 Category: Volume 16
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Mathematical screening of nutritional parameters for enhancement of insecticidal proteins production by Bacillus sp.
K. Ennouri^{1}
R. Ben Ayed^{1*}
H. Ben Hassen^{2}
^{1 }Centre of Biotechnology of Sfax, PB ‘1177’, 3018 Sfax, Tunisia
^{2 }Laboratory of Physics, Mathematics and Applications. Faculty of Sciences of Sfax, Tunisia
Abstract  The bacterium Bacillus thuringiensis (Bt) is a spore forming microorganism that produces an insecticidal crystalline protein (ICP) making it a famous biopesticide. The ICPs are also referred to as Cry proteins and include deltaendotoxins, which cause mortality of insects classified to several orders, namely, Coleoptera, Diptera and Lepidoptera.
Statistical methods were carried out to ameliorate the fermentation medium composition for the production of bacterial deltaendotoxins in submerged cultures. An experimental statistical design was used to measure the effects of different components in the medium. The concentrations of starch and soybean meal, considered as the main carbon and nitrogen sources for bacterial growth, respectively, FeSO_{4} and MgSO_{4} were found to increase Bacillus sp. deltaendotoxin production. Different mathematical models were developed and interaction between all ingredients was studied. In concordance with coefficient of determination (R²) value, well known as the most important criterion for predictive models success, the best model was validated and thus demonstrated the effect of interaction and then can precisely predict the production of deltaendotoxins by studied bacterium. With a limited number of experiments, this method allowed to obtain promoting results.
Keywords: Bacillus thuringiensis / deltaendotoxins / coefficient of determination / interaction / statistical design.
1. Introduction
The evolution of insecticide resistance and the developing alertness of environmental problems caused by agrochemical insecticides have spurred research into biologicallybased, environmentally kindly choices. Among the compounds identified are proteins from microbes, predators, and plants that having selective toxicity to insects. Most popular among these insecticidal proteins are the B.thuringiensis crystal (Cry) deltaendotoxin proteins produced by Bacillus thuringiensis that form crystalline inclusions throughout sporulation (Schnepf et al. 1998). Cry proteins bind to receptors and insert into the membranes of insect midgut epithelial cells, forming pores and causing cellular lysis and serious damage to the midgut epithelium (Bravo et al. 2007). Because of the elevated effectiveness of B. thuringiensis endotoxins against pest larvae, these toxins are of high economic importance and strain selection and changing cultural settings have been investigated to boost B. thuringiensis deltaendotoxins production (Dulmage and Rhodes 1982; Holmberg and Sievanen 1980). To acquire the optimal conditions for a reaction, it is usually important to evaluate numerous parameters. The use of mathematical methods and experimental designs enables the determination of the influence of all parameters with a minimum of trials and the method has been applied to numerous fields. The basic approach has been derived by statisticians. Indeed the methodology enables one to obtain information with a minimum of experiences leading to the optimization of a process. Therefore, we present in this work an original example for the optimization of the medium ingredients for particular bacterial toxins production using experiment matrices. In the present work, an isolated strain which has high entomopathogenic activity was studied and some fermentation conditions such as carbon and nitrogen sources and various metal ions on deltaendotoxins production were investigated. A modified medium was defined for high production of deltaendotoxins.
2. Experimental Methods
2.1. The B. thuringiensis strain
The studied strain of B. thuringiensis subsp. kurstaki is provided from the collection of bacterial strains (Center of Biotechnology of Sfax, Tunisia), known for its toxicity against Lepidoptera insects (Ennouri et al. 2013). The bacterial strain was grown for maintained on Luria Bertani (LB) agar medium composed of 10 g l^{1} peptone, 5g l^{1} NaCl, 5g l^{1} yeast extract and 15 g l^{1} agar and then stored at 4 °C.
2.2. Microorganism and cultivation media
For fermentation medium, an economic complex medium (Ghribi et al. 2007) was used containing the following components (g l^{1}): starch, 25; soybean meal, 20; MgSO_{4}, 0.3; MnSO_{4}, 0.02; FeSO_{4}, 0.02; K_{2}HPO_{4}, 1; KH_{2}PO_{4}, 1;. CaCO_{3} (20 g l^{1}) was added for keeping pH stability. All media used in this study were adjusted to pH 7.0 ± 0.01 before autoclaving.
2.3. Culture conditions
