating the importance to use a robust internal control. [START_REF] Cinquin | Microspectrometric insights on the uptake of antibiotics at the single bacterial cell level[END_REF] The Innovative Medicine Initiative-funded consortium Translocation [START_REF]TRANSLOCATION | Molecular basis of the bacterial cell wall permeability[END_REF] (www.imi.europa.eu/content/translocation) has defined as its main objective the study of antibiotic translocation across bacterial membranes. [START_REF] Stavenger | TRANSLOCATION Project: How to get good drugs into bad bugs[END_REF] The consortium uses, new approaches, and more traditional ones, to improve our understanding of drug transport and to support future strategies in order to face the antibiotic resistance crisis. In this context, it is important to define common standards and/or protocols to validate the new methods and for future correlation with the antibacterial activities. [START_REF] Masi | Mechanisms of envelope permeability and antibiotic influx and efflux in Gram-negative bacteria[END_REF][START_REF] Vergalli | Spectrofluorimetric quantification of antibiotic drug concentration in bacterial cells for the characterization of translocation across bacterial membranes[END_REF] This is the main objective of this study that proposes a joint protocol for spectrofluorimetry and mass spectrometry analyses associated to biological/biochemical characterizations of bacterial samples. From this work, a new perspective emerges on how to measure kinetics of antibiotic uptake inside bacterial cells and correlate them to the antibiotic mode of action in order to (i) understand and combat the emergence and spread of resistant strains and (ii) extend the activity of antibiotics or (iii)

upgrade the design of new molecules. In addition, this study contributes to the recently proposed concepts, "Resident Time Concentration Close to Target" (RTC2T) and "Structure Intracellular Concentration Activity Relationship" (SICAR). 10

Materials and methods

Bacteria and Media

Escherichia coli strains used in this study are listed in Figure 1. These isogenic strains have been previously described regarding their antibiotic susceptibility. 30

Immunodetection

Exponential-phase bacteria in liquid Mueller Hinton II medium were centrifuged and the pellet was solubilized in loading buffer. [START_REF] Pagès | Efflux Pump, the masked side of ß-Lactam resistance in Klebsiella pneumoniae clinical isolates[END_REF] Total cell protein (OD600 = 0.02 corresponding to equal protein per well) was loaded onto a SDS-polyacrylamide gel (10% polyacrylamide (w/v), 0.1% SDS (w/v)). Proteins were electro-transferred onto nitrocellulose membranes in transfer buffer. An initial saturating step was performed overnight at 4°C with Tris-buffered sodium (TBS: 50 mM Tris-HCl, pH 8.0, 150 mM NaCl) containing skimmed milk powder (10%). The nitrocellulose sheets were then incubated in TBS + skimmed milk powder + Triton X-100 (0.2%) for 2 h at room temperature in the presence of polyclonal antibodies (1:5,000, 1:2,000 and 1:10,000 dilution for anti-AcrA, anti-AcrB, OmpC and OmpF respectively) directed against denatured AcrA, AcrB, OmpC and OmpF respectively. [START_REF] Pagès | Efflux Pump, the masked side of ß-Lactam resistance in Klebsiella pneumoniae clinical isolates[END_REF] The detection of antigen-antibody complexes was performed with horseradish peroxidase secondary antibody conjugated Immune-Star goat anti-rabbit IgG antibodies (BioRad) and revelation was performed using a ChemidocXRS+ (BioRad).

Drug susceptibility assays

Ciprofloxacin and fleroxacin were assayed to study the antibiotic susceptibility of E. coli strains. MIC values of antibiotics were determined by the microdilution method (CLSI) in liquid Mueller Hinton II medium by using the twofold standard microbroth dilution method (microplates and automatic analyses Tecan®) (CLSI, http://clsi.org/). MIC values were read after 18 h of incubation at 37°C. Experiments were carried out in triplicate and the resulting medians were presented.

Accumulation protocol

Bacteria grown at 37°C in Luria-Bertani broth in its exponential-phase (0.6 optical density units at 600 nm) were concentrated 10-fold. The bacterial suspension was centrifuged at 6000 × g for 15 min at 20 °C and pellets were re-suspended in 1/10 of the initial volume in a sodium phosphate buffer (50 mM) at pH 7 supplemented with MgCl2 (5 mM) (NaPi-MgCl2 buffer) to obtain a density of 6.10 9 cfu.mL -1 (colony-forming-unit). In 96-well deep well plates, 1.44 mL of the bacterial suspension was incubated 2 or 10 min at 37°C (final volume 1.8 mL per well) with different concentrations of fleroxacin and ciprofloxacin (0 to 5 mg/L), in the absence or in the presence of the efflux blocker cyanide-m-chlorophenylhydrazone (CCCP) at 10 μM for the efflux pump overproducer strain AG102. CCCP collapses the energy-driven force needed by the efflux pump to expel antibiotics in the resistant strain. [START_REF] Vergalli | Fluoroquinolone structure and translocation flux across bacterial membrane[END_REF] Bacterial suspensions incubated without antibiotics, with or without CCCP, were used as controls. Suspensions (800 μL) were then loaded on 1 M sucrose cushions (1.1 mL) in two deep well plates (one for the spectrofluorimetry analysis and the other for the mass spectrometry analysis) and centrifuged at 2 700 × g for 20 min at 4°C to eliminate extracellular-adsorbed compounds and collect washed bacteria. [START_REF] Vergalli | Spectrofluorimetric quantification of antibiotic drug concentration in bacterial cells for the characterization of translocation across bacterial membranes[END_REF] The same incubation mixtures were used to performed spectrofluorimetry and mass spectrometry analyses, in three replicates each. This accumulation assay was repeated three times.

To control that the bacterial cells are alive during the experimental time, the number of cfu was determined by sampling the bacterial suspension at 2 and 10 min during antibiotic incubation. The cfu numbers were determined and no change in cell viability was observed during this period that corresponds to accumulation assay (data not shown). It must be noted that the ratio "bacterial cell/antibiotic concentration" was different in the MIC assay and in accumulation assay (about 10-20 times higher in accumulation conditions compared to MIC assays). Furthermore, the accumulation assay was carried out using starving conditions during a limited incubation time (2-10 min) as previously determined. 27

Spectrofluorimetry assay

To follow the compound uptake by bacterial population, the fluorimetric assay previously described was used. [START_REF] Kaščáková | Antibiotic transport in resistant bacteria: Synchrotron UV fluorescence microscopy to determine antibiotic accumulation with single cell resolution[END_REF] Pellets corresponding to 800 μL of bacterial suspensions were lysed with 500 μL of 0.1 M Glycin-HCl pH 3 buffer overnight at room temperature. The lysis efficacy has been checked by cfu determination as previously mentioned. [START_REF] Vergalli | Spectrofluorimetric quantification of antibiotic drug concentration in bacterial cells for the characterization of translocation across bacterial membranes[END_REF] After a centrifugation in deep wells for 20 min at 2 700 × g at 4°C, 100 μL of lysates were analyzed by spectrofluorimetry at λex 290 nm and λem around 450 nm for fleroxacin and λex 275 nm and λem around 450 nm for ciprofloxacin. To quantify the fluoroquinolone fluorescence intensity in bacteria lysate, spectra were normalized using the tryptophan peak at 356 nm and subtracted from control sample spectra. [START_REF] Cinquin | Microspectrometric insights on the uptake of antibiotics at the single bacterial cell level[END_REF] Fluoroquinolone concentrations in bacterial lysate were calculated according to a calibration curve (See paragraph 'Standard curves'). 29

Mass spectrometry determination

Sample preparation for Mass spectrometry analysis

Pelleted bacteria were thawed during 10 min at 37°C and resuspended in 200 µL of 0,1 M Glycin-HCl pH 3 buffer. Samples were sonicated during 5 min (sonic batch) and incubated at 37°C during 2 hours under gentle agitation. The lysis efficacy has been checked by cfu determination (data not shown). After a first centrifugation at 6,100 g (10 min, room temperature) 150 µL of the supernatant were recover and centrifuged a second time in the same conditions. 40 µL of these final supernatants were then put in a 96 well plate for MS analysis.

