Antimicrobial Efficacy of Un-Ionized Ammonia (NH3) against Salmonella Typhimurium in Buffered Solutions with Variable pH, NH3 Concentrations, and Urease-Producing Bacteria

ABSTRACT The presence of Salmonella in poultry litter, when used as a biological soil amendment, presents a risk for the preharvest contamination of fresh produce. Poultry litter is rich in organic nitrogen, and previous studies have suggested that ammonia (NH3) in poultry litter may affect the survival of Salmonella. Salmonella enterica serovar Typhimurium was inoculated into buffer solutions to characterize the pH dependency, minimum antimicrobial concentration, and efficacy of NH3 production. In solutions with 0.4 M total ammonia nitrogen (TAN) at various pH levels (5, 7, 8, and 9), significant inactivation of Salmonella only occurred at pH 9. Salmonella was reduced by ∼8 log CFU/mL within 12 to 18 h at 0.09, 0.18, 0.26, and 0.35 M NH3. The minimum antimicrobial concentration tested was 0.04 M NH3, resulting in an ∼7 log CFU/mL reduction after 24 h. Solutions with urea (1% and 2%) and urease enzymes rapidly produced NH3, which significantly reduced Salmonella within 12 h. The urease-producing bacterium Corynebacterium urealyticum showed no antagonistic effects against Salmonella in solution. Conversely, with 1% urea added, C. urealyticum rapidly produced NH3 in solution and significantly reduced Salmonella within 12 h. Salmonella inactivation data were nonlinear and fitted to Weibull models (Weibull, Weibull with tailing effects, and double Weibull) to describe their inactivation kinetics. These results suggest that high NH3 levels in poultry litter may reduce the risk of contamination in this biological soil amendment. This study will guide future research on the influence of ammonia on the survival and persistence of Salmonella in poultry litter. IMPORTANCE Poultry litter is a widely used biological soil amendment in the production of fresh produce. However, poultry litter may contain human pathogens, such as Salmonella, which introduces the risk of preharvest produce contamination in agricultural fields. Ammonia in poultry litter, produced through bacterial degradation of urea, may be detrimental to the survival of Salmonella; however, these effects are not fully understood. This study utilized aqueous buffer solutions to demonstrate that the antimicrobial efficacy of ammonia against Salmonella is dependent on alkaline pH levels, where increasing concentrations of ammonia led to more rapid inactivation. Inactivation was also demonstrated in the presence of urea and urease or urease-producing Corynebacterium urealyticum. These findings suggest that high levels of ammonia in poultry litter may reduce the risk of contamination in biological soil amendments and will guide further studies on the survival and persistence of Salmonella in poultry litter.

the NH 3 concentration, urease, and urease-producing bacteria experiments were fitted to nonlinear survival models to describe the inactivation kinetics of each treatment.

