A predictive model of Vibrio cholerae for combined temperature and organic nutrient in aquatic environments

Authors


Correspondence

Songzhe Fu, No.833 Lijing road, Honggutan district, Nanchang Center for Disease Control and Prevention, Nanchang 330038, China. E-mail: fusongzhe@hotmail.com

Abstract

Aims

To develop a predictive model for Vibrio cholerae in sea water.

Methods and Results

The growth curves of V. cholerae NE-9 at different temperatures (range from 10 to 30°C) and chemical oxygen demand (COD) concentration (range from 5 to 40 mg l−1) were determined. The modified logistic model and Baranyi model were chosen to regress the growth curves. A new method for modelling effects of temperature and COD on the specific growth rate (μ) was successfully developed by a combination of modified square root–type equation and saturation growth rate model. The coefficient of determination (R2), bias factor (Bf) and accuracy factor (Af) were taken to assess the performance of the established model. Logistic model produced a good fit to the observed data (R2 = 0·952). However, the Baranyi model provided biologically plausible parameter estimates. The overall predictions for V. cholerae NE-9 growth agreed well with observed plate counts, and the average R2, Bf and Af values were 0·967, 1·198 and 1·201, respectively.

Conclusion

The predicted model agreed well with observed data, and the result can be applied for the prediction of Vcholerae in actual environments.

Significance and Impact of the Study

The results of this study provide the basis for the prediction of V. cholerae in sea water.

Introduction

Vibrio cholerae is a life threatening and therefore important aquatic pathogen and has been found to survive for extended periods of time in both estuarine and sea waters (Xu et al. 1982). Among the serotype of this species, only serotype O139 and O1 caused serious cholera outbreaks (Fields et al. 1992; Nair et al. 1994). Between 1998 and 2001, the WHO reported 578 infectious disease outbreaks in 132 countries, where acute diarrhoea with cholera was the most frequent (Ashbolt 2004). Generally, the transmission of V. cholerae is through contaminated food and water in communities that do not have access to adequate sewage and water treatment systems. In Latin American, Haiti experienced a nationwide outbreak of cholera caused by Vcholerae O1 serotype Ogawa which began in October 2010 following the January earthquake (Centers for Disease Control and Prevention (CDC) 2010). The origin of the Haitian cholera outbreak was associated with contaminated water (Chin et al. 2011). In addition, food borne outbreaks caused by this bacterium have also been reported in several Asian countries (Wei et al. 2008).

In aquatic outbreaks, the illness is related to consumption of the contaminated water and infected aquatic animals. The rapid growth of the bacterium often leads to the persistence of Vibrio sp. in aquaculture systems. The results obtained from Anand et al. (2010) showed that the V. cholerae populations in the sediment of a aquaculture pond ranged from 1·9 × 107 to 2·3 × 107 CFU g−1. Many other factors, such as the discharge of pollutants and environmental change, have further contributed to the persistence and increased occurrence of the infectious disease (Trinidad and Sedas 2007).

Most aquaculture farmers try to control Vibrio population in their ponds in order to control their pathogenicity to human and aquatic animal health. Many attempts have been carried out to describe V. cholerae growth and survival in various sea water environments. The growth of V. cholerae is affected by many factors, including temperature, organic nutrient concentration, pH and salt level. Singleton et al. (1982a) found that the temperature and organic nutrient concentration are key factors for controlling and limiting further outbreaks (Singleton et al. 1982a,b). Huq et al. (1984) investigated the influence of water temperature, salinity and pH on the multiplication of toxigenic Vibrio cholerae serovar O1, suggesting that an alkaline pH (8·5) was optimal both for attachment and multiplication of V. cholerae. The results from Huq et al. (2005) revealed significant correlations of water temperature, water depth, rainfall, conductivity and copepod counts with the occurrence of cholera toxin-producing bacteria (presumably V. cholerae).

