Modeling the Temperature Effect on the Growth of Uropathogenic Escherichia coli in Sous-Vide Chicken Breast

Abstract

Uropathogenic Escherichia coli (UPEC) is known to cause 65–75% of human urinary tract infection (UTI) cases. Poultry meat is a reservoir of UPEC, which is suspected to cause foodborne UTIs. In the present study, we aimed to determine the growth potential of UPEC in ready-to-eat chicken breasts prepared by sous-vide processing. Four reference strains isolated from the urine of UTI patients (Bioresource Collection and Research Center [BCRC] 10,675, 15,480, 15,483, and 17,383) were tested by polymerase chain reaction assay for related genes to identify their phylogenetic type and UPEC specificity. A cocktail of these UPEC strains was inoculated into sous-vide cooked chicken breast at 10^3–4 colony-forming unit (CFU)/g and stored at 4°C, 10°C, 15°C, 20°C, 30°C, and 40°C. Changes in the populations of UPEC during storage were analyzed by a one-step kinetic analysis method using the U.S. Department of Agriculture [USDA] Integrated Pathogen Modeling Program-Global Fit [IPMP-Global Fit]. The results showed that the combination of the no lag phase primary model and the Huang square-root secondary model fitted well with the growth curves to obtain the appropriate kinetic parameters. This combination for predicting UPEC growth kinetics was further validated using it to study additional growth curves at 25°C and 37°C, which showed that the root mean square error, bias factor, and accuracy factor were 0.49–0.59 (log CFU/g), 0.941–0.984, and 1.056–1.063, respectively. In conclusion, the models developed in this study are acceptable and can be used to predict the growth of UPEC in sous-vide chicken breast.

Introduction

Uropathogenic Escherichia coli (UPEC) is the most common causative agent of human urinary tract infections (UTIs), with prevalence rates of 75% and 65% in cases of uncomplicated and complicated UTIs, respectively (Flores-Mireles et al., 2015). UPEC is an extraintestinal pathogenic Escherichia coli (ExPEC), which differs from commensal Escherichia coli with respect to phylogenetic background and virulence attributes. Previous studies found genetic similarities between E. coli from food animals, particularly chickens, and ExPEC causing community-acquired UTIs in humans (Bergeron et al., 2012; Vincent et al., 2010). Another case–control study indicated that frequent consumption of chicken was significantly relevant to woman's UTI caused by antimicrobial-resistant E. coli (Manges et al., 2007). Animal studies also demonstrated that inoculation with E. coli isolates (phylogroup B2 or D) from broiler chicken meat could cause UTI in mice (Jakobsen et al., 2010a; Jakobsen et al., 2010b). Thus, retail chicken meat products are suspected to be a reservoir of UPEC, and may be responsible for foodborne UTIs due to their zoonotic potential (Mitchell et al., 2015; Nordstrom et al., 2013).

Ready-to-eat (RTE) foods meet the urban consumers' demand for a time-saving diet, with a growing global market valued at US$ 90 billion in 2020 (QYResearch, 2020). Chicken breast cooked by sous-vide is one of the most popular RTE food products in Taiwan, because it meets the demand for high-protein and low-calorie meals of people who exercise. Sous-vide is a novel method of cooking in vacuumized plastic pouches using a water bath or convection steam oven (Baldwin, 2012). To prevent nutrient loss and retain moisture and flavor compared to conventional cooking, the cooking temperature of sous-vide is often maintained around 60°C or lower, and the product is kept isothermally for a long time (Bhat et al., 2020; Dominguez-Hernandez et al., 2018). However, inadequate sous-vide processing, such as cooking at low temperatures for a short time, may allow the survival of vegetative forms of pathogenic bacteria in food, leading to foodborne illnesses (Dogruyol et al., 2020).

Moreover, RTE foods are expected to be consumed without prior heating, which increases the risk of foodborne infections caused by cross-contamination of pathogens after cooking (Sheen and Hwang, 2010; Sinh et al., 2018). To the best of our knowledge, there is no predictive model for the UPEC growth in sous-vide RTE foods until now. It is worthwhile to investigate the growth kinetics of UPEC in sous-vide chicken breast since the predictive microbiology approach has been recognized as a critical component of microbial risk assessment in foods (FAO/WHO, 2021).