RESULTS
pH treatments. The survival of Salmonella in solutions at various pH levels (5, 7, 8, and 9) with and without ammonium sulfate added (0.4 M TAN) is shown in Fig. 1. The calculated un-ionized ammonia concentrations (M NH 3 ) corresponding to each pH treatment with 0.4 M TAN added are reported in Table 1. The mean ST populations (log CFU/mL), pH, TAN (ppm), and un-ionized ammonia concentrations (M NH 3 ) at each sampling time are reported in Tables S1, S5, S6, and S7 in the supplemental material, respectively. After 24 h, ST populations in all treatments under pH 9 remained above 7 log CFU/mL. Increases were observed in PBS (pH 7) at 18 h and 0.4 M TAN (pH 8) at 12 h, although these increases were not significant (P . 0.05) compared to the other treatments under pH 9. Significant reductions (P , 0.05) of 1.16 and 5.07 log CFU/mL were observed after 6 h in the N-cyclohexyl-2aminoethanesulfonic acid (CHES; pH 9) and 0.4 M TAN (pH 9) treatments, respectively. After 12 h, ST populations in the 0.4 M TAN (pH 9) treatment fell below the limit of detection (LOD; 0.30 log CFU/mL). In the CHES (pH 9) treatment, ST populations were reduced to 3.70 log CFU/mL (4.25-log reduction) after 24 h (Fig. 1). Among the treatments with 0.4 M TAN added, the pH 9 CHES solution had the highest concentration of un-ionized ammonia. In these treatments, over 50% of the TAN was in the form of NH 3 at pH 9 compared to less than 10% in solutions at a pH of #8 (Table 1).  Un-ionized ammonia treatments. Salmonella inactivation at various levels of un-ionized ammonia (M NH 3 ) fitted to Weibull curves is shown in Fig. 2. The mean ST populations (log CFU/mL), pH, TAN (ppm), and un-ionized ammonia concentrations (M NH 3 ) at each sampling time are reported in Tables S2, S5, S6, and S7, respectively. Salmonella populations in all treatments, except the control (CHES, pH 9; Fig. 2A), approached the LOD within 12 to 24 h. In the 0.04 M NH 3 treatment, the ST concentration was reduced to 0.26 log CFU/mL (7.40-log reduction) after 24 h (Fig. 2B). The 0.09 M NH 3 treatment approached the LOD at 12 h (Fig. 2C). The 0.18 and 0.26 M NH 3 treatments were the quickest to fall below the LOD at 12 h ( Fig. 2D and E, respectively). In the 0.35 M NH 3 treatment, mean ST populations were reduced to 0.36 log CFU/mL (7.62-log reduction) at 6 h, followed by increased recovery (0.57-log increase) at 12 h. However, this increase was not significant   (36), the Weibull model with tailing effects was selected to be comparable with model fits for the other treatments. The resulting Weibull curve was slightly concave (P = 1.12) with a tailing effect (N res ) starting at 3.62 log CFU/mL ( Fig. 2A). The double Weibull model represented the best fit for the 0.04 M NH 3 treatment. This survival curve was concave (P = 1.85) until it reached an inflection point after the 12-h sampling point (Fig. 2B). The 0.09 M NH 3 treatment was best fitted to the Weibull model and the bilinear and Geeraerd models with shoulder effects, where all three models had the same AIC and BIC values of 233.97 and 233.38, respectively. The Weibull model was selected as the preferred model. The 0.18 and 0.26 M NH 3 treatments were best fitted to Weibull survival curves, with no shoulder or tailing phenomena observed. The fitted curve for the 0.09 M NH 3 treatment was concave (P = 1.46), whereas the 0.18 and 0.26 M NH 3 treatment curves were convex (P , 1) ( Fig. 2C to E). Overall, the values of d (time [h] to the first decimal reduction of the microbial population) and p (shape of the inactivation curve) decreased as the level of un-ionized ammonia increased. The 0.26 M NH 3 treatment had the lowest d and p values of 0.17 and 0.49, respectively (Table 2).