For preinoculum preparation, a loopful of B. thuringiensis grown on LB plate was used to inoculate a 3 ml of sterilised LB medium and incubated in a rotary shaker at 30 °C and 200 rates per minute overnight (1418h). For inoculum preparation, 250 ml erlenmeyer flasks containing 50 ml of LB medium were inoculated with 1% (v/v) of the preinoculum and incubated in a rotary shaker at 30°C and 200 rates per minute for 6 h. The volume of culture inoculum was calculated on the basis of a final absorbance of 0.15 measured at 600 nm. The 250 ml shake flasks including 20 ml of complex lowcost medium were incubated with estimated inoculum volume. In such media, the initial OD was not measured after inoculation but calculated on the basis of the OD measured in the inoculum. Samples taken regularly from the incubated cultures were subjected to microscopical observation. The fermentation process was considered as ended when 90 % (or more) of the B. thuringiensis cells had been destroyed, liberating the crystals and spores.
2.4. Determination of deltaendotoxins
At the end of fermentation, one ml of collected samples was centrifuged at 13000×g for 10 min at a temperature of 4 °C. The supernatants were removed. The pellets were washed twice with 1 ml of 1 M NaCl solution and twice with 1 ml of bidistilled autoclaved water. The crystal proteins in the pellet were dissolved with 50mM NaOH (pH 12.5) for 2 h at 30 °C with vigorous shaking. The suspension was centrifuged at 13000×g for 10 min at 4 °C and the pellet was removed. The supernatant, containing the alkalisoluble insecticidal crystal proteins was used to define the deltaendotoxin concentration by Bradford method using bovine serum albumin as standard protein (Bradford 1976). Deltaendotoxins concentration was measured at 595 nm using a UVvisible spectrophotometer (BioRad Laboratories, Inc.). The obtained values are the mean of triplicate runs of two separate experiments.
2.5. Statistical experimental design
The significance of the various media constituents towards deltaendotoxins production was further tested using PlackettBurman statistical experimental designs (1946). This method is based upon the existence of Hadamard matrices, which are square matrices of order N with entries at two levels, +1 and −1. These matrices are orthogonal such that for each column the number of +1 is equal to the number of −1. This experimental design is suitable for screening the effect of a large number of factors in an experiment and ideal for the determination of main effects. The design assumes that there are no interactions between different media constituents, X_{i}, in the range of variables under consideration and a linear approach is considered sufficient for screening:
Where Y is the calculated target function and i are the regression coefficients.
With such experimental design, N factors can be screened with only N+1 trials and screening up to 100 variables (Castro et al. 1992) is feasible with the aid of this method. In the present study, effect of 7 factors of the medium on deltaendotoxin production was determined.
Trials were carried out in triplicate and at two different times and the responses considered for study represent mean of the responses. The effect of each variable was estimated by the standard equation:
Where R(H) characterizes all responses when constituent was at high levels, R(L) corresponds to all responses when constituent was in low levels, N is the total number of runs.
The standard error (S.E.) represents the square root of the variance of an effect and the (pvalue) or significance level of each concentration effect is estimated using student’s ttest:
Where, E(xi) is the effect of the variable xi.
The coefficient of determination (R²) determines the degree of collinearity between simulated and measured data. Similarly, R² determines the proportion of the variance in experimental data explained by the model. R² ranges from 0 to 1, with higher values indicating less error variance, and typically values greater than 0.5 are considered acceptable (Santhi et al. 2001). Although R² have been widely used for model evaluation, these statistics are oversensitive to high extreme values (outliers) and insensitive to additive and proportional differences between model predictions and measured data (Legates and McCabe 1999).
3. Results and discussion
Table 1 represents the independent variables and their respective high and low concentrations used in the optimization study, whereas Table 2 represents the experimental design for 12 trials with two levels of concentrations for each variable, which was followed for the optimization of medium components for deltaendotoxins production.
Table 1: Medium components (variables) and the respective high and low concentration levels used in experimental design 

