The pharmacokinetics and pharmacodynamics of cefquinome against Streptococcus agalactiae in a murine mastitis model

Cefquinome is a new generation cephalosporin that is effective in the treatment of mastitis in animals. In this study, we evaluated the associations between the specific pharmacokinetics and pharmacodynamics (PK/PD) of cefquinome and its antibacterial activity against Streptococcus agalactiae in a mouse model of mastitis. After a single intramammary dose of cefquinome (30, 60, 120, and 240 μg/mammary gland), the concentration of cefquinome in plasma was analysed by liquid chromatography with tandem mass spectrometry (HPLC/MS–MS). The PK parameters were calculated using a one-compartment first-order absorption model. Antibacterial activity was defined as the maximum change in the S. agalactiae population after each dose. An inhibitory sigmoid Emax model was used to evaluate the relationships between the PK/PD index values and antibacterial effects. The duration for which the concentration of the antibiotic (%T) remained above the minimum inhibitory concentration (MIC) was defined as the optimal PK/PD index for assessing antibacterial activity. The values of %T > MIC to reach 0.5-log10CFU/MG, 1-log10 CFU/MG and 2-log10 CFU/MG reductions were 31, 47, and 81%, respectively. When the PK/PD index %T > MIC of cefquinome was >81% in vivo, the density of the Streptococcus agalactiae was reduced by 2-log10. These findings provide a valuable understanding to optimise the dose regimens of cefquinome in the treatment of S. agalactiae infections.


Introduction
Bovine mastitis (BM) is an inflammatory condition of the mammary gland that is caused by trauma or infection and results in the reduced production of both casein proteins and milk

Drugs, bacteria, and animals
Cefquinome sterile powder was obtained from Dr. Ehrenstorfer (lot number G130285; Augsburg, Germany). S. agalactiae 3-64 were isolated from dairy cows infected with mastitis. Kunming mice were purchased from the Hunan Silaike Jingda Laboratory Animal (Hunan, China). The mice were maintained in compliance with the American Association for Accreditation of Laboratory Animal Care guidelines [23]. All animal studies were approved by the Laboratory Animal Welfare and Ethics Committee of the Northeast Agricultural University (NEAUEC20191011).

Analysis of minimum inhibitory concentration (MIC), minimum bactericidal concentration (MBC) and mutant prevention concentration (MPC)
MICs were determined by microdilution in compliance with the Clinical Laboratory Standards Institute guidelines [24]. Briefly, colonies were transferred into MHB supplemented with 5% mouse serum and incubated at 37˚C on a shaking incubator (220 rpm). The final count was approximately 1×10 8 CFU/mL. 10 μL (1×10 6 CFU/mL) of the culture was used to inoculate each well of a 96-well plate containing broth with different concentrations of cefquinome. A series of two-fold dilutions was achieved by adding 100 μL culture aliquots to a 96-well plate.
The MIC was considered the lowest concentration of cefquinome that inhibited bacterial growth in broth after 24 hrs incubation. MBC was determined using a single set of doubling dilutions. The MIC well and four other wells with drug concentrations higher than the MIC were used to establish the MBC using the spot plate count method. The lowest drug concentration that reduced the bacterial count by 99.9% of the original count after 18 hrs was defined as the MBC [25]. Mutant prevention concentrations were determined by applying a high count bacterial suspension (1.5×10 11 colony-forming units (CFU)/mL) on to an agar plate containing different drug concentrations (1,2,4,8,16,32,64 and 128 multiples of the MIC for each isolate). The concentration ranges were narrowed down. The plates were incubated at 37˚C for 72 h and checked for bacterial growth every 24 h. The MPC was defined as the lowest concentration of cefquinome that completely inhibited bacterial growth after 72-hrs [26]. All susceptibility tests were repeated in triplicates.