The first objective of the present study was to examine how storage temperature affects the growth of UPEC in sous-vide chicken breasts. The second objective was to develop mathematical models to predict the effect of storage temperature on the growth of UPEC in sous-vide chicken breast. We used the USDA IPMP-Global Fit to perform one-step kinetic analysis to develop the models (Huang, 2017). The performance of the developed models was further validated by additional growth experiments.

Materials and Methods

UPEC strains and polymerase chain reaction identification

The reference strains of UPEC isolated from patients' urine (Bioresource Collection and Research Center [BCRC] 10,675, 15,480, 15,483, and 17,383) were purchased from the Bioresource Collection and Research Center (Hsinchu, Taiwan). The UPEC strains were cultured in LB-Miller broth (BioShop, Canada) at 35°C for 24 h and stored in Brain-Heart Infusion broth (Becton Dickinson, Sparks, MD, USA) containing 30% of glycerol at −80°C until use. The phylogroups, and the presence of UPEC-specific genes in these reference strains, were identified using multiplex polymerase chain reaction (PCR). For phylogroup classification, specific primers were used for four genes: arpA, chuA, yjaA, and TspE4.C2 (Clermont et al., 2013; Clermont et al., 2000). To determine the specificity of UPEC, primers were designed for three UPEC-specific marker genes: c3509, c3686, and chuA. These are virulence genes present in UPEC, but absent in commensal E. coli and other uropathogenic bacteria. Concomitantly, an E. coli-specific marker gene, uidA, was used as an internal control (Brons et al., 2020). All primers were purchased from MDBio, Inc. (Taipei, Taiwan). The primer sequences are listed in Supplementary Table S1.

The DNA of the four UPEC strains was extracted using EZ-Pure Plasmid Prep ver.2 (Integrated Bio, Taiwan). PCR mixtures (10 μL each) were composed of 5 μL of PowerAmp 2X PCRmix-Green (Bioman Scientific Co., Ltd, Taiwan), 2 μL of template DNA, 1.6 μL of primer, and 1.4 μL of double-distilled water. The mixtures were incubated in a PCR thermal cycler (Kyratec, Queensland, Australia) to amplify the DNA under the following conditions: initial denaturation of double stranded DNA for 5 min at 95°C; 30 cycles consisting of 2 min at 95°C, 2 min at 55°C, and 1 min/kb at 72°C; and final extension for 10 min at 72°C. All amplicons were analyzed by electrophoresis in 2.0% agarose gels containing a nucleic acid stain (BioGreen, Bioman Scientific Co., Ltd., Taiwan) and visualized using a ultraviolet (UV) light documentation system (Slite 200W 15 model, Blueberry Co., Ltd., Taiwan). The sizes of the amplicons were determined using a loading dye containing 100 bp DNA ladder (Bioman Scientific Co., Ltd, Taiwan).

Inoculum preparation

A cocktail of UPEC reference strains was used for the inoculation. The four UPEC strains were cultured in 5 mL of LB-Miller broth in a 15 mL centrifuge tube separately at 37°C, with shaking at 180 rpm for 18–24 h (LM-570RD; Yihder Co., Ltd, Taiwan). The cocktail was prepared by mixing 5 mL of the strain and centrifuging at 3500 × g for 10 min (Z300K; Hermle, Germany). The supernatant was discarded, and the pellet was suspended in 0.1% sterilized peptone water (BioShop, Ontario, Canada).

Sous-vide cooking and inoculation of chicken breast meat

Skinned chicken breasts (99% fat free) were purchased from a local supermarket (Taipei, Taiwan). The chicken samples were divided into 5 ± 0.1 g per package (8 cm × 12 cm), sterilized by UV light, frozen at −80°C, and used for 1 month. Before sous-vide cooking, the frozen samples (5 g each) were thawed at 4°C overnight and smashed into flat-thin sizes using a stomacher (BagMixer 400; Interscience, France). All the samples were vacuumized using a vacuum sealer (NutriFresh; Hamilton Beach, Southern Pines, NC, USA) and cooked at 60°C for 5 min using a sous-vide cooker (33970-TW; Hamilton Beach). The samples were then immediately placed on ice for cooling. E. coli was not detected in any of the samples.