Urea, urease, and Corynebacterium urealyticum treatments. The survival of ST in CHES buffer solutions (pH 9) with urea (1% and 2%), urease, and C. urealyticum (CU) is shown in Fig. 3. The mean ST populations (log CFU/mL), CU populations (log CFU/mL), pH, and TAN (ppm) at each sampling time are reported in Tables S3, S4, S5, and S6, respectively. The un-ionized ammonia concentrations (M NH 3 ) at each sampling time are reported in Table 3. After 24 h, ST populations in the 1% and 2% urea and urease control treatments were reduced to 3.23, 3.83, and 4.37 log CFU/mL, respectively (Fig. 3A, C, and D). Both treatments with urea (1% and 2%) and urease fell below the LOD at 12 h, representing 7.81-and 7.82-log reductions, respectively ( Fig. 3E and F). At 12 h, the mean un-ionized ammonia concentrations in the 1% and 2% urea with urease treatments were 0.153 and 0.316 M NH 3 , respectively. After 24 h, the 1% and 2% urea with urease treatments produced un-ionized ammonia concentrations of 0.165 and 0.375 M NH 3 , respectively (Table 3). In the CU with 1% urea treatment, the rate of ammonia production remained constant at approximately 0.04 M NH 3 every 6 h until 18 h, when this rate decreased (Table 3). ST populations were reduced to 3.36 log CFU/mL in the CU control treatment after 24 h. In the CU with 1% urea treatment, ST populations fell below the LOD after 12 h (7.92-log reduction) (Fig. 3G). The mean un-ionized ammonia concentrations in this  (Table 3). Ammonia production in the urea with urease and C. urealyticum with urea treatments increased the pH up to 9.25 (Table S5). NH 3 did not have a major effect on the CU inoculum, which decreased by only 1.66 log CFU/mL after 24 h (Table S4). The un-ionized ammonia concentrations in the urea, urease, and CU control treatments were less than 0.001 M NH 3 at each sampling time (Table 3). Table 4 shows parameter estimates, 95% confidence intervals, and goodness-of-fit measures (AIC and BIC) for the fitted Weibull curves of ST survival in urea (1% and 2%), urease, and CU solutions. ST survival in the urease control solution was best fitted to the double Weibull model, where the survival curve was slightly concave (P = 1.16) with a minor inflection point between 12 and 18 h (Fig. 3A). The CU control was fitted well to both the trilinear With only slight differences between AIC and BIC, the Weibull model with tailing effects was selected to allow for comparisons with the other treatments. The resulting model for the CU control treatment was concave (P = 1.59) with the tailing effect (N res ) starting at 3.25 log CFU/mL (Fig. 3B). The Weibull model, without shoulder or tailing effects, was best fitted to ST inactivation data for the urea (1% and 2%) controls and 2% urea with urease treatment. For the 1% urea with urease and CU with 1% urea treatments, identical AIC and BIC values indicated three best-fitting models: the Weibull, Geeraerd with shoulder effects, and bilinear with shoulder effects models. The Weibull model was selected as the preferred model. The 1% and 2% urea controls were both fitted to convex (P , 1) survival curves with d values of 3.89 and 4.38, respectively ( Fig. 3C and D). The urease and CU treatments with 1% urea were both fitted by concave (P . 1) survival curves with d values of 2.88 and 3.73, respectively ( Fig. 3E and G). The 2% urea with urease treatment showed the most rapid decline of Salmonella among this group of treatments, with d and p values of 0.26 and 0.54, respectively ( Fig. 3F and Table 4).

DISCUSSION
Several studies have demonstrated the antimicrobial effects of NH 3 on Salmonella in poultry litter and solutions (19,28,31,(33)(34)(35). However, previous work in poultry litter has often been performed using NH 3 gas. As a result, key aspects of the interaction between NH 3 and Salmonella are not fully understood. This research sought to examine these aspects by characterizing the pH dependency, minimum antimicrobial concentration, and efficacy of NH 3 production in buffer solutions inoculated with S. Typhimurium (ST).   Payne et al. (37) observed the growth of Salmonella in poultry litter at pH 7 and 9 under favorable conditions (i.e., a w and temperature). Several poultry litter surveys have observed the average pH of litter to be approximately 8 (38)(39)(40). In this current study, buffer solutions at pH 5, 7, and 8 with and without ammonium sulfate added showed no detrimental effects on the survival of ST in the solutions. However, at pH 9 with and without ammonium sulfate added (0.4 M TAN), ST populations were significantly reduced. Koziel et al. (19) reported that NH 3 treatments at low pH levels (4.4 to 4.6) failed to show any antimicrobial effect on S. Typhimurium in solution. In their study, Salmonella reductions were not observed in the control solution of PBS at pH 9 (19). Given that the CHES buffer did not exhibit any antimicrobial effects on the inoculum at any lower pH level (5 to 8), with or without the addition of ammonium sulfate, the reduction seen in this current study may be a strain-dependent pH sensitivity. This type of strain-dependent sensitivity to alkaline conditions has been previously observed in a study that tested 99 strains of Salmonella enterica in alkaline solutions (pH 11), where authors reported that reductions ranged from 0 to 5 log CFU/mL after 2 h (41). Despite this pH effect, the addition of ammonium sulfate to the variable pH solutions demonstrated that the antimicrobial efficacy of NH 3 was dependent on alkaline pH levels ($9).