Establishment of an LC-ESI-MS/MS method for the analysis of cefquinome
The plasma concentrations of Cefquinome were determined by LC-ESI-MS/MS as described previously [27]. Briefly, 100 μl of water containing 0.1% (v/v) formic acid and 100 μL of plasma were combined and vortexed for 3 min. The samples were then centrifuged at 5000 × g for 15 min and the supernatants were harvested. 20 μL of the supernatant was injected into the HPLC system. The limit of detection (LOD) and limit of quantification (LOQ) values for this assay were 0.005 and 0.01 μg/ml, respectively. The recoveries of cefquinome in the plasma samples were >85%. All inter-and intra-assay variations were measured by calculating the relative standard deviation (%RSD) and ensuring that it was <10%.

Establishment of a murine mastitis model
A murine mastitis model was established based on previous studies [28,29]. 8-12 day old pups were removed and lactating mice were anaesthetised with 1% pentobarbital sodium delivered by i.p injection. After 0.15 hrs, the L4 (4 th on the left) and R4 (4 th on the right) abdominal MGs were disinfected with 75% ethanol and the teat tip was cut using scissors. To prevent environmental bacterial contamination, <1 mm of the tissue was removed. Each teat was held with fine forceps and the duct orifice was located. 100 μL of S. agalactiae (5.2×10 5 CFU/mL) was slowly injected through the orifice using a syringe with a blunt needle (<30 gauge).

In vivo antibacterial efficacy
After S. agalactiae was injected into the mice, four mice were euthanized by CO 2 asphyxiation and MG samples were collected at 3, 6, 9, 12, 24, 48, and 72 h. MG samples were homogenized and the visible bacterial colonies were counted to establish in vivo bacterial growth curves for four experimental groups and one control group. In the mastitis model, a single dose of cefquinome was administered to the MG at a range of concentrations (30, 60, 120, or 240 μg/gland). The control group was treated with saline solution. The limit of detection for the bacteria was 300 CFU/MG.

The pharmacokinetics of cefquinome in murine plasma
PK experiments were performed on lactating Kunming mice. The mice were randomized into four experimental groups (n = 6 each). Sedation and analgesia management were performed as described by Zeng et al. [30]. Briefly, mice were added to an induction chamber (oxygen flow rate = 0.5-1.0 L/min). At the same time, 3%-5% of isoflurane vapour was applied for induction and then reduced to 1%-3% for maintenance. As stated above, after intramammary administration (30, 60, 120, and 240 μg/MG), retro-orbital blood samples (200 μL at each time point) were harvested at 0.083, 0.167, 0.25, 0.5, 0.75, 1, 2, 4, 6, 8, 10, and 12 h after cefquinome administration. The plasma samples were isolated by centrifugation for 10 min (2500 × g, 4˚C). The supernatants were stored at -20˚C for 2 weeks and the plasma cefquinome concentration was established via HPLC-MS/MS. The linearity of cefquinome quantitation was from 0.01-5 μg/mL and R 2 was >0.99. Cefquinome extraction recovery in the plasma was >80%, and the coefficient of variation was <10% within and between runs. The respective limitations of quantification and detection were 0.01 μg/mL and 0.005 μg/mL. The main PK parameters were harvested using WinNonlin version 5.2.1 (Pharsight, MO, USA). These parameters were the half-life of first-order elimination (T 1/2e ), the half-life of absorption (T 1/2α ), peak plasma concentration (C max ),and time of maximum plasma concentration (T max ).

PK/PD integration
The PK/PD indexes comprised the AUC/MIC (area under the time-concentration curve divided by MIC), %T > MIC (the percentage time for which the drug concentration exceeded MIC), and C max /MIC (peak concentration divided by MIC). The relationship between in vivo antibacterial effects (4log CFU/MG) and the PK/PD indexes were described using an inhibitory sigmoid E max model [31,32].
where E denotes the antibacterial effect determined based on the maximum change in the bacterial counts (log 10 CFU/MG) during 72 h after treatment; E max indicates the maximum change in the bacterial counts in the control group; E 0 represents the maximum change in the bacterial counts in the various experimental groups; EC 50 is the PK/PD index values that produced antibacterial effects equal to 50% of the maximum; C e is the PK/PD index; and N is the Hill coefficient, corresponding to the steepness of the effect curve associated with each of the PK/PD indexes.

Statistical analyses
Statistical analyses were conducted by the analysis of variance. Significant differences in the data were analysed using Bonferroni correction and with a P-value threshold of <0.05 set for statistical significance [33].