Mass spectrometry analysis

Quantitative analysis was performed on a Waters ACQUITY UHPLC HSS T3 column (1.8 μ m 50 x 2.1 mm) at room temperature with the flow rate of mobile phase set at 0.5 mL/min.

The mobile phase consisted of (A) 0. 1.

Standard curves

Mass spectrometry

Solutions of each compound for calibration were freshly prepared in bacteria lysate. From a first concentration of 5 mg/L, 4-time serial dilutions were done in bacteria lysate to a final concentration of 0.076 ng/mL, leading to 9 solutions used for mass spectrometry calibration curves (Figure S1).

Spectrofluorimetry

Various known concentrations of fleroxacin and ciprofloxacin were mixed with bacteria lysates at OD=4.8 and samples were measured with spectrofluorimeter (n=3) at λex 290 or 275 nm respectively and λem around 450 nm. The trend lines and the slopes of the fleroxacin and ciprofloxacin standard curves were determined in the various studied bacteria lysates (Figure S2). The corrected fluorescence value of each spectrofluorimetry sample (corrected with the fluorescence signal from bacteria as previously described) [START_REF] Cinquin | Microspectrometric insights on the uptake of antibiotics at the single bacterial cell level[END_REF] was divided by the slope of the trend line to obtain the fleroxacin and ciprofloxacin concentrations.

Results and Discussion

Fluoroquinolone susceptibility and AcrAB expression

The activity of fleroxacin and ciprofloxacin were assayed on E. coli AG100, AG100A, a derivative strain devoid of the AcrAB efflux pump, and AG102, a strain that overproduces AcrAB (Figure 1a). The same strains were used for both detection methods. In general, AG100A was more susceptible to the drugs than the wild type, while AG102 was more resistant. Immunoblots confirmed the absence of AcrAB in AG100A and a more intense signal in AG102 (Figure 1b). The porins, OmpC and OmpF, are present at an equivalent level of expression in the 3 strains (Figure 1b).

Mass Spectrometry versus spectrofluorimetry to evaluate the fluoroquinolone accumulation

In order to compare the two approaches for determining the antibiotic accumulation in various efflux backgrounds, an experimental protocol was designed (see Figure S3). In this protocol, we generated duplicate samples for each experimental point (e.g. strain, time, drug concentration). Each sample was analyzed in triplicate (corresponding to 3 independent wells) using spectrofluorimetry or mass spectrometry method (blind assay).

Ciprofloxacin accumulation

The analysis was performed on measurements of ciprofloxacin concentrations accumulated in all studied strains (AG100, AG100A, AG102, AG102 incubated with CCCP) at 2 min and 10 min incubations (Figure 2). The consistency between spectrofluorimetry and mass spectrometry was quantified by Bland-Altman calculations (Figure 2). The difference is centered around zero with neither absolute systematic error nor strong dependency on the magnitude of measurements. The observed bias is relatively low (297 ± 5477 molecule/cell) and not significant, and biases are similar between incubations at 2 min and 10 min (data not shown). Under the conditions used, the two methods give equivalent results.

Fleroxacin accumulation

The results are presented in Figure S4. As observed with ciprofloxacin, the Bland-Altman plot demonstrated the consistency of the measurements obtained with spectrofluorimetry and mass spectrometry (Bias of 263 ± 4008 molecule/cell). The difference is centered around zero and no proportional error is present in the comparison between the two methods.

It must be noted that only in the case of fluorimetry assay, as reported previously, the internal signal corresponding to intrinsic bacterial fluorescence (tryptophan fluorescence) was systematically used to correct the data about the variation of cellular masses presented in the various samples. [START_REF] Cinquin | Microspectrometric insights on the uptake of antibiotics at the single bacterial cell level[END_REF][START_REF] Vergalli | Spectrofluorimetric quantification of antibiotic drug concentration in bacterial cells for the characterization of translocation across bacterial membranes[END_REF] The fact that spectrofluorimetry measurements are corrected with the bacterial internal standard, unlike mass spectrometry data, can explain the ranges of agreement obtained on the Bland-Altman plots. Another specific point concerns the detection limit of spectrofluorimetry: it cannot be used to detect accumulations performed with concentration lower than 500 ng/mL under the conditions used. In contrast, mass spectrometry gives access to a wider range of low concentrations (down to 25 ng/mL) in our conditions.

Concentration effect, influx and efflux activity

The measure of the accumulation of compounds inside the E. coli AG100A strain devoid of AcrAB pump can be used to determine the respective efficacy of ciprofloxacin and fleroxacin uptake. The results presented in Figure 3 indicate that ciprofloxacin is about 2-fold more efficiently accumulated compared to fleroxacin in the absence of AcrAB efflux. A quite similar value has been calculated using spectrofluorimetry assay and previously proposed for the concept SICAR IN . [START_REF] Vergalli | Fluoroquinolone structure and translocation flux across bacterial membrane[END_REF] In this study, the mass spectrometry assay also shows a difference in uptake for ciprofloxacin and fleroxacin (Kruskal-Wallis test, p<0.01, n=27).

To evaluate the impacts of external concentration effect and/or of efflux level on the rate of intracellular accumulation, a large range of ciprofloxacin concentrations was incubated with the parental strain, the AcrAB-derivative and the AcrAB overproducer isogenic strains. The data obtained with mass spectrometry analyses are presented in Figure 4. A strong difference was observed between the accumulations in the different AcrAB strains: the maximal accumulation, whatever the concentration used, was obtained with AG100A or with AG102 in the presence of CCCP; in contrast the minima was obtained with AG102 (p<0.001).

Moreover, the overproduction of AcrAB in AG102 has a noticeable effect on ciprofloxacin accumulation at high concentrations (3.75 and 5 µg/mL) compared to the pump basal expression obtained in AG100 (p<0.05).

The fold-increase (FI) was defined as the ratio:

F[AG102+CCCP] / F[AG102],
where /AG102] and FI [AG100A/AG102] was observed (from about 4.4 to 2.7 and 3.6 to 2.4, respectively)(Figure 5). These results suggest that a saturation of the efflux ability to expel the internalized molecules can be reached in the E. coli strain that overproduced AcrAB when high concentration of ciprofloxacin is used.

These data explain the key contribution of efflux pump in fluoroquinolone resistance in clinical strains where the uptake of antibiotic can be impaired by alteration of the membrane permeability as previously hypothesized. 10

Conclusion

A variety of methods has been previously reported to follow the intracellular accumulation of antibiotic in enterobacterial cells that feature membrane-associated mechanisms of resistance affecting many or all antibiotic classes, including reduction of outer membrane permeability or increase of levels of efflux pumps . [START_REF] Masi | Mechanisms of envelope permeability and antibiotic influx and efflux in Gram-negative bacteria[END_REF][START_REF] Blair | How to measure export via bacterial multidrug resistance efflux pumps[END_REF] Until now and despite recent methodology efforts, no comparative assays have been carried out in order to have an independent validation of the proposed protocols or at least to check their consistency and robustness.

In this study, our aim was to determine the internal concentration of fluoroquinolones, ciprofloxacin and fleroxacin and to measure the effect of antibiotic concentrations on bacteria expressing various levels of AcrB pump, using fluorimetric and mass spectrometric (LC&MS/MS) methods.

For the first time, a robust consistency was described between these two approaches, spectrofluorimetry and mass spectrometry, whatever the efflux activity, the molecule or the concentration of antibiotic used in the assays. Moreover, by combining the spectrofluorimetry measurement, that contains a solid internal standard [START_REF] Vergalli | Spectrofluorimetric quantification of antibiotic drug concentration in bacterial cells for the characterization of translocation across bacterial membranes[END_REF] , with LC&MS/MS determination, that allows studying low concentrations of molecule, these two methods can be viewed as complementary. Our study is especially important in view of recent papers reporting the accumulation of antibacterial molecules using mass spectrometry assay when this assay lacks robust internal control for normalization. [START_REF] Richter | Predictive compound accumulation rules yield a broad-spectrum antibiotic[END_REF] The development of LC&MS/MS assays in microplates allows to determine the relationship between a large range of antibiotic concentrations and the amount of intra-bacterial accumulation in different efflux backgrounds without and with the presence of an efflux poison (CCCP). Importantly, the data demonstrate that ciprofloxacin penetrates and accumulates more than fleroxacin in an AcrAB-strain The measurement of uptake in the absence of efflux activity, defined by SICAR IN as previously proposed, [START_REF] Vergalli | Fluoroquinolone structure and translocation flux across bacterial membrane[END_REF] is thus confirmed.