Field surveys of poultry litter offer conflicting reports on the relationship between Salmonella and ammonia in litter, with studies observing negative (42) Previous studies in poultry litter and manure have used various levels of NH 3 gas to demonstrate its antimicrobial effects on Salmonella (28,31,33). However, these concentrations of NH 3 gas may not be feasibly generated as a result of natural ammonia production in commercial poultry litter. Ammonia production and volatilization in poultry litter increases significantly at pH levels higher than 8 (15,25,44). Turnbull et al. (28) reported that the salmonellacidal efficacy of NH 3 gas increased as the a w of the litter approached 1.00. Given the pH dependency and the potential effects of a w , the minimum antimicrobial concentration of NH 3 in poultry litter may differ considerably from the level reported in this study of buffer solutions.
Schefferle (45) demonstrated that strains of Corynebacterium, Nocardia, Streptomyces, Pseudomonas, Micrococcus, Alcaligenes, Achromobacter, and Cytophaga recovered from poultry litter had the ability to break down uric acid and urea into ammonia. Urease-producing bacteria may be present in litter at levels of 6 to 8 log CFU/g (46). Corynebacterium represent a major genera of urease-producing bacteria commonly found in poultry litter, and the species Corynebacterium urealyticum has been previously identified in litter samples (45,(47)(48)(49). At present, urease-producing bacteria have not been studied in relation to the prevalence or concentration of Salmonella in poultry litter. A recent study by Bucher et al. (50) reported that S. Heidelberg concentrations in poultry litter microcosms exhibited a negative correlation with Nocardiopsis and a positive correlation with Bacillaceae in the litter. They also isolated a consortium of five Bacillus subtilis strains from the poultry litter that reduced the growth of S. Heidelberg in a poultry litter extract solution by an average 0.2 log CFU/mL (50). In the present study, CU had no antagonistic effects on the ST inoculum. The constant rate of ammonia production in the CU with 1% urea treatment suggests that urease enzyme activity in the CU population reached its maximum within the first 6 h of the experiment and that the enzymes were fully saturated by urea from 0 to 18 h. At each sampling time, the CU treatment produced less NH 3 than the urease treatment, suggesting that the CU inoculum produced a urease concentration of ,50 U/mL, the concentration of urease added directly into the other treatments. The results of this study demonstrated that urease and C. urealyticum can produce NH 3 in solution under these conditions (pH 9, 30°C) and effectively reproduce the antimicrobial activity observed in the previous experiments. Further investigations are needed to examine the relationship between urease-producing bacteria and Salmonella survival in poultry litter.
Previous studies modeling the survival of Salmonella in poultry litter have examined the effects of heat treatments, storage time, and storage conditions using stacked or composted litter (51)(52)(53). In these various studies, Chen et al. (51)(52)(53) used the exponential, Geeraerd (with shoulder and/or tailing effects) (54), biphasic (55), and double Weibull models (56) to describe the inactivation kinetics of Salmonella in litter. Payne et al. (37) used the exponential and Churchill models (57) to describe the growth and inactivation of Salmonella in poultry litter under various pH and a w conditions. Whereas the current study compared seven models to determine the best fit, these previous studies only used one or two models to fit their inactivation data. The results of this study demonstrated that the inactivation kinetics of S. Typhimurium in NH 3 solutions were well described by the Weibull, double Weibull, and Weibull with tailing effects models. The CHES (pH 9) and CU control treatments were both fitted to the Weibull model with tailing effects. Tailing in survival curves typically implies either the existence of a more resistant subpopulation of cells or that cells are adapting to the stress during exposure (58). The urease control and 0.04 M NH 3 treatments were fitted by the double Weibull model. The double Weibull model assumes that the microbial population is composed of two groups with different resistance levels toward a stress treatment (56). Except for the 0.04 M NH 3 treatment, all NH 3 and NH 3 -producing treatments were best fit to the Weibull model, where d and p values generally decreased as NH 3 concentrations increased. At NH 3 levels of $0.9 M, Salmonella populations fell below the LOD within 12 h. The use of three time points (0, 6, and 12 h) to fit several treatment models represents a significant limitation of this current study. Given that Salmonella populations may have fallen below the LOD between 6 and 12 h in these treatments, additional observations within these times would likely change the model parameters. Koziel  Overall, this modeling effort may serve as a primer for further studies on the interactions between Salmonella and NH 3 in poultry litter and solutions.