Modelling the growth and survival of pathogenic microorganisms is a basic tool for the prediction of a Vcholerae outbreak. Accuracy is important when predicting the growth responses of the V. cholerae in aquatic environment and developing its mathematical models to correlate contamination level and environmental conditions. This will serve as a basis for developing more efficient disease control strategies. However, there have been attempts to formulate a predictive model for this organism. Many models have successfully been applied to predict the population dynamics of other Vibrio sp. in foods. Hsieh et al. (2008) described the dynamics of total Vibrio spp. concentrations in the Neuse River Estuary and derived the predictive models for estuarine environments. A mathematical model of the square root type was developed by Yang et al. (2009) to predict generation times of V. parahaemolyticus strain for the temperature range (0–35°C) in salmon meat based on temperature. Yoon et al. (2008) also modelled the effect of temperature on lag time and the specific growth rate of V. parahaemolyticus in broth and oyster slurry, they found that the growth of V. parahaemolyticus was delayed in oyster slurry when compared to growth in broth, and inactivation was observed at 10 or 15°C. The risk assessment of Vibrio sp. in foods was also undertaken recently (FAO/WHO 2009). However, the model for the prediction of the growth of V. cholerae under different organic nutrient concentration, especially in aquaculture environment, has not been developed. As far as we know, only three studies have been published where growth rates of V. cholerae O1 were investigated and compared in sterile-filtered natural water (Mouriño-Pérez et al. 2003; Worden et al. 2006; Vital et al. 2007). The results from Mouriño-Pérez et al. (2003) and Vital et al. (2007) suggested that dissolved organic matter has the potential to support explosive growth of V. cholerae. The results demonstrate a positive trend between the assimilable organic carbon concentration and final cell concentration. Kirschner et al. (2008) also found that the rapid growth of planktonic Vibrio cholerae non-O1/non-O139 strains in a large alkaline lake depended on temperature and dissolved organic carbon quality. However, the growth characteristics for the pathogenic Vibrio cholerae O139 have not been described.

To indicate the level of organic pollution in water, chemical oxygen demand (COD) is normally measured as a rapid indicator in both municipal and industrial wastewater treatment plants (Clescer et al. 1998). The objectives of this study were to model a pathogenic V. cholerae strain NE-9 in sea water at temperatures from 10 to 30°C and COD from 5 to 40 mg l−1 using the mathematical equations and to establish secondary model of growth kinetic parameters response to temperatures and COD. Furthermore, the predicted growth rates from the model developed in this study were compared with the results from Vital et al. (2007) under constant and variable temperatures or COD in laboratory to assess the performance of the model.

Materials and methods

Bacterial strains and culture media

Pathogenic V. cholerae NE-9 strain (serotype O139) and nonpathogenic V. cholerae NE-1 strain (serotype O1 Ogawa) were isolated from coastal sea water from Qingdao (Fu et al. 2009). Virulence cholera toxin (ctx) gene and toxin-coregulated pilus A (tcpA) gene were confirmed positive by PCR method for NE-9 strain and negative for NE-1 strain (Singh et al. 2002). Bacterial strains were stored in 10% (w/v) glycerol broth at −70°C. Sterilized aquaculture sea water, comprising fish faeces and unconsumed feed, was used as a substrate solution for the growth of V. cholerae NE-9 (salinity level is 2·7%). The composition of this wastewater was described previously (Fu et al. 2012). Sucrose (C12H22O11) was used as a carbon source to control the concentration of COD from 5 to 40 mg l−1. NH4Cl was used as a nitrogen source to control the concentration of total ammonium chloride at 1·0 mg l−1. Natural sea water was used as a substrate solution for the growth of V. cholerae NE-1.

Growth in sea water at constant temperatures and COD concentration

Vibrio cholerae NE-9 or V. cholerae NE-1 was grown in 100 ml of LB broth in 250 ml flasks, and starvation of cells was ensured using procedures described in Fu et al. 2012. Starved cells were added to sterilized aquaculture sea water with different COD concentration to a final concentration of 105 CFU ml−1 and then were stored at 10° for 18 h (for V. cholerae NE-1, cells were added to natural sea water). This step ensured that the behaviour of bacteria cells would be similar to that in nature sea water. The inoculated sea water was aseptically divided into 300-ml glass bottles with 100 ml sea water in each bottle and stored at 10, 15, 20, 25 and 30°C, respectively. Sampling was generally carried out at 2 h intervals for the storage of 20, 25 and 30°C, and 6 h intervals for 15 and 10°C. Samples of 1 ml were taken at each interval. After sampling, each of the content was suspended in 10 ml phosphate-buffered saline containing sterile glass beads (0·1 mm; BioSpec Products, Bartlesville, OK, USA) and was resuspended and homogenized for 2–5 min to dislodge the attached bacteria, and the homogenates were used for direct plating. Each sampling experiment consisted of six counts (three trials with two replicates per trial) at each time interval.