With increasing external concentrations of compound, the effect of efflux on internal accumulation was altered and the accumulation ratio obtained between efflux-and efflux ++ strains was significantly decreased, showing that efflux can be saturated. This effect must be taken into consideration when assessing the impact of efflux on new antibacterial agents.

In addition, the fact that efflux pumps can indeed be saturated supports the strategy previously proposed by several authors to generate a substrate competition on the binding sites of efflux pumps by using molecular lures or adjuvants to restore the intracellular antibiotic concentration. [START_REF] Pagès | Efflux Pump, the masked side of ß-Lactam resistance in Klebsiella pneumoniae clinical isolates[END_REF][START_REF] Ruggerone | RND efflux pumps: Structural information translated into function and inhibition mechanisms[END_REF][START_REF] Ramaswamy | Computational modelling of efflux pumps and their inhibitors[END_REF][START_REF] Nikaido | Broad specificity efflux pumps and their role in multidrug resistance of Gram negative bacteria[END_REF][START_REF] Pagès | Efflux pumps of gram-negative bacteria, a new target for new molecules[END_REF] Intrinsic bacterial fluorescence has been previously used to standardize/normalize the data in the quantification assays for fluorescent drugs. [START_REF] Kaščáková | Antibiotic transport in resistant bacteria: Synchrotron UV fluorescence microscopy to determine antibiotic accumulation with single cell resolution[END_REF] In this study, the good correlation between mass spectrometric determination and fluorimetric analyses demonstrated the advantage of this internal measure for monitoring the efficacy of lysis protocol and correcting the crude signals for protocol validation. [START_REF] Masi | Mechanisms of envelope permeability and antibiotic influx and efflux in Gram-negative bacteria[END_REF][START_REF] Masi | Fluorescence enlightens RND pump activity and the intrabacterial concentration of antibiotics[END_REF] In the future, it will be necessary to develop additional assays using similar methods as the one described here to measure in whole bacteria the apparent affinities of various antibiotics for the different bacterial transporters involved in the influx step (e.g. porins) or involved in the efflux (e.g. other AcrAB family members).

To conclude, with this method the concept of "structure intracellular concentration activity relationship" (SICAR) previously proposed [START_REF] Masi | Mechanisms of envelope permeability and antibiotic influx and efflux in Gram-negative bacteria[END_REF][START_REF] Masi | Fluorescence enlightens RND pump activity and the intrabacterial concentration of antibiotics[END_REF] is now applied to a large concentration range.

In SAR studies for biologically active molecules, SICAR will correlate the chemical structure to the efficacy of translocation through bacterial membrane and the resulting intracellular accumulation; while taking into account recently proposed key parameters, such as globularity and charge, as reported by Richter et al. [START_REF] Richter | Predictive compound accumulation rules yield a broad-spectrum antibiotic[END_REF] Thus, the role of chemical side chains involved in the membrane permeation (IN) or in the efflux transport (OUT) can be dissected and allow the design of drug that fit better the translocation constraints present in resistant clinical isolates. Ciprofloxacin was accumulated for 2 min and 10 min in AG100 (AcrAB+), AG100A (AcrAB-), AG102 (AcrAB++) and AG102 cells incubated in the presence of CCCP (10 µM).

Figures

The ciprofloxacin intracellular concentrations (molecules/cell) obtained in the various isogenic strains were determined with the spectrofluorimetry and mass spectrometry methods.

The figure shows the Bland-Altman plot of the differences between mass spectrometry and spectrofluorimetry quantification against the averages of the two methods with bias of 297 ± 5477 units. The bias is represented by the gap between the X axis, corresponding to a zero difference, and the parallel dotted line to the X axis. The 95% limits of agreement corresponding to +/-1.96 SD are represented in dashed lines.

.

F

  [AG102+CCCP] corresponds to the ciprofloxacin accumulated in AG102 in the presence of CCCP and F[AG102] corresponds to the ciprofloxacin accumulated in the same strain in the absence of CCCP. The F[AG100A] / F[AG102] was also calculated and the different ratios were plotted for the given external ciprofloxacin concentration in Figure 5. Interestingly, with increasing ciprofloxacin concentration, a significant decrease (p<0.05) of FI [AG102+CCCP

Figure 1 .a

 1 Figure 1. Expression of AcrAB efflux components and porins, and fluoroquinolone

Figure 2 .

 2 Figure 2. Bland and Altman plot for mass spectrometry and spectrofluorimetry measurements

Figure 3 .

 3 Figure 3. Amount of intrabacterial concentrations of ciprofloxacin and fleroxacin measured

Figure 4 .

 4 Figure 4. Accumulation and concentration effect of ciprofloxacin measured by mass

Figure 5 .

 5 Figure 5. Determination of ciprofloxacin accumulation ratios in E. coli strains expressing

Table 1 :

 1 Mass spectrometry parameters used during analyses.

	Ion source	Ciprofloxacin	Fleroxacin
	Spray Voltage Positive Ion (V)	3500	3400
	Sheath Gas (Arb)	40	45
	Auxiliary Gas (Arb)	15	5
	Sweep Gas (Arb)	2	1
	Ion transfert Tube Temperature (°C)	350	350
	Vaporizer Temperature (°C)	400	400
	SRM	Ciprofloxacin	Fleroxacin
	Collision Energy (V)	18	18
	Dwell Time (ms)	50	50
	RF lens (V)	75	77
	Q1 Resolution (FWHM)	0.7	0.7
	Q3 Resolution (FWHM)	0.7	0.7
	CID Gas (mTorr)	1.5	1.5

Acknowledgements

We thank Anne Davin-Regli, Muriel Masi, Robert Stavenger and Mathias Winterhalter for their fruitful discussions, Anne-Marie Tran for their assistance during microbiological assays.

Funding

This work was supported by the TRANSLOCATION consortium and has received support from the Innovative Medicines Initiatives Joint Undertaking under Grant Agreement (grant number 115525), resources which are composed of financial contribution from the European Union's seventh framework program (FP7/2007-2013) and EFPIA companies in kind contribution. This work was also supported by Aix-Marseille Univ and Service de Santé des Armées, and by Soleil program (projects # 20141262, 20150318, 20160173).

Transparency declarations

The authors (L.C., C.T., A.V. and M.M.) declare competing financial interests: L.C., C.T., A.V. and M.M. are former/current employees of Sanofi R&D. All other authors: none to declare.


Mateusz Szczepanski
email: szczepanski@laplace.univ-tlsefrmalec@laplace.univ-tlsefrmaussion@laplace.univ-tlsefr

David Malec

Pascal Maussion

Philippe Manfé
email: philippe.manfe@mailnidec.com

Design of Experiments (DoE) predictive models as a tool for lifespan prediction and comparison for enameled wires used in low voltage inverter-fed motors

Keywords: lifespan prediction, comparative method, design of experiments, accelerated aging, rotating machines, partial discharge, electrical insulation system, inverter-fed motors, PWM, Weibull distribution

Since the development of power electronic components, which allowed the manufacturing of reliable and efficient inverters, variable speed drives using inductive motors have become more and more popular. The PWM technique has proven to be a very effective method of rotational speed control. However, the fast changing voltage pulses, with very steep slopes (in the order of a few kV/ s), has brought new hazards for the electrical insulation system of such motors. Very high frequency harmonic components of PWM voltage will result in significant overvoltage due to an impedance mismatch between the cable and the motor. As an effect, the voltage seen by some parts of the insulation system may exceed the Partial Discharge Inception Voltage (PDIV) stating localized partial discharges activity. The aim of this paper is to investigate and analyze the aging process of the enameled wire exposed to different factors and to propose a method allowing to predict their lifespans in g iven conditions. This study introduces a prediction based on the Design of Experiments method and the statistical Weibull distribution. Thanks to the model obtained with short multi-stress aging tests, it is possible to predict the results of significantly longer ones. Moreover, the adapted methodology is proposed that allows to predict the scatter of the long tests basing on the short-time results dispersion. The same approach is used to compare different products between each other and rank them. All model predictions are compared with the experimental data in order to prove the model accuracy.