To obtain initial populations of 10^3–4 CFU/g, sous-vide cooked samples were inoculated with aliquots (0.6 mL) of the UPEC cocktail, which was diluted before inoculation. The inoculated samples were ground using a sterilized mortar and pestle. After inoculation, the samples were transferred to plastic dishes, sealed with parafilm, and incubated at 4°C, 10°C, 15°C, 20°C, 30°C, and 40°C for different durations of time. The experiment was repeated thrice.

Bacterial enumeration

After incubation, 5 g of the inoculated sample was aseptically transferred to a sterile bag (3 cm × 15 cm; 3M, Seoul, Korea) with 45 mL of sterilized 0.1% peptone water to obtain 1:10 dilution and stomached by a stomacher for 1 min. The sample was serially diluted with 0.1% sterilized peptone water before loading on Petrifilm Rapid E. coli/Coliform Count Plate (3M, St. Paul, MN, USA). The plates were incubated at 35°C for 24 h, and blue colonies (with and without gas) were then counted for determining the cell number of UPEC.

Model development

The growth curves obtained at each storage temperature were analyzed using the USDA IPMP Global Fit, a free software tool to perform one-step global regression analysis for the determination of kinetic parameters in predictive microbiology (Huang, 2017). To construct tertiary models, a total of six different combinations of primary and secondary models were tested using the software. The primary models used were the Huang full growth model [Eq. (1)], and no lag phase model [Eq. (2)], which can analyze growth curves with or without a lag phase (Fang et al., 2013; Huang, 2013). $\begin{matrix} y (t) = y_{0} + y_{m a x} - ln \{e^{y_{0}} + [e^{y_{m a x}} - e^{y_{0}}] e^{- μ_{m a x} B (t)}\} \\ B (t) = t + \frac{1}{4} ln \frac{1 + e^{- 4 (t - λ)}}{1 + e^{4 λ}} \end{matrix}$ (1)

y (t) = y_{0} + y_{m a x} - ln \{e^{y_{0}} + [e^{y_{m a x}} - e^{y_{0}}] e^{- μ_{m a x} t}\}

(2)

In Eqs. (1) and (2), y ₀, y_max , and y(t) are the bacterial populations (ln CFU/g) at initial, maximum, and time t, respectively; μ_max is the specific growth rate (ln CFU/h) at a constant temperature; and λ is the lag phase duration (h).

The secondary models used in conjunction with each of the primary models included the Ratkowsky square root (RSR) model [Eq. (3)], Huang's square root (HSR) model [Eq. (4)], and cardinal parameter model [Eq. (5)] (Huang et al., 2011; Ratkowsky et al., 1982; Rosso et al., 1993). A secondary model for λ was required for the Huang primary growth model. An empirical model was used to describe the effect of temperature on the lag phase duration [Eq. (6)] (Huang, 2017). $\sqrt{μ_{m a x}} = a (T - T_{0})$ (3)

\sqrt{μ_{m a x}} = a {(T - T_{m i n})}^{0.75}

(4)

μ_{m a x} = \frac{μ_{o p t} (T - T_{m a x}) {(T - T_{m i n})}^{2}}{\begin{matrix} [(T_{o p t} - T_{m i n}) (T - T_{o p t}) \\ - (T_{o p t} - T_{m a x}) (T_{o p t} + T_{m i n} - 2 T)] (T_{o p t} - T_{m i n}) \end{matrix}}

(5)

ln (λ) = A - m \times ln (μ_{m a x})

(6)

In Eqs. (3) and (4), a is the regression coefficient, T is the incubation or storage temperature (°C), T ₀ is the nominal growth minimum temperature (°C) in the RSR model, and T_min is the estimated minimum growth temperature (°C) in the HSR model. In Eq. (5), μ_opt is the optimal growth rate (ln CFU h⁻¹) at the optimal temperature, T_opt (°C), and T_min and T_max are the estimated minimum and maximum temperatures, respectively. In Eq. (6), A and m are the coefficients.