Variable 
Medium components 
Lower level (g l^{1}) 
Higher level (g l^{1}) 
X1 
KH_{2}PO_{4} 
1.5 
0.5 
X2 
K_{2}HPO_{4} 
1.5 
0.5 
X3 
MgSO_{4} 
0.1 
0.5 
X4 
MnSO_{4} 
0 
0.002 
X5 
FeSO_{4} 
0 
0.002 
X6 
Starch 
25 
35 
X7 
Soybean meal 
20 
30 
The variables X_{1}, ..., X_{7} represented the medium constituents. Table 3 represents the results of statistical experiment with respect to endotoxins production, the effect, standard error, t and pvalue (confidence level) of each component. The components were screened at the confidence level of 95% on the basis of their effects. If the component showed significance at or above 95% confidence level and its effect was negative, it indicated that the component was effective in deltaendotoxins production but the amount required was lower than the indicated as low () concentration in studied statistical experiment. If the effect was positive, a higher concentration than the indicated high value (+) concentration was required during further optimization studies. According to Table 2, deltaendotoxins concentrations ranged from 457 mg l^{1} to 2426 mg l^{1}.
Table 2: Deltaendotoxins concentrations according to experimental design 

KH_{2}PO_{4} 
K_{2}HPO_{4} 
MgSO_{4} 
MnSO_{4} 
FeSO_{4} 
starch 
soybean meal 
Deltaendotoxins (mg l^{1}) 
1,5 
1,5 
0,1 
0,02 
0 
25 
20 
457±58 
0,5 
1,5 
0,5 
0,02 
0 
35 
30 
1808±64 
0,5 
0,5 
0,5 
0,02 
0,02 
25 
30 
1568±31 
1,5 
1,5 
0,1 
0,02 
0,02 
25 
30 
1671±55 
1,5 
0,5 
0,5 
0,02 
0 
35 
20 
915±47 
0,5 
0,5 
0,1 
0 
0 
25 
20 
1375±26 
1,5 
1,5 
0,5 
0 
0,02 
35 
20 
1368±28 
1,5 
0,5 
0,5 
0 
0 
25 
30 
1253±34 
1,5 
0,5 
0,1 
0 
0,02 
35 
30 
2426±57 
0,5 
1,5 
0,5 
0 
0,02 
25 
20 
1618±44 
0,5 
0,5 
0,1 
0,02 
0,02 
35 
20 
1626±20 
0,5 
1,5 
0,1 
0 
0 
35 
30 
601±36 
The confidence level of all components were below 95% in deltaendotoxin production and hence, were considered insignificant (Table 3). Starch, considered as principal source of carbon, soybean meal (source of nitrogen), FeSO_{4} and MgSO_{4 }enhanced the deltaendotoxin production whereas K_{2}HPO_{4}, KH_{2}PO_{4} and MnSO_{4} inhibited the production of deltaendotoxins.
Table 3: Prediction model from regression analysis 

Predictor 
Coefficient 
SE 
t 
p 
Rank 
Constant 
208 
1415 
0.15 
0,001 

KH_{2}PO_{4} 
84.4 
328.5 
0,26 
0,810 
6 
K_{2}HPO_{4} 
273.2 
328.5 
0,83 
0,452 
3 
MgSO_{4} 
155.4 
821.2 
0,19 
0,859 
7 
MnSO_{4} 
4974 
16424 
0,30 
0,777 
5 
FeSO_{4} 
32248 
16424 
1.96 
0,121 
1 
Starch 
13.37 
32.85 
0,41 
0,705 
4 
Soybean meal 
32.77 
32.85 
1.00 
0,375 
2 
S = 568.960 
R² = 59.60% 
R²(adj) = 0,0%




Analysis of Variance (ANOVA) 





Source 
DF 
SS 
MS 
F 
p 
Regression 
7 
1910312 
272902 
0,84 
0,605 
Residual Error 
4 
1294861 
323715 


