Predictive Model for Growth of Listeria monocytogenes on the Surface of Fresh Beef

This study was sought to establish a predictive model for Listeria monocytogenes growth on the surface of fresh beef. Fresh beef were totally disinfected with ozone water prior to inoculate with L. monocytogenes and box-packaged to store at 5, 10, 15, 20, 25 and 30°C to calculate the CFU to predict the growth trend. The results showed that the growth trend of L. monocytogenes on fresh beef surface could be well fitted with modified Gompertz models (R 2 >0.98). Temperature effect on maximum specific growth rate and lag phase was demonstrated by the square-root model as a good linear relationship with R 2 values of 0.93 and 0.87, respectively. Conclusively, a predictive growth model for L. monocytogenes on surface of fresh beef stored at various temperature from 5 to 30°C was established effectively as follows: LgNt = lgN0+lg(Nmax/N0)×Exp{-Exp[2.718×(-0.002137+0.002203t) 2/lg(Nmax/N0)×( (0.004544+0.015048t) -2 -t)+1]}.


INTRODUCTION
Predictive food microbiology was a new discipline based on microbiology, mathematics, statistics and computer science (Li et al., 2001;Xu, 1995;Ross, 1996;Liu et al., 2007).It can use mathematical model to quantitative analyze the growth and survival trends of food pathogens or spoilage bacteria under different environmental conditions, make a reasonable forecast for possible risk.Therefore, it is significant to establish dynamic growth models of the microorganism which related to the food quality and can describe microbial behavior under various temperature conditions (Dalgaard, 1995).
Listeria monocytogenes, one of zoonotic foodborne patheogen (Ding et al., 2010), has a low incidence but high death rate of 20%-30%.People who are pregnant, infants, the elderly or immunocompromised will get higher risk of infection.Furthermore, L. monocytogenes is also one of the main pathogens in frozen food since it can still keep survival and proliferation at low temperature.Inadequate cold chain system which enables to accelerate the potential detrimental pollution due to a rapid proliferation of L. monocytogenes during transmitting process will threaten the quality and safety of beef production.Therefore, to develop a predictive model for forecasting the microbial growth is helpful to ensure the quality and safety of food.However, the established predictive models are usually based on data derived from the meat material that washed with sterile water or sterilized at high temperature and high pressure (Zhu, 2008;Armitage, 1997;Mcmeekin et al., 2008), which can not depict the real microbiogical growth on crude materials.This study was to establish a mathematical model that accurately predicted the growth of L. monocytogenes on the surface of crude fresh beef under different temperature conditions and provide the useful suggestions for risk assessment of L. monocytogenes in the beef.

Fresh samples preparation and pretreatment:
The fresh beef obtained from Zhejiang Suichang beef processing company, were packaged into sterile bags and directly frozen in -20°C.Prior to inoculation with L. monocytogenes, the fresh beef have been shaped into 1 cm-diameter pieces (approx 1 g weight).In order to eradicate the possible microbe existing on the surface, the fresh samples have been disinfected with 10 mg/L ozone water for 5 min under the sterile operation environment (Qiu and Fang, 2007).This disinfection method has been evaluated for reliability by the daily sterile observation on the bacterial culture medium.
Test organisms preparation: L. monocytogenes ATCC19114-3 was inoculated in tryptic soy agar-yeast extract (TSB-YE) liquid medium, shocked at 37°C overnight.Concentration was adjusted to 10 3 cfu/mL for subsequent study.
Temperature variation studies: 0.1 ml L. monocytogenes liquid culture with 10 3 cfu/mL ultimate concentration was added on the surface of beef samples, then they were incubated in 2×2 cm sterile medicine box for subsequent growth observation with various temperature treatments described as follows.
Treatments under 5°C incubated for 28 d were counted with CFU every 2 d.Treatments under 10°C incubated for 14 d were counted with CFU every 24 h, Treatments under 15°C incubated for 156 h were counted with CFU every 12 h, Treatments under 20°C incubated for 88 h were counted with CFU every 8 h; Treatments under 25°C incubated for 40 h were counted with CFU every 4 h; Treatments under 30°C were counted with CFU by 2,4,6,8,10,15,20,25,30 and 35 h, respectively.All tests were repeated three times.All samples were washed by 3 mL physiological saline then the liquid residues were incubated on the Brian Heart Infusion (BHI) agarose for CFU-counting with the Chinese national standards (GB 47892, 2010).

