Diane Borselli

Jean Michel Brunel

Olivier Gorgé

Jean Michel Bolla

Polyamino-isoprenyl derivatives as antibiotic adjuvants and motility inhibitors for Bordetella bronchiseptica porcine pulmonary infection treatment

Keywords: Antibiotic resistance, Combination therapy, Whole-cell screening, motility, virulence, Bordetella bronchiseptica

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In Europe, the overall sales of veterinary antimicrobial agents used in food producing animals represented 7680 tons in 2016 (https://bi.ema.europa.eu/analyticsSOAP/saw.dll?PortalPages), and the main use (around 60%) concerns the pig industry [START_REF] Schwarz | Use of antimicrobial agents in veterinary medicine and food animal production[END_REF][START_REF] Chauvin | A survey of group-level antibiotic prescriptions in pig production in France[END_REF]. The release of antibiotics in the environment by livestock production is one of the major contributing factors for the emergence of bacterial resistance in pathogens affecting both humans and animals [START_REF] Jechalke | Fate and effects of veterinary antibiotics in soil[END_REF][START_REF] Wichmann | Diverse antibiotic resistance genes in dairy cow manure[END_REF][START_REF] Bártíková | Veterinary drugs in the environment and their toxicity to plants[END_REF][START_REF] Albero | Persistence and availability of veterinary antibiotics in soil and soil-manure systems Andrade[END_REF]). Thus, it is crucial to decrease the antibiotic consumption in veterinary field and particularly in livestock without affecting animal health (Wellington et al. 2014, Pruden et al. 2014). Consequently, strategies have been proposed, and one of the most successful consists of a dual drug approach allowing an efficient enhancement of antibacterial activity while minimizing the drug concentration [START_REF] Brooks | Therapeutic strategies to combat antibiotic resistance[END_REF]Brooks 2014, Collignon et al. 2016).

The World Health Organization and the European Commission have published guidelines concerning the prudent use, in food production animals, of cephalosporin of 3 rd and 4 th generation and fluoroquinolones, which are considered as "critically important" antimicrobial agents in human medicine (https://bi.ema.europa.eu/analyticsSOAP/saw.dll?PortalPages, [START_REF] Briyne | Antibiotics used most commonly to treat animals in Europe[END_REF]. According to the international recommendations, the antimicrobials that could be used to treat porcine respiratory tract infections are tetracyclines, phenicols, macrolides, fluoroquinolones or a combination of trimethoprim and sulfonamides (Kadlec et al. 2004[START_REF] Kadlec | Efflux-mediated resistance to florfenicol and/or chloramphenicol in Bordetella bronchiseptica: identification of a novel chloramphenicol exporter[END_REF]. It is noteworthy that respiratory diseases in swine such as pneumonia and atrophic rhinitis are caused by the Gram-negative coccobacillus Bordetella bronchiseptica that requires a tetracycline treatment even if resistance can occur [START_REF] Prüller | Antimicrobial Susceptibility of Bordetella bronchiseptica Isolates from Swine and Companion Animals and Detection of Resistance Genes[END_REF][START_REF] Kadlec | Antimicrobial Resistance in Bordetella bronchiseptica[END_REF]. Otherwise, florfenicol is a good alternative [START_REF] Chauvin | A survey of group-level antibiotic prescriptions in pig production in France[END_REF], because this antibiotic has a good distribution in the body and few side-effects. However, although florfenicol was only used in veterinary medicine, a cross-resistance by efflux with its non-fluorinated analogue, chloramphenicol has been evidenced [START_REF] Kadlec | Efflux-mediated resistance to florfenicol and/or chloramphenicol in Bordetella bronchiseptica: identification of a novel chloramphenicol exporter[END_REF].

In an ongoing project dedicated to reducing the florfenicol consumption from breeding pig holdings, we screened polyamino-isoprenyl compounds that were previously described [START_REF] Borselli | Polyamino-Isoprenyl Derivatives Block Intrinsic Resistance of P. aeruginosa to Doxycycline and Chloramphenicol in vitro[END_REF] for their ability to potentiate florfenicol activity. The objective of this study is to identify a compound with significant activity and to elucidate its mechanism of action on the membrane physiology and to evaluate its impact on the bacterial motility.

Materials and methods

Bacterial strains and growth conditions

The B. bronchiseptica strain used in this study comes from the Institut Pasteur collection, CIP 55.110. Ten isolates from pig husbandries in France were obtained from Labofarm (Loudéac France) (Table 1). The bacterial identification was carried out by matrix-assisted laser desorption ionization-time of flight (MALDI-TOF) Biotyper (Brüker, Billerica, Germany) with comparison with the manufacturer's bacterial database. All the strains were grown either on Columbia agar at 35°C for 24h to 48h or in Columbia broth at 35°C for 24h.

Antibiotics and Chemicals

The antibiotic florfenicol was supplied by the pharmaceutical company Virbac (Carros, France). The antibiotic imipenem was purchased from Sequoia Research Products (Pangbourne, UK). All the chemicals Polymyxin B, Polymyxin B nonapeptide (PMBN), Phenylalanine-arginine beta-naphthylamide (PAßN), Carbonylcyanide mchlorophenylhydrazone (CCCP), Cetyl trimethylammonium bromide (CTAB), Dimethyl sulfoxide (DMSO), 3,3'-Dipropylthiacarbocyanine iodide (DiSC 3 (3)), Hydroxyethyl piperazineethanesulfonic acid (HEPES), Ethylene diamine tetraacetic acid (EDTA) and Benzalkonium chloride were purchased from Sigma Aldrich (St Quentin Fallavier, France). The polyamino-isoprenyl derivatives chemolibrary was described previously [START_REF] Bolla | Preparation of polyaminoisoprenyl derivatives for use in medical and nonmedical antibiotic or antiseptic treatment[END_REF].

MIC determination

Minimal inhibitory concentrations of antibiotics (MIC) were measured by the microdilution broth method in 96-well microtiter plates using the two-fold dilution method and according to the NCCLS guidelines. The inoculum was adjusted at 5x10 5 CFU/mL in a final volume of 200 µL. MIC was visually determined after 24 hours incubation at 37°C. Assays were performed in three independent biological experiments.

High content screening

The polyamino-isoprenyl derivatives chemical library was screened at 10 µM final concentration in the absence and in the presence of sub-inhibitory concentration of florfenicol (MIC/4) to identify only antibiotic adjuvants. We also added control molecules as polymyxin B, PAßN, CCCP, CTAB and benzalkonium chloride at 10 µM. The screening was performed in 96-well microtiter plates in Columbia broth with a final volume of 200 µL and a DMSO final concentration of 2.5%. The bacterial inoculum was adjusted to 5x10 5 CFU/mL. Microtiter plates were read at 600 nm on an Infinite M200 Pro plate reader (Tecan, Lyon, France) after 24h incubation at 35°C. Assays were performed in three independent biological experiments.

General procedure for the synthesis of compounds for the hit to lead procedure

The general synthetic pathway is illustrated for the preparation of compound 1. A mixture of farnesal (345 mg, 2.27 mmol), titanium(IV)isopropoxide (645 mg, 2.27 mmol) and spermine (2.27 mmol) in absolute methanol (5 mL) was stirred at room temperature for 12 hours. Sodium borohydride (172 mg, 4.5 mmol) was then added at 0ºC and the resulting mixture was stirred for an additional 2 hours. The reaction was then quenched by adding water (1 mL). Stirring was maintained at room temperature for 20 minutes. After filtration over a pad of Celite washing with methanol and ethylacetate, the solvents were removed under vacuum and the crude amine was purified by flash chromatography on silicagel. using CH2Cl2/MeOH/ NH4OH (7/3/1) as eluent affording the expected coupling product 1 in 64% yield (see also supplementary material).

Checkerboard assay

Combinations of polyamino-isoprenyl derivatives with florfenicol were tested by using the previously described microdilution checkerboard method [START_REF] Kadlec | Antimicrobial Resistance in Bordetella bronchiseptica[END_REF]. Briefly, an inoculum (100 µL) of 5x10 5 CFU/mL of B. bronchiseptica strain was added to 96-well microtiter plates containing a serial two-fold dilution of antimicrobial agents in Columbia broth. After incubation of plates during 24 h at 35°C, we determined the MIC for each combination and calculated the fractional inhibitory concentration indexes (FICIs) allowing us to characterize the level of efficiency of the combination. The FICIs are calculated as follows: FICI = FIC A + FIC B, where FIC A= MIC antibacterial A in combination/ MIC antibacterial A alone and FIC B= MIC antibacterial B in combination/ MIC antibacterial B alone. The antibacterial combination was considered synergistic when the FICI was ≤0.5, indifferent when 0.5 < FICI ≤ 4 and antagonistic when FICI > 4 [START_REF] Odds | Synergy, antagonism, and what the chequerboard puts between them[END_REF]. Outer membrane permeabilization assay 100 milliliters of Columbia broth were inoculated with an overnight culture of a B. bronchiseptica isolate producing ß-lactamases (isolate 77-A12). Once the cultures reached an the mid-logarithmic phase, imipenem was added (0.125 mg/L final concentration) for 2 hours, then cells were recovered by centrifugation (3,600 X g, 20 min, 20°C) and washed twice in 20 mM potassium phosphate buffer (pH 7.2) 1 mM MgCl 2 (PPB) supplemented with 30 µM of CCCP that allows the inactivation of active efflux [START_REF] Nagano | Kinetic behavior of the major multidrug efflux pump AcrB of Escherichia coli[END_REF]. After the second centrifugation, the cell suspension was adjusted to 0.5 OD 600 nm. One hundred microliters of the bacterial suspension were mixed with 50 µL of compound derivatives dilutions already set up in microplates, to give final concentrations ranging from 1.56 to 200 µM. Then, 50 µL of nitrocefin was added to obtain a final concentration of 50 µg/mL. The absorbance at 490 nm was monitored to follow the nitrocefin hydrolysis using a Sunrise microplate reader (Tecan) over 2 hours and 30 minutes. Experiments were performed in triplicate. For each compound, the efficacy of permeation was determined using the slope in the linear range, relatively to the control slope obtained with 100 µM polymyxin-B.

Real Time efflux assay

The strain CIP55.110 was inoculated into 20 mL of Columbia broth and grown for 24 h at 35°C to reach the stationary phase. Cells were recovered by centrifugation (3,600 X g 20 min, 20°C) and washed twice in PPB. The cell suspension was adjusted to 0.5 OD 600 nm and loaded with 1,2' dinaphthylamine (TCI-Europe SA, Zwinjndretch, Belgium) 32 µM final concentration, supplemented with the proton dissipator CCCP 30 μM. After overnight incubation, cells were washed in PPB and the bacterial suspension was adjusted to 0.5 OD 600 nm. In a 96-well Greiner black microplate (Greiner, Courtaboeuf, France) 50 µL of the desired tested compounds were mixed with 100 µL of the cell suspension yielding final concentration ranging from 12.5 to 200 µM. The dye transport was triggered after addition of 5 µL of Columbia broth and the fluorescence was monitored each 22 second during 30 min on an Infinite M200 microplate reader (Tecan) (excitation wavelength 370 nm and emission wavelength 420 nm). Polymyxin B is used as control in our experiments, this antibiotic is able to rapidly disrupt the proton-motive force without interfering with fluorescence measurements. Assays were performed in three independent biological experiments.