The statistical indices of Akaike information criterion (AIC) [Eq. (7)] and root mean square error (RMSE) [Eq. (8)] were used to evaluate the goodness-of-fit of each combination of primary and secondary models. $\begin{matrix} A I C & = n \times l n [\frac{\sum_{0}^{n - 1} {(y_{i} - ŷ_{i})}^{2}}{n}] + 2 (p + 1) \\ + \frac{2 (p + 1) (p + 2)}{d f - 2}, d f > 2 \end{matrix}$ (7)

R M S E = \sqrt{\frac{\sum_{i = 1}^{n} {(y_{i} - ŷ_{i})}^{2}}{n - p}}

(8)

In Eqs. (7) and (8), y_i and $ŷ_{_{i}}$ are the observed and predicted microbial populations (log CFU/g), n is the number of observed values, p is the number of parameters in the model, and df or $n - p$ indicates the degree of freedom. A lower AIC and RMSE scores indicate a better fit of the predictive building models and that the predictions are reliable (Lee et al., 2023).

Validation of predictive models

Additional growth experiments at 25°C and 37°C, not used in the estimation of kinetic parameters, were performed to obtain growth curves for validating the combination of models. We selected 25°C and 37°C because they were close to average room temperature and summer's extreme temperature in Taiwan, allowing UPEC to grow well in sous-vide chicken breast. To evaluate the error and performance of the developed models, the RMSE, the bias factor (B_f ), [Eq. (9)], and the accuracy factor (A_f ), [Eq. (10)], were determined (Lu et al., 2020; Park et al., 2019; Ross, 1996). $B_{f} = 1 0^{[\frac{\sum_{i = 1}^{n} log (o b s e r v e d_{i} ∕ p r e d i c t e d_{i})}{n}]}$ (9)

A_{f} = 1 0^{[\frac{\sum_{i = 1}^{n} |log (o b s e r v e d_{i} ∕ p r e d i c t e d_{i})|}{n}]}

(10)

In Eqs. (9) and (10), predicted is the microbial population calculated from the developed models, and observed is the microbial population observed in the growth experiment at 25°C or 37°C. A perfect agreement between the predictions and observations leads to B_f and A_f values equal to 1.0.

Results and Discussion

Phylogroup and specificity of UPEC reference strains

The four clinically isolated UPEC reference strains were first identified for their phylogenetic groups using Clermont's assignment method (Clermont et al., 2013). The quadruplex genotypes corresponding to the presence (+)/absence (−) of four genes, arpA (400 bp), chuA (288 bp), yjaA (211 bp), and TspE4.C2 (152 bp), were determined for each strain. The results showed that BCRC 10,675, 15,483, and 17,383 had genotypes of − + + +, − + + +, and − + + −, respectively, regarding the presence/absence of arpA, chuA, yjaA, and TspE4.C2 (Table 1). Accordingly, these three strains were assigned to phylogroup B2.

Table 1.

Identification of the Phylogenetic Types of the Escherichia coli Strains Used in the Present Study

BCRC strains	ArpA (400 bp)	chuA (288 bp)	yjaA (211 bp)	TspE4C2 (152 bp)	Phylogroup ^a
10,675	−	+	+	+	B2
15,480	+	+	−	+	D^b
15,483	−	+	+	+	B2
17,383	−	+	+	−	B2

According to Clermont's phylogroup assignment method.

Confirmed by an additional polymerase chain reaction assay using an E-specific primer pair (ArpAgpE.f and ArpAgpE.r) for arpA (301 bp).

BCRC, Bioresource Collection and Research Center.

In contrast, the quadruplex genotype of BCRC 15,480 was + + − +, indicating that further screening is required to determine phylogroups D and E. An additional PCR assay was performed using the E-specific primer pair ArpAgpE.f (5′-GATTCCATCTTGTCAAAATATGCC-3′) and ArpAgpE.r (5′-GAAAAGAAAAAGAATTCCCAAGAG-3′), which generate 301-bp fragments of arpA. Since the PCR results indicated the absence (−) of arpA (301 bp), BCRC 15,480 was assigned to phylogroup D. Therefore, all the BCRC strains were classified as either phylogroup B2 or phylogroup D. This was consistent with previous epidemiological studies demonstrating that ExPEC strains were frequently categorized into phylogroup B2 and, to a lesser extent, phylogroup D, whereas commensal strains are usually categorized in phylogroups A and B1 (Dadi et al., 2020; Lara et al., 2017).

