AP (CVCC259) was purchased from Chinese Veterinary Culture Collection Center (Qingdao, China). Danofloxacin mesylate powder (content >99%) was provided by Guangdong Dahuanong Biotechnology (Guangdong, China). Tryptic soy broth (TSB) and Mueller–Hinton Agar (MHA) were obtained from Guangdong Huankai Microbiology Technology (Guangdong, China). Nicotinamide adenine dinucleotide (NAD) was sourced from Beijing Puboxin Biotechnology (Beijing, China). Newborn bovine serum was provided by Guangzhou Ruite (Guangzhou, China).

A peristaltic pump (BT100-1F), pump head (DG-2-B/D; 10 roller), and rubber hose (inner diameter ≤3.17 mm; wall thickness = 0.8–1 mm) were purchased from Longer Precision Pump (Baoding, NC, USA). Fiber dialysis tubes (Float-A-Lyzer^® 1,000 kD; 10 mL) were sourced from MilliporeSigma (Burlington, MA, USA).

MHA and TSB were supplemented with 4% newborn bovine serum and NAD (1 mg/mL).

The MIC was tested by an agar-dilution method according to criteria set by the Clinical and Laboratory Standards Institute (25). Briefly, after being cultured for 8 h in a constant-temperature shaker (180–200 rpm, 37°C), the bacterial suspension was diluted to 10⁶ CFU/mL by TSB. Then, the bacterial suspension (100 μL) was added to an MHA plate containing danofloxacin (0.016–1 μg/mL after twofold dilution). After drying, the MHA plates were placed in an incubator in an atmosphere of 5% CO₂ for 18–20 h at 37°C. The MIC was determined as the minimum concentration of drug that did not result in bacterial growth.

Next, we determined MIC₉₉. Briefly, a series of MHA plates containing drugs were prepared based on the MIC (90% × MIC, 80% × MIC, 70% × MIC, 60% × MIC, 50% × MIC). After the logarithmic-phase bacterial suspension had been diluted tenfold (10⁻¹, 10⁻², 10⁻³, 10⁻⁴, 10⁻⁵, 10⁻⁶), the dilutions were inoculated to MHA and cultured as described for determination of the MIC. Then, the bacterial populations were counted and compared between drug-containing plates and the blank plate. Percent recovery growth of bacteria was obtained, and a linear formula between the drug concentration and percent recovery was obtained. MIC₉₉ was determined as the value which inhibited the growth of bacteria by 99% (1% recovery).

We also tested the MPC. Briefly, after being cultured for 8 h, a logarithmic-phase bacterial suspension (100 mL) was centrifuged (5,000 × g, 20 min, 4°C). Then, the supernatant was removed and blank TSB (1 mL) was added for a bacterial population of 1.5 × 10¹¹ CFU/mL. Then, the bacterial solution (100 μL) was inoculated on MHA plates (1 × MIC, 2 × MIC, 4 × MIC, 8 × MIC, 16 × MIC, 32 × MIC, 64 × MIC) and incubation allowed to proceed for 72 h. The minimum concentration of danofloxacin that did not elicit bacterial growth was defined as MPC_pr. Then, based on MPC_pr, the drug concentration was reduced linearly from 10%MPC_pr to 50% × MPC_pr, and the procedure repeated as described for measurement of MPC_pr. The MPC was defined as the lowest concentration of danofloxacin that could inhibit the growth of bacteria. All tests were repeated thrice.

The peristaltic pump that we employed has been described in detail previously (26). A storage chamber, central chamber, and elimination chamber were connected through the peristaltic pump and rubber tube. The storage chamber consisted of a blue-cap bottle (500–5,000 mL) for storage of blank TSB broth. The central chamber comprised a modified three-necked flask containing blank TSB broth (290 mL), a dialysis tube, and magnetic rotor. The three-necked flask consisted of an inlet tube, sampling tube, and outlet tube with rubber stoppers. The sampling tube comprised an elongated syringe needle and nylon filters (0.22 μm) for collection of the TSB sample and contamination prevention. The central chamber was placed in a large beaker with water at a constant temperature (37°C) and magnetic-stirring apparatus (100 rpm). The elimination chamber consisted of a blue-cap bottle (500–5,000 mL) for collection of waste liquid. The dialysis tube contained a bacterial suspension (10 mL) and “floated” in blank TSB and 1-cm above TSB thanks to a foam gasket.

The PK parameter of danofloxacin in pigs was in reference to the work of Yang et al. (27). We set the elimination half-life (t_1/2) of danofloxacin at 7 h. The elimination rate constant (Kel) was calculated to be 0.693/t_1/2. The flow rate of the peristaltic pump (Q) was calculated as Kel × V_C (broth volume in the central chamber and dialysis tube). After the flow rate had been set, the device was run for 2 h to enable stabilization. Then, logarithmic-phase AP (10⁸ CFU/mL) was added to the central chamber. The in vitro DIM was established if the bacterial population stabilized at ~10⁸ CFU/mL.

We wished to study the antibacterial effect in different parts of the MSW. Hence, seven dosage groups (0 × MIC₉₉, 1/2 × MIC₉₉, 1 × MIC₉₉, 2 × MIC₉₉, 4 × MIC₉₉, 8 × MIC₉₉, 16 × MIC₉₉) were set up and administrated thrice every 24 h. To balance the drug concentration between the dialysis tube and peripheral chambers rapidly, both compartments were administered drugs to ensure that the drug concentration was identical upon experiment initiation. The bacterial suspension (0.1 mL) was collected from the dialysis chamber with a 1-mL sterile syringe. Then, it was diluted and dropped onto a blank MHA plate for bacterial counting at 0, 3, 6, 9, 12, and 24 h after each dose as well as at 48 and 72 h after the final dose. The limit of detection of the bacterial count was 50 CFU/mL. Each dose was repeated thrice. The kill curve of danofloxacin against AP was drawn as the logarithmic value of the bacterial population at different times.