Enumeration of bacteria in sea water

For direct plate count analyses of V. cholerae, serially diluted samples were spread onto Thiosulfate-citrate-bile salts-sucrose (TCBS) agar and incubated at 37°C for 24 h. Only statistically valid plates, those that have between 25 and 250 colonies per plate were considered for the determination of the viable counts. The viable counts were determined by colony counter (Wiggens Galaxy 230; Roswell, GA, USA). The validation of the effect of homogenization was performed by inoculating a known number of cells into the wastewater and 3·5% saline water, respectively, and conducted in accordance with the description of Epstein and Rossel (1995). Bacterial counts of the homogenates were compared with counts of un-homogenized saline water. A relative standard deviation in the range of ±5% is considered acceptable.

Construction of the predictive model

Primary model

Population means of the viable counts (log10 CFU ml−1) were used for developing growth curves at each experimental temperature as a function of time. Each data point represents the average of three trials (from three trials with two replicates per trial). For growth curves, the data were fitted by the modified logistics equation (Eqn), which is often used to describe the bacterial growth curves (Juneja et al. 2007). In this equation (Eqn (1)), Y(t) represents the increase in microbial cell density at a certain time (log10 CFU ml−1), t is the time of incubation. A = Ymax − Y0, where Ymax is the cell density at stationary phase when growth, while Y0 represents initial inoculated microbial cell density (log10 CFU ml−1) which is a constant value for each experiment. The parameter A, μ and λ represent the maximum increase in microbial cell density (log10 CFU ml−1), specific growth rate (h−1) and growth lag time (h), respectively.

display math(1)

For the Baranyi model (Eqn (2)), the models were employed to regress the data and the goodness-of-fit of these models were evaluated and compared. The Baranyi model is a traditional approach for describing microbial growth curves in foods (Baranyi and Roberts 1994). This model can be written as

display math(2)

where X(t) represents the microbial cell density at a certain time (ln CFU ml−1), X0 and Xmax represent initial inoculated microbial cell density and asymptotic cell density (ln CFU ml−1), respectively. F(t) = t + 1/v × ln (evt + e−h − evt−h); ν is rate of increase in the limiting substrate, assumed to be equal to μ; h is equal to μ × λ.

Secondary model

Secondary models describe the effects of environmental conditions, such as temperature, on the parameters of a primary model, particularly growth rate and lag time. For the logistic model, a square root–type model (Ratkowsky et al. 1982), expressed as Eqn (3), was used to analyse the effect of temperatures on specific growth rate (μ in Eqn (1)). A proportional relation between the lag time and growth rate has been reported (Delignette-Muller 1998), so the relation between the lag time and specific growth rate is expressed as Eqn (4). In this study, we assume the lag time and growth rate are not influenced by inoculation sizes. Therefore, the lag time (λ) can be calculated by Eqns ((3) and (4)).

display math(3)
display math(4)

where Cg and Ag are regression coefficients at constant COD concentration (but varied at different COD concentration), T represents temperature (°C), Tmin is the theoretical minimum temperature required for growth of the organism.

To describe a proportional relation between the specific growth rate and COD, we hypothesized that the specific growth rate and COD can be fitted to a saturation growth rate model generated by Curve Expert software (Eqn (5)), where a and b are constant coefficients. This model is often used to describe the population growth rate under limiting conditions where the population levels off (saturates) as COD increases.

display math(5)

This model can be linearized by inverting the values of specific growth rate and COD to give linear equations. Further, if the hypothesis holds true, the varying patterns of derived parameter Cg and Ag are more likely to be described by a saturation growth rate model because they are positively correlated with the values of μ. The values of Cg and Ag were calculated using Eqns (3) and (4) based on different COD concentration, respectively. The derived parameter Cg was fitted in Eqn (6), where c and d are constant coefficients. For the derived parameter Ag, it was also described by the saturation growth rate model in Eqn (7), where e and f are constant coefficients. The values of parameter Ag versus the temperatures (°C) were plotted, and the influence of temperature on these parameters was described by linear regression equations.