In conclusion, this study provides a fundamental understanding of the production of NH 3 , its pH dependency, and the response of Salmonella to various concentrations of NH 3 in solution. This study observed that the antimicrobial activity of ammonia was dependent on alkaline conditions (pH $ 9), where NH 3 concentrations of $0.04 M resulted in significant Salmonella reductions. Urease and C. urealyticum were shown to be capable of rapidly breaking down urea into ammonia under alkaline conditions, replicating this antimicrobial effect. The results of this study suggest that high NH 3 levels in poultry litter may reduce the risk of Salmonella contamination in this biological soil amendment. However, future laboratory and field studies are needed to determine the feasibility of NH 3 demonstrating this salmonellacidal effect in commercial poultry litter environments, given the need for alkaline conditions and sufficient ammonia production.

MATERIALS AND METHODS
Bacterial strains and inoculum preparation. A Salmonella enterica serovar Typhimurium (ST) isolate (AG100R) previously recovered from poultry litter (38) was used to inoculate the solutions in this study. Antimicrobial resistance to 200 mg/mL rifampicin (RIF; Sigma-Aldrich, St. Louis, MO) was induced in the ST isolate using stepwise exposures. The urease-producing bacteria Corynebacterium urealyticum ATCC 43044 (CU) was also used in this study. This urease-producing bacterium has been found naturally in poultry litter (47). To facilitate recovery and enumeration of CU, resistance to 120 mg/mL ampicillin (AMP; Fisher Scientific, Fair Lawn, NJ) was induced using stepwise exposures. To prepare the ST inoculum, a frozen culture was transferred to 10 mL of tryptic soy broth (TSB; BD, Difco, Sparks, MD) with 80 mg/mL RIF and incubated at 37°C for 18 to 24 h in a shaking incubator at 100 rpm. This overnight culture was transferred once more into 10 mL of TSB with 80 mg/mL RIF and incubated under the same conditions. The final culture was prepared by transferring the overnight culture to 25 mL of TSB with 80 mg/mL RIF in a 50-mL conical centrifuge tube (Fisher Scientific) and incubating under the same conditions. Similarly, the CU inoculum was prepared using Mueller-Hinton broth (MHB; BD, Difco) with 10% rabbit serum (Gibco, Dublin, Ireland) and 80 mg/mL AMP as the culture broth. Cells were collected by centrifugation (1,789 Â g, 10 min) and washed twice in 0.5 M N-cyclohexyl-2-aminoethanesulfonic acid (CHES; Acros Organics, Fair Lawn, NJ) buffer or phosphate-buffered saline (PBS; MP Biomedicals, Irvine, CA). The CHES buffer and PBS washing solutions were adjusted to pH 9.0, 8.0, 7.0, or 5.0 using 10 N NaOH or 6 N HCl, depending on the desired pH of each treatment. Enumeration of the ST inoculum was performed by spreading 0.1 mL of 0.1% peptone water (PW; BD, Difco) serial dilutions onto tryptic soy agar (TSA; BD, Difco) with 80 mg/mL RIF, in duplicate, and incubating at 37°C for 18 to 24 h before counting. The CU inoculum was enumerated similarly, using Mueller-Hinton agar (MHA; BD, Difco) with 10% rabbit serum and 80 mg/mL AMP as the plating medium and incubated at 37°C for 48 h. Each bacterial inoculum yielded a final average concentration of approximately 9 log CFU/mL. Ammonia, urea, and control treatments. All the treatments performed in this study are shown in Table 5. No ammonia or urea was added to control treatments. Solutions for the pH and ammonia trials