Predictive model development:
• Growth predictive model of colonies number as primary growth model: Gompertz model can well describe the growth trend of microorganism.In this study, a modified Gompertz equation was developed to describe the growth of L. monocytogenes under various temperatures.The equation is following: where, N t = The number of viable microorganisms at various temperature N 0 = The initial microbial number N max = The maximum microbial number in stable phase µ max = The maximum specific growth rate of microbe λ = Microbial lag phase time • Square root model as secondary growth model: The square root equation, presented by Ratkowsky et al. (1982), Buchanan et al. (1997) and Baranyi and Roberts (1994) as an experience model which could describe the linear relationship of microorganisms under different temperature conditions between growth rate or inverse square root of lag phase and effective temperature, could well illustrate the growth of microorganisms under different temperature conditions.The formula is as follows: In the Eq. ( 2) and ( 3), where T is the Celsius temperature (°C) and T min is a hypothetical value, represented the temperature when specific growth rate is zero, parameter b is the constant value.
• Statistics analysis: All analysis and statistics in this study were performed by DPS software (Tang and Feng, 2002).

RESULTS AND DISCUSSION
Growth curve of L. monocytogenes under various temperatures condition: Growth curves of L. monocytogenes under various temperatures were illustrated in Fig. 1.A, B, C, D represented the growth curve of L. monocytogenes at 30, 25, 20 and 15°C, respectively.These curves showed as a steep rise in the  Primary growth model of L. monocytogenes: Figure 2 showed that the modified Gompertz equation can better predict the dynamic growth of L. monocytogenes at 30, 25, 20, 15, 10 and 5°C, respectively.Gompertz model was used to fit the experimental data by the optimized method of Marquardt.Additionally, Kinetic parameters in Table 1 demonstrated that maximum number in stable phase (N max ) of L. monocytogenes was 11.9015±0.6322at the condition of 20°C and the minimum value was 9.8324±0.4249at the condition of 30°C.The maximum specific growth rate (µ max ) increased with the temperature increasing.The maximum value of µ max was 0.004399153/h at the condition of 30°C, the minimum value was 0.00020901/h at the condition of 5°C as well.The time of lag phase (λ) was decreasing as the temperature increasing.The maximum value was 131.974 at 5°C; the minimum value was 2.3799 h occurred at 30/ °C.

Development and verification of secondary growth model:
As the limits of primary model (demonstrated as Gompertz model above), square root equation was In those equations, correlation coefficients (R 2 ) are 0.93 and 0.87, respectively.b = 0.002203 and T min = 0.97041 can be calculated according to the Eq. ( 4).So we infer that L. monocytogenes could grow at 0.97°C theoretically.By merging Eq. ( 4) and (5) into Eq.( 1), the growth kinetics model of L. monocytogenes at 5-30°C in fresh beef could be acquired.The equation is as follow:

CONCLUSION
Conclusively, the primary growth model of Gompertz equation could well describe the growth of L. monocytogenes under various temperatures on the surface of fresh beef and secondary model of square root could fit well the bacteria growth rate and the time of lag phase.In addition, the results showed that L. monocytogenes could grow at 0.97°C which consistent with one of their biological traits (could grow under low-temperature) and this could improve their health hazard being a food borne pathogen.Therefore, our experimental data have embodied the general trend of the bacterial growth and can predict the growth of L. monocytogenes under various temperatures, enrich the database of L. monocytogenes proliferation in various meats.However, this study only developed the predictive model about the growth of L. monocytogenes at multiple constant temperatures but not at the variable temperature, so the influence of temperature fluctuation during transportation on their growth in beef still need further research.

Fig. 2 :
Fig. 2: Growth tendency of L. monocytogenes on the surface of fresh beef at various temperatures (Solid dots: observation values, solid line: fitted curve).The equation shows the estimated parameter of modified Gompertz model under relevant temperatures.All parameters are highly significant (p<0.01) and the correlation coefficient (R 2 ) is more than 0.98 first 96 h culture period obviously suggested that L. monocytogenes could rapidly grow at the range of 15 to 35°C and the concentration may reach the risk threshold of food safety during those culture periods.The upward trend of the curves E and F (the growth curve of L. monocytogenes at 10 and 5°C) were not showed up obviously but began to rise rapidly after 96 h.It showed that L. monocytogenes could also cause huge risks in low temperature condition as the time extended.

Table 1 :
Kinetic parameters of L. monocytogenes grown on the surface of fresh beef at various temperatures based on modified Gompertz model