Chromatogram of cefquinome
The chromatograms for cefquinome in a cefquinome standard solution and the experimental samples are shown in Fig 1. This method had good specificity and was used for the determination of cefquinome.

The PKs of cefquinome in murine plasma
Due to the low protein binding (8%) [34] and precipitation in the samples, we believe that the cefquinome was almost entirely unbound in plasma. The concentration-time data are shown in Table 1. The cefquinome concentration-time curves for the different doses were generated (Fig 2). A one-compartment model with first-order absorption was fitted to calculate the PK parameters ( Table 2). The time of the maximum plasma concentration (T max ) was 0.20-0.25 hrs (mean, 0.22 hrs). The half-life of first-order elimination (T 1/2e ) was 0.47-0.69 hrs (mean, 0.65 hrs). The peak plasma concentration (C max ) increased proportionately with increasing doses of cefquinome along with the area under the time-concentration curve (AUC).

In vitro killing curves
The in vitro killing curves are presented in Fig 3 and show that cefquinome is a classical timedependent drug. The killing rate and bactericidal effects did not increase with an increase in drug concentration. In the low-concentration group (< 4 × MIC), cefquinome did not have a bactericidal effect. When the concentration reached >4 × MIC, in the low-concentrationpathogens group, the maximum bactericidal effect achieved a 3-log 10 CFU/mL reduction.
However, in the high-concentration-pathogens group, the maximum bactericidal effect only achieved a 1.2-log 10 CFU/mL reduction.

In vivo antibacterial effect
The in vivo killing curves are shown in Fig 4. The killing rate of cefquinome in mice was lower than that observed in Mueller-Hinton Broth. However, the killing curve of cefquinome against S. agalactiae showed a classical time-dependent pattern. The 30, 60, 120, and 240 μg/MG experimental groups achieved 1.1-log 10 , 1.2-log 10 , 2.5-log 10 , and 2.8-log 10 CFU/MG reductions, respectively at 72 h. The 120 μg/gland and 240 μg/gland experimental groups almost achieved bactericidal effects but these did not change significantly within increasing drug concentration increased (P>0.05).

PK/PD integration and analysis
PK/PD integration of the various PK/PD indexes versus the antibacterial effectiveness for the inhibitory sigmoid E max model are shown in Figs 5-7. The R 2 values between the observed PD and predicted PD data of %T > MIC, AUC/MIC, and C max /MIC were 0.9863, 0.9582, and 0.8774, respectively. The key PK/PD parameters are summarized in Table 3. The target values

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of the PK/PD indexes to produce a 0.5-log 10 CFU/MG reduction, 1-log 10 CFU/MG reduction, and 2-log 10

Discussion
In veterinary drug research, PK and PD data are often established in separate parallel studies to formulate the drug delivery scheme which is evaluated and verified in subsequent clinical trials [35]. However, with the widespread use of antibiotics, bacterial resistance has gradually emerged. PK/PD modelling is a vital approach to optimise the use of antibacterial drugs. The elimination half-life (T1/2e) identified in this study (0.49±0.083 hrs) was similar to that previously reported i.e. 0.4 hrs for intramammary administration in an experimental mouse model of S. aureus mastitis and 0.43 hrs for the intramuscular injection in the black swan model [27,36]. However, the value was significantly lower than reported for intramammary administration in lactating Chinese dairy cows (4.63 hrs) which detected the drug concentration in milk and for intramammary administration in an Escherichiacoli lactating mouse mastitis model (12.63 hrs) that detected the drug concentration in the MGs [29,37]. Compared to the cefquinome concentration in MGs, the cefquinome concentration in plasma was much lower which also occurs in cows. This may be related to the chemical properties of cefquinome. Cefquinome is an organic acid with low fat solubility and pKa values of 2.51 and 2.91 [38]. This causes the distribution of cefquinome to be less extensive and so it cannot penetrate membranes and cross the blood-MG barrier, preventing the drug from reaching the blood from the MG. The T 1/2α of 0.07±0.05 hrs was identical to the 0.07 hrs previously reported [36]. In addition to oral administration, the body can rapidly absorb other forms of cefquinome. After metabolism in vivo, cefquinome is mainly excreted in the urine through the kidneys [38].
In the present study, after 9 hrs of inoculation in mice MGs, the S. agalactiae bacterial burden reached approximately 10 7 CFU/MG. These data showed that the S. agalactiae-induced mastitis model could sufficiently replicate acute mastitis for bacterial evaluations. Low and high-concentration groups were designed to observe the bactericidal effect of cefquinome on S. agalactiae. The low-concentration group achieved bactericidal efficacy when the drug concentration was >4 × MIC. However, for the high-concentration group, cefquinome achieved only a bacteriostatic effect. These data agree with a previous report [39]. Significant differences were observed between the low-concentration and high-concentration groups (p<0.05) that