display math(6)
display math(7)

In the same way, the relation between the maximum increase in microbial cell density (A) and COD was also described by a saturation growth rate model (Eqn (8)), where g and h are constant coefficients.

display math(8)

Evaluation of model performance

Seven cases were measured on artificially V. cholerae NE-9 contaminated wastewater stored at isothermal conditions (15, 18, 20, 25, 27 and 30°C), with different COD levels. Two cases stored at 20°C were designed to assess model performance under two COD levels, one in which stored at COD = 20 mg l−1 for 48 h, another in which stored at COD = 40 mg l−1 for 64 h. Four cases stored at COD = 20 mg l−1 under different temperature conditions (15, 18, 20, 25, 27 and 30°C).One case stored at COD = 20 mg l−1, 18°C for 100 h. The bias factor (Bf) and the accuracy factor (Af) which were defined by the Eqns (9) and (10) (Ross 1996; Giffel and Zwietering 1999; Braun and Sutherland 2003), were used as overall measures of model prediction bias and accuracy, respectively. Where n is the number of prediction cases used in the calculation.

display math(9)
display math(10)

Data analysis

The performance of primary model and secondary models was evaluated using the coefficient of determination (R2) and standard deviation (SD) provided by Curve Expert software ver. 1.3 or DMFit software (Baranyi and Roberts 1994).The parameter μ, λ, R2 and SD were calculated for each trial and averaged the results of three trials. All statistics were performed with spss for Windows, ver. 11.5 (SPSS Inc, Chicago, IL, USA).

Results

Primary modelling of V. cholerae growth in sea water

A total of 532 experimental data points on the growth of V. cholerae in sea water under different conditions (temperatures range from 0 to 30°C and COD concentration range from 5 to 40 mg l−1, three trials at each condition) were obtained. The V. cholerae growth in sea water developed with S-type pattern, so the process can be described with logistic curve. Growth curves were fitted from experimental data using Eqns (1) or (2), and goodness-of-fit parameters are presented in Tables 1 and 2. The results revealed that the specific growth rate (μ) increased with temperature and COD, suggesting that temperature and organic carbon were the key parameters promoting growth of V. cholerae.

Table 1. Parameter values of the modified logistic model of Vibrio cholerae NE-9
 Parameter R 2 SD
Temperature (°C)Aλμ
  1. COD, chemical oxygen demand; ND, not determined.

COD = 5 mg l−1
10ND56·20·00900·98410·077
152·821·30·01700·93860·183
202·93·860·04500·95750·182
252·763·140·05470·94380·162
302·832·200·09600·98190·080
COD = 10 mg l−1
10ND54·10·01000·90290·014
152·2321·30·02100·87030·107
203·252·920·08020·94750·160
253·451·870·15610·94670·213
303·221·780·21700·99300·107
COD = 20 mg l−1
10ND45·10·01100·90290·039
153·2519·70·03500·96710·176
203·522·960·12320·98490·145
253·391·940·17980·98330·162
303·671·740·26500·98600·152
COD = 40 mg l−1
10ND35·40·01300·90290·052
153·4418·60·04150·94480·184
203·442·810·14280·98230·170
253·472·040·21540·92290·207
303·781·670·27400·99460·160
Table 2. Parameter values of the Baranyi model of Vibrio cholerae NE-9
Temperature (°C)λμ R 2 SD
  1. COD = chemical oxygen demand.

COD = 5 mg l−1
1050·20·00900·8920·0452
1526·450·02090·9870·1911
200·46610·06990·9840·1381
256·723 × 10−80·14080·9860·1570
308·174 × 10−90·08230·9960·0829
COD = 10 mg l−1
1046·40·00410·9920·0452
150·27530·01680·9750·1011
201·396 × 10−70·04870·9800·1133
251·076 × 10−80·04520·9820·1819
309·713 × 10−90·17830·9950·0607
COD = 20 mg l−1
1043·00·03990·9720·1193
150·00002230·02890·9900·1603
204·506 × 10−80·11960·9950·1008
252·164 × 10−80·17730·9920·1072
302·572 × 10−80·17020·9940·1137
COD = 40 mg l−1
1040·510·04350·9850·0848
150·0000022720·03280·9900·2000
200·0000062890·10280·9900·1164
251·298 × 10−80·13540·9830·2297
306·104 × 10−90·21000·9940·0712

