Int.J.Curr.Microbiol.App.Sci (2014) 3(1): 127-139
ISSN: 2319-7706 Volume 3 Number 1 (2014) pp. 127-139
http://www.ijcmas.com
Original Research Article
Adjusting a primary survival model of Enteric Bacteria "E. coli " in
coastal environment : Oualidia lagoon
M.Hennani1*, N.Hassou1, A. Aajjane2 and O.Assobhei1
1
Laboratory of marine biotechnology and environment, department of biology, Faculty of
Sciences, University Chouaib Doukkali, El Jadida, Morocco.
2
Laboratory of Marine Geosciences and Soil Sciences, Unit associated CNRST (URAC 45)
Team of Soil Science and Heritage, department of geology, University Chouaib Doukkali, El
Jadida, Morocco.
*Corresponding author
ABSTRACT
Keywords
Survival
Bacteria;
Escherichia
coli;
Oualidia;
linear model;
non-linear
model;
AIC criterion.
Enteric Bacteria especially Escherichia coli in natural environment present an
important health risk. Adequate modeling of the bacteria survival in such systems
can provide a valuable tool in assessing water quality. This study quantified and
modeled the survival of Escherichia coli in coastal environment; Oualidia lagoon.
The survival experimental data used in this research were obtained from diffusion
culture of Escherichia coli along the Oualidia lagoon at different parts and time of
the year. Two primary models, linear and non-linear regression were analyses and
compared. The statistical analyses test using the RSS, R²adj et AIC criterion was
applied to compare the survival curves of two models fitted to experimental data.
The results of this study revealed that the survival model of Escherichia coli in
Oualidia found by non-linear regression. Although the AIC values for the two
distributions in question were close to each other, the non-linear model which had
the lowest AIC value was determined at the most suitable model.
Introduction
The enteric bacteria dispersed in coastal
areas are completely depending on their
environment. It has been observed that
bacterial concentration decreases over
time once introduced in the coastal
environment (Chraibi, 1996; Chedad et
Assobhei 2007). Because into coastal or
marine environments, bacteria are exposed
to numerous factors which cause stress
(Rozen and Belkin, 2001; Chedad et
Assobhei, 2007; Rippy et al., 2013). Based
on a large number of laboratory studies,
various physicochemical factors such as
visible light, temperature, pH, Salinity,
turbidity, toxicity of heavy metals, are
believed to have a significant impact on
bacterial mortality (Sinton et al., 2002;
Noble et al, 2004; Richard et al, 2004;
Chedad et Assobhei, 2007; Semenov et al.,
2007). A bacterial decrease can present
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Int.J.Curr.Microbiol.App.Sci (2014) 3(1): 127-139
different shapes of survival curves. Linear
curves, frequently concave curves may
become convex or sigmoidal when the
intensity of the stress varies (Whiting et al,
1996; Koutsoumanis et al., 1999; Samelis
et al., 2001; Virto et al, 2005; Hajmeer et
al., 2006). An understanding of the
survival of fecal indicator organisms and
the enteric bacteria in coastal water is
basic to the meaningful interpretation of
sanitary environment quality. In almost all
areas of water quality, the preventive
mathematical models are currently used to
predict and estimate the pollution risk and
defining the spatial-temporal factors
dispersion
of
bacterial
pollution
introduced in natural environments to
provide useful management information
for minimizing fecal pollution in these
areas.
Materials and Methods
Study area and sampling experiments
Lagoon Oualidia is located on the Atlantic
coast of Morocco (Fig. 1). Three distinct
parts can be characterized (Rharbi et al,
2001):
The lower zone which ranges from 2.5 km
at low tide to 4 km at high tide seems to be
strongly influenced by the sea (low
variations of temperature and salinity);
The upper zone which ranges from 1.5 km
at high tide to 3 km at low tide looks much
more confined and presents a pool for the
nitrogen elements, suspended particles and
organic matter as well;
The intermediary zone appears to be under
both marine and continental influences.