were prepared using ammonium sulfate [(NH 4 ) 2 SO 4 ; Fisher Scientific] dried in an oven for 1 h at 100°C. In the pH trial, 26.19 g/L (NH 4 ) 2 SO 4 was added to autoclaved CHES or PBS buffers to achieve 0.4 M nominal concentrations of total ammonia nitrogen (TAN). The calculated corresponding concentrations of un-ionized ammonia (NH 3 ) in each pH trial solution are shown in Table 1. For the ammonia trial, solutions were prepared by adding dried (NH 4 ) 2 SO 4 to autoclaved CHES buffer to achieve 0.04, 0.09, 0.18, 0.26, and 0.35 M nominal concentrations of NH 3 . Table 6 shows the amounts of (NH 4 ) 2 SO 4 added to achieve the desired TAN and NH 3 concentrations in each solution. Urea solutions (1% and 2%, wt/vol) were prepared by adding urea to bottles of autoclaved CHES buffer. Urease solutions were prepared to a concentration of 50 U/mL by adding 0.025 g of urease from Canavalia ensiformis (jack bean) (specific activity of 40,150 U/g; Sigma-Aldrich) to 20 mL of CHES. The pH of each solution was adjusted to the desired pH for each treatment, as indicated in Table 5, using 10 N NaOH or 6 N HCl. For all treatments, except those with urease or CU inoculum, 9 mL of each solution was transferred to five 15-mL screw-cap conical centrifuge tubes (Fisher Scientific), followed by the addition of 1 mL of ST inoculum. For treatments with urease, 8 mL of each solution was transferred to five 15-mL screw-cap conical centrifuge tubes, followed by the addition of 1 mL of both the urease solution and ST inoculum. For urease-producing bacteria treatments, 8 mL of each solution was transferred to five 15-mL screw-cap conical centrifuge tubes, followed by the addition of 1 mL of both the CU and ST inoculum. All tubes were incubated in a shaking incubator at 30°C and 120 rpm. All treatments were performed in triplicate.  Sampling procedure. One tube from each treatment was sampled at each sampling time (0, 6, 12, 18, and 24 h). Bacterial enumeration was performed by transferring 1 mL from the experimental tube to 9 mL of 0.1% PW, serially diluting, and spread plating 0.1 mL onto TSA with 80 mg/mL RIF for ST and plating onto MHA with 10% rabbit serum and 80 mg/mL AMP for CU. As ST and CU populations approached the limit of detection (LOD) (1 CFU/mL), four 250-mL subsamples from the treatment tubes were plated onto TSA with 80 mg/mL RIF and MHA with 10% rabbit serum and 80 mg/mL AMP, respectively. Plates were incubated at 37°C for 18 to 24 h and 48 h for ST and CU, respectively. All treatment tubes were filter sterilized (product number 430320; Corning, Corning, NY) before measuring pH and TAN. For urease and urease-producing bacteria treatments, pH was measured after filtration, and filtrates were stored at 220°C to stop urease activity until TAN was measured. The pH (model HI72911B, Hanna Instruments, Smithfield, RI) and TAN (model HI4101, Hanna Instruments) of each tube were measured using a pH/oxidation-reduction potential (ORP)/ion-selective electrode (ISE) meter (model HI98191, Hanna Instruments). TAN was measured in parts per million according to the manufacturer's instructions for the ammonia combination ISE. During the pH trial, PBS buffer treatments (pH 5.0 and 7.0), with and without ammonia added, were measured at 0 and 24 h for pH. For these treatments, TAN was measured in duplicate from samples of the prepared bulk PBS solutions without ammonia added and from tubes sampled at 0 h for treatments with 0.4 M TAN added.