Regarding the UPEC specificity, the presence of three genetic markers, c3509, c3686, and chuA, was determined in the BCRC reference strains. These genes are potentially associated with virulence and are crucial for UTI pathogenesis (Lloyd et al., 2007). Genes c3509, c3686, and chuA were predicted to encode a putative ATP-binding protein of an ABC transport system, a D-arabinose 5-phosphate isomerase, and an outer membrane heme/hemoglobin receptor, respectively (Brons et al., 2020). Our PCR results showed that at least one of these genes was present in all four BCRC strains (Table 2). The internal amplification control, uidA, specific for E. coli and encoding β-D-glucuronidase, was also present in all four BCRC strains. The PCR results of UPEC specificity and phylotyping indicated that these four strains were genetically UPEC and could be clinically associated with common UTIs. Therefore, they were added to the cocktail for inoculation.

Table 2.

Identification of Uropathogenic Escherichia coli-Specific Genes for the E. coli Strains Used in the Present Study

BCRC strains	UPEC-specific			E. coli-specific
BCRC strains	c3509	c3686	chuA	uidA
10,675	−	+	+	+
15,480	−	+	+	+
15,483	−	+	+	+
17,383	−	−	+	+

UPEC, uropathogenic Escherichia coli.

Growth kinetics analysis and selection of models

In the inoculation study, the growth of UPEC in sous-vide chicken breast was observed at all incubation temperatures except 4°C for up to 168 h (7 days). With an initial inoculum of 3–4 log CFU/g, the population of UPEC in sous-vide chicken breast reached a maximum level of ∼9.5 to 10.5 log CFU/g at 10°C, 15°C, 20°C, 30°C, and 40°C, indicating that the storage time was sufficient for the growth to reach stationary phase. The set of five growth curves collected between 10°C and 40°C, including 49 data points, was submitted to IPMP-Global Fit for one-step kinetic analysis to minimize the global error.

Figure 1 shows a comparison between the data and regression curves of UPEC growth at each incubation temperature. Tables 3 and 4 list the estimated parameters of the primary Huang full growth and no lag phase models in combination with secondary models, including the HSR, RSR, and cardinal parameter models, respectively. The lag phase was short and almost invisible in each growth curve (Fig. 1). Fitting with the Huang full growth model could not reliably estimate the lag phases of these growth curves. This is reflected in the large standard errors and p-values for estimates of coefficients A and m, regardless of the combination with HSR, RSR, or cardinal parameter models (Table 3).

FIG. 1.

The experimental populations of UPEC in sous-vide chicken breast stored at (A) 4°C and growth curves fitted with no lag phase model at (B) 10°C, (C) 15°C, (D) 20°C, (E) 30°C, and (F) 40°C. L95PCI, lower 95% confidence interval; U95PCI, upper 95% confidence interval. CFU, colony-forming unit; UPEC, uropathogenic Escherichia coli.

Table 3.