I. INTRODUCTION

A. Form-and random-wound machines

The windings of the machines can be divided into two groups: form-wound or random-wound. [START_REF]E ngineering Report: Form-Wound Coils[END_REF] Form windings use rectangular magnet wires. The position of each individual turn inside the slot is well controlled. As a result a turn-to-turn voltage stress as well as temperature distribution are more uniform compared to random-wound machines. Due to much higher cost, both of materials and labor, this type of winding is used almost only for high voltage or high power (typically more than hundreds of kW) low voltage machines and thus will not be further discussed in this review.

Low voltage and/or low power machines are almost exclusively random-wound. The windings are made with insulated round copper conductors, called magnet wire. As their arrangement in the coil during skeining or insertion cannot be controlled, the winding is called random. As a result, wires from one turn can touch any other turn and therefore the maximum turn-to-turn voltage can be significantly higher than for formwound machines. In the worst-case scenario the beginning and the end of the winding can be adjacent. According to some studies [START_REF] Mihaila | Prediction of the turnto-turn voltages in parallel connected wires configuration for motor coils fed by steep fronted pulses[END_REF] the probability of such a situation can be higher than 90%. Moreover, this type of winding is much more vulnerable to mechanical damages due to vibrations or loose wire. Further problems can be caused by uneven resin build-up, non-uniform temperature distribution or higher accumulation of moisture and contaminates due to unsteady air circulation. B. Electrical insulation system of low voltage motors Electrical insulation system is an insulating structure containing one or more insulating materials together with associated conducting parts employed in an electrotechnical device [START_REF]International Electrotechnical Vocabulary -Part 212: Electrical insulating solids, liquids and gases[END_REF]. The IEC standard [START_REF]Rotating electrical machines -Part 18-41: Partial discharge free electrical insulation systems[END_REF] divides the electrical insulation systems used in electric machines into 2 main categories, called type I and type II. The type I system consists in the materials that are not expected to experience any partial discharges (PDs) activity within specified conditions in their service lives. It is generally used in random-wound low voltage machines (rated voltage 700 VRMS) and is based almost uniquely on organic polymer materials. By contrast, systems expected to withstand PDs in any part of the insulation throughout their service lives, are classified as type II [START_REF]Rotating electrical machines -Part 18-42: Partial discharge resistant electrical insulation systems (Type II) used in rotating electrical machines fed from voltage converters -Qualification tests[END_REF]. These systems are usually used in form-wound high voltage machines and use both the organic polymer materials and inorganic materials. In this review we concentrate only on type I electrical insulation system in random-wound machines.

Insulating components in low voltage machines can be divided according to their function into the following groups [START_REF] Stone | Electrical Insulation for Rotating Machines. Design, Evaluation, Aging, Testing, and Repair[END_REF]:

Phase-to-ground insulation Phase-to-phase insulation Turn-to-turn insulation Impregnating varnish or potting resin

The first three components are often called primary or major insulation, as opposed to impregnating liquid, which is a secondary insulation. The overview of the components of a lowvoltage insulation system is shown in Fig. 2. Fig. 2. Overview of materials in a low-voltage insulation system: 1 turn insulation, 2 slot liner, 3 slot separator, 4 wedge, 5 phase separator, 6 lead sleeving, 7 coil-nose tape, 8 connection tape, 9 cable, 10 tie cord and 11 bracing. [START_REF] Chapman | Insulation Systems for Rotating Low-Voltage Machines[END_REF] The phase-to-ground insulation prevents the winding coils from touching the stator core. Each slot of the stator is lined with a slot liner made most commonly of so-called insulating "paper", such as aramid paper (well-known under its Dupont trade name Nomex TM ), polyester film (known as Mylar TM ) or polyester fleece (known as Dacron TM ). Generally, they present high breakdown strength, good mechanical properties, such as tear resistance and they resist well to chemical attack. The choice of the insulating material is often defined by the thermal class of the machine. The slot liners are available in wide range of thicknesses, depending of their voltage class [START_REF] Stone | Electrical Insulation for Rotating Machines. Design, Evaluation, Aging, Testing, and Repair[END_REF] [START_REF] Chapman | Insulation Systems for Rotating Low-Voltage Machines[END_REF].

The phase-to-phase insulation prevents the any two coils of different phases from touching one-another. At the end winding the coils are separated by the phase separators. For those winding configurations with two different phases in the slots, their coil are separated by the slot separators. For phase-to-phase insulation, the same materials are used as for the phase-toground insulation. The insulators are typically slightly thicker due to higher voltage that they need to support.

In order to further improve the properties of the insulating papers they can be piled together into flexible laminates. These laminates are best known under their trade names, e.g. NMN (Nomex/Mylar/Nomex) or DMD (Dacron/Mylar/Dacron). The role of turn-to-turn insulation is to electrically separate the turns of the same coil from each other. In low voltage machines this insulation consists in the thin enamel layer on the copper wire. For each diameter of a magnet wire there are several enamel thicknesses available, called grades. Typically grades 1 or 2 are used (higher grade= thicker enamel), but higher grades (up to 9 [START_REF]Specifications for particular types of winding wires -Part 0-7 : general requirements -Fully insulated (FIW)[END_REF]) are commercially available. All the wire dimensions are standardized in [START_REF]2013 Specifications for particular types of winding wires -Part 0-1: General requirements -Enamelled round copper wire[END_REF] or [START_REF] Nema Mw | Magnet Wire[END_REF].

Polymer materials are easily eroded by a partial discharges activity. The enamel of conventional wires is also highly vulnerable to PDs. On the other hand, inorganic materials can withstand a partial discharges activity for a long time, but are hard to process and thus expensive. Magnet wire manufacturer desired to combine the advantages of those two groups of materials. As a result, composite materials were developed, where the micro-or nano-inorganic particles, such as TiO2, SiO2 or Al2O3, are dispersed in the polymer matrix. The wires enameled with such composites are often referred to as "corona resistant". Although they are not completely resistant to a PD activity, they have significantly higher breakdown strength and lifespan in a partial discharges regime than the conventional wires [START_REF] No | Proprieties of Polymer Composites Used in High-Voltage Applications[END_REF]. The impregnation serves in the machines as a secondary insulation. Naturally it strengthens the primary insulation, but also improves heat transfer (better thermal conductor than the air) as well as mechanically blocks the winding and protects it toward vibrations and environmental conditions. Usually the low-voltage machines are dip or trickle impregnated. Due to high slot fill factor the varnish cannot easily penetrate in-between the wires and often multiple air voids can be found inside the slots or at the coil outhangs. There are techniques allowing better covering of the winding, such as VPI (vacuum-pressure impregnation) of potting, but are still rarely used for low-voltage machines.