To detect AP mutants, each sample was plated in MHA containing 1 × MIC of danofloxacin 24 h after each dose as well as 48 and 72 h after the final dose. AP with increasing MICs was passed through five generations in MHA to monitor the stability of the mutant. Then, the MIC of mutant AP was tested as described above.

The concentration of danofloxacin at different time points was tested by high-performance liquid chromatography, but the data were lost because of damage to software. Therefore, the PK of drugs in the model were simulated using a first-order elimination rate and calculated using Equation 1:

C: drug concentration at time t,

C₀: initial concentration of danofloxacin,

K: constant of elimination rate,

t: time of sample collection after drug administration.

The drug concentration at each time point after each dose administration was calculated, and drug concentration–time curves were drawn. Values of area under concentration-time curve (AUC_24h) and maximum concentration (C_max) during 24 h were obtained based on a non-compartment model using WinNonlin (version 5.2.1, Pharsight, MO, USA).

The antibacterial effect (E) was defined as the maximum change in the number pf bacteria during the interval of each administration. The antibacterial effect was split into a bacteriostatic effect (0 log₁₀ CFU/mL), bactericidal effect (3 log₁₀ CFU/mL), and eradication effect (4 log₁₀ CFU/mL).

AUC_24h/MIC₉₉ and C_max/MIC₉₉ were obtained directly by the values of AUC_24h and C_max divided by MIC₉₉. The percentage of time that the drug concentration was above MIC₉₉ during the dosing interval of 24 h (i.e., %T >MIC₉₉) was calculated by PD models using WinNonlin.

The relationship between PK/PD parameters and the antibacterial effect was fitted by an inhibitory sigmoid E_max model by WinNonlin using Equation 2:

E: change in the bacterial count in different drug concentrations after administration of each dose,

E_max: change in the bacterial count in the control group after administration of each dose,

E₀: maximum change in the bacterial count in the treatment group after administration of each dose,

C_e: PK/PD parameters, AUC_24h/MIC₉₉, C_max/MIC₉₉, %T >MIC₉₉,

EC₅₀: value of the PK/PD parameter to reach half of E_max,

N: Hill coefficient, the slope of the PK/PD parameter, and E curves.

The fitting relationships between PK/PD parameters and E were expressed by the correlation coefficient (R²). The greater the value, the better was the fitting. PK/PD parameters were calculated to make the bacterial population decrease by 0 log₁₀ CFU/mL, 3 log₁₀ CFU/mL, and 4 log₁₀ CFU/mL.

The MIC, MIC₉₉, and MPC were 0.0625, 0.05, and 0.4 μg/mL, respectively.

According to Equation 1, the danofloxacin concentration at each time point was obtained by extrapolation. Concentration–time curves were drawn (Figure 1). The values of C_max and AUC_24h after administration of each dose were obtained using WinNonlin.

Drug concentrations were distributed in different parts of the MSW. The groups of 0.025 μg/mL and 0.05 μg/mL were located outside the MSW. The groups of 0.1 μg/mL and 0.2 μg/mL were located in the lower part of the MSW. The group of 0.4 μg/mL was located in the middle of the MSW. The group of 0.8 μg/mL group was located in the middle and upper parts of the MSW.

Kill curves at different dosing concentrations are shown in Figure 2. The antibacterial effect after each dose is shown in Table 1. The groups of 0.025 μg/mL and 0.05 μg/mL could produce a bacteriostatic effect. The group of 0.1 μg/mL could reach a bactericidal effect. The group of 0.2 μg/mL could reach an eradication effect.

The antimicrobial effect of three-times administration was not significantly different for the group of 0.025 μg/mL compared with that of the control group (Table 1). If the dose >0.025 μg/mL, then the reduction in the bacterial count after the first-time dose was significantly greater than that after the second-time dose and third-time dose. The higher the dose, the greater was the difference, but the difference between the second-time dose and third-time dose was not significant. Changes in the MIC at each dose are shown in Figure 3. The MIC of AP did not change significantly if the drug concentration was lower than MIC₉₉ and higher than the MPC. If the drug concentration was in the middle of the MSW, then the MIC of AP was increased significantly if the frequency of drug administration increased (eightfold increase for the groups of 0.1, 0.2, and 0.4 μg/mL) and recovery to the initial value was observed in the group of 0.05 μg/mL after the final administration.

Using the sigmoid E_max model, AUC_24h/MIC₉₉ had the highest correlation with E (R² = 0.7992) (Figure 4). R² of %T >MIC₉₉ with E was 0.7935 (Figure 5). The values of AUC_24h/MIC₉₉, C_max/MIC₉₉, %T > MIC₉₉, and E are shown in Table 1. Therefore, AUC_24h/MIC₉₉ was selected as the PK/PD parameter to predict the corresponding E. The PK/PD parameters and AUC_24h/MIC₉₉ values for different antibacterial effects were obtained (Table 2). The predicted values of AUC_24h/MIC₉₉ to produce a bacteriostatic effect, bactericidal effect, and eradication effect were 2.68 h, 33.67 h, and 71.58 h, respectively.