Total 
11 
3205172




In fact, Nickerson and Bulla (1974) reported that the change in the carbon source affects the biological activity and the morphology of the crystals. The phenomenon could be possibly due to alteration on the rate of synthesis of the different Cry proteins (Yudina et al. 1992). On the other hand, free amino acids containing basic form of assimilated nitrogen by cell; have to be supplied in the medium in order to obtain good parasporal crystal formation in Bacillus thuringiensis (Egorov et al. 1984).
In addition, the regression is not linear (according to Table 3) because the amount of Fstatistic for determination of effective factors on deltaendotoxin production is 0.84 with the significance level of p = 0.605. The results are presented in Table 3 which shows the regression model with coefficient of determination of 0.596 and adjusted coefficient of determination of 0 which means that constructed model explains two plausible cases: the first is that there is no linear competitive advantage between the seven components and the second is that the production is totally influenced by other factors.
The goodness of fit of a linear regression model is popularly measured by the sample coefficient of determination known as R². This measure has a tendency to rise and to reach its upper limit as the number of explanatory variables in the model increase. Such an uncomfortable feature is controlled to a large extent through an application of a correction for the degrees of freedom. This leads to another measure of the goodness of fitted model known as adjusted R². Both the high adjusted R² value and the close to zero pvalue in the Analysis Of Variance (ANOVA) (Box et al. 1978; DeVor et al. 1992; Montgomery 2001) show that this model has a satisfactory goodness of fit. The use of R², the coefficient of determination, also called the multiple correlation coefficient, is well established in classical regression analysis (Rao 1973). Its definition as the proportion of variance explained by the regression model makes it useful as a measure of success of predicting the dependent variable from the independent variables. Generally, R² value is accepted as a standard criterion for the predictive success of the models (Hakanson et al. 2003). Multivariate models capable of assessing large number of variables and interrelations are therefore, more successful in defining and predicting biological processes such as deltaendotoxins production. In the present study, the relationships between nutrients having positive effect on deltaendotoxins production have been investigated using a linear multivariate approach. Thus, in order to increase secretion of deltaendotoxins by Bacillus thuringiensis strain, our major focus is to investigate the relationships between parameters having positive effect on deltaendotoxins production by Bacillus thuringiensis. In this study, MgSO_{4}, FeSO_{4}, starch and soybean meal will be more studied. The variable with confidence level above 95% is considered a significant factor. According to Table 4, we showed that all ingredients significantly affect the deltaendotoxin production independently for a significance level α=0.05.
Table 4: Prediction model (with interaction) from regression analysis


Predictor 
Coefficient 
SE 
t 
p 
Rank 
Constant 
4414.3 
167.7 
26.32 
0.024 

KH_{2}PO_{4} 
1061.24 
38.27 
27.73 
0,023 
3 
K_{2}HPO_{4} 
703.69 
38.27 
18.39 
0,035 
8 
MgSO_{4} 
4490.8 
144.6 
31.05 
0,020 
1 
MnSO_{4} 
29477 
1446 
20.38 
0,031 
5 
FeSO_{4} 
367751 
18398 
19.99 
0,032 
6 
Starch 
62.037 
4.091 
15.16 
0.042 
10 
Soybean meal 
87.198 
5.010 
17.40 
0.037 
9 
FeSO_{4} × starch 
7302.4 
375.8 
19.43 
0.033 
7 
FeSO_{4 }× soybean 
10644.8 
433.9 
24.53 
0.026 
4 
MgSO_{4} × FeSO_{4} 
283982 
9395 
30.23 
0.021 
2 
S = 35.4291 
R² =100.0% 
R²(adj) = 99,6% 



Analysis of Variance (ANOVA) 





Source 
DF 
SS 
MS 
F 
p 
Regression 
10 
3203917 
320392 
255.25 
0,049 
Residual Error 
1 
1255 
1255 