Inner Membrane depolarization assay

An overnight culture of bacterial strain CIP 55.110 was diluted 50-fold into 20 mL Columbia broth. After reaching an OD 600 nm of 0.5, cells were recovered by centrifugation (3,600 X g, 20 min, 20°C) and incubated 5 min at room temperature in 5 mM HEPES-10 mM EDTA (pH 7.0). They were then centrifuged (3,600 X g for 20 min at 20°C) and re-suspended in 5 mM HEPES (pH 7.0) supplemented with Columbia Broth 2.5% and adjusted to an OD 600 nm of 0.29. Fluorescence was monitored every 30 seconds (excitation wavelength 622 nm, emission wavelength 690 nm) after addition of 5 µL of a 160 µM solution of DiSC 3 (3) to 100 µL of the cell suspension to reach a final concentration of 7.6 µM. After a period of incubation (16.5 min) to allow the dye incorporation into the polarized membranes, 10 µL of compound dilutions were added. The difference in the relative fluorescence values (RFU) from the control containing only buffer and the control containing untreated bacteria in buffer is taken as the maximum level of depolarization. Assays were performed in three independent experiments.

Motility assay

Swimming motility was evaluated on tryptone-agar plates (tryptone (1% w/v), 0.5 % NaCl (w/v), yeast extract 0.5 % (w/v)) supplemented with agar 0.3 % (w/v) [START_REF] Murray | FlhF is required for swimming and swarming in Pseudomonas aeruginosa[END_REF]. Swarming motility was evaluated on tryptone-agar plates supplemented with agar 0.5 % (w/v) [START_REF] Murray | FlhF is required for swimming and swarming in Pseudomonas aeruginosa[END_REF]. For both assays, sterilized tryptone-agar was dispensed to Petri dishes containing either no compound or compound 1 (Cpd1) at 10 µM and left to dry at room temperature for 2h. An inoculum obtained after dilution of an overnight culture was adjusted to an OD 600 nm of 1.1. The plates were inoculated with a sterile toothpick and incubated in a non-reverse position at 35°C during the indicated times (24h, 48h or 72h) and halo diameters corresponding to bacterial growth were measured and reported. Assays were performed in three independent biological experiments.

Microscopy live tracking and acquisition

A drop of each bacterial culture in exponential growth was deposited on a microscope slide and Cpd1 was added where indicated and immediately observed. Acquisition was performed in resonant mode with the LEICA SP5 CLS by using a laser HeNe at 633nm and a transmission PMT. The scans were recorded at a 512x512 resolution size and time laps over 200 frames. Their subsequent analysis was realized with the free software ImageJ using the MtrackJ plugging permitting to determine the average speed in µm/sec of each bacterium followed. The results reported correspond to mean values obtained from 15 tracking's measurement for each condition analyzed.

Time kill study

The effectiveness of Cpd1 and florfenicol combination against the reference strain CIP 55.110 was determined by the time-kill assay. An overnight culture was diluted to 50-fold into 5 mL of Columbia agar and grown until the cell suspension reached the mid-logarithmic phase. The inoculum was then adjusted to 10 7 CFU/mL in Columbia broth supplemented with either, no addition, sub-inhibitory concentration of florfenicol (MIC/4), sub-inhibitory concentration of Cpd1 (7.5 µM) and sub-inhibitory concentration of both. Each tube containing 1 mL was incubated at 35°C and the bacterial count was determined after several times of incubation: 0, 1, 3, 6, 9, and 12 h by spreading the appropriate dilutions on Columbia agar plates. The plates were incubated overnight at 35°C before colonies counting. The curves obtained are the result of two independent experiments.

Libraries construction for bioinformatic analysis

Libraries were prepared with NebNext kit (New England Biolabs, Ipswich, MA) after Covaris ME220 Covaris Focused-ultrasonicator (Covaris, Woburn, MA) shearing, according to manufacturer protocol, and sequenced on a NextSeq550 (Illumina, San Diego, CA) with High Output 300 cycles V2 cartridge (ref. FC-404-2004). Antibiotic resistance profiles of the four strains were tested against CARD (22) and oneCodex, with confirmation of phenotypic resistance except for florfenicol.

Results

High content screening: selection of florfenicol antibiotic chemosensitizer

The MICs to florfenicol of 10 clinical strains and the reference one were determined, value ranged from 2 to 32 mg/L showing different level of resistance to this antibiotic (Table 1).

A polyamino-isoprenyl chemical library containing 60 molecules has been tested at a 10 µM concentration in combination with florfenicol at sub-inhibitory concentration (MIC/4 = 1 mg/L) on the reference strain of B. bronchiseptica CIP 55.110 to identify compounds able to decrease florfenicol MIC below 1mg/L. To avoid compounds with intrinsic activity, a control experiment was performed in the absence of florfenicol. We then identified compounds that could only kill bacteria in the presence of florfenicol. Amongst the tested compounds, only Cpd1 led to an 85% inhibition of the bacterial growth under these experimental conditions.

Efficacy of compounds on animal isolates

To extend our study, we evaluated the efficacy of Cpd1 on ten animal isolates. This compound was able to restore the susceptibility of 8/10 isolates to florfenicol. Nevertheless, two of them were still resistant to florfenicol alone and in combination (Figure 1). It is noteworthy that, as already reported in literature (Corbière-Priot and Duménil 1996), a difference in MICs values was observed, depending on the method used for the evaluation; the MIC value being higher by using the microdilution broth method with respect to the one obtained by agar plate method.

Hit to lead procedure

In the perspective of improving the efficiency of Cpd1, several derivatives were synthetized (compounds 2-7, Figure 2) as their corresponding water-soluble tartrate salts to increase their solubility in bacteria growth media and reduce solvent detrimental side-effects. Compounds 1-4 possess a common farnesyl moiety whereas derivatives 5-7 a geranyl one. Moreover, each pair Cpd2 / Cpd6, Cp3 /Cpd5 and Cpd4 /Cpd7 have in common the same polyamine group (Figure 2). The MIC of these compounds were determined for each strain, no significant intrinsic activity was observed for any of these new compounds (Table 1).

Checkerboard assay

To determine both the minimal efficient combinations of the designed compounds and florfenicol that are necessary to inhibit the bacterial growth, we performed a checkerboard assay on animal isolates, the strain CIP 55.110 being used as control. The results are summarized in Table 2. Cpd1 exhibited a FIC index of about 0.5 that reflects the strong synergy between Cpd1 and florfenicol used at MIC/2. We noticed that higher concentrations are necessary to observe a synergy using florfenicol at MIC/4. We also observed the same range of FIC index for the farnesyl compounds (Cpd2-Cpd4). On the other hand, we were unable to determine the FIC indexes for the geranyl ones (Cpd5-Cpd7) due to the high concentrations needed to inhibit the bacterial growth as mentioned by ND in Table 2.

Presence of an active efflux in B. bronchiseptica

For all the strains tested, we observed a MIC for florfenicol ranging from 2 to 4 µg/mL except for two strains 42-F10 and SR11-14 exhibiting a MIC over the resistance breakpoint of 8 µg/mL [START_REF] White | Characterization of Chloramphenicol and Florfenicol Resistance in Escherichia coli Associated with Bovine Diarrhea[END_REF]. We previously reported that efflux mechanisms are produced at a basal level in Gram negative bacteria [START_REF] Mamelli | Prevalence of efflux activity in low-level macrolide-resistant Campylobacter species[END_REF], Borselli et al. 2016) and can account for the observed low-level of resistance that can be strongly induced when exposed to toxic compounds [START_REF] Hay | Antibiotic Inducibility of the mexXY Multidrug Efflux Operon of Pseudomonas aeruginosa: Involvement of the MexZ Anti-Repressor ArmZ[END_REF][START_REF] Ghisalberti | Chloramphenicol and expression of multidrug efflux pump in Enterobacter aerogenes[END_REF]. To evaluate the presence of an active efflux in B. bronchiseptica, we measured the ability of the strain CIP55.110 to expel the 1,2'dNA, a fluorescent dye which is a substrate of efflux pumps [START_REF] Bohnert | Determination of Real-Time Efflux Phenotypes in Escherichia coli AcrB Binding Pocket Phenylalanine Mutants Using a 1,2'-Dinaphthylamine Efflux Assay[END_REF]. According to our previous report [START_REF] Borselli | Polyamino-Isoprenyl Derivatives Block Intrinsic Resistance of P. aeruginosa to Doxycycline and Chloramphenicol in vitro[END_REF], we first observed an accumulation of the dye after addition of CCCP at a 30 µM final concentration whereas no accumulation was observed in its absence. This suggested that de-energization of the cytoplasmic membrane by CCCP blocked dye releasing. Conversely, pre-loaded bacteria incubated with culture media led to a fluorescence decrease suggesting an active efflux as shown in Figure 3 (black lane) where the strain CIP55.110 can expel about 75% of the pre-loaded dye. This result allowed us to compare the ability of the different compounds to inhibit this efflux. Action of the derivatives on dye efflux Some combinations between compounds 1-7 and florfenicol were found to restore susceptibility of the strains towards this antibiotic. This might suggest that the action of the compounds contributed to a better accumulation of florfenicol into the bacteria, increasing the intracellular concentration over the threshold of susceptibility.

To understand how the derivatives and especially the farnesyl ones could potentiate the antibiotic activity, we evaluated their ability to block the efflux activity in B. bronchiseptica (Figure 3). An example of the results obtained with compounds used at 100 µM is presented in Figure 3A. As shown on this graph, the strain CIP55.110 is able to expel the dye (black lane) and this transport is dependent of energy (violet lane) and compounds exhibit different level of efflux-inhibition. To better compare the efficiency of compounds, we performed a dose-response assay ranging from 200µM to 12.5µM, the results are summarized in figure 3B. We observed that inhibition mainly concern compounds 1 to 4 and that no inhibition was found in our conditions, below 25µM. In addition, we observed a significant increase of inhibition, from 25µM to 200µM for compound 1-4. At 100 µM, the dye efflux was inhibited by 50% by using Cpd1 and Cpd2 whereas Cpd3 and Cpd4 led to a 30% and 17% efflux inhibition, respectively. Under similar experimental conditions, Cpd5-7 did not present any significant effect.

The other parameter that could modulate the antibiotic intracellular concentration is the outer-membrane permeability. Thus, we evaluated the permeabilization activity of the polyamino-isoprenyl derivatives by using previously reported nitrocefin hydrolysis method [START_REF] Jechalke | Fate and effects of veterinary antibiotics in soil[END_REF]. We took advantage of the isolate 77-A12 that produces a ß-lactamase (not shown). Interestingly, geranyl compounds (Cpd5-Cpd7) did not exhibit any permeabilization activity while farnesyl ones (Cpd1-Cpd4) increased the permeability of the outer membrane from 30 to 50% considering that a maximum rate of permeation was obtained by using polymyxin B (100 µM) (Figure 4A). However, no influence of the amine structure was detected, Cpd4 (branched amine) presenting a similar activity with respect to the three other farnesyl compounds bearing a linear amine.