C. Partial discharges in low voltage motors

A partial discharge (PD) is an electric discharge that only partially bridges the insulation between two conductors [START_REF]International Electrotechnical Vocabulary -Part 212: Electrical insulating solids, liquids and gases[END_REF]. In low-voltage machines powered directly from the grid, the voltage seen by any part of the insulation system is lower than the minimum required in order to start a partial discharges activity, called partial discharge inception voltage (PDIV). Thus the problem of partial discharges was associated only with high voltage machines. Since the introduction of power electronic inverters the stress seen by the insulation system has raised significantly. Very short surges produced by such sources creates voltage transients having very short rise times (as short as a fraction of s), which can result in a partial discharges activity. High dV/dt of the slope is a source of very high frequency harmonics in the FFT spectrum of a PWM signal. The input impedance of the machine is usually significantly larger than the characteristic impedance of the cable connecting the inverter and the motor, especially for smaller machines. This impedance mismatch, completely negligible for low frequency harmonics (associated with fundamental frequency and its harmonics), is the reason for a significant increase of the peak voltage at the motor terminals. Fig. 3 shows how the overvoltage at the machine terminals is influenced by the impulse rise time and the length of the cable between the inverter and the motor. Generally speaking the longer the cable and the smaller the rise time, the higher the overvoltage factor (defined as the ratio between the peak voltage at motor terminals and at the inverter output). The introduction of new wide-bandgap semiconductors based on silicon carbide (SiC), gallium nitride (GaN) or diamond, which will further reduce the rise time, will result in even higher stress applied to machine insulation system. More recent studies [START_REF] Taghia | Advanced Analysis of Transient Overvoltage in Electromechanical Chain Fed by SiC Inverter[END_REF] show that the overvoltage factor can exceed 2 in case of unfavorable superposition of overvoltages at the inverter output or of the resonance for certain harmonics of the PWM signal. Fig. 3. Overvoltage at the motor terminals as a function of cable length for different risetimes [START_REF] Feldmeier | Applying dV/dT filters with AFDs, Application Paper AP043001EN[END_REF] If this voltage exceeds the PD inception voltage, the activity of partial discharges will start causing very accelerated aging As a result of these pre-mature breakdowns the lifespan of inverterfed machines is still unsatisfactory. [14][16]. When a very steep impulse voltage is applied to a stator winding, the voltage distribution is nonlinear, contrary to equal distribution at power frequency (i.e. 50 or 60 Hz). As a result, a much greater percentage of the voltage appear across the first turns. This nonuniformity occurs because the pulse voltage goes through the winding not instantaneously but at the speed given by = , where L is the lineic inductance and C the lineic capacitance. Consequently, first turns are energized before the others and a very high voltage appears across the turn insulation in the first few turns of the winding. [START_REF] Stone | Electrical Insulation for Rotating Machines. Design, Evaluation, Aging, Testing, and Repair[END_REF] Fig. 4 shows the voltage waveform for 6 different parts of the coil of the same phase. E is a voltage at the phase terminal, V1 after the first of the turns in this coil, V2 after the following , etc. The resulting turn-to-turn voltages confirms that the electric stress across the first few turns is significantly higher than for the rest of the coil. As a result, the thin enamel layer is particularly endangered by inverter powering and is often the weakest link leading to machines' breakdown. [START_REF]Rotating electrical machines -Part 18-42: Partial discharge resistant electrical insulation systems (Type II) used in rotating electrical machines fed from voltage converters -Qualification tests[END_REF] Fig. 4. Transient voltage waveforms at the different parts of the coils (left) and the resulting turn-to-turn voltage calculated between these parts [START_REF] Bidan | Development of a New Off-line Test Procedure for Low Voltage Rotating Machines Fed by Adjustable Speed Drives (ASD)[END_REF]

II. THE DESIGN OF EXPERIMENTS (DOE) METHOD

A. General information

Most commonly used test methods change only one factor, while other are kept constant (so called One Factor At Time, or OFAT). If it is needed to test the influence of several factors, the test must be repeated for each factor separately. The Design of Experiments (DoE), first introduced by R.A. Fisher in 1935 [START_REF] Fisher | The Design of Experiments[END_REF], uses a different approach. At the same time, all factors do have a significant role and all of them might be changed from one experimental point to the other. Interaction may exist between factors, consequently the effect of two (or more) combined factors may be larger, or smaller, than the sum of the two (or more) effects taken separately. The DoE method can take into account these interactions between the factors. Thanks to this approach, we can significantly reduce the number of the experiments and at the same time increase the analysis accuracy as well as draw more persistent conclusions from the test campaign. The DoE is thus a very efficient method to organize the experiments allowing to process optimization or model estimation. The method has already proven its potency in many different fields of electrical engineering ([18]- [START_REF] Zernig | Optimal design of experiments for semiconductor lifetime data[END_REF]) also for modeling the insulation lifespan ([22]- [START_REF] Salameh | Parametric and Nonparametric Models for Lifespan Modeling of insulation Systems in Electrical Machines[END_REF]). DoE is a very costeffective and efficient approach, as it allows to strictly limit the number of needed experiments.

B. DoE model construction

The DoE model ( 1) describes the relationship between the system response Y and levels of factors Xi influencing it. The effect of each of those factors and the interactions between them is denoted by the coefficients in a vector E.

E X Y

This relation needs to be linear or linearized, like in the case of all the factors studied here. It is described in section V. The coefficients in the "effect" vector E must be calculated, based on the experimental data of system responses Y. If [X] is square matrix, by the simple modification of the above equation, one gets (2).

Y X E

1 A design, in which all combinations of factors are investigated in each replicate of the experiment, is called a full factorial design or full factorial experiment. It is the only means to completely and systematically study interactions between factors in addition to identifying significant factors [START_REF]Experiment Design & Analysis Reference[END_REF]. The most widely used parametrical model is based on 2 levels of each factor. In case of k factors the model requires 2 k parameters and thus 2 k experimental points [START_REF] Khuri | Response surfaces: designs and analyses[END_REF]. In order to be able to compare the influence of different factors between each other, the "direct" factor are replaced by dimensionless factor levels, normalized to the range [-1,1]. Level "+1" is assigned to the maximum level of factor, while "-1" to the minimum. For the DoE with 2 factors, X becomes a matrix of 2 2 ×2 2 elements, while Y the vector of 2 2 elements, as shown in [START_REF]International Electrotechnical Vocabulary -Part 212: Electrical insulating solids, liquids and gases[END_REF].

AB B A I E E M Y Y Y Y 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 2 1
As it can be seen above, the construction of the model depending on 2 factors and their interaction requires 4 experiments in order to determine the system responses Y1 to Y8. The first column of matrix X refers to the mean value of all the system responses M. The second and third column refer to the levels of factors, respectively EA and EB. The last column is the multiplication of second and third column and denotes the level of factors interaction IAB. Analogically, in case of the DoE with 3 factors, X is a matrix of 2 3 ×2 3 elements, as shown in [START_REF]Rotating electrical machines -Part 18-41: Partial discharge free electrical insulation systems[END_REF]. Similarly to 2 factors models, here the first column of X refers to the mean value of all the system responses M. Next 3 columns describe levels of factors A -C. Columns 5 to 7 describe the interaction between 2 of the factors, respectively AB, AC and BC and their level X is a simple multiplication of corresponding factors levels. Last column is the interaction of all 3 factors.

C. Model extrapolation

In its standard form, the model obtained by the DoE, as described in the previous paragraph, is valid only in the range defined by the minimum and maximum of each factor. This means that the reduced factor levels X should be in the range of [-1, 1]. The extrapolation of the model means that the reduced factor levels X need to exceed their natural validity range of natural [-1, 1]. In our case, the model is contracted for relatively high stress levels in order to assure that the needed experiments are as short as possible. It is particularly interesting to extrapolate the model towards longer lifespan. As a result, the chosen factor levels will be smaller than the model's minimum "-1" (true for all factors, that decrease the system response, which is the case for all the factors studied in this paper). If we were to cover the whole range of operating conditions within one factorial design, the tests for very low stress levels would be far too time and energy consuming and costly, while those for very high stress level might be too short to give reliable results.

As it is necessary to control the stress parameter levels as precisely as possible, otherwise all the model experimental points would not be reliable, it might be necessary to use different test equipment for different tests thus adding additional source of results dispersion.

III. WEIBULL DISTRIBUTION AND SCATTER ANALYSIS

A. Weibull distribution

Among multiple statistical distribution functions, the normal (Gaussian) distribution is most commonly used. Due to the fact that it has a finite probability for negative values, which is physically impossible, normal distribution in not adapted to be used with electrical breakdown data. What is more, as a random variable (here: breakdown data) follows an extreme value distribution (such as Weibull distribution), so does the m i n i m u m . [ 2 8 ] . I n t h i s pa pe r w e u s e d t h e t w o -pa r a m e t e r Weibull distribution. The cumulative density function for this distribution is shown in (5):

t t F exp 1 ) , , (
Variable t denotes in the case of this paper a measured lifespan. The two parameters: and are, respectively, scale and shape parameter (both positive). The scale factor (called also a characteristic value represents the time for which the failure probability F is equal to 63.2%. It can be considered as an analogous to mean value of the normal distribution. is a shape parameter or slope and depends mostly on the dispersion of results (the higher is, the smaller the dispersion). Standard [START_REF]Guide for the statistical analysis of electrical insulation breakdown data[END_REF] gives detailed explanation of how to calculate those Weibull parameters, depending on the sample size.