In order to model survival bacteria curve,
numbers of primary models were
proposed. Among these models, we can
find the models based on a log-linear
decrease such as the vitalistic models
(Cole et al., 1993; Little et al., 1994;
Skandamis et al., 2002), the exponential
models (Membre et al., 1997), log- linear
with latency time (Buchanan et al.,
1994)...ect, and the models based on a
sigmoidal inactivation such as Weibull
model (Mafart et al, 2002). The purpose of
this research is to determine the primary
survival model of Escherichia coli
introduced in the Moroccan oyster area;
Oualidia lagoon, on three different season
(winter, spring and summer), where the
climatic condition were almost constant
for each season. Two primary models (loglinear model and Weibull model) of
survival bacteria; were compared based on
an experimental data.
The lagoon watershed area is not well
recognized; the area is characterized by
diffuse pollution. The main sources of
pollution are due to tourism, shellfishes,
agriculture or related to sewages
infiltration from septic tanks (Hennani et
al, 2012). There are no other industrial
activities (Gonenc et al, 2006).
They are two main reasons for choosing
Oualidia lagoon in this study:
The area is located in nutrient rich coastal
waters which are sheltered from currents
and waves, they are often vulnerable to
bacterial pollution;
The economic impact of shellfishing and
the high cost of purification are two
reasons why more com-prehensive and
predictive tools should he developed.
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Int.J.Curr.Microbiol.App.Sci (2014) 3(1): 127-139
Fig.1 Map of Oualidia lagoon (Google Maps, 2013)
Fig.2 Survival experiments schema
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Int.J.Curr.Microbiol.App.Sci (2014) 3(1): 127-139
The experiments were carried out to
establish the survival of enteric bacteria
"Escherichia coli" in the lagoon for three
season of the year 2012: winter, spring and
summer. Along the lagoon, three zones
characterized by different hydrodynamical
and environmental conditions were
investigated (Fig. 2).
µl of Trypan blue (TB, 0.4%). The sample
was loaded into a sterilized Neubauer
hemocytometer, and the cells lying within
a 1 mm² area, were counted using a light
microscope. Blue stained cells were
counted non-viable and non stained cell as
viable.
Tested primary models
Inoculum preparation and survival
experiments
Based on a shape of decrease curve, we
have chosen in this study to evaluate two
primary survival models of bacteria. The
firstly is the classical primary model based
on a Log-linear decrease (Chick, 1910).
The secondly is the Weibull model based
on a sigmoidal decrease (Mafart et al,
2002).
The strain used in this study was
Escherichia coli isolated from sewages, by
solid media; Eosin Methylene Blue agar
(EMB, Biokar Diagnostic). Vegetative
cells were recovered in 250 ml of Nutrient
Broth (NB, Biokar Diagnostic) incubated
at 37°C.
After 24 h of incubation,
cultivable bacteria were recovered in 100
ml of Ringer solution after centrifugation
(4°C - 15 min). Bacterial suspension was
prepared and was inoculated into sterilized
diffusion chamber (1ml per chamber). The
diffusion chamber is a Plexiglas box (250
ml) with a capped opening midway to
allow sampling of the chamber. Each
chamber was closed at both ends with a
Nuclepore membrane (0.47 µm), held in
place between two Plexiglas retainers.
Te on O rings ensured water tightness.
Leaks were checked by slowly immersing
each empty chamber in lagoon water and
allowing them to gradually ll via the
Nuclepore membranes at each end. The
Prepared diffusion chambers were
introduced in the lagoon by describe
experiments points into Fig. 2, that were
been exposed in the environment
conditions for various lengths of time.
Log-linear model
Based on a simple linear regression, the
model equation is derived from the model
proposed by (Chick, 1910), confirmed by
(Esty et al., 1922; Esty and Williams,
1924) et transformed on the familiar form
by (Katzin et al, 1943; Ball and Olson,
1957) (Eq. 1).