In Gram negative bacteria, the PMF drives many of the efflux pumps and inner membrane transporters, and our compounds are able to inhibit efflux of the fluorescent dye used (Figure 3). Consequently, it is interesting to determine if the derivatives could alter the proton motive force across the inner membrane of B. bronchiseptica. As shown in figure 4B, addition of polyamino-isoprenyl derivatives lead to an increase of the level of fluorescence that reflects the decrease of the proton-motive force. In this case, Cpd1 and Cpd2 cause the most important depolarization at about 60% of the inner membrane. Surprisingly, derivative Cpd6 and Cpd4 were also able to depolarize the inner membrane up to 40%. Nevertheless, we observe a slight effect for Cpd5 and Cp7 which depolarized the inner membrane up to 20% and 10%, respectively. Molecules responsible for the most important depolarization remained the farnesyl ones while the geranyl compounds displayed the lower rate of depolarization. In addition, the presence of a branched amine on the farnesyl moiety greatly influence the activity (compare Cpd1/Cpd4, Cpd2/Cpd4) except for Cpd3, but one must consider that it is due to the presence of only 3 amino groups instead of Cpd4, as it is encountered for the other compounds. Thus, conversely to the results obtained from the outer membrane permeation assays, herein the activity not only depends on the isoprenyl moiety of the compound but also of the polyamine structure.

Cpd1 and motility inhibition

As the derivatives can largely impair the proton-motive force and, particularly Cpd1, we were wondering if this compound could influence the flagella-driven motility that is highly dependent from the energy triggered by the PMF. We tested here the ability of Cpd1 to inhibit the swimming and swarming of two strains of B. bronchiseptica, the CIP 55.110 which is susceptible to florfenicol and the SR11-14 which is resistant both to florfenicol and to the combination florfenicol/Cpd1. Thus, we measured the diameter of the motility halo after 24 hours of incubation at 25°C to assess the functioning of the flagella. The motility of each strain was evaluated in the presence and absence of Cpd1 and/or NaCl by considering that the flagella could use both the proton and the sodium gradient. We observed that Cpd1 inhibited the swimming motility at about 40% for both strains (Figure 5A) whereas a slight effect was encountered towards the swarming motility ranging from 20% and 30% inhibition depending on the considered strain (Figure 5B). Nevertheless, it is noteworthy that the swarming inhibition by Cpd1 is stronger in the absence of NaCl (up to 40%, (Figure 5B). To further characterize the motility inhibition by Cpd1, we performed a real time assay by monitoring the motility speed of bacteria after extemporaneous addition of the compound under the microscope. As shown in figure 5C, a dramatic decrease of speed motility was observed for both strains. The observed inhibition of motility for both strains CIP55.110 and SR11-14 correlated with the phenotype observed previously, strongly suggests that Cpd1 inhibits flagella motilities by disrupting the PMF.

Time effect on bacterial growth

To further characterize the Cpd1/florfenicol combination, its in vitro pharmacodynamic (PD) parameters were evaluated using time-kill kinetics assays (Fig 6). Curves were obtained by plotting the number of CFU at every time point for the synergistic concentrations of the drugs.

As expected, the use of florfenicol at a sub-inhibitory concentration (MIC/4) had no effect on the cell growth such as the Cpd1 used at a concentration of 7.5 µM which corresponds to its MIC/32. Nevertheless, the combination of both totally inhibits the cell growth and, after 9 hours of incubation, the reduction of bacterial cell count was around two Log compared to the bacteria incubated with florfenicol or Cpd1 alone. After 12 hours of incubation, the cell count was still reduced of four Log demonstrating a significant effect of the combination compared to the same antimicrobials administered alone (Figure 6). The combination florfenicol/Cpd1 appeared to be bacteriostatic as florfenicol used alone.

Florfenicol resistance mechanism investigation

Two of the strains included in our study (42F10 and SR11-14) exhibited resistance to florfenicol (MIC = 8 and 32 µg/mL, respectively). Such resistance is not common but has already been described and the floR gene was identified in some isolates as responsible for this resistance [START_REF] Kadlec | Efflux-mediated resistance to florfenicol and/or chloramphenicol in Bordetella bronchiseptica: identification of a novel chloramphenicol exporter[END_REF][START_REF] Kadlec | Antimicrobial Resistance in Bordetella bronchiseptica[END_REF]. To check if floR could be associated with florfenicol resistance in these two strains, we designed primers to amplify the gene according to the sequence previously described in the study of [START_REF] Kadlec | Efflux-mediated resistance to florfenicol and/or chloramphenicol in Bordetella bronchiseptica: identification of a novel chloramphenicol exporter[END_REF]. No amplification was detected despite several attempts suggesting that another mechanism of resistance was involved in these strains. Taken together, our data suggested that another mechanism was involved in florfenicol resistance in these two strains. We thus decided to determine the complete sequenced genomes of those two strains, as well as two other strains, our reference CIP55-110 and 77A12 which was resistant to ß-lactams, were realized (SRA accession: PRJNA551886). In order to be able to highlight a new gene of resistance or a floR derived one, we mapped our two libraries made from resistant strains against reference strain B. bronchiseptica 253, by using BWA MeM software (version 0.7.16a-r1181) with a minimum seed length of 28, all other options kept to standard. Owing the fact that this strain does not have resistance to florfenicol, we selected reads that did not map to this strain. We reconstructed de novo the two other strains CIP55-110 and 77H12 with SPAdes version 3.9.1 [START_REF] Bankevich | SPAdes: a new genome assembly algorithm and its applications to single-cell sequencing[END_REF] and we mapped the remaining reads to the obtained contigs with the same goal. We ended with 581 k-reads and 377 k-reads for SR11-14 and 42F10, respectively (Supplemental Material). We reconstructed de novo contigs with those remaining reads, keeping in mind the hypothesis that genes responsible for florfenicol resistance would be present in such contigs. We ended with 416 contigs and 331 contigs, respectively, that were mapped against all the florfenicol and/or chloramphenicol resistance associated genes published until now (634 sequences). Unfortunately, we found any match. As a last attempt, considering that protein sequence is better preserved than nucleotide sequence, we performed a blastx of all our contigs against all the available florfenicol resistance related protein sequences but even there unsuccessfully. Genes associated with resistance to antibiotics specifically detected in those two strains were found, indicating that our pipeline was able to detect genes present only in those strains and not in the reference and non-resistant ones (sul2 in SR11-14 and TEM-116 in 42F10). Interestingly, genes sharing homology with ABC transporters and OptrA [START_REF] Tamang | Detection of novel oxazolidinone and phenicol resistance gene optrA in enterococcal isolates from food animals and animal carcasses[END_REF], that have been described to be associated with florfenicol resistance in Enterococcus faecium have been detected colocalized on same contigs, that also exhibit plasmid associated features. Interestingly, OptrA was shown to afford cross-resistance to chloramphenicol and florfenicol in E. faecium [START_REF] Wang | A novel gene, optrA, that confers transferable resistance to oxazolidinones and phenicols and its presence in Enterococcus faecalis and Enterococcus faecium of human and animal origin[END_REF][START_REF] Bender | Rapid emergence of highly variable and transferable oxazolidinone and phenicol resistance gene optrA in German Enterococcus spp. clinical isolates[END_REF][START_REF] Na | Detection of oxazolidinone and phenicol resistant enterococcal isolates from duck feces and carcasses[END_REF]) that can be correlated with the cross-resistance to these two antibiotics in the two strains studied herein (see Supplementary Table 1).

Discussion

The international and European authorities requested to use with parsimony antibiotics which can favor emergence of resistance in human and veterinary medicine. For the first time, an alternate way is studied by using adjuvant molecules that enhance florfenicol antibiotic activity. This strategy allowed us to decrease by four the MIC of the majority of strains tested here with small amounts of polyamino-isoprenyl derivatives, previously known to potentiate antibiotics by acting on membrane functions [START_REF] Blanchet | Polyamine derivatives: a revival of an old neglected scaffold to fight resistant Gram-negative bacteria?[END_REF]. Thus, even if florfenicol is only used to treat animal infections it presents cross resistance with chloramphenicol and it appears important to prevent the spread to human pathogens.

Today, it is recognized that human health is directly related to animal health and the environment. The dramatic increase in antibiotic resistance and the scarcity of new drugs on the market in recent decades highlight the threat of moving to the past era of antibiotics, with a significant increase in infection mortality. In this context, taking into account the "One Health" problem becomes an urgent need. This must allow collaborative efforts between health actors, but also breeders and those involved in environmental management.

This includes the involvement of a research at the interface between chemistry and microbiology, to develop new infection control strategies, by developing molecules that target specific new bacterial processes and / or new molecules that block / inhibit resistance mechanisms already under way. In recent decades, the efflux mechanisms have become increasingly important for human and animal health, we propose to block the mechanisms of resistance by efflux of Gram-negative bacteria.

According to our previous work [START_REF] Borselli | Polyamino-Isoprenyl Derivatives Block Intrinsic Resistance of P. aeruginosa to Doxycycline and Chloramphenicol in vitro[END_REF], we evaluated enhancing activity of our polyamino-isoprenyl chemical library (used at a 10 µM concentration) in the presence of florfenicol at a sub-inhibitory concentration against B. bronchiseptica, CIP 55.110 reference strain. Thus, Cpd1 was identified as an interesting chemosensitizer of B. bronchiseptica to florfenicol and evaluated against ten animal isolates leading to the restoration of susceptibility for 8 of these 10 strains. Two isolates were resistant to the combination, and the mechanism of resistance involved remains unknown.

Subsequently, a pharmacomodulation study was performed to try to improve the encountered activity. In this context, six derivatives, three geranyl ones and their corresponding farnesyl homologues were prepared and evaluated in a checkerboard assay. First, we noticed that Cpd1 remained the better tested compound needing the lowest concentration to potentiate florfenicol activity. It is also noteworthy than all farnesyl compounds showed better efficiency than geranyl ones. As polyamines are well known agents to disrupt membranes [START_REF] Blanchet | Polyamine derivatives: a revival of an old neglected scaffold to fight resistant Gram-negative bacteria?[END_REF], we investigated the effect of the compounds on membranes physiology and stability. We investigated the permeability of the outer membrane which play a key role in antibiotic accumulation into Gram-negative bacteria and as expected, all the tested polyamino-isoprenyl compounds increase the outer membrane permeability, farnesyl compounds being better permeabilizers than geranyl ones.