B. Scatter of results and how to cope with it

Electrical breakdown, especially due to long aging, is a very complex phenomenon. It is influenced by many factors, some relatively easy to control, while others far more difficult or too expensive to precisely control. As a result, the results are often strongly dispersed. For very simplified models, where many technical details of the sample can be scrupulously verified, the scatter of results can be reduced. The disadvantage of those sample is that they might not be representative for the real object and the aging and breakdown mechanisms can be completely different from the final product. Generally speaking the more complex the sample is, the better it represent the final product but for the price of higher dispersion. For electrical insulation system faults in motors one can easily expect as much as ten-toone difference between the lifespan of samples tested in the identical conditions [START_REF] Stone | Electrical Insulation for Rotating Machines. Design, Evaluation, Aging, Testing, and Repair[END_REF].

Such a high results dispersion can significantly constrict the lifespan modeling and may bias the final conclusions. A standard DoE model enables only to predict characteristic value ( ), but cannot give any confidence bounds of such prediction. To enable the scatter prediction for the long-term experiments, it is only possible to base it on the scatter of the short-term results, that were used to obtain the DoE model. Same as in [START_REF] Szczepanski | Prediction of the lifespan of enameled wires used in low voltage inverter-fed motors by using the Design of Experiments[END_REF], the coefficient of variation (CV), called relative standard deviation (RSD), was chosen for this purpose. The coefficient of variation is defined as the standard deviation divided by the characteristic value , defined in [START_REF] Stone | Electrical Insulation for Rotating Machines. Design, Evaluation, Aging, Testing, and Repair[END_REF] for the Weibull distribution:

1 1 1 2 1 2 CV where 0 1 ) ( dx x e n n x
The coefficient of variation is calculated for all of the DoE model experimental points. The average of all those CVs is then assumed to describe the scatter of long-term results.

IV. SAMPLES PREPARATION AND EXPERIMENT DESCRIPTION

A. Accelerated aging tests

An electric machine is typically designed to reach tens of years. Due to such a long time, the test are rarely performed under normal operating conditions, as they would be far too time-and energy-consuming. Taking into consideration all these difficulties, yet still the need to lead to product breakdown in order to better understand machine failure mode, the aging process needs to be somehow accelerated. In order to do so one or more aging parameters are modified so that the measured lifespan of the sample is shorter. Naturally the best compromise needs to be found between the reasonable diminution of tests duration and the reliable simulation of the real-life conditions. The methodology presented here enables to correctly predict the results of time-absorbing experiments yet keeps the necessary tests reasonably short.

B. Comparison of materials

The modeling and the prediction of the lifespan is only one of the concerns in the field of electrical insulation system. In the highly competitive market of electric machines, the primary products, such as magnet wires, insulating papers or varnishes are constantly modified and improved and their prices are also fluctuating. The machine manufacturers usually have a range of typically used insulating materials in the existing solutions. For different reasons it might be necessary to replace one product with the other, for example change the supplier of a magnet wire or the thickness of the insulating papers. As there can be significant differences between different batches of the same product, not to mention the differences between different suppliers, this can influence the final reliability of the machine. It is thus essential to regularly control the quality control of those primary products. As it is not possible to test the complete machine in its nominal conditions each and every time any of its components changes, a quick and reliable comparative test is needed in order to assure that the applied changes are for the better, not for worse.

C. Sample type

As stated in the introduction, the stress that needs to be withstand by the electrical insulation system of inverter-fed machines is significantly higher than with the sinusoidal power supply. The interturn insulation is particularly endangered by fast changing pulses generated by the inverter. As the winding is rarely perfectly impregnated and the varnish layer can be missing is same places it is up to the thin enamel layer on the magnet wire to ensure the turn-to-turn insulation. Some FEM simulations [START_REF] Benmamas | Contribution to Partial Discharge Analysis in Inverter-fed Motor Windings for Automotive Application[END_REF] shows that the PDIV of the interturn insulation were the varnish has correctly penetrated in-between the wires, but with air voids present, can be as low as for the nonimpregnated configuration. The same situation may arrive is case of a winding fault if the paper assuring the phase-to-ground or phase-to-phase insulation has slipped or is missing. In such a situation the last insulating layer is the enamel on the wire. For all the reasons mentioned above in this paper we concentrated on the evaluation of the enameled wire insulation.

Twister pair is the most commonly used sample to test the magnet wire quality. Its manufacturing is controlled by the standard [START_REF]Winding wires -Test methods -Part 5: Electrical properties[END_REF], as it was primarily designed for testing the breakdown voltage. Thank to well-established manufacturing protocol, twisted pairs have quite good reproducibility. Moreover, it is advised as one of the sample types for turn-toturn insulation tests in standard [START_REF]Rotating electrical machines -Part 18-41: Partial discharge free electrical insulation systems[END_REF].

D. Corona-resistant magnet wire

Tests without partial discharge activity, in low voltage range, would be extremely time-and energy-consuming and thus it was necessary to perform the accelerated aging above the PDIV. In order to be able to obtain both the short-and longterm results it was not possible to use the conventional magnet wires, as their lifespan in the partial discharge regime the does not exceed few hours. However, as mentioned in the introduction; the wires covered with enamel with inorganic nano-fillers (e.g. SO2, ZnO, Al2O3,…), called corona-resistant, are far more resistant and can sustain the partial discharges activity for about 1000 times longer than the conventional ones. Thus, for this campaign of measurements a corona resistant wire was chosen. All information concerning the used magnet are presented in Table I.

E. Description of the accelerated aging testbench

A special test bench was constructed in order to recreate the real-life stress submitted to the insulation of an inverter-fed machine. It allows to recreate inverter-type stress by delivering square waves of the desired amplitude, frequency and duty cycle. Depending on the chosen high voltage pulse generator it can deliver up to 1.75 kV (3.5 kV peak-to-peak) with the maximum switching frequency of 30 kHz, or even up to 3 kV with slightly lover frequency, max. 10 kHz. It allows to cover the whole range of switching frequencies typically used in the frequency inverters. Accelerated aging tests usually demand a special test bench adapted to their special requirements. The most critical parameter is a long duration of test: in case of insulating materials for electrical machines those tests can last weeks, months or even years. We need to assure that all devices can function for such a long time without any stops or failures. The other, but equally important challenge, is to assure that the applied stress parameters will not change during the aging process. Assuring these two key factors may be particularly difficult as the aging processes, naturally far less rapid, will apply to all the components of a test bench: power supplies, cables, connectors, probes, detectors, heaters, fans, etc.

In order to recreate the real-life stress submitted to the insulation of an inverter-fed machine, a special test bench was constructed. It allows to deliver square waves of the desired amplitude, frequency and duty cycle, thus simulating the PWM waveform withstood by the insulation. Depending on the chosen high voltage pulse generator it can deliver up to 1.75 kV (3.5 kV peak-to-peak) with the maximum switching frequency of 30 kHz, or even up to 3 kV with slightly lover frequency, max. 10 kHz. This allows to cover the whole range of switching frequencies typically used in the frequency inverters.

Temperature is also an important factor influencing the aging process. To better control the experimental conditions, all the test were conducted inside a climate chamber to assure controlled ambient temperature during all tests. This is particularly important for the tests at very high stress level, where the partial discharge activity can significantly increase the temperature of the samples. This would result to shorter lifespan due to local overheating of the enamel. As ozone generated during PD activity can also influence the lifespan [START_REF] Szczepanski | Ozone concentration impact on the lifespan of enameled wires (conventional and corona-resistant) for low voltage rotating machines fed by inverters[END_REF] the climate chamber needs to be strongly ventilated.

The automatic system of failure detection allowed to assure stable conditions thanks to the possibility of performing experiments on multiple samples without stopping the test. The lifespan was measured automatically for each sample with the accuracy of 1 s. The end of life was stated when the mean DC current flowing through the sample exceeded 100 mA. Such sample was considered as short-circuited and automatically disconnected from the powering source.