Both logistic model and Baranyi model provided a good statistical fit to the observed data, and the average R2 value was 0·952 and 0·969, respectively. Parameter values and performance statistics of Eqn (1) at each tested temperature and COD were shown in Table 1. For the logistic model, the fitted growth curves at 10 and 15°C had lower R2 value than that of 20, 25 and 30°C when V. cholerae was initially inoculated at a concentration of 5·0 log10 CFU ml−1 resulting in approximately increase of 3·22 log10 CFU ml−1. The average maximum increase in microbial cell density (A) was positively correlated with COD concentration regardless of the incubation temperatures. The value of μ increased with temperatures and varied between 0·021 and 0·91 h−1, the lag time (λ) decreased from 42·5 to 1·9 h when incubation temperatures increased from 15 to 30°C.

Nevertheless, the traditional Baranyi model failed to estimate the lag time, especially in the temperature of 20, 25 and 30°C. Some curves were calculated a lag time <10−8 h by employing Baranyi model, which was not accordance with that real value of growth curve obvious (Table 2).

Secondary modelling of the effect of temperature on V. cholerae growth in sea water

The square root analysis (Eqn (3)) was carried out to determine the relationship between μ and the storage temperature of V. cholerae. As a result, the relationship between μ and temperature was linear with a high coefficient of determination regardless of COD concentration (Fig. 1) (R2 equals to 0·9703, 0·9831, 0·9860 and 0·9719, respectively); the regression equations and performance statistics were shown in Table 3. Based on the performance of the calculated equations, SD and SSE (sum of squares due to error) for each model were given (Table 3). For the regression Eqn (3), the calculated theoretical minimum temperature (Tmin) for V. cholerae growth in sea water was close to 6·4°C in average.

Table 3. Relationships between the parameters and temperatures or chemical oxygen demand (COD)
ParametersCOD (mg l−1)EqnsSecondary modela R 2 SDSSE
  1. a

    T is the temperature (° C); NA: not applicable.

The equations for Vibrio cholerae NE-9
μ5 (3) μ0. 5 = 0·0216T–0·09520·97030·0160·080
 10 (3) μ0. 5 = 0·0211 T–0·10630·98310·0150·075
 20 (3) μ0. 5 = 0·0232 T–0·20490·98600·0410·0202
 40 (3) μ0. 5 = 0·0141 T–0·10280·97190·0360·0060
λ5 (4) μ × λ = 0·44310·98920·0140·070
 10 (4) μ × λ = 0·39540·96170·0430·215
 20 (4) μ × λ = 0·32430·94000·1100·550
 40 (4) μ × λ = 0·19520·95620·0570·285
CgNA (6) Cg = 0·02575 × COD/(5·078 + COD)0·92540·00240·0096
AgNA (7) Ag = 0·5236 × COD/(7·515 + COD)0·98470·00290·0116
ANA (8) A = COD/(0·4224 + 0·2672 × COD)0·98240·00420·0168
The equations for V. cholerae NE-1
μNatural sea water (3) μ0. 5 = 0·0217 T–0·12670·95990·03740·187
λNatural sea water (4) μ × λ = 0·67710·96890·03530·176
Figure 1.

The effect of temperature on parameter μ of modified logistic model of Vibrio cholerae NE-9 △ (chemical oxygen demand (COD) = 40 mg l−1); ▲ (COD = 20 mg l−1); □ (COD = 10 mg l−1); ■ (COD = 5 mg l−1).

The relationship between μ and lag time (λ) was described by a modified rule of λ constant (Eqn (4)). A simple model (Eqn (4)), which assumed a constant value of λ under constant COD, was applied to describe the lag time λ (Fig. 2), and the results showed satisfactory goodness-of-fit of the model (average R2 = 0·973). Based on Eqns (3) and (4), the equations for the relationship between μ and λ of V. cholerae NE-9 at four COD levels were calculated in Table 3. Compared with the Arrhenius model which is often used in describing temperature effect on lag time (Diez-Gonzalez et al. 2007), this simplified model was fewer parameters and is more efficient in prediction.