The presence of an active efflux in B. bronchiseptica was demonstrated by using CCCP allowing an efficient dye loading into the bacterial membranes. These results corroborate the genome sequence analysis from B. pertussis (a human and animal pathogen closely related to B. bronchiseptica) suggesting the presence of putative RND efflux pumps coding sequences (Andrade et al. 2014). To our knowledge, it is also the first time that efflux was determined in B. bronchiseptica. Thereby, we evaluated the effect of Cpd1 and its derivatives on the efflux activity of B. bronchiseptica. The molecules able to inhibit the dye efflux were the farnesyl ones while the geranyl derivatives demonstrated no ability to block the efflux activity (Cpd1 and Cpd4 leading to 50 % inhibition (used at 100 µM)). Moreover, we observed a dose response effect for each farnesyl compound as encountered in a previous work on Pseudomonas [START_REF] Borselli | Polyamino-Isoprenyl Derivatives Block Intrinsic Resistance of P. aeruginosa to Doxycycline and Chloramphenicol in vitro[END_REF]. It also appeared that the farnesyl moiety was essential to obtain high activities. All these data led us to envision that these compounds could act against PMF, which is required for many cell processes, as efflux pump systems but also the flagella motors.

The flagella that potentially contribute to virulence, could be considered as a new target for the development of motility inhibitors to circumvent the spread of bacterial infections [START_REF] Malapaka | High-Throughput Screening for Antimicrobial Compounds Using a 96-Well Format Bacterial Motility Absorbance Assay[END_REF]). Effect of Cpd1 was studied and a significant inhibition on the flagella-dependent motilities was observed. Nevertheless, since B. bronchiseptica can also use the sodium gradient, we were unable to discriminate if Cpd1 targets preferentially the proton or sodium gradient. We concluded that this effect is probably due to a general inhibition. On the other hand, we noticed that the inhibition of motility occurred in an independent way of the resistance level of the strain. Indeed, a resistant strain (SR11-14) and the reference strain CIP55.110 gave the same response to inhibition of motility after treatment with Cpd1. More interestingly, the study of the resistance mechanism of these strains by bioinformatic investigations showed the presence of a gene sharing homologies with the gene coding the ABC-F type ribosomal protection protein OptrA, known to confer florfenicol and chloramphenicol resistance in Enterococcus faecium and to use ATP as a source of energy [START_REF] Wang | A novel gene, optrA, that confers transferable resistance to oxazolidinones and phenicols and its presence in Enterococcus faecalis and Enterococcus faecium of human and animal origin[END_REF][START_REF] Bender | Rapid emergence of highly variable and transferable oxazolidinone and phenicol resistance gene optrA in German Enterococcus spp. clinical isolates[END_REF][START_REF] Na | Detection of oxazolidinone and phenicol resistant enterococcal isolates from duck feces and carcasses[END_REF]. This is consistent with our results demonstrating that Cpd1 targets the PMF and correlates with the absence of efficacy towards the strains exhibiting this mechanism of resistance. In the strain SR 11-14 one might consider that OptrA and/or efflux pumps are overexpressed in this strain. We can hypothesize that florfenicol resistance could have been acquired through horizontal transfer from Enterococcus, and this hypothesis is strengthened by the fact that the contig containing resistance associated genes showed high homology with plasmids found in such bacteria.

Finally, to better characterize the antibiotic/derivative combination we did time kill assays at the concentrations which have shown synergistic effect. This florfenicol/Cpd1 combination reduces the antibiotic efficient concentration four times and so could allow to reduce drastically the amount of the antibiotic used. Because Cpd1 did not modify the bacteriostatic activity of florfenicol, but increased its efficiency, one may consider that Cpd1 allows an increase of the intra-cellular concentration of the antibiotic [START_REF] Vergalli | Spectrofluorimetric quantification of antibiotic drug concentration in bacterial cells for the characterization of translocation across bacterial membranes[END_REF]. Experiments are in progress to evaluate this hypothesis and results will be reported in due course.

Figures legend

Figure 1: The ability of B. bronchiseptica reference strain CIP55,110 (5 µL of 5 10 5 CFU were spotted on the plates) to grow under various experimental conditions was assessed in solid media containing (left to right) no compound, Cpd1 (compound 1) (10 µM), FF (Florfenicol) (2µg/mL), FF (2µg/mL) + Cpd1 (10 µM). Figure 2: Structure of farnesyl and geranyl polyamine derivatives Cpd1-Cpd7. Figure 3: Inhibition of the efflux of the 1,2' dinaphthylamine dye by derivatives 1-7. 3A. Efflux was triggered after 200s by the addition of culture media. The intensity of fluorescence emission for 1,2' dinaphthylamine is given in relative fluorescence units (RFU). Each compound was tested at 100 µM concentration; as controls an experiment without addition of compounds and culture media (purple curve) was also included. 3B. Percentage of efflux inhibition obtained for each compound. Error bars represent standard deviations of 3 independent biological experiments. Figure 4: Effect of polyamine derivatives on membrane functions 4A) Outer membrane permeabilization by the different compounds at 100 µM. Nitrocefin hydrolysis was followed at 490nm. 4B) Inner membrane depolarization measured by the increase fluorescence of DisC 3 (5) in the presence of the different compounds at 100 µM. Error bars represent standard deviations of 3 independent biological experiments. Figure 5: Effect of 10 µM of the hit compound on bacterial motility of a susceptible strain (CIP55.110) and a florfenicol resistant isolate (SR11-14) +/-NaCl. Graph represent the percentage of inhibition of the motility halo in presence of Cpd1. 5A) Picture taken after 24h incubation of the swimming plate. 5B) Swarming motility, halo measured after 48 h incubation. 5C) Picture taken after 24h of incubation of swimming plate with NaCl inoculated with SR11-14, containing no compound (left) and 10 µM of Cpd1 (right). In all cases, error bars represent standard deviations of 3 independent experiments. Figure 6: Time-kill curves of florfenicol (FF) (0.5 mg/L), Cpd1 (7.5 µM) and of the combination FF (0.5 mg/L)+Cpd1 (7.5 µM) over a 12 hours period against strain CIP55.110. Errors bars represent standard deviations of 2 independent biological experiments.

Table 1 :

 1 Susceptibilities to florfenicol (FF) and polyamine derivatives (Cpd1-Cpd7) of 641 various B. bronchiseptica strains. 642 643

	Strains	Source	MIC (µg/mL)	MIC (µM)
			FF	Cpd1 Cpd2 Cpd3 Cpd4 Cpd5 Cpd6 Cpd7
	CIP55.110

Conflict of interest Statement

The author(s) declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Authors contribution statement

All authors conceived the approach; DB carried out all the experiments related to bacteria; JM Brunel carried out the synthesis, purification and analyses of the compounds; OG performed the DNA sequencing and the sequence analyses; DB, JM Brunel and JM Bolla wrote the main manuscript text; DB and JM Brunel prepared the figures; all authors reviewed the manuscript. Funding This research was supported by Aix-Marseille Université, Service de Santé des Armées, the SATT-SE and the Virbac company. DB was supported by a French Agency of Research and Technology fellowship (Conventions industrielles de formation par la recherche (Cifre)).

Acknowledgements

The authors thank Dr Jean-Marie Pagès for helpful discussions in the course of this work and for commenting on the manuscript; Dr Pascal Weber for his numerous advices and his excellent contribution in confocal microscopy.


Abdessalem Abidi

Qianxue Wang

Belgacem Bouallègue

Mohsen Machhout

Christophe Guyeux

Quantitative Evaluation of Chaotic CBC Mode of Operation

Keywords: Cipher Block Chaining, Mode of operation, Block cipher, Chaos, Devaney's chaos, sensivity, expansivity

In cryptography, block ciphers have a very simple principle. They do not treat the original text bit by bit but they manipulate blocks of text. This manipulation follows various ways which are called block cipher modes of operation. Each one of these modes possesses owns characteristics and its specific security properties. Among them, we quote the Cipher Block Chaining (CBC) mode. This paper presents a complete topological study of the CBC block cipher mode of operation. To do this, we began by proving the chaotic behavior of this mode according to Devaney.

Introduction

Block ciphers have a very simple principle. They do not treat the original text bit by bit but they manipulate blocks of text -for instance, a block of 64 bits for the DES (Data Encryption Standard) or a block of 128 bits for the AES (Advanced Encryption Standard) algorithm. In fact, the original text is broken into blocks of N bits. For each block, the encryption algorithm is applied to obtain an encrypted block that has the same size. Then we gather all blocks, which are encrypted separately, to obtain the complete encrypted message. For decryption, we proceed in the same way, but this time starting from the cipher text to obtain the original message using the decryption algorithm instead of the encryption function. So, it is not sufficient to put anyhow a block cipher algorithm in a program. We can instead use these algorithms in various ways according to their specific needs. These ways are called the block cipher modes of operation. There are several modes of operation and each mode has owns characteristics and its specific security properties. In this paper, we will consider only one of these modes, which is the cipher block chaining (CBC) mode, and we will study it according to chaos.

The chaos theory we consider in this paper is the Devaney's topological one [START_REF] Devaney | An Introduction to Chaotic Dynamical Systems[END_REF]. In addition to being recognized as one of the best mathematical definition of chaos, this theory offers a framework with qualitative and quantitative tools to evaluate the notion of unpredictability [START_REF] Jacques M Bahi | Efficient and cryptographically secure generation of chaotic pseudorandom numbers on gpu[END_REF]. As an application of our fundamental results, we are interested in the area of information safety and security. In this research work, which is an extension of our previous article [START_REF] Abidi | Proving chaotic behavior of cbc mode of operation[END_REF], the theoretical study of the chaotic behavior for the CBC mode of operation is deepened by evaluating its level of sensibility and expansivity [START_REF] Bahi | Discrete Dynamical Systems and Chaotic Machines: Theory and Applications[END_REF].

The remainder of this research work is organized as follows. In Section 2, we will recall some basic definitions concerning chaos and cipher-block chaining mode of operation. Section 3 is devoted to the recall of our previous research works. In Section 4 quantitative topological properties for chaotic CBC mode of operation is studied in detail. This research work ends by a conclusion section in which our contribution is recalled and some intended future work are proposed.

Basic recalls

This section is devoted to basic definitions and terminologies in the field of topological chaos and in the one of block cipher mode of operation.

Devaney's Chaotic Dynamical Systems

In the remainder of this article, S n denotes the n th term of a sequence S while X N is the set of all sequences whose elements belong to X . V i stands for the i th component of a vector V . f k = f • ... • f is for the k th composition of a function f . N is the set of natural (non-negative) numbers, while N * stands for the positive integers 1, 2, 3, . . . Finally, the following notation is used: 1; N = {1, 2, . . . , N }.

Consider a topological space (X , τ ) and a continuous function f : X → X on (X , Z).

Definition 1 The function f is topologically transitive if, for any pair of open sets U, V ⊂ X , there exists an integer k > 0 such that

f k (U ) ∩ V = ∅. Definition 2 An element x is a periodic point for f of period n ∈ N, n > 1, if f n (x) = x.
f is regular on (X , τ ) if the set of periodic points for f is dense in X : for any point x in X , any neighborhood of x contains at least one periodic point.