F. Description of the experimental conditions

As mentioned before the tests need to be performed in the partial discharge regime. For the purpose of model creation, the parameters were chosen so that the lifespan of samples was in the order of few hours, which is sufficiently short to reasonably shorten the tests duration. The points used to verify the predictions made thanks to model extrapolation had significantly longer lifespan, in the order of hundreds of hours. In each series up to 8 samples were tested in order to be able to perform a statistical analysis of the experimental data.

Table II presents the experimental conditions for the tests for the DoE model. The chosen parameters allowed to keep the experiments short, yet still providing the necessary interval between the results achieved for the different tests of the DoE matrix. All 3 magnet wires A-C were tested in exactly the same conditions. G. Flowchart of the methodology Fig. 6 shows the flowchart explaining how the methodology presented in this article can applied.

V. EXPERIMENTAL RESULTS

A. Model linearization

The DoE method requires that the relation between system response Y (a function of the lifespan) and the factor level (a function of the stress amplitude) is linear. The most commonly used model describing the effect of the electric stress on the lifespan of the insulation in the presence of partial discharge is an inverse power model [START_REF] Stone | Electrical Insulation for Rotating Machines. Design, Evaluation, Aging, Testing, and Repair[END_REF][33] [START_REF] Montanari | Aging Phenomenology and Modeling[END_REF] where lifespan L is proportional to field strength E to the power of -n. Thus the relation between the lifespan and voltage amplitude is linear in log-log plot [START_REF] Lahoud | Electrical aging of the insulation of low-voltage machines: model definition and test with the design of experiments[END_REF] [START_REF] Salameh | Parametric and Nonparametric Models for Lifespan Modeling of insulation Systems in Electrical Machines[END_REF]. In order to confirm this fact, the linearity of the model was tested in much larger range and for several measurement points. The results are shown in Fig. 7. The relation between the lifespan and the switching frequency is not linear. The studies [22][25] have shown that this function has the same nature as the one for the voltage amplitude, so the inverse power law. Results are in Fig. 7Fig. [START_REF]Specifications for particular types of winding wires -Part 0-7 : general requirements -Fully insulated (FIW)[END_REF]. It is intuitive to say that the relation between the lifespan and the switching frequency is inversely proportional. If one assumed that each pulse generates the same number of PD of the same energy and that the lifespan in inversely proportional to the number of PDs (i.e. a number of PDs to breakdown is constant), this would indeed mean that L ~ 1/f. In logL -logf plot this relation is still a straight line, with the slope (exponent in the inverse power law) equal to -1. In other words doubling the switching frequency would mean cutting lifespan in half. As it can be seen in Fig. 8 the slope of the lifespan line is much more steep: doubling the frequency results in the lifespan more than 5 times shorter. This can mean that PD become more detrimental as the frequency increases. If we assumed that the energy of PD at every pulse is the same (independent of frequency), it would mean that the same quantity of energy needs to be dissipated in shorter time, as the frequency (this the repetition rate of PDs) is increased. As a result, the effects of PDs would accumulate the lifespan decrease faster than 1/f.

As the influence of frequency on the partial discharge activity and the aging process is still the object of multiple research, the chosen here inverse power law seems to be the best compromise between the simplicity of the model and its accuracy. The most commonly used model describing the effect of temperature on the lifespan of the insulation is based on the Arrhenius law, as presented in equation ( 7), [START_REF] Stone | Electrical Insulation for Rotating Machines. Design, Evaluation, Aging, Testing, and Repair[END_REF] 9). The obtained results show that the relationship between the lifespan and the stress level can be linearized for the large range of lifespan (2-3 orders of magnitude). This means that short tests may enable to predict the results of long ones. % 4 .

CV

In order to verify whether the predictions of lifespan made using the short-time DoE model are correct and if the scatter prediction is effective, several long-time experiments were achieved. In those experiments, the level of at least one aging factor, typically voltage amplitude, was significantly lower the natural validity range of DoE model, i.e. [-1, +1]. The other factor in some cases was higher than the +1 maximum in order to accelerate the test. Finally, factor levels were calculated using ( 9) and [START_REF] Nema Mw | Magnet Wire[END_REF]. *test G was not performed in the climate chamber but in a laboratory oven without the possibility of cooling; due to lack of ventilation, the temperature was not as stable as for the other tests.

All those tests, except the last one (G*), were performed in the climate chamber where the temperature was kept constant at 30°C (±2ºC). Thanks to high ventilation, the influence of the local overheating of insulation due to partial discharge activity as well as ozone concentration on the test results was minimized. The last measurement, noted as G* was on purpose not performed inside the climate chamber but in a laboratory oven without the possibility of cooling by ventilation. It was done so in order to verify whether at this relatively low stress level the temperature will be stable only thanks to heat dissipation losses. No significant increase of average temperature inside the oven was noted due to this test, however the fluctuations of temperature were higher than for climate chamber (±2ºC in the oven in comparison to ±0.1 ºC in the climate chamber). It is however highly possible that locally, on the sample surface, the temperature was slightly higher. The additional heat generated locally was not high enough to change the temperature inside the oven, but were enough to bias the lifespan results. At the same time lack of ventilation caused the increase in ozone concentration which could also influence the experimental data [START_REF] Szczepanski | Ozone concentration impact on the lifespan of enameled wires (conventional and corona-resistant) for low voltage rotating machines fed by inverters[END_REF]. For each of the experimental points A to G, the predicted lifespan was based only on the short-time 2factor model extrapolation, where system response (Y=logL) was calculated according to [START_REF]Specifications for particular types of winding wires -Part 0-7 : general requirements -Fully insulated (FIW)[END_REF]. Following the hypothesis about the constant coefficient of variation (paragraph III), the standard divination was calculated as [START_REF] Persson | Transient Effects in Application of PWM Inverters to Induction Motors[END_REF].

CV

The calculated standard deviations were used to estimate the scatted of the results for the predicted lifespan values. Upper and lower limits of dispersions, here defined as + andrespectively, were also calculated. The calculated standard deviations were used to estimate the scatted of the results for the predicted lifespan values. The results are presented in Table VII. For each experimental point A to G, the extrapolation factor was presented in order to show how much longer the predicted lifespan is in comparison to the average lifespan of short-time model. Finally, the results predicted by the model were compared with the experimental ones. For all the seven experimental points A-G, the long-time aging tests were performed. In each test, up to eight samples were tested at the same time. All those results were then presented in Fig. 12. Axis of abscissa represents the modeled lifespan (from the learning set), thus the one calculated in Table VII, while axis of ordinates shows the measured lifespan, thus the experimental data from the long-time measurements (test set). The diagonal, marked in red shows the DoE model line. The dash line below and above it, are the lower and upper limits of the predicted dispersion of results, based on the hypothesis of a constant CV. The experimental points used for the DoE model construction are marked in blue in the left bottom corner of the graph. These points show how far are the long-time measurements from the short-time experiments which have been used to create the DoE model. The obtained results show that the proposed method is a very efficient tool for predicting much longer lifespan. The maximum relative error is 33% (excluding series G), which is similar the results obtained is some much more short-term studies [START_REF] Lahoud | Electrical aging of the insulation of low-voltage machines: model definition and test with the design of experiments[END_REF] [START_REF] Salameh | Parametric and Nonparametric Models for Lifespan Modeling of insulation Systems in Electrical Machines[END_REF]. Taking into consideration that the analyzed stress levels are far from the range used to construct the model, with the extrapolation factor even higher than 100 for the longest tests, the accuracy of the outcome is even more impressive. The suggested methodology of including the scatter of the results has proven to be effective. The spans of the dispersion intervals of the test sets are close to the ones predicted by the model. Naturally not all the experimental points are included in the predicted triangle of dispersion, but always some experimental points are within this zone (excluding series G).