Analysis of the Huang Full Growth Model

Parameter	Estimate						Evaluation
Parameter	Value	SE	t	p	L95CI	U95CI	AIC	RMSE
3-A: with Huang square-root model							−43.2	0.536
A	9.73 × 10⁻²	7.69 × 10⁻³	12.66	2.18 × 10⁻¹⁵	8.18 × 10⁻²	1.13 × 10⁻¹
T_min	5.10	1.03	4.98	1.35 × 10⁻⁵	3.03	7.18
A	−6.39 × 10⁻¹	3.44	−0.19	8.53 × 10⁻¹	−7.59	6.31
M	1.41	1.83	0.77	4.47 × 10⁻¹	−2.30	5.12
y₀, T_10°C	3.40	6.98 × 10⁻¹	4.87	1.87 × 10⁻⁵	1.99	4.81
y₀, T_15°C	3.96	6.38 × 10⁻¹	6.21	2.64 × 10⁻⁷	2.67	5.25
y₀, T_20°C	4.03	6.78 × 10⁻¹	5.94	6.27 × 10⁻⁷	2.66	5.40
y₀, T_30°C	4.05	5.78 × 10⁻¹	7.00	2.13 × 10⁻⁸	2.88	5.22
y₀, T_40°C	3.25	5.30 × 10⁻¹	6.14	3.32 × 10⁻⁷	2.18	4.32
y_max	10.6	2.61 × 10⁻¹	40.45	1.84 × 10⁻³³	10.0	11.1
3-B: with Ratkowsky square-root model							−37.7	0.567
A	3.93 × 10⁻²	3.98 × 10⁻³	9.88	3.60 × 10⁻¹²	3.13 × 10⁻²	4.74 × 10⁻²
T₀	1.93	1.27	1.51	1.38 × 10⁻¹	−6.49 × 10⁻¹	4.50
A	−5.12	2.48 × 10²	−0.02	9.84 × 10⁻¹	−5.07 × 10²	4.96 × 10²
M	−6.64	3.08 × 10²	−0.02	9.83 × 10⁻¹	−6.30 × 10²	6.16 × 10²
y₀, T_10°C	2.97	5.53 × 10⁻¹	5.36	3.95 × 10⁻⁶	1.85	4.09
y₀, T_15°C	3.91	4.92 × 10⁻¹	7.94	1.12 × 10⁻⁹	2.91	4.90
y₀, T_20°C	3.98	4.90 × 10⁻¹	8.11	6.78 × 10⁻¹⁰	2.98	4.97
y₀, T_30°C	3.86	9.59 × 10⁻¹	4.02	2.54 × 10⁻⁴	1.92	5.80
y₀, T_40°C	3.68	6.37 × 10⁻¹	5.77	1.07 × 10⁻⁶	2.39	4.97
y_max	10.5	2.60 × 10⁻¹	40.58	1.63 × 10⁻³³	10.0	11.1
3-C: with cardinal parameters model							−43.6	0.509
μ_opt	1.57	4.23 × 10⁻¹	3.72	6.66 × 10⁻⁴	7.14 × 10⁻¹	2.43
T_opt	36.9	1.81	20.37	1.05 × 10⁻¹	33.2	40.5
T_min	3.29	2.48	1.33	1.92 × 10⁻¹	−1.73	8.31
T_max	44.9	13.0	3.46	1.39 × 10⁻³	18.6	71.2
A	−8.35 × 10⁻¹	4.20	−0.2	8.43 × 10⁻¹	−9.34	7.67
M	1.46	2.16	0.68	5.03 × 10⁻¹	−2.92	5.84
y₀, T_10°C	3.44	7.21 × 10⁻¹	4.77	2.83 × 10⁻⁵	1.98	4.90
y₀, T_15°C	3.93	6.91 × 10⁻¹	5.69	1.63 × 10⁻⁶	2.53	5.33
y₀, T_20°C	3.88	7.11 × 10⁻¹	5.45	3.46 × 10⁻⁶	2.44	5.32
y₀, T_30°C	3.84	6.29 × 10⁻¹	6.11	4.44 × 10⁻⁷	2.57	5.12
y₀, T_40°C	3.73	6.20 × 10⁻¹	6.01	6.07 × 10⁻⁷	2.47	4.98
y_max	10.7	2.75 × 10⁻¹	38.89	1.30 × 10⁻³¹	10.2	11.3

AIC, Akaike information criterion; RMSE, root mean square error; SE, standard error.

Table 4.