Definition 3 (Devaney's formulation of chaos [START_REF] Devaney | An Introduction to Chaotic Dynamical Systems[END_REF]) The function f is chaotic on (X , τ ) if f is regular and topologically transitive.

The chaos property is strongly linked to the notion of "sensitivity", defined on a metric space (X , d) by: Definition 4 The function f has sensitive dependence on initial conditions if there exists δ > 0 such that, for any x ∈ X and any neighborhood V of x, there exist y ∈ V and n > 0 such that

d (f n (x), f n (y)) > δ.
δ is called the constant of sensitivity of f . Indeed, Banks et al. have proven in [START_REF] Banks | On devaney's definition of chaos[END_REF] that when f is chaotic and (X , d) is a metric space, then f has the property of sensitive dependence on initial conditions (this property was formerly an element of the Devaney's definition of chaos). Additionally, the transitivity property is often obtained as a consequence of the strong transitivity one, which is defined below [START_REF] Guyeux | A topological study of chaotic iterations. application to hash functions[END_REF]. Definition 5 f is strongly transitive on (X , d) if, for all point x, y ∈ X and for all neighborhood V of x, it exists n ∈ N and x ∈ V such that f n (x ) = y.

Finally, a function f has a constant of expansivity equal to ε if an arbitrarily small error on any initial condition is always magnified until ε [START_REF] Guyeux | A topological study of chaotic iterations. application to hash functions[END_REF]. Mathematically speaking,

Definition 6 The function f is said to have the property of expansivity if ∃ε > 0, ∀x = y, ∃n ∈ N, d(f n (x), f n (y)) ε.
Then, ε is the constant of expansivity of f. We also say that f is ε-expansive.

CBC properties

Like some other modes of operation, the CBC mode requires not only a plaintext but also an initialization vector (IV) as input. In what follows, we will show how this mode of operation works in practice.

Initialisation vector IV

As what has been already announced, in addition to the plaintext, the CBC mode of operation requires an initialization vector (denoted as IV in what follows) in order to randomize the encryption. This vector is used to produce distinct ciphertexts even if the same plaintext is encrypted multiple times, without the need of a slower re-keying process [START_REF] Huang | A novel structure with dynamic operation mode for symmetric-key block ciphers[END_REF].

An initialization vector must be generated for each execution of the encryption operation, and the same vector is necessary for the corresponding execution of the decryption operation, see Figure 1. Therefore the IV, or information that is sufficient to calculate it, must be available to each party of any communication. The initialization vector does not need to be secret, so the IV, or information sufficient to determine the IV, may be transmitted with the cipher text. In addition, the initialization vector must be unpredictable: for any given plaintext, it must not be possible to predict the IV that will be associated to the plaintext, in advance to the vector generation [START_REF] Dworkin | Recommendation for block cipher modes of operation. methods and techniques[END_REF].

CBC mode characteristics

Cipher block chaining is a block cipher mode that provides confidentiality but not message integrity in cryptography. The CBC mode offers a solution to the greatest part of the problems presented by the ECB (Electronic codebook) for example [START_REF] Schiltz | Les modes opératoires de la cryptographie symétrique[END_REF] as, due to the CBC mode, the encryption will depend on the context. Indeed, the cipher text of each encrypted block will depend not only on the initialization vector IV but also on the plaintext of all preceding blocks. Specifically, the binary operator XOR is applied between the current bloc of the plaintext and the previous block of the cipher text, as depicted in Figure 1. Then, we apply the encryption function to the result of this operation. For the first block, the initialization vector takes place of the previous cipher text block.

CBC mode has several advantages. In fact, this mode encrypts the same plaintext differently with different initialization vectors. In addition, the encryption of each block depends on the preceding block and therefore, if the order of the cipher text blocks is modified, the decryption will be impossible and the recipient realizes the problem. Furthermore, if a transmission error affects the encrypted block C i , then only the blocks m i and m i+1 are assigned, the other blocks will be determined correctly.

The main objective of this series of articles regarding the chaotic topological behavior of the CBC mode of operation is to understand in which extent this mode depends on its inputs. More precisely, is it possible to understand this dependence, in such a way that the effects of a modification of the IV and/or the message can be predicted? If so, this kind of weakness could be considered in the design of specific attacks, while if the converse is proven, that is to say, if the mid-to-long term effects of a slight modification of the input cannot be predicted, that chaotic dependence will make such attacks inefficient. In what follows, we will summarize the results which proof the chaotic behaviour of the CBC mode of operation.

Previously obtained results

In this section, we are interested to recall our previous results. They have been detailed in [START_REF] Abidi | Proving chaotic behavior of cbc mode of operation[END_REF], in which we have proven that some well chosen block ciphers can lead to a chaotic behavior of the CBC mode of operation. Indeed, this mode can be seen as a discrete dynamical system (recurrent sequence), whose evolution can thus be studied using common tools taken from the mathematical analysis [START_REF] Bahi | Evaluating quality of chaotic pseudo-random generators. application to information hiding[END_REF].

Modeling the CBC mode as a dynamical system

Our modeling follows a same canvas than what has be done for hash functions [START_REF] Bahi | Hash functions using chaotic iterations[END_REF][START_REF] Guyeux | A topological study of chaotic iterations. application to hash functions[END_REF] or pseudorandom number generation [START_REF] Bahi | Evaluating quality of chaotic pseudo-random generators. application to information hiding[END_REF]. Let us consider the CBC mode of operation with a keyed encryption function ε k : B N → B N depending on a secret key k, where N is the size for the block cipher, and D k : B N → B N is the associated decryption function, which is such that ∀k, ε k • D k is the identity function. We define the Cartesian product X = B N × S N , where:

• B = {0, 1} is the set of Boolean values,
• S N = 0, 2 N -1 N , the set of infinite sequences of natural integers bounded by 2 N -1, or the set of infinite N-bits block messages, in such a way that X is constituted by couples of internal states of the mode of operation together with sequences of block messages. Let us consider the initial function:

i : S N -→ 0, 2 N -1 (m i ) i∈N -→ m 0
that returns the first block of a (infinite) message, and the shift function:

σ : S N -→ S N (m 0 , m 1 , m 2 , ...) -→ (m 1 , m 2 , m 3 , ...)
which removes the first block of a message. Let m j be the j-th bit of integer, or block message, m ∈ 0, 2 N -1 , expressed in the binary numeral system, and when counting from the left. We define:

F f : B N × 0, 2 N -1 -→ B N (x, m) -→ (x j m j + f (x) j m j ) j=1..N
This function returns the inputted binary vector x, whose m j -th components x mj have been replaced by f (x) mj , for all j = 1..N such that m j = 0. In case where f is the vectorial negation, this function will correspond to one XOR between the clair text and the previous encrypted state. So the CBC mode of operation can be rewritten as the following dynamical system:

X 0 = (IV, m) X n+1 = (E k • F f0 (i(X n 1 ), X n 2 ) , σ(X n 1 )) (1)
For any given g : 0, 2 N -1 × B N -→ B N , we denote G g (X) = (g(i(X 1 ), X 2 ); σ(X 1 )) (when g = E k • F f0 , we obtain one cypher block of the CBC, as depicted in Figure 1). So the recurrent relation of Eq.( 1) can be rewritten in a condensed way, as follows.

X n+1 = G E k •F f 0 (X n ) . (2)
With such a rewriting, one iterate of the discrete dynamical system above corresponds exactly to one cypher block in the CBC mode of operation. Note that the second component of this system is a subshift of finite type, which is related to the symbolic dynamical systems known for their relation with chaos [START_REF] Lind | An introduction to symbolic dynamics and coding[END_REF]. We now define a distance on X as follows: d((x, m); (x, m)) = d e (x, x) + d m (m, m), where:

         d e (x, x) = N k=1 δ(x k , xk ) d m (m, m) = 9 N ∞ k=1 N i=1 |m i -mi | 10 k .
This distance has been introduced to satisfy the following requirements:

• The integral part between two points X, Y of the phase space X corresponds to the number of binary components that are different between the two internal states X 1 and Y 1 .

• The k-th digit in the decimal part of the distance between X and Y is equal to 0 if and only if the k-th blocks of messages X 2 and Y 2 are equal. This desire is at the origin of the normalization factor 9 N .

Proofs of chaos

As mentioned in Definition 3, a function f is chaotic on (X , τ ) if f is regular and topologically transitive. We have began by stating some propositions that are primarily required in order to proof the chaotic behavior of the CBC mode of operation.

Proposition 1 Let g = ε k • F f0
, where ε k is a given keyed block cipher and f 0 :

B N -→ B N , (x 1 , ..., x N ) -→ (x 1 , ..., x N )
is the Boolean vectorial negation. We consider the directed graph G g , where:

• vertices are all the N-bit words.

• there is an edge m ∈ 0, 2 N -1 from x to x if and only if g(m, x) = x.

So if G g is strongly connected, then G g is strongly transitive.

proving by doing so the strong transitivity of G g on (X , d).

We have then proven that, Proposition 2 If G g is strongly connected, then G g is regular.

According to Propositions 1 and 2, we can conclude that, if the directed graph G g is strongly connected, then the CBC mode of operation is chaotic according to Devaney, as established in our previous research work. In that article and for illustration purpose, we have also given some examples of encryption functions making this mode a chaotic one.

We have previously recalled that the mathematical framework of the theory of chaos offers tools to measure this unpredictable behavior quantitatively. The firsts of these measures are the constants of sensitivity and of expansitivy, recalled in the definitions section. We now intend to investigate these measures.

Quantitative measures

Let us firstly focus on the sensitivity property of the CBC mode of operation.

Sensitivity

Proposition 3 The CBC mode of operation is sensible to the initial condition, and its constant of sensibility is larger than the length N of the block size.

Proof Let X = (x; (m 0 , m 1 , ...)) ∈ X and δ > 0. We are looking for X = (x ; (m 0 , m 1 , ...) and n ∈ N such that d(X, X ) < δ and d(G n g (X), G n g (X )) > N . Let us define k 0 = -log 10 (δ) + 1, in such a way that all X of the form:

(X 1 , (m 0 , m 1 , ..., m k0 , m k0+1 , m k0+2 , ...)) are such that d(X, X ) < δ. In other words, all messages m whose k 0 first blocks are equal to (m 0 , m 1 , ..., m k0 ) are δ-close to X. where D k is the keyed decryption function associated to E k , and z is the negation of z. We thus define X as follow:

• X 1 = x, • ∀k k 0 , m k = m k , • m k0+1 = m , • ∀k k 0 + 2, m k = m k , so d(G k0+1 g (X), G k0+1
= N + 9 N ∞ k=k0+2 m k -m k 10 k = N + 9 N ∞ k=k0+2 N 10 k = N + 9 ∞ k=k0+2 1 10 k = N + 1 10 k0+1 > N,
which concludes the proof of the sensibility of G g .

The second important tool that reinforces the chaotic behavior of the CBC mode of operation is the expansivity. The study of this property, which has been recalled in Definition 6, will be regarded below.

Expansitivity

In this section we offer the proof that: Proposition 4 The CBC mode of operation is not expansive.