In case of the G series, the error of p rediction is visibly more important. All the experimental points had the lifespans shorter than model predictions, and none of them were in the zone predicted by the scatter analysis. As for this series the experiment was not conducted inside the climate chamber but in a laboratory oven, the temperature of enamel might have been locally slightly higher due to absence of ventilation. This temperature rise, undetectable at the scale of the oven (temperature sensor measures the average temperature inside the oven), might have been the cause of the lifespan shortening. Also the higher ozone concentration, due to no ventilation, has probably contributed to shorter lifespans [START_REF] Szczepanski | Ozone concentration impact on the lifespan of enameled wires (conventional and corona-resistant) for low voltage rotating machines fed by inverters[END_REF]. These results show that even in the case of such a long test (predicted lifespan >400h) the temperature must be rigorously kept constant as well as assuring a sufficient ventilation in order to assure the reliable results of accelerated aging tests.

In conclusion, the Design of Experiments (DoE) method proved to be effective even for the extrapolation of the model far from its initial range of validity. This shows that, based only on short-time results, it is possible to effectively predict both the lifespan value and scatter of results for the lifespans, tens of times longer than the duration of the needed experiments. This obviously means that the method is not only time-but also money-saving. The extrapolation permits also to approach much closer the nominal conditions of the machines exploitation.

E. Extrapolation limits

Naturally the model presented in the paper cannot be extrapolated without any limits. The aging mechanism must be at least similar for both short-and long-time results in order for the prediction to be corrects. Thus the extrapolation must be limited to the reasonable range of stress levels. We can apply simple mathematical consideration. In case of all the factors studied here we can assume that an increase in stress level should always decrease (or at least never increase) the lifespan of the samples. For all the factors, the response of the system Y should decrease when the factor level Xi is increasing (otherwise it would mean that an increased voltage or a higher frequency can prolong the insulation lifespan, which is not the case). Thus the partial derivatives of the model equation ( Y/ Xi) should be negative. As a result of such approach the obtained stress limits are very low, thus cannot be taken into consideration due to aging mechanism changes, as explained before. On the other hand, they show that the method is mathematically stable for a very wide range of stress levels. Some lifespan models (e.g. [START_REF] Simoni | A general multistress life model for insulating materials with or without evidence for thresholds[END_REF][37] [START_REF] Starr | Searching for threshold in voltage endurance[END_REF]) postulate the existence of a threshold level, below which no aging takes place. This effect can be neglected if we are far enough from this threshold, but if we operate close to it the DoE method might not be well adapted in such a case. In the particular case of the voltage amplitude, the PDIV level for example can be considered as a threshold. On the other hand, there are very few studies describing the influence of voltage without partial discharges activity on the lifespan of insulation systems. However, it is well known that the aging mechanism with and without partial discharges is not the same, thus the PDIV level creates the natural barrier for model extrapolation.

F. Long-term comparisons based on short-term DoE models

By applying the same technique of extrapolation as for the wire A we can compare the performance of wires A-C. Two points of different voltage amplitude and frequency were chosen to compare the DoE models predictions for all 3 wires with experimental values. Test voltage for each test (I-II) was significantly lower than those used for the construction of the DoE model, with corresponding voltage level XV largely exceeding the natural validity range of DoE of [-1, 1]. Similarly to model for wire A we used the assumption of constant CV in order to predict the dispersion of the extrapolated results. Table VIII shows the average coefficients of variation for each of the 3 wires (A-C). Fig. 13 shows the comparison between the model predictions (in blue) and the experimental results (in red) for 3 magnet wires A-C tested at the above-mentioned test conditions (see As presented in Fig. 13, the predicted model intervals always intersect with the experimental data. Relative errors of the prediction of the mean values are similar to those obtained with short-time tests within the DoE domain of validity. Both for points in test I and test II the difference between the wire A and B is not statistically significant as the model predictions overlap, i.e. the bottom confidence bound of the prediction for wire A is below the upper confidence bound for wire B. This statement is true also for the experimental values obtained for those 2 wires: we are not able to conclude than the wire A is 'stronger' than the wire B. However, for both test I and test II the wire C stands out as the 'weakest' of 3 tested wires. It is statistically significant for both model predictions and experimental values.

VI. CONCLUSIONS AND PERSPECTIVES

As already shown in several publications on this topic, the DoE proved its usefulness in the field of modeling accelerated aging of different insulating materials. However, up to now, almost only short-time models were presented for which the stress levels have been significantly higher than those that might be seen by the insulation system during normal operating conditions in order to accelerate the test.

The results presented in this paper show that DoE models can be successfully extrapolated towards much lower stress levels and that they give satisfyingly accurate predictions of much longer test results. Thanks to the original methodology proposed for the scatter of short-time results, the DoE model extrapolation was enriched with the prediction of the dispersion of long-time results. The predicted lifespans correspond well with the experimental data, especially if we take into consideration that the short DoE tests were even more than 100 times shorter than the predictions.

Finally, the DoE short-time models can be used as a comparative tool for different products available on the market. Thanks to the proposed methodology it was possible to rank the products regarding their lifespan, from the best to the worst, using only a quick test campaign. This classification was confirmed by long-time predictions and correlated well with the experimentally obtain results for those points.

The study presented here was based entirely on the enameled wires and their insulation. Future work will be directed towards wider range of insulating materials in order to be able to study the aging of the insulating systems of low voltage machines as a whole. It will enable to analyze the behavior of each element of insulating system but also the interactions between them. As presented in this paper the use of the Design of Experiments (DoE) method can be an effective tool in lifespan modeling as well as its prediction. Further work will verify if the same methodology as presented here can be applied to other than insulating material domains, such as LEDs, OLEDs or fuel cells.

Fig. 1 .

 1 Fig.1. Cross-section of a slot: form winding (left) and random winding (right)[START_REF]E ngineering Report: Form-Wound Coils[END_REF]

Fig. 5 .

 5 Fig. 5. The automatized test bench for the accelerated aging tests: climate chamber (left) and high voltage pulse generator with the lifespan counters (right)

Fig. 6 .

 6 Fig. 6. Flowchart showing the methodology of short-time modeling and longtime prediction

Fig. 7 .

 7 Fig. 7. The experimental verification of the linearity of the function between the lifespan and the voltage in log-log plot (other parameters are constant: f = 10 kHz, T = 30 C)

Fig. 8 .

 8 Fig. 8. The experimental verification of the linearity of the function between the lifespan and the frequency in log-log plot (other parameters are constant: V = 1.75 kV, T = 30 C)

  [START_REF] Endicott | Application of the Erying Model to Capacitor Aging Data[END_REF][34]: =A where A and B are constants and T denotes absolute temperature [K]. This equation becomes linear in log(L)reciprocal(T) plot. (see Fig.

Fig. 12

 12 Fig.12The comparison between the model predictions and the real experimental data.

TABLE VII EXPERIMENTAL

 VII POINTS USED TO COMPARE THE WIRES

		Voltage	Voltage		Frequency
				Frequency
		amplitude	level		level
		V	XV	f	Xf
	Test	[kV]	[-]	[kHz]	[-]
	I	1 32	-8 06	12 487	1 64
	II	1 23	-9 25	7 153	0 03

Table VII )

 VII . Confidence intervals are presented as a line where bottom bar denotes -, upper + and middle one characteristic lifespan . The values for test parameters I are shown in solid lines, for test II in dotted lines.

TABLE VIII COEFFICIENTS

 VIII OF VARIATION FOR WIRES A-C

	No.	Voltage level	Frequenc y level	A	CV	Magnet wire B CV	C	CV
				[-]	[%]	[-]	[% ]	[-]	[%]
	1	-1	-1	8 5 0	16 4	4 26	26 5	2 24	47 2
	2	-1	1	3 8 2	29 4	20 2 3	6 1	4 99	22 9
	3	1	-1	5 3 4	21 7	3 65	30 5	10 1 4	11 9
	4	1	1	3 7 1	30 1	11 1 8	10 8	7 17	16 4
	Average coefficient of variation	24. 4		18. 5		24. 6

Fig. 13 Comparison between the model predictions and the real experimental data for wires A-C at given stress level (see

Table VII); test I -solid line; test II -dotted line

ACKNOWLEDGMENT

The authors would like to thank both Nidec-Leroy Somer and the ANRT (French Agency for Research and Technology) for their financial contribution to this research.