Figure 2.

The relationship between μ and lag time (λ) for Vibrio cholerae NE-9. △ (chemical oxygen demand (COD) = 40 mg l−1); ▲ (COD = 20 mg l−1); □ (COD = 10 mg l−1); ■ (COD = 5 mg l−1).

Secondary modelling of the effect of COD on V. cholerae growth in sea water

The impact of organics on the specific growth rate was evaluated by inoculating V. cholerae into sea water under four different COD concentrations (5, 10, 20 and 40 mg l−1). In this study, a modified saturation growth rate model (Eqn (5)) was employed to predict the relationship between specific growth rate and COD. This equation is often employed to model population growth under conditions where the population levels off (saturates) as nutrient concentrations increases. To linearize the equation, we inverted it to give a linear regression equation. Therefore, the equation can be written in terms of the new variables 1/μ and 1/COD. Similar models had been predicted the relationship between nitrification rate and COD (Zhu and Chen 2001). Our results suggested that 1/μ and 1/COD were adequately described by a linear regression equation, regardless of temperature (Fig. 3a,b). The average R2 value for 10, 15, 20, 25 and 30 was 0·9926, 0·9831, 0·9892, 0·9110 and 0·9914, respectively (Fig. 3). These results support our hypothesis that the specific growth rate and COD are linearly related in the saturation growth rate model.

Figure 3.

The effect of chemical oxygen demand (COD) on parameter μ of modified Logistic model of Vibrio cholerae NE-9 (a, b). □ (10°C);△ (15°C); ▲ (20°C); ■ (25°C); ♦ (30°C).

Secondary modelling of the effects for a combination of temperature and COD

To describe a proportional relation between the temperature and COD, saturation growth rate models (Eqns (6), (7) and (8)) were used to describe the formulation of the parameter Cg, Ag and A. By inverting the values of Cg and COD (or Ag and COD) to 1/Cg and/1COD (or/1Ag and/1COD), Cg (or Ag) and COD values can be plotted to check for a linear relation. The formulation of the parameter Cg and Ag (Eqns (6) and (7)) was written as follows:

Cg = 0·02575 × COD/(5·078 + COD)

Ag = 0·5236 × COD/(7·515 + COD)

The average R2 values for the formulation of parameter Cg and A were 0·9254 and 0·9824, respectively (Fig. 3a,b). Combined with Eqns ((3), (4), (6) and (7)), lag time λ can be calculated. In the same way, the parameter A can be written as: A = COD/(0·4224 + 0·2672 × COD) or1/A = 0·4224/COD + 0·2672 (Figs 3c and 4).

Figure 4.

The effect of chemical oxygen demand (COD) on parameters Cg (a), Ag (b) and A (c) of modified logistic model of Vibrio cholerae NE-9.

Evaluation of the model for the prediction of V. cholerae NE-9

For the seven varied temperature and COD cases, our results suggest that most predictions for V. cholerae were in agreement with the observed data (Fig. 5a–g). Generally, the accuracy of the prediction is acceptable when Bf value ranges from 0·75 to 1·25, and Af value ranges from 1·1 to 1·9 (Ross 1996; Giffel and Zwietering 1999; Braun and Sutherland 2003). In the present study, the validation of the model with observed data showed that most of the predicted data agreed well with observed plate counts (Table 4), except for Case b and Case c (Bf values were 1·30 and 1·265, respectively, slightly higher than 1·25). For other cases, Af and Bf values were close to 1·2, which indicated good agreement between the predicted and observed values. Nevertheless, the values of Af and Bf in this study were relatively higher for enumeration results, which means the predictions exceeded the observed data by 20% on average in terms of log10 (CFU ml−1). These results showed that the established models may be useful for predicting V. cholerae in wastewater in the low-nitrogen conditions. For other environments, more extensive growth data for various water conditions that possess different organic pollution levels are needed for the model validation.

Table 4. Validation of the model of Vibrio cholerae NE-9 with additional seven sets of observed data
CaseEnvironmental factors N R 2 BfAf

Temperature

(°C)

COD (mg l−1)
  1. COD, chemical oxygen demand; N, Number of the data points.

a2040200·9961·1601·200
b2020100·9921·3001·250
c1520130·9611·2651·190
d2720200·9201·1601·163
e1818150·9881·1011·208
f2520150·9741·1711·195
g3020150·9391·2301·201
Figure 5.