(Eq.1)
where
is the initial number of Bacteria,
the number of surviving bacteria after a
duration of heat exposed stress, is the
time, and the classical value presents a
simple biological significance: time that
leads to a tenfold reduction of surviving
population.
Non Log-linear model
After the exposed time of bacteria in the
lagoon, the viable cells are defined based
on the assessment technique using a
standard method. Briefly, 20 µl of
bacterial suspension was mixed with 100
Based on a nonlinear regression, the
Weibull model has been widely used to
describe resistance to thermal stress during
the past few decades in heat treatment
studies but also in non-thermal treatment
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Int.J.Curr.Microbiol.App.Sci (2014) 3(1): 127-139
studies (Peleg and Cole, 1998; Van
Boekel, 2002). Different forms of this
model were present, but the familiar form
is that described by (Mafart et al., 2002;
Van Boekel, 2002), (Eq. 2).
computed: The Akaike Information
Criterion (AIC) (Akaike, 1977) and the
adjusting Correlation coefficient (R²adj).
Results and Discussion
(Eq.2)
The results of models analysis were fitted
to experimental data are shown in the Fig.
3, 4, 5. Based on a curves of experimental
survival data of Escherichia coli, were
showed that bacterial concentration
decreases according time, when they were
exposed to natural stress. Several aspects
of the effects of environmental condition
were
considered,
including
water
temperature, salinity, turbidity, solar
radiation.... etc. The incident of
unfavorably environmental condition
increases from winter to summer and from
surface water to depth. Visually, the nonlinear model (Weibull model) fitted better
than linear model. The fitted line plot of
non-linear regression shows that the raw
data follow a nice tight function which
looks pretty good. However, the linear
regression systematically adjusting at an
experimental data in the curve indicates a
bad fit.
where
is the initial number of
Bacteria, the number of surviving
bacteria after a duration of heat exposed
stress,
is the time,
is to the first
reduction time that leads a tenfold
reduction of survival population, and is
a shape parameter.
For the traditional case where the survival
curve, originated from a first order, is
linear p equal 1 and the
parameter
correspond to the classical value.
Adjusting and Model evaluation
Generally, the evolution function of
survival curves during time can be
expressed as follows:
(Eq.3)
Generally, the estimates from non-linear
model are near to experimental data than
the estimates from the linear model (Table
1). Indeed, the experimental concentration
of bacteria introduced at
was 8.60
, however, this value is
estimated in an interval of 8.7 to
,
and
6
to
8.4
, respectively for non-linear
and linear model.
where
is the decimal logarithm of
and f is the regression function. is the
vectors of parameters of models, were
estimated by minimization of the sum of
square of the residual values defined by
:
(Eq.4)
The primary models were adjusted by the
polyfit function (Polyfit, MATLAB 6.1)
for linear regression (Eq. 1), and by
nonlinear fitting module (NLINFIT,
MATLAB 6.1, Optimization Toolbox; The
Math-Works) for nonlinear regression (Eq
(2). The fit of the two models was
compared using the statistical analysis,
MATLAB 6.1. Two parameters were
These parameters provide valuable
information to model bacterial survival in
natural environment but we cannot use for
the selection of a reliable model. It was
interesting to perform a statistical analysis
for choosing the better of these two
models tested.