Proof Consider for instance two initial vectors x = (1, 0, . . . , 0) and x = (0, 1, 0, . . . , 0), associated to the messages m = ((0, 1, 0, . . . , 0), (0, . . . , 0), (0, . . . , 0), . . .) and m = ((1, 0, . . . , 0), (0, . . . , 0), (0, . . . , 0), . . .): all blocks of messages are null in both m and m , except the first block. Let X = (x, m) and X = (x , m ).

Obviously, x = x , while x⊕m 0 = x ⊕m 0 . This latter implies that X 0 1 = X 0 1 , and by a recursive process, we can conclude that ∀i ∈ N, X i 1 = X i 1 . So the distance between points X = (x, m) and X = (x , m ) is strictly positive, while for all n > 0, d G n g (X), G n g (X ) = 0, which concludes the proof of the non expansive character of the CBC mode of operation by the mean of the exhibition of a counter example.

Conclusion and future work

In this paper, both expansivity and sensibility of symmetric cyphers are regarded, in the case of the CBC mode of operation. These quantitative topology metrics taken from the mathematical theory of chaos allow to measure in which extent a slight error on the initial condition is magnified during iterations. It is stated that, in addition to being chaotic as defined in the Devaney's formulation, the CBC mode of operation is indeed largely sensible to initial errors or modifications on either the IV or the message to encrypt. Its expansivity has been regarded too, but this property is not satisfied, as it has been established thanks to a counter example.

In future work, we intend to deepen the topological study of the behavior of the CBC mode of operation. We will study whether this mode of operation possesses other qualitative properties of disorder like the topological mixing. Additionally, other quantitative evaluations will be performed, and the level of topological entropy will be evaluated too.

Figure 1 :

 1 Figure 1: CBC mode of operation

Figure 2 :

 2 Figure 2: k 0 + 1-th iterate of G g

  G g (y; (m k0+1 , m k0+2 , ...)) , G g (y; (m , m k0+1 , m k0+2 , ...))) = d ((z; (m k0+2 , m k0+3 , ...)) , (E k (y ⊕ m ); (m k0+1 , m k0+2 , ...))) = d ((z; (m k0+2 , m k0+3 , ...)) , (E k (y ⊕ (y ⊕ D k (z))); (m k0+1 , m k0+2 , ...))) = d ((z; (m k0+2 , m k0+3 , ...)) , (E k ((y ⊕ y) ⊕ D k (z)); (m k0+1 , m k0+2 , ...))) = d ((z; (m k0+2 , m k0+3 , ...)) , (E k (0 ⊕ D k (z)); (m k0+1 , m k0+2 , ...))) = d ((z; (m k0+2 , m k0+3 , ...)) , (E k (D k (z)); (m k0+1 , m k0+2 , ...))) = d ((z; (m k0+2 , m k0+3 , ...)) , (z; (m k0+1 , m k0+2 , ...))) = d e (z, z) + d m ((m k0+2 , m k0+3 , ...), (m k0+1 , m k0+2 , ...))


Zhuosheng Lin
email: zhuoshenglin@163.com

Christophe Guyeux
email: christophe.guyeux@univ-fcomte.fr

Qianxue Wang
email: wangqianxue@gdut.edu.cn

Simin Yu
email: siminyu@163.com

Diffusion and confusion of chaotic iteration based hash functions

Keywords: hash function, security flaws, chaotic iterations, diffusion and confusion

To guarantee the integrity and security of data transmitted through the Internet, hash functions are fundamental tools. But recent researches have shown that security flaws exist in the most widely used hash functions. So a new way to improve their security performance is urgently demanded. In this article, we propose new hash functions based on chaotic iterations, which have chaotic properties as defined by Devaney. The corresponding diffusion and confusion analyzes are provided and a comparative study between the proposed hash functions is carried out, to make their use more applicable in any security context.

I. INTRODUCTION

Hash functions, as one of the key technologies in information security and cryptographic application domain, are widely used in digital signatures, file integrity checking, authentication, password protection, and so on. At the same time, the analysis of hash functions has recently made some breakthroughs. Xiaoyu Wang and her team presented new collision search attacks on SHA0 and SHA1 [START_REF] Wang | Collisions for hash functions md4, md5, haval-128 and ripemd[END_REF]- [START_REF] Wang | Efficient collision search attacks on sha-0[END_REF]. These research results not only shocked people, but also encouraged researchers to construct more secure hash functions.

Chaos, with its high sensitiveness to small changes and initial conditions and long-term unpredictable characteristics, has become an important branch of modern nonlinear science and applications. For instance, a lot of one-way hash functions that are based on chaotic characteristics have been recently proposed [START_REF] Wang | One-way hash function construction based on 2d coupled map lattices[END_REF], [START_REF] Guo | Cryptanalysis on a parallel keyed hash function based on chaotic maps[END_REF]. However, through research, we found that most of these chaotic systems are on real domain. Due to the limited-length when realized in computer or digital devices, this will inevitably lead to finite precision effects and result in dynamical degradation of chaotic systems [START_REF] Li | On the dynamical degradation of digital piecewise linear chaotic maps[END_REF]. Such flaws will make the security performance of hash function declines.

Chaotic iterations (CIs), defined on integer domains, have been proven to achieve a real chaotic system under the definition of Devaney topological chaos [START_REF] Devaney | An introduction to chaotic dynamical systems[END_REF], which solves degradation of chaotic dynamic properties fundamentally. CIs have been applied to pseudorandom number generation, information hiding, symmetric cryptography, and so on [START_REF] Guyeux | Introducing the truly chaotic finite state machines and theirs applications in security field[END_REF], [START_REF] Guyeux | Improving random number generators by chaotic iterations. application in data hiding[END_REF]. In this article, we intend to construct a one-way keyed hash function with CIs. Then the diffusion and confusion are analyzed.

The remainder of this article is organized as follows. The basic recalls of CIs and hash function are given in Section II. Our CI-based hash function is proposed and reformulated in Section III. Section IV shows its experimental evaluation. This research work ends by a conclusion section in which our article is summarized and intended future work is outlined.

II. BASIC RECALLS

This section gives some recalls on topological chaotic iterations and hash functions.

A. Chaotic iterations

Let us first define some notations that are used in the remainder of this article. N is the set of natural (non-negative) numbers. The domain N * = {1, 2, 3, . . .} is the set of positive integers and

B = {0, 1}. [[1; N ]] = {1, 2, 3, . . . , N }. A sequence which elements belong in [[1; N ]] is called a strategy.
The set of all strategies is denoted by S . S n denotes the n th term of a sequence S , X i stands for the i th components of a vector X . Definition 1. Let f : B N → B N be a function and S ∈ S be a strategy. The so-called chaotic iterations are defined by:

x 0 ∈ B N , ∀n ∈ N * , ∀i ∈ [[1; N ]] , x n i = x n-1 i , if S n = i f x n-1 S n , if S n = i (1)
In other words, at n th iteration, only the S n -th component of vector x n is updated.

For a given function f , let us define a function

F f : [[1; N ]]× B N → B N by: F f (k, x) = x j • δ (k, j) + (f (x)) k • δ (k, j) j=1,2,3,...,N (2)
where δ (k, j) = 0 ⇔ k = j. Consider the phase space: X = [[1; N ]] × B N , and the map defined on X by:

G f (S, E) = (σ (S) , F f (i (S) , E)) , (3)
where σ is the shift function that removes the fist term of the strategy. So the chaotic iterations defined in Equ.1 can be described by the following iterations:

X 0 ∈ X X k+1 = G f (X k ) (4)
arXiv:1708.02793v1 [nlin.CD] 9 Aug 2017

For given two points X = (S, E) , Y = Š, Ě ∈ X , we define the distance between these two points by: Considering the distance between d on X , it has already been proven that [START_REF] Guyeux | Topological chaos and chaotic iterations application to hash functions[END_REF]:

d (X, Y ) = d e E, Ě + d s S, Š , where        d e E, Ě = N k=1 δ E k , Ěk d s S, Š = 9 N ∞ k=1 S k -Šk 10 k (5) in which d (X, Y ) = d e E, Ě
• G f is continuous. • Iterations defined in Equ.4 are regular. • G f is topologically transitive.
• G f has sensitive dependence on initial conditions. Thus, according to the Devaney's definition [START_REF] Devaney | An introduction to chaotic dynamical systems[END_REF], [START_REF] Banks | On devaney's definition of chaos[END_REF], G f is chaotic.

B. Hash functions

Let k ∈ K be a key in a given key space K. So a function h k () that maps a key k and a binary bit string x to a string of a fixed length l is a Secure Keyed One-Way Hash Function (SKOWHF) [START_REF] Bakhtiari | Keyed hash functions[END_REF], if it satisfies the following properties:

• Given k and x, it is easy to compute h (k, x).

• Without knowledge of k, it is hard to compute h (k, x).

• For any x or given (possibly many) pairs x and h (k, x), it is hard to compute k. • For a given k, it is hard to find two values x and y such that h (k, x) = h (k, y), but x = y. • Length l has to be larger than 128 bits in order to counter birthday attack.

• Key space K has to be sufficiently large in order to counter exhaustive key search.

III. CI-BASED HASH FUNCTIONS

Let us now present our hash function

H h : K × B * → B N which is based on chaotic iterations recalled before. The key k = {k 1 , k 2 , prng type} is in key space K = B k1 × B k2 × N.
All the steps are described in the following paragraphs.

The first step of the algorithm is to choose the traditional hash function h that we will use in our own hash function. For our implementations, we have chosen MD5, SHA-256, and SHA-512. And the selective traditional hash function determines the length (N ) of the output hash value. For MD5, N = 128, for SHA-256, N = 256, and for SHA-512, N = 512.

Then for the input message x, we need to transform the it into a multiple normalized N bits sequence. This pre-treatment is similar to the SHA-1 case. After that, the length of the treated sequence X is L.

In the third step, we use k 2 as a seed to generate L bits pseudorandom numbers m. In our implementation, the Pseudo-Random Number Generator can be Mersenne Twister (MT), Blum Blum Shub (B.B.S.), XORshift, or Linear Congruential Generator (LCG). This is the prng type in key space K. The generated pseudorandom numbers are used to construct the strategies. As 2 n = N , we split its sequence to be m = S 0 S 1 . . ., where the length of S i is n. Then the strategy is S = S 0 S 1 . . . , where S i is transformed to the decimal value.

In the forth step, we first transform the input k 1 to binary value which length is N . Here we split X into X = X 0 X 1 . . . . Each X i will be combined with k 1 using exclusive-or operation. Then we combine the result with pseudorandom numbers m using exclusive-or operation too. After that, we use this result as the input of traditional hash function h.

Lastly, to construct the digest, chaotic iteration of G f are realized with the traditional hash function output h(k 1 , X, m) and strategies S as defined above. The result of these iterations is a N bits vector. It is translated into hexadecimal numbers to finally obtain the hash value.