Un-ionized ammonia calculations. Un-ionized ammonia (NH 3 ) concentrations were calculated using TAN (ppm), pH, and temperature (°C) according to the following equations (equations 1 and 2) derived from the Henderson-Hasselbalch equation (pH = pK a 1 log 10  Statistical analysis. Bacterial plate counts (CFU/mL) were log transformed (log 10 [CFU/mL 1 1]) for statistical analysis. The log-transformed LOD was 0.30 log CFU/mL (log 10 [1 1 1]). Negative samples were assigned a value of 0 CFU/mL and were represented by 0 log CFU/mL (log 10 [0 1 1]). A one-way analysis of variance (ANOVA) followed by Tukey's honestly significant difference test was used to compare mean ST populations for all treatments and un-ionized ammonia concentrations (M NH 3 ) for the urea, urease, and CU treatments. Welch's t test was used to compare mean CU populations at each sampling time. Statistical analyses were performed in R version 4.0.4 (59) with a significance level of 0.05.
Inactivation models, parameter estimation, and goodness-of-fit. Several primary inactivation models were fitted to the survival data to determine the best-fitting model. The following models were considered: log-linear (60), bilinear (with and without tailing or shoulder effects) (61), trilinear (61), Geeraerd (with and without tailing or shoulder effects) (54), Weibull (62), Weibull with tailing effects (63), and double Weibull (56). ST concentration (log CFU/mL) data from the NH 3 , urea, urease, and urease-producing bacteria experiments were fitted to these models using the nls() function in R (59). Bootstrapped confidence intervals were generated for the fitted model parameters using the nlsBoot() function from the nlsMicrobio R package (61). For each treatment, ST concentrations were modeled for sampling times between inoculation (0 h) and the first sample time approaching the LOD. Survival data from the 0.35 M NH 3 treatment were not modeled because the data could not be fitted reliably. The goodness-of-fit among fitted models was compared according to the Akaike information criterion (AIC; equation 3) (64) and the Bayesian information criterion (BIC; equation 4) (65).
In equations 3 and 4, RSS is the residual sum of squares, p is the number of data points used to fit the model, and k is the number of parameters in the model. Lower AIC and BIC scores indicate a better fitting model.
Inactivation kinetics in this study were described by the Weibull, Weibull with tailing effects, and double Weibull models. The Weibull model (equation 5) is an empirical inactivation model used to fit microbial survival curves that exhibit non-log-linear behavior (66).
In this model (equation 5), N t is the microbial population (CFU/mL) at time t, N 0 is the initial microbial population (CFU/mL), t is the time (h), p is the shape of the inactivation curve (dimensionless), and d is the time (h) to the first decimal reduction of the microbial population.
Albert and Mafart (63) proposed a modified Weibull model that incorporated parameters for modeling shoulder (delayed response) and/or tailing (stabilized decline) phenomena observed in microbial survival curves. This model is presented here with only tailing incorporated (equation 6). log 10 ðN t Þ ¼ log 10 ðN 0 2 N res Þ10 2 t d ð Þ p 1 N res h i (6) In this model (equation 6), N t , N 0 , t, p, and d have the same meaning as previously described, while N res is the microbial population (CFU/mL) at the starting point of the tail, which is supposed to be fully resistant against inactivation.
Coroller et al. (56) proposed a new primary inactivation model based on two mixed Weibull distributions, which could be used to describe survival curves where the microbial population is assumed to be composed of two subpopulations with different levels of resistance to stress (equation 7). In this double Weibull model (equation 7), N t , N 0 , t, and p have the same meaning as previously described, while a is the fraction of the first subpopulation remaining in the total population, and d 1 and d 2 are the times to the first decimal reduction of subpopulations 1 and 2, respectively (67).