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Int.J.Curr.Microbiol.App.Sci (2014) 3(1): 127-139
Table.1 Estimate parameter for linear model (1) and non-linear model (2)
Estimate parameter
Model 1
Area
Inlet
Period
Winter
Spring
Summer
Oyster farm
Winter
Spring
Summer
Agricultural
Area
Model 2
Winter
Spring
Summer
Surface water
Depth
Surface water
Depth
Surface water
Depth
Surface water
Depth
Surface water
Depth
Surface water
Depth
Surface water
Depth
Surface water
Depth
Surface water
Depth
Log 10 N0
(FCU/ml)
7.93
7.48
7.47
8.17
6.81
7.17
8.38
8.4
8.46
8.64
8.44
8.46
8.58
8.68
8.48
8.65
8.45
8.55
D (h)
-7.81
-10.34
-7.81
-7.99
-7.45
-8.16
-12.27
-15.2
-9.48
-16.5
-8.67
-12
-11.6
-17.18
-11.96
-15.72
-10.15
-12.79
Log 10 N0
(FCU/ml)
8.9
8.92
8.83
8.87
8.85
8.86
8.85
8.85
8.91
8.78
8.83
8.9
8.93
8.79
8.83
8.82
8.89
8.85
(h)
1.52
2.32
1.52
3.34
0.41
0.7
6.09
11.18
4.79
13.39
5.29
6.2
7.02
14.71
7.23
12.21
5.57
8.22
p
0.51
0.54
0.51
0.69
0.43
0.45
0.68
0.8
0.72
0.84
0.79
0.7
0.76
0.92
0.75
0.83
0.74
0.77
Table.2 Statistical parameter for testing Linear Model (Model1) and non-linear model
(Model2)
Model 1
RSS
Inlet
Winter
Surface water
Depth
spring
Surface water
Depth
Summer Surface water
Depth
Oyster
Winter
Surface water
farm
Depth
spring
Surface water
Depth
Summer Surface water
Depth
Agricultural Winter
Surface water
area
Depth
spring
Surface water
Depth
Summer Surface water
Depth
4.2982
5.3106
5.333
2.2255
11.3327
8.459
1.7203
1.076
1.8223
0.3824
1.8245
1.927
1.955
0.4821
0.9991
0.6982
2.439
0.9876
132
AIC
-4.65
-2.75
-2.71
-10.58
4.07
1.44
-12.89
-17.12
-12.37
-26.43
-12.36
-11.87
-11.74
-24.34
-17.78
-21.01
-9.75
-17.89
R²adj
0.7568
0.8169
0.8165
0.9119
0.6917
0.7152
0.8489
0.854
0.8997
0.9332
0.9148
0.8395
0.8468
0.9116
0.9113
0.8947
0.8468
0.9009
RSS
2.5059
2.0202
1.5723
1.0984
3.1281
2.5879
1.1773
0.9511
1.1394
0.3251
1.4355
1.3796
1.6028
0.3717
0.6878
0.6179
1.9282
0.748
Model 2
AIC
-7.51
-9.45
-11.70
-14.93
-5.51
-7.22
-14.31
-16.23
-14.60
-25.89
-12.52
-12.88
-11.53
-24.68
-19.14
-20.11
-9.87
-18.39
R²adj
0.8654
0.8667
0.9368
0.9493
0.9007
0.8984
0.8791
0.8492
0.9266
0.9337
0.9216
0.8658
0.8533
0.9275
0.9291
0.8912
0.8644
0.9126
Int.J.Curr.Microbiol.App.Sci (2014) 3(1): 127-139
Fig.3 Shape of the survival curves fitting for Escherichia coli in lower Zone (Inlet) of the Oualidia Lagoon. (a): surface water, (b): Depth.
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Fig.4 Shape of the survival curves fitting for Escherichia coli in Intermediary Zone (oyster farm) of the Oualidia Lagoon.
(a): surface water, (b): Depth
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Int.J.Curr.Microbiol.App.Sci (2014) 3(1): 127-139
Fig.5 Shape of the survival curves fitting for Escherichia coli in upper Zone (agricultural area) of the Oualidia Lagoon.
(a): surface water, (b): Depth
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Int.J.Curr.Microbiol.App.Sci (2014) 3(1): 127-139
In this study, the non-linear model gives
the lowest RSS for each analysis point
(100%), while the traditional linear model
never gave the lowest RSS value (Table
2). According to the R²adjusting test, nonlinear model showed significantly
correlation to experimental data than linear
model in 16 out of 18 cases (88.89%). The
results of the AIC (Table 2) model
comparison procedures indicate for
majority experimentation that the nonlinear model (Model 2) present the lowest
AIC value than linear model (Model 1).