Analysis of the No Lag Phase Model

Parameter	Estimate						Evaluation
Parameter	Value	SE	t	p	L95CI	U95CI	AIC	RMSE
4-A: with Huang square-root model							−45.9	0.544
a	9.64 × 10⁻²	6.51 × 10⁻³	14.82	4.56 × 10⁻¹⁸	8.33 × 10⁻²	1.10 × 10⁻¹
T_min	5.24	8.10 × 10⁻¹	6.47	9.35 × 10⁻⁸	3.60	6.88
y₀, T_10°C	3.05	5.55 × 10⁻¹	5.49	2.26 × 10⁻⁶	1.93	4.17
y₀, T_15°C	3.75	4.90 × 10⁻¹	7.64	2.06 × 10⁻⁹	2.76	4.74
y₀, T_20°C	3.86	4.84 × 10⁻¹	7.97	7.24 × 10⁻¹⁰	2.88	4.84
y₀, T_30°C	3.90	4.02 × 10⁻¹	9.70	3.56 × 10⁻¹²	3.09	4.72
y₀, T_40°C	3.09	4.37 × 10⁻¹	7.07	1.31 × 10⁻⁸	2.20	3.97
y_max	10.6	2.63 × 10⁻¹	40.25	1.38 × 10⁻³⁴	10.1	11.1
4-B: with Ratkowsky square-root model							−39.8	0.578
a	3.74 × 10⁻²	3.12 × 10⁻³	11.99	5.58 × 10⁻¹⁵	3.11 × 10⁻²	4.37 × 10⁻²
T₀	1.43	1.22	1.17	2.47 × 10⁻¹	−1.03	3.89
y₀, T_10°C	2.91	5.52 × 10⁻¹	5.27	4.62 × 10⁻⁶	1.80	4.03
y₀, T_15°C	3.94	4.87 × 10⁻¹	8.09	4.97 × 10⁻¹⁰	2.96	4.93
y₀, T_20°C	4.03	4.77 × 10⁻¹	8.44	1.65 × 10⁻¹⁰	3.07	4.99
y₀, T_30°C	3.91	4.04 × 10⁻¹	9.67	3.90 × 10⁻¹²	3.09	4.73
y₀, T_40°C	2.93	4.53 × 10⁻¹	6.47	9.39 × 10⁻⁸	2.02	3.85
y_max	10.5	2.61 × 10⁻¹	40.44	1.15 × 10⁻³⁴	10.0	11.1
4-C: with cardinal parameters model							−47.4	0.513
μ_opt	1.53	4.12 × 10⁻¹	3.72	6.35 × 10⁻⁴	6.98 × 10⁻¹	2.37
T_opt	36.7	1.69	21.72	2.17 × 10⁻²³	33.3	40.1
T_min	3.57	2.15	1.66	1.05 × 10⁻¹	−7.83 × 10⁻¹	7.92
T_max	44.9	12.2	3.69	6.92 × 10⁻⁴	20.3	69.5
y₀, T_10°C	3.13	5.62 × 10⁻¹	5.57	2.05 × 10⁻⁶	1.99	4.26
y₀, T_15°C	3.74	5.62 × 10⁻¹	6.66	6.28 × 10⁻⁸	2.61	4.88
y₀, T_20°C	3.73	5.61 × 10⁻¹	6.64	6.66 × 10⁻⁸	2.59	4.86
y₀, T_30°C	3.71	4.90 × 10⁻¹	7.56	3.69 × 10⁻⁹	2.72	4.70
y₀, T_40°C	3.61	4.88 × 10⁻¹	7.39	6.31 × 10⁻⁹	2.62	4.59
y_max	10.7	2.79 × 10⁻¹	38.47	1.25 × 10⁻³²	10.2	11.3

Owing to statistical insignificance, A and m should be ignored, and the entire dataset can be analyzed using the no lag phase model. As shown in Table 4A, the regression results of the no lag phase model with the HSR model showed that all the parameters were statistically significant (p < 0.05), indicating that Eq. (4) can be used to estimate the μ_max for use in Eq. (2), to predict UPEC growth. The estimated minimum growth (T_min ) was 5.2°C, which was in agreement with the observation that UPEC did not grow in the inoculated samples when stored at 4°C. It was also in agreement with a previous study, which reported that UPEC inoculum could not grow in raw chicken meat at 4°C for up to 120 h, and the estimated T_min was 5.1°C (Sommers et al., 2018). Moreover, the estimated initial and maximum cell populations (y _o and y_max ) were 3.1–3.9 log CFU/g and 10.6 log CFU/g, respectively. This is in close agreement with the growth curves.