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may be related to the fact that cefquinome is a beta-lactam which is a bactericidal drug at the exponentialstage of bacteria. Penicillin-binding proteins (PBPs) are needed for the survival, growth, and reproduction of bacteria. PBPs are also the binding sites for beta-lactam antibiotics [40] which cause bacterial death by creating defects in bacterial cell walls [41]. In this study, based on the bacterial killing curves, the low-concentration group had a higher growth rate (more bacteria were present at the exponential stage) compared to the high-concentration group. The greater number of exponential growing bacteria means that more PBPs could combine with the cefquinome. Hence, the bactericidal effect in the low-concentration group was greater than that in the highconcentration group.
Different bacteria have been used to describe the association between PK/PD indexes and cefquinome antibacterial activity in different animal infection models. A prior report used

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Haemophilus parasuis to study the antibacterial activity of cefquinome. The data suggested that the %T > MIC required for 3-log 10 drop and 4-log 10 drop were 61% and 71%, respectively [42]. A later study investigated the effects of cefquinome on Actinobacillus pleuropneumoniae using a piglet tissue cage model and reported that %T > MIC achieved 11.59%, 27.49%, and 59.81% with respective 1/3-log 10 , 2/3-log 10 , and 1-log 10 reductions [43]. The same group also used Escherichia coli to examine cefquinome antibacterial efficacy and calculated that the values of %T > MIC to achieve 1/6-log 10 reductions, 1/3-log 10 reductions, and 1/2-log 10 reductions were 3.97%, 17.08%, and 52.68%, respectively [44]. The efficacy of cefquinome was also reported for Klebsiella pneumonia and Staphylococcus aureus in an ex vivo dog model and an in vivo rabbit tissue cage infection model [21,45]. All these studies demonstrated that

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cefquinome had effective antimicrobial activity against these pathogens. However, to the best of our knowledge, no previous study has reported on the efficacy of cefquinome against S. agalactiae.
In the current study, we used an experimental S. agalactiae mastitis model system to investigate the interactions between the PK/PD indexes and cefquinome activity against S. agalactiae. The %T>MIC was the PK/PD index that most effectively described the antibacterial activity of cefquinome against S. agalactiae. When the in vivo %T > MIC values were 31%, 47%, and 81%, there were 0.5-log 10 units, 1-log 10 units, 2-log 10 units reductions observed, respectively. Studies have shown that %T > MIC is a vital index for describing the PK/PD relationship of the cefquinome concerning bactericidal activity [46,47]. Here, the correlation coefficient (R 2 )

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values of %T > MIC, AUC/MIC, and C max /MIC were 0.9863, 0.9582, and 0.8774, respectively. AUC/MIC has been used to describe the relationship between PK and PD for concentrationdependent drugs. However, in this study, the R 2 of %T > MIC and AUC/MIC were very close showing that both indexes were useful in this model. These data are in agreement with a previous report by Yu et al. [28]. The cefquinome concentrations in the blood and MG were not identical due to the blood-milk barrier which explains this result.
In this study, we showed that specific doses of cefquinome cause different therapeutic impacts on the S. agalactiae-induced mastitis model. We also demonstrated that cefquinome can cause a reduction of 2.8-log 10 CFU/MG in the in vivo killing-time curve to achieve a bactericidal effect in vivo.