Validation of the model of Vibrio cholerae NE-9 with additional seven sets of observed data. The observed data in (a, b, c, d, e, f and g) (Case a to g) were measured on V. cholerae at constant temperature ranging from 10 to 30°C. Experimental data points are the average of 12 counts (from three trials with two replicates per trial and two plates per replicate). The growth curves were obtained using the modified logistic model. The dotted curves are upper and lower prediction limits at a 95% confidence level.

Validation of the methodology of the modelling for the growth prediction of V. cholerae O1 in natural sea water

Only three studies have been published to investigate the growth rates of V. cholerae O1 in sterile-filtered natural water (Mouriño-Pérez et al. 2003; Worden et al. 2006; Vital et al. 2007). However, the growth rates for V. cholerae O139 are lack of data. To validate if there is a systematic error for the modelling method that influence all independent variables, nonpathogenic V. cholerae NE-1 was chosen to validate the model and compared with the reported specific growth rates. In the same way of modelling for V. cholerae NE-9, it can be seen that the logistic model provided a good statistical fit to the observed data for V. cholerae NE-1, and the average R2 values for parameter μ and λ were 0·9689 and 0·9599, respectively (Fig. 6). The lag times were 35·83, 11·546, 8·12, 5·72 and 2·1 at 10, 15, 20, 25 and 30°C, respectively. While the specific growth rates were 0·0138, 0·04075, 0·0682, 0·155 and 0·32 at corresponding temperatures, respectively. Based on Eqns ((3) and (4)), the calculated equations for V. cholerae NE-1 were exhibited in Table 3. Overall, predictions for V. cholerae NE-1 growth at tested temperatures agreed well with reported specific growth rates. Reported specific growth rates (determined by microscopic cell counting) ranged from 0·013 to 0·596 h−1 for V. cholerae O1 at temperatures between 15 and 28°C (Mouriño-Pérez et al. 2003; Worden et al. 2006), while the predicted value of μ at 15 and 28°C was 0·0397–0·2313 h−1 in our experiments. The predicted value of μ at 30°C was 0·28 h−1. The predicted values fell inside the range of observed values.

Figure 6.

The effect of temperature on parameter and λ (a) and μ (b) of modified logistic model of Vibrio cholerae NE-1.

Discussion

Although there have been significant research efforts on predictive model for pathogens, information relative to V. cholerae kinetics is still lacking, especially for the impact of organic matter on its growth in sea water. In this study, we proposed to develop a new methodology for modelling the effects of temperature and COD by a combination of modified square root–type equation and saturation growth rate model. Our results revealed that specific growth rates, growth yield, and maximum increase in cell density increased markedly with increasing concentrations of COD and temperatures, indicating that dissolved organic matter and temperatures have the potential to support explosive growth of V. cholerae. The results obtained showed a high R2 values (0·91–0·99) using a modified logistic model. Juneja et al. (2007) compared three primary growth models of the Baranyi, modified Gompertz and logistic models and concluded that the modified Gompertz model was the best primary model to predict the growth of Salmonella in chicken as a function of time. In this study, the logistic model was the best predictor of V. cholerae growth in sea water.

In an intensive aquaculture farm, there is high concentration of waste produced by the animals' normal metabolic processes. High concentration of fish faeces and unconsumed feed promoted the growth of V. cholerae. The ability to maintain a pathogen-free system is a very difficult task; however, predicting levels of pathogens to below the infective levels and establishing an early warning system would decrease the chance of people becoming infected. One of the key aspects for improving the sanitation of such aquaculture farm is having the ability to ‘manage’ these pathogen populations. Michaud et al. (2006) have reported the bacterial community structure and composition related in aquaculture systems. The findings revealed that organic carbon plays an important role in determining the relative abundance and the impact of prokaryotes in aquatic systems. In the present study, we neglected the effect of microbial interaction and organic nitrogen on the growth of V. cholerae. Nevertheless, these results showed that the established models may be useful for predicting the growth of V. cholerae in aquaculture sea water with low organic nitrogen.