Table 4B shows the regression results of the no lag phase model and the RSR model. The nominal minimum growth temperature (T ₀) was not statistically significant, indicating that it could not reliably estimate the μ_max . When the growth data were analyzed with the combination of the no lag phase model and cardinal parameters model, most parameters were found to be statistically significant (Table 4C). The T_opt and T_max were 36.7°C and 44.9°C, respectively. However, the T_min was not statistically significant, implying that data points at a lower temperature between 4°C and 10°C are required to reduce the uncertainty in estimating the kinetic parameter. Hence, the HSR model was considered more suitable than the RSR and cardinal parameter models to estimate the parameters in the no lag phase model for predicting the growth of UPEC.

Validation

Since data for UPEC growth in sous-vide chicken breast were not available in the literature, the accuracy of the developed models (combination of no lag phase model and HSR model) was validated using two additional growth curves obtained at 25°C and 37°C, after the determination of kinetic parameters. Table 5 lists the predicted growth versus observed cell population sampling during 72 h (at 25°C) or 12 h (at 37°C) of incubation. The RMSE of prediction was 0.49 or 0.59 log CFU/g. The B_f and A_f values for 25°C were 0.984 and 1.056, respectively, whereas the values for 37°C were 0.941 and 1.063. B_f < 1 represented fail-safe predictions, and both the values were closed to 1.0. The A_f values were all lower than 1.30. Accordingly, the result suggested that the predicted growth agreed closely with the experimental observations, and the performance of the developed models was acceptable (Oscar, 2005; Ross et al., 2000).

Table 5.

Validation of the Performance of the Developed Models Using Additional Sous-Vide Chicken Breast Samples Stored at 25°C and 37°C

Time (hours)	Observation ^a	Prediction ^b	RMSE ^c	B_f ^d	A_f ^e
5-A: 25°C			0.59	0.984	1.056
0	4.18	4.18
1	4.15	4.53
2	4.26	4.89
19	9.88	10.43
27	10.60	10.60
43.5	11.12	10.60
48.5	11.15	10.60
72	11.17	10.60
5-B: 37°C			0.49	0.941	1.063
0	3.83	3.83
0.5	3.85	4.19
1	3.78	4.55
1.5	4.43	4.91
2	4.83	5.27
4	6.10	6.72
6	8.16	8.16
8	9.38	9.56
10	10.09	10.47
11	10.19	10.57
12	10.35	10.60

Observed populations (log CFU/g) of UPEC growth were obtained from an additional storage experiment at 25°C for 72 h or 37°C for 12 h.

Predicted populations (log CFU/g) of UPEC growth were calculated using the no lag phase model, Huang square-root model, and estimated parameters, shown in Table 4A.

RMSE (log CFU/g).

B_f , bias factor.

A_f , accuracy factor.

CFU, colony-forming unit.

Conclusion

In the present study, we identified the phylogenetic type and specificity of four UPEC reference strains by PCR and used them to develop mathematical models for the prediction of UPEC growth in sous vide RTE chicken breast meat. The set of five growth curves collected between 10°C and 40°C was submitted to IPMP-Global Fit for one-step kinetic analysis. Among the six different combinations of primary and secondary models, the combination of the no lag phase model and the HSR model could reliably estimate all growth parameters. Moreover, the accuracy of the developed models was validated by a growth curve obtained at 25°C and 37°C, producing acceptable values of RMSE (0.49–0.59 log CFU/g), B_f , (0.941–0.984), and A_f (1.056–1.063). Thus, such models will be useful for conducting risk assessment of UPEC in sous-vide chicken products. For the food industry, they can be used to develop temperature controls for inhibiting the proliferation of UPEC and reasonable products' shelf lives for preventing the overgrowth of UPEC during food storage, thereby reducing the risk of UTI caused by this pathogen.

Footnotes

Authors' Contributions

K.-H.L. conceived the idea, acquired the funding, conducted the research, and edited the main article. A.H. performed the experiments, analyzed the data, and wrote the first draft of the article. Y.-C.P. collected the data for validation and revised the article. Y.-J.H. provided the technical support. L.-Y.G. and C.-Y.K. collected the data for model development. L.-Y.S. supervised the project, provided the resources, and reviewed the article.

Disclosure Statement

The authors have no conflicts of interest to declare.

Funding Information

This study was supported by the National Science and Technology Council, Taiwan (MOST 109-2314-B-002-282-MY2; MOST 111-2320-B-218-001-MY3).

Supplementary Material

Supplementary Table S1

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