Total 
11 
3205172 



In order to obtain a higher R² value, we deduct from several constructed models that only three 2factor interaction terms among these variables also significantly affect the deltaendotoxins production for α=0.05, i.e., (FeSO_{4} × MgSO_{4}), (FeSO_{4} × starch), and (Soybean × FeSO_{4}). The statistical significance of the second order equation was checked by an Ftest (ANOVA) and data were shown in Table 4. The regression model for deltaendotoxins production was highly significant (pvalue= 0.049) with a satisfactory value of determination coefficient (R^{2}^{ }= 1), indicating that total variability in the response could be explained. The closer the value of R^{2}^{ }is to 1.0, the stronger the model and the better it predicts the response. The model Fvalue of 255.25 indicated that the model terms were significant. Furthermore, the signs of the parameters in the model presented in Table 4 are examined. Positive signs mean that the production value will go in the same direction as the parameter, and negative signs imply the opposite. Therefore, the endotoxins production by Bacillus thuringiensis will be improved due to increases of MgSO_{4}, K_{2}HPO_{4}, interaction of FeSO_{4} and soybean meal, and interaction of starch and FeSO_{4}. Moreover, the positive effect of Magnesium ions on enhancement of deltaendotoxins production has been kept. In fact, the addition of macronutrients such as Mg^{2+} has been reported to increase the yield and insecticidal activities of B. thuringiensis (Goldberg et al 1980). However, interaction of FeSO_{4} and MgSO_{4} seems to decrease the production of deltaendotoxins. This finding suggests that when iron, coupled with magnesium ions, are able to prevent the formation of deltaendotoxins. Thus, on the basis of obtained results, we conclude that negative individual effects of starch, FeSO_{4}, and soybean meal, were converted in positive effect when interactions were applied. Iron is an element required in trace amounts for most of the microorganisms in order to run their number of crucial biochemical reactions including reduction of the oxygen for synthesis of ATP, detoxification of oxygen radicals etc. These restrictions of availability under limited environmental conditions and biological requirements have disposed microorganisms to synthesize particular molecules that can compete with hydroxyl ion for the ferric state of iron, a nutrient which is present and biologically unavailable. Siderophores are lowmolecularmass (5001000 Daltons) ironchelating ligands that are produced by most microorganisms under ironlimited circumstances (Hider 1984), which bind ferric ions with high similarity (Neilands 1995). Siderophore solubilize the nonsoluble surrounding iron in order to make it biologically available. Microorganisms, which produce siderophore have molecular systems to transport iron by siderophore – iron complexes into the cells through iron regulated outer membrane proteins (Braun et al. 1998). The obtained results may explain the positive relationship (FeSO4 × starch) and (FeSO4 × soybean) by the fact that Fe^{3+} agents have a highly specific chelating potency. Siderophores are synthesized by microorganisms to sequester iron from the culture medium, and carbon and nitrogen sources in a second time. The media used for the industrial production of B. thuringiensis are composed of complex carbon and nitrogen sources. Starch is considered as suitable carbon sources and a proteinrich material such as soybean flour is among the cheap sources of nitrogen used. Anderson (1990) suggested a relationship between carbon:nitrogen ratio and production of deltaendotoxins. According to Table 4, starch and soybean meal increased the deltaendotoxins production only when iron ions (Fe^{3+}) were present in the culture medium. Several medium components such as nitrogen and carbon sources influence the metabolic and biochemical behaviour of the microbial strain and subsequent metabolite production pattern, such as deltaendotoxins secretion. Thus, the assimilation of Carbon and Nitrogen by Bacillus thuringiensis was more suitable with the presence of accessible iron ions. In planning a factorial experiment prior knowledge may suggest that some interactions are potentially important and should therefore be estimated free of the main effects.
4. Conclusion
In this study, the coefficient of determination (R²) has been considered as the most important criterion for better choice of interactions between culture components. Interaction permitted to discover hidden biological relationships between culture ingredients composing the bacterial environment and the studied microorganism. Our findings suggest that Iron is perhaps the most important micronutrient used by Bacillus thuringiensis strain and is essential for the metabolism. Iron actions have been highlight because of the potential role of microbial siderophores in facilitating uptake of iron ions and their mobilisation under specific growth conditions.
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