So we define the keyed hash function H h : K × B * → B N by the following procedure

Algorithm 1 The proposed hash function H h

Input:

The key, k = (k 1 , k 2 , prng type) ∈ K;

The input message x ∈ B * ; Output:

Hash value H; 1: Transforming x to sequence X which length is L; 2: Use PRNG to generate m which using k 2 as a seed and construct strategy S = S 0 S 1 . . . with m; 3: Use standard hash function to generate hash value H = h(k 1 , X, m); 4: for i = 1 . . . do

5:

Chaotic iterations, to generate hash value: H = G f (S i , H); 6: end for 7: return H; Thus H h is a chaotic iterations based post-treatment on the inputted hash function. If h satisfies the collision resistance property, then it is the case too for H h . Moreover, if h satisfies the second-preimage resistance property, then it is the case too for H h , as proven in [START_REF] Guyeux | Introducing the truly chaotic finite state machines and theirs applications in security field[END_REF].

IV. EXPERIMENTAL EVALUATION

Before discussing diffusion and confusion, we will give some examples of hash values.

A. Hash Value

Let us now consider that the input message is the poem Ulalume (E.A.Poe), which is constituted by 104 lines and 3582 characters. The traditional hash function used here will be the From simulation results, we can see that any change in key space K seems to cause a substantial modification in the final hash value, which is coherent with the topological properties of chaos.

For a security hash function, the repartition of its hash values should be uniform. In other words, the algorithm should make full use of cryptogram space to make that the hash values are evenly distributed across the cryptogram space. The parameter we use here is the same as in Case 1. In Figure 1a, the ASCII codes are localized within a small area, whereas in Figure 1b the hexadecimal numbers of the hash values are uniformly distributed in the area of cryptogram space.

We will now test our hash function with some changes in the input message, and observe the distribution of hash values. The hash function is set with k 1 = 50, k 2 = 50, and prng type is B.B.S.. The hash function used here will be the MD5.

Case 1. The input message is the poem Ulalume (E.A.Poe). Case 2. We replace the last point '.' with a coma ','. Case 3. In "The skies they were ashen and sober", 'The' become 'the'. Case 4. In "The skies they were ashen and sober", 'The' become 'Th'. Case 5. We add a space at the end of the poem. The corresponding hash values in binary format are shown in Figure 2. Through this experiment, we can check that the propose hash function is sensitive to any alteration in the input message, which will cause the modification of the hash value.

B. Diffusion and Confusion

In cryptography, diffusion and confusion are two important properties of a secure cipher that has been identified by Claude Shannon in his 1945 classified report "A Mathematical Theory of Cryptography". Diffusion means that the redundancy of the plain text must be dispersed into the space of cryptogram space so as to hide the statistics of plain text. Confusion refers to the desire to make the statistical relationship between plain text, ciphertext, and keys as complex as possible, which makes

∆P = 1 N -1 N i=1 ( Bi L -P ) × 100%
, where N denotes the statistical times, and B i denotes the changed bits of hash value in i th test, while L denotes the bits of hash value in binary format.

We use again the poem Ulalume (E.A.Poe) as input message. Using our hash function H h , we will get the original hash value. For this sequence, we toggle only one bit each time. Then we will obtain another hash values. Let k 1 = 50, k 2 = 50, and prng type is B.B.S. The hash function h used is MD5 while test times N = 1000. The distribution of B i is shown in Figure 3. From the figure, we can see that a one bit change in the plain text will modify about 64 bits in the 128 bits hash value. In other words, the proposed hash function achieves desired value for such properties. The desired distribution of hash algorithm should be that small toggle in plain text causes 50% change of hash value. ∆B and ∆P show the stability of diffusion and confusion properties. The hash algorithm is more stable if these two values are close to 0. Observing Table I, both the mean changed bit number B and the mean changed probability P are close to the desired value. ∆B and ∆P are quite small. Both of them illustrates the diffusion and confusion of our hash function H h and these capabilities are quite stable. From Table I, we can also know that when prng type = LCG or prng type = B.B.S, all P are larger than 50%. But when prng type = LCG, ∆B and ∆P are smaller. To sum up, in our proposed hash function, it is better to choose B.B.S. as pseudorandom number generator. Furthermore, compared with the performance of standard hash functions which is shown in Table II, the proposed one in some situations shows better results.

V. CONCLUSION AND FUTURE WORK

In this article, a new hash function based on chaotic iterations has been presented. We used pseudorandom number generator to construct a strategy S. Then we simulated the proposed hash function's sensitivity to keys and plain text. At last, the performance of diffusion and confusion is discussed. The experimental results show that this hash function is a secure keyed one-way hash function. Through the statical performance of the proposed hash function, we found that B.B.S is a better pseudorandom number generator to construct strategies.

In future work, we will try to apply chaotic iteration to construct pseudorandom number generators. Then we will use this kind of PRNG to construct strategies for hash functions. At the meantime, other properties induced by CIs will be explored.

Fig. 2 :

 2 Fig. 1: Distribution of Ulalume poem

Fig. 3 :

 3 Fig. 3: Distribution of changed bit numbers B i

  is the Hamming distance between E and Ěk . So d (X, Y ) -d (X, Y ) = d s S, Š measures the difference between strategies S and Š. More precisely, this floating part is lower than 10 -k if and only if the first k terms of the two strategies are equal. Moreover, if the k th digit is nonzero, then S k = Šk .

  MD5. So N = 128. To give illustration of the keys properties, we will use this hash function H h to generate hash values in the following cases: Case 1. k 1 = 50, k 2 = 50, prng type is B.B.S.. Case 2. k 1 = 51, k 2 = 50, prng type is B.B.S.. Case 3. k 1 = 50, k 2 = 51, prng type is B.B.S. Case 4. k 1 = 50, k 2 = 50, prng type is LCG. Case 5. k 1 = 50, k 2 = 50, prng type is MT. Case 6. k 1 = 50, k 2 = 50, prng type is XORshift.

	The corresponding hash values in hexadecimal format are:
	Case 1. D8ED0DDD1A611C1AEDE0915BE2CA91D3.
	Case 2. 54B7B1E2C2239CF0FBC327D55CFA7BF2.
	Case 3. 8453BA95FB088DA84219F1AFCD14E9EE.
	Case 4. 663F90CB4ECD5E8AF53D2760E01491C8.
	Case 5. 01C142B339413DEF49E7A65FF43A50DF.
	Case 6. FD2B8ABC6BE956718669D92367E1680A.

TABLE I :

 I Statical performance of the proposed hash function

	prng type	hash type	B	P (%)	∆B	∆P (%)
		MD5	64.008	50.006	5.788	4.522
	B.B.S	SHA-256	128.085 50.033	7.880	3.078
		SHA-512	256.353 50.069 10.911	2.131
		MD5	63.977	49.982	5.452	4.260
	Mersenne Twister	SHA-256	128.316 50.123	7.858	3.070
		SHA-512	255.534 49.909 11.691	2.283
		MD5	64.355	50.277	5.795	4.528
	LCG	SHA-256	128.056 50.022	7.842	3.063
		SHA-512	256.106 50.021 11.539	2.254
		MD5	63.963	49.971	5.648	4.412
	XORshift	SHA-256	127.596 49.842	8.036	3.139
		SHA-512	255.955 49.991 11.573	2.260

TABLE II :

 II Statical performance of the standard hash function

	standard hash function	B	P (%)	∆B	∆P (%)
	MD5	63.893	49.916	5.437	4.248
	SHA-256	127.746 49.901	8.405	3.283
	SHA-512	256.084 50.016 11.232	2.194


Nadine Boudargham
email: nboudargham@ndu.edu.lb

Jacques Bou Abdo
email: jbouabdo@ndu.edu.lb

Jacques Demerjian
email: jacques.demerjian@ul.edu.lb

Christophe Guyeux
email: christophe.guyeux@univ-fcomte.fr

Abdallah Makhoul
email: abdallah.makhoul@univ-fcomte.fr

Investigating Low Level Protocols for Wireless Body Sensor Networks

Keywords: WBAN, Static TDMA, Dynamic TDMA, FDMA, CSMA/CA, DS-CDMA, Delay, Scalability, OPNET

The rapid development of medical sensors has increased the interest in Wireless Body Area Network (WBAN) applications where physiological data from the human body and its environment is gathered, monitored, and analyzed to take the proper measures. In WBANs, it is essential to design MAC protocols that ensure adequate Quality of Service (QoS) such as low delay and high scalability. This paper investigates Medium Access Control (MAC) protocols used in WBAN, and compares their performance in a high traffic environment. Such scenario can be induced in case of emergency for example, where physiological data collected from all sensors on human body should be sent simultaneously to take appropriate action. This study can also be extended to cover collaborative WBAN systems where information from different bodies is sent simultaneously leading to high traffic. OPNET simulations are performed to compare the delay and scalability performance of the different MAC protocols under the same experimental conditions and to draw conclusions about the best protocol to be used in a high traffic environment.

I. INTRODUCTION

The rapid advances in medical sensors enabled miniaturized computing devices called sensor nodes to be implanted in or placed around the human body. These sensors gather physiological and activity data from the human body and its environment, and send them wirelessly to a personal device like PDA (Personal Digital Assistant) or a smartphone that acts as a gateway to health care [1,17]. This network is called Wireless Body Area Network (WBAN) or Wireless Body Sensor Network (WBSN). A general architecture of WBAN is shown in Figure 1.

The main aim of WBAN is to enhance peoples life, thus many applications for WBAN can be found. In general, these applications can be categorized into medical and non-medical ones. Medical applications involve monitoring physiological attributes of the human body to detect any abnormal condition, Fig. 1: WBAN General Architecture allowing therefore appropriate personnel to take action before it is too late. Whereas examples of non-medical applications include entertainment applications, emotion detection, secure authentication, and non-medical emergencies through gathering data from the environment and warning people in case of danger like fire [2]. WBAN are mostly used to monitor a single body but it can be extended to monitor a group of individuals known as collaborative WBAN systems [3,18,19].

In these Wireless Body Sensor Networks, sending data with adequate Quality of Service (QoS) like designing a high scalable system and sending data with a minimal delay is crucial. The [14], [16]. However, non of these researches compare the delay and the scalability characteristics of the five listed protocols simultaneously under the same experimental conditions in WBAN. In this study, each of the listed protocols is analyzed and compared with respect to two QoS metrics: delay and scalability. The aim of this comparison is to show which technique offers the lowest delay and highest scalability in a high traffic environment. Such scenario can be induced in case of emergency for example, where physiological data collected from all sensors on human body should be sent simultaneously to properly assess the person's case and take action accordingly. This study can also be extended to cover collaborative WBAN systems where information from different bodies is sent simultaneously leading to high traffic.

This research work is organized as follows. A general review of basic MAC protocols for WBAN is presented in Section II. A survey on the delay and the scalability performance of different MAC protocols is summarized in Section III. The experimental evaluation is presented in Section IV, while conclusion and future work are drawn in Section V.