1990, Hellweger and al., 2009; Green et
al., 2011, Fioravanti et al, 2011, Blaustein
et al, 2012) or an estimate of the lag phase
of decay (Gameson, 1984; Barcina et al,
1986, 1991; Baranyi, 2010). However, our
results (Fig.3, 4, 5) confirmed by some
research show that enteric bacterial
(E.coli) survival curve follow a sigmoidal
curve when the logarithm of cell number is
plotted against time (Gonzales, 1995;
Mafaret et al., 2002; Van Boekel, 2002;
Buzrul and alpas, 2005; Coroller, 2006;
Bialka et al. 2008; Izquier and GómezLópez, 2011; Keklik et al. 2012). Two
models; linear and non-linear function
have been analyzed against experimental
data to select the best approach for
modeling and quantifying Escherichia
Coli survival in coastal environment;
Oualidia lagoon. Linear model may be
considered acceptable since they give
significant linear regression, when we
compared to non-linear model, we find
that the latter model fitted the
experimental data better than linear model.
This confirmed with many research
suggested that the Weibull model was
more successful than the log-linear model
in estimating the inactivation for all
poultry products evaluated (Coroller,
2006; Keklik et al., 2012). So the classical
decay rate constant D for bacterial
decrease is not suitable for quantifying and
modeling the survival of enteric bacteria.
The environmental factor and lagoon
conditions present a clear and regular
influence on the shape the parameters
and p . For each area study in this work,
the shapes of p and
were estimated
(table 1) suggests that the environmental
conditions of Oualidia lagoon along year
influences their values. This observation is
in agreement with the works of Couvert et
al., 2005 and Coroller, 2006. Constant p
value means that the Weibull probability
density function curves presents the same
The environmental conditions may have a
predictable effect on bacteria survival in
coastal area. That is important as this
information could be used for estimating
and modeled the survival bacteria at
different time of the year. Generally, for
Escherichia Coli, diffusion culture may be
a more useful tool for establishing factorssurvival relationships [Lessard and
Sieburth, 1983; Salomon and Pommepuy,
1990; Pommepuy and al., 1992; Chraibi,
1996; Chedad et Assobhei 2007; Chandran
et al., 2010]. In membrane diffusion
chamber, the bacteria under investigation
come in contact with continuous
exchanges of and solutes and the
membrane prevent the entry of
autochthonous bacteria and pathogens into
diffusion culture. Numerous studies have
demonstrated the negative impacts of
natural environmental condition on
allochthonous bacteria (Chraibi, 1996;
Chedad and Assobhei 2007, Chandran et
al , 2010). The intensity of decrease
change according the climate condition.
Linear regression model is the most
common way of estimating a survival of
bacteria exposed to environmental stress
used in majority research. Until now,
Escherichia coli survival has been
quantified and modeled by either a decay
rate constant (Rhodes and Kator, 1988,
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Int.J.Curr.Microbiol.App.Sci (2014) 3(1): 127-139
convex shape. These parameters models
were easily conducted by maximum
likelihood estimators.
Marines Sciences Network in Morocco),
Ministry of scientific research, faculty of
science of Chouaib Doukkali university,
BIOMAR laboratory and Geosciences
Marine and Soil Sciences laboratory.
Special thanks to Louis COROLLER for
her help of uses Matlab software. The
authors are grateful to the reviewers of the
journal for helpful comments.
Statistical analysis conducted to compare
the log linear and non-log linear models
for each experiments confirmed that the
non-log linear model is the best. The
residual same of square, associate at
correlation coefficient R2 adj and AIC
criterion of the non-linear model were
smaller, showing that was the better
estimation of parameters and better
goodness of fit. This agrees with previous
studies reporting sigmoid survival plots for
the total number of enteric bacteria in
aquatic
systems
(Gonzales,
1995;
Blaustein, 2012, Keklik et al., 2012).
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