Compared with other models of Vibrio sp. reported previously, the lag time of V. cholerae in sea water was much shorter. In the report of Yang et al. (2009), the lag time was 9·6098 and 3·4344 h for 20 and 30°C, while in our study that of values were 2·960 and 1·744 h, respectively. The rapid diffusion of organic matters in water may be the reason for that. Generally, foods have various degrees of buffering capacity due to the many carboxyl and ammonium groups on the amino acid fragments. Diffusion limitation of organic matter acts as a constraint on growth and leads to a longer lag time, while in sea water, the growth of V. cholerae is directly influenced by the substrate concentration. Therefore, the dynamics of V. cholerae are more sensitive to the change of environmental conditions in an aquatic environment. However, this effect could be offset by the decrease in growth rate at lower temperatures. In our study, there was no significant difference for specific growth rate among the different COD concentration at 10°C.

As far as we are aware, only three studies have been published concerning growth rates of V. cholerae O1 and compared in natural water (Mouriño-Pérez et al. 2003; Worden et al. 2006; Vital et al. 2007). The results from Vital et al. (2007) showed that the salinity levels impacted the value of μ of V. cholerae O1. At moderate salinity levels, the estimated value of μ of V. cholerae was much higher (5 g NaCl l−1, μ = 0·84 h−1), whereas the value was significantly reduced at high salinity levels (30 g NaCl l−1, μ = 0·30 h−1). The predicted value of μ for V. cholerae NE-1 at 30°C was 0·28 h−1 in our experiments. The reported value was similar with our results at similar salinity levels (2·7%). Whereas compared with that value in freshwater, the reported value of V. cholerae O1 at 30°C (μ = 0·49 h−1) was considerably higher than our results. However, due to the fact that the nutrient level is not equally distributed throughout the whole sea water, the actual growth rates differ probably distinctly between sites. The modelling results for the growth prediction of V. cholerae O1 were reasonable.

However, compared with the results from Vital et al. (2007) and the growth rates of V. cholerae NE-1 reported here, that values of V. cholerae NE-9 in this study were relatively lower. The specific growth rates increased with temperatures or COD concentration and varied between 0·0096 and 0·274 h−1. In contrast to these results, Mouriño-Pérez and colleagues (2003), who monitored growth of the V. cholerae O1 in sterilized red tide waters off California and reported growth rates between 0·0125 and 0·596 h−1, suggesting that nutrients released during phytoplankton blooms promote growth of V. cholerae.

The growth behaviour of pathogenic and nonpathogenic Vibrio strains was compared previously. Interesting in this respect is the report of Provenzano et al.(2000) who observed that the growth rates of V. cholerae with a plasmid expressing virulence factors were noticeably reduced compared with the wild-type strains, suggesting that the nonpathogenic V. cholerae increased more rapidly than that of pathogenic V. cholerae at identical temperature. Similarly, Yoon et al. (2008) found that nonpathogenic V. parahaemolyticus showed more rapid growth than the pathogenic V. parahaemolyticus. Growth of pathogenic V. parahaemolyticus in oyster slurry was not observed at 10°C, and slight growth was observed at 15°C. The present models were based on the growth of one single strain of a pathogenic V. cholerae. At present, it is not clear whether nonpathogenic V. cholerae O1 showed more rapid growth than the pathogenic V. cholerae O139 due to the lack of virulent genes. It is notable that, however, some environmental changes may trigger their virulence potential (Rivera et al. 2001). Therefore, more extensive growth data for various pathogenic strains that possess different toxin genes, as well as other nonpathogenic strains, are needed for establishing a model for the prediction of total V. cholerae in the future study.

Conclusion

In summary, the results of this study indicated that the predictive model for combined temperature and organic nutrient provided reliable predictions for V. cholerae in the aquatic environment. The models could be used to predict the dynamics of the pathogen and establish a monitoring system in controlling these bacterial infections.

Acknowledgements

We wish to thank two anonymous reviewers for their helpful criticisms and valuable suggestions to improve the manuscript. This work was supported by a grant from the National Natural Science Foundation of China (30972267), CAS Knowledge Innovation Project (KZCX2-EW-Q212), Public Service Sectors (Agriculture) Special Project (201003024) and Atlantic Salmon Research Fund (Y12605101I).We would especially like to thank Ms Shaoshao Liu for sampling assistance.

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