II. GENERAL REVIEW OF MAC PROTOCOLS IN WBAN

There are two main classes for MAC protocols: "contentionbased" and "contention-free". In "contention-based" protocols, also known as "random access" protocols, nodes do not coordinate with each other to access the channel; so transmitted data may collide, forcing colliding nodes to backoff for a certain time before trying to access the channel again. Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) is an example of "contention-based" protocols. As for "contentionfree" protocols, nodes follow a certain schedule to avoid collisions during transmission.

D. FDMA

FDMA is another "contention-free" protocol in which nodes are assigned different frequency bands to transmit their data through the medium. Each frequency band is separated from its adjacent bands by a guard band to avoid interference. Therefore, nodes can transmit their data without any need for further process [6]. The FDMA access scheme is shown in Figure 5 [8].

E. DS-CDMA

In Direct Sequence Code Division Multiple Access (DS-CDMA), every node is assigned a unique code [10]. All nodes send their data over the same frequency, but they are still distinguished from one another by the different codes assigned to them. The users generated code is multiplied with the users original signal to form his encoded signal, i.e., encoded signal = (original signal) x (code). Hence the nomination Direct Sequence-CDMA or DS-CDMA. The DS-CDMA access scheme is shown in Figure 6 [8].

III. DELAY AND SCALABILITY PERFORMANCE SURVEY

Reliability in WBAN is very important, and end-to-end delay is a major key performance metric in critical healthcare applications [11]. Studying the delay performance of different MAC protocols is specifically important in emergency cases requiring simultaneous transmission of critical data from all sensors in or on the body to take fast action accordingly. Scalability or system capacity is another important QoS metric in WBAN since sensor nodes might be added to the system at anytime based on the medical need or on the type of physiological data that should be gathered. Scalability reflects the performance of the MAC protocol when more sensor nodes are added to the system and shows how flexible it is to add them. As mentioned earlier, many articles discuss the QoS characteristics of MAC protocols in WBAN, but non of these researches compare the five protocols concurrently in the same environment. In the following, we combine the findings from different studies analyzing the delay and scalability performance for Static TDMA, Dynamic TDMA, FDMA, CSMA/CA and DS-CDMA.

A. Delay Analysis

In [12], the authors present a comparison between FDMA and Static TDMA techniques. They demonstrate that in general, Static TDMA induces less delay than FDMA since the transmission of a TDMA packet takes only one slot, whereas the transmission in FDMA lasts for a whole frame. Also, authors prove that the difference in delay between the two protocols is variable since in Static TDMA, a packet has to wait for its appropriate slot even when the queue is empty, whereas the packet is instantly transmitted without further delay in FDMA. Nevertheless, this same literature proves that when the load increases, the ratio of the delays of both schemes become close to one, so Static TDMA and FDMA will have similar performances. Authors of [6] state that in Static TDMA, the generated packets experience three types of delays before reaching the receiver: transmission delay, queuing delay, and propagation delay. In this literature, a comparison of delay as a function of throughput in WBAN is assessed for various protocols including Static TDMA, FDMA, and CSMA/CA. The comparison shows that in low traffic, both Static TDMA and FDMA offer low delay, and Static TDMA outperforms FDMA. However the delay significantly increases in both schemes when the load increases. As for CSMA/CA, the delay is the highest among the other protocols even when the traffic is low since CSMA/CA continuously senses the medium and waits for it to become free before transmitting the packets. Literature [7] examines the delay characteristics of different protocols used in Wireless Sensor Networks under varying traffic loads. It shows that the average message delay of Static TDMA increases with increasing traffic load due to queuing that is originated from the limited bandwidth available since every node is transmitting one message per frame. This literature also explains that the delay induced by CSMA/CA is due to two factors: the "contention-based" nature of CSMA/CA when the node renounces from sending its data after finding the channel busy, and the retransmission of the messages due to collision. Authors of [13] analyze the performance of DS-CDMA and Static TDMA when bursty voice traffic is sent, and prove that even though Static TDMA outperforms DS-CDMA in low traffic, the delay of DS-CDMA when bursty data is applied is much lower than that of Static TDMA. Literature [14] compares DS-CDMA based protocols to other protocols in Wireless Sensor Networks and states that the delay of DS-CDMA is induced by assigning different codes for every node. Authors of [10] introduce a Dynamic TDMA scheme for WBAN, and show that the delay in Dynamic TDMA is lowest delay realizable by TDMA mechanism.

Table I summarizes the protocols studied in every reference in terms of delay. It shows that none of the references compared the delay performance of the five protocols simultaneously. Table II presents the delay analysis results based on the literature findings.

B. Scalability Analysis

Many articles show that scalability is poor in TDMA based system. For instance, authors of [5] state that scalability is a main disadvantage in TDMA based systems since adding a sensor node requires performing modifications in the central controller. For example, if a medical staff decided to add sensor nodes to monitor additional physiological data, he has to change the transmission time frame from the central controller which is not practical. This literature suggests that TDMA is suitable for small WBAN systems with limited number of nodes. Also, authors of [10], [14] and [9] state that TDMA has limited scalability and ability to adapt to changes such as adding sensor nodes. Literature [12] shows that in both FDMA and Static TDMA, the delay increases with the number of users. So the performance of both protocols degrades when increasing the number of nodes which reflects a poor scalability. Authors of [6] show that CSMA/CA has good scalability in WBAN, as it maintains a constant delay when increasing the offered load. Also, literature [5] and [10] state that scalability is one of the important advantages of CSMA/CA as it can easily accommodate different traffic sources with different rates. Article [16] states that capacity is a main advantage of DS-CDMA as it can handle more nodes than the other technologies.

Table III summarizes the protocols studied in every reference in terms of scalability. It shows that none of the references compared the scalability performance of the five protocols simultaneously. Table IV presents the scalability analysis results based on the literature findings.

IV. EXPERIMENTAL EVALUATION A. Motivations

To fairly assess the performance of Static TDMA, Dynamic TDMA, FDMA, DS-CDMA and CSMA/CA protocols, the five techniques should be tested under the same experimental conditions, which has not been done previously as shown in Table I & Table III. Therefore in this section, delay and scalability will be simulated simultaneously for all the listed protocols in the same high traffic environment. Simulation results will be compared to those presented in Table II & Table IV in order to draw appropriate conclusion about the best protocol to be used in a high traffic environment.

B. Simulation Environment and Parameters

Testing the performance of the five listed MAC protocols is done using OPNET simulator [20]. In the simulation, eight nodes are placed in a star topology architecture around the sink node as shown in Figure 7. The OPNET default parameters for the physical layer and wireless link were used. The transmission rate is set to 250kbps, and the packet arrival time between packets is set to 5ms in order to induce high traffic. The simulation parameters are summarized in Table V.

C. Obtained Results and Discussion

The delay simulation results are presented in Figure 8. They show that DS-CDMA outperforms the other "contentionfree" protocols since it induces the lowest delay. This delay is generated from assigning different codes to nodes. Static TDMA and FDMA are very close in performance in a high traffic environment as they both induce high delays due to queuing. The delay of Dynamic TDMA is high, but less than that of Static TDMA since it uses the slots more efficiently, and therefore minimizes queuing. As for CSMA/CA, the "contention-based" protocol, the delay is unmanageable since in high traffic, the probability of collision in CSMA/CA increases, so the number of retransmissions accumulate. Also, the medium is very busy, therefore the nodes have to wait for a long backoff time. The obtained results agree with the delay analysis results obtained in Table II. In order to test the scalability of different protocols, simulations are repeated with different number of nodes, and the average end-to-end delay induced by each protocol was evaluated accordingly. Figure 9 shows the scalability performance of each protocol with respect to different number of nodes. Results show that the delay in Static TDMA, Dynamic TDMA and FDMA increases with the number of nodes. For instance, the average end-to-end delay of Static TDMA increased from 8.93 seconds to 21.6 seconds when the number of nodes is doubled from eight to sixteen. Similarly, the average delay of Dynamic TDMA increased from 5.35 seconds to 19.77 seconds, and that of FDMA increased from 9.91 seconds to 23.85 seconds. This implies a degradation in the performance of these three protocols when more nodes are added to the system, and reflects a poor scalability. On the other hand, the delay in DS-CDMA and CSMA/CA protocols remains almost constant when increasing the number of nodes, therefore these two protocols offer good scalability. The results obtained in the simulation agree with the scalability analysis results presented in Table IV.

Both the delay and scalability studies showed that DS-CDMA MAC protocol outperforms the other protocols when high traffic is generated in WBAN since it offers the lowest delay and the highest scalability.

V. CONCLUSION AND FUTURE WORK

In this paper, the delay and scalability performance of Static TDMA, Dynamic TDMA, FDMA, DS-CDMA and CSMA/CA MAC protocols were analyzed and simulated in a high traffic WBAN environment. Simulation results showed that DS-CDMA protocol performs better than the other techniques in terms of delay and scalability, which agrees with the survey analysis. Therefore DS-CDMA should be considered to be used in high traffic WBAN systems. Future work includes analyzing and comparing the performance of these five protocols in terms of other QoS metrics like probability of collision, hardware complexity and energy consumption for better assessment. In addition, the study presented in this paper is based on a single body WBAN, so it can be extended to analyse the behavior of the different protocols in collaborative WBAN systems.

  delay and scalability of WBAN largely depend on the design and choice of the Medium Access Control (MAC) protocol. Standard MAC protocols for WBANs include Static Time Division Multiple Access (Static TDMA), Dynamic Time Division Multiple Access (Dynamic TDMA), Frequency Division Multiple Access (FDMA), Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) and Direct Sequence Code Division Multiple Access (DS-CDMA). In the literature, many studies discuss the QoS characteristics of different MAC protocols [5], [6], [7], [9], [10], [12], [13],

  Example of "contention-free" protocols include Static Time Division Multiple Access (Static TDMA), Dynamic Time Division Multiple Access (Dynamic TDMA), Frequency Division Multiple Access (FDMA), and Direct Sequence Code Division Multiple Access (DS-CDMA) [4].A. CSMA/CACSMA/CA is a random "contention-based" protocol. It is commonly known as the ON DEMAND access protocol since the sensor node access the transmission channel only when it has some information to send[5]. Traditionally, CSMA nodes sense the medium prior to transmitting data. If the medium is free, they transmit the packet. However a hidden problem might occur in this case if another node is already sending data at the same time and will eventually result in collision[6]. CSMA/CA is an enhancement over the traditional CSMA protocol in terms of collision avoidance capability. Improved CSMA/CA algorithm is shown in Figure2. When a sensor node has data to send, it first senses the channel. If the channel is busy, the node waits for a random backoff time; once the

Fig. 2 :

 2 Fig. 2: CSMA/CA Algorithm

Fig. 4 :

 4 Fig. 4: Dynamic TDMA Access Scheme

Fig. 6 :

 6 Fig. 6: DS-CDMA Access Scheme

Fig. 7 :

 7 Fig. 7: OPNET Star Topology

Fig. 8 :

 8 Fig. 8: Delay Performance of MAC Protocols

Fig. 9 :

 9 Fig. 9: Scalability Performance of MAC Protocols