ISSN 0798 1015

Vol. 38 (Nº 04) Año 2017. Pág. 24

Adjust of linear and nonlinear models in the study of neutralization of snake venom Bothrops pauloensis by aqueous extracts Jathropha curcas and Hedychium coronarium

Ajuste de modelos lineares e não-lineares no estudo da neutralização da peçonha da serpente Bothrops pauloensis pelos extratos aquosos Jathropha curcas e Hedychium coronarium

Naiani TARTARINE 1; Janser Moura PEREIRA 2; Quintiliano Siqueira Schroden NOMELINI 3; Veridiana de Melo Rodrigues ÁVILA 4; Luiz Fernando Moreira IZIDORO 5

Recibido: 15/08/16 • Aprobado:25/09/2016

Content

1. Introduction

2. Methods

3. Results

4. Discussion

5. Conclusions

References

Acknowledgment

1. Introduction

Brazil’s snake fauna is considered one of the richest in the world, being currently known 371 species belonging to 10 families: Anomalepididae, Leptotyphlopidae, Typhlopidae, Aniliidae, Tropidophiidae, Boidae, Colubridae, Dipsadidae, Elapidae and Viperidae (BÉRNILS, 2012). Of these species, 15% are considered venomous, they are distributed in the families Viperidae and Elapidae (BERNARDE, 2011).

The snakebites accidents have medical importance because of its high frequency and severity, and recently they were introduced by the World Health Organization in the list of neglected tropical diseases (OMS, 2008). In Brazil, according to data of the Ministério da Saúde occur on mean 24,000 cases of accidents by snakes accidents per year, with lethality close to 0.4%. Between 2000 and 2009 was notified in the Southeast an mean of 6000 cases of cases per year accidents per year, Minas Gerais is the most responsible state for this statistic with 50% of all reported cases (BRASIL, 2015).

The species of Bothrops snakes, which accidents are called botropic, are currently distributed in five genres: Bothriopsis, Bothrocophias, Bothrops, Bothrops, Rhinocerophis (BERNARDE, 2011) and are responsible for 90% of accidents in the country (BRASIL, 2015).

The botropic envenomations are characterized in general by immediate local reactions and systemic effects. Systemic effects involve changes in blood coagulation and cardiovascular system, and local reactions characterized by hemorrhage, necrosis and severe inflammation with prominent edema and pain (LUNA; SILVA; PEREIRA, 2011). These pathological phenomena are complex due to additive or synergistic effects of active enzymes and toxins.

Therefore, many researchers have been searching for medicinal herbs as an alternative therapy because of its antiophidic role (IZIDORO et al. 2003). According to MATSUDA et al., (2002) of the plant Hedychium coronarium has been isolated some types of diterpenes, which may be used to neutralize the pathological symptoms derived from ophidian accidents. BORGES et al., (2005) observed that the sap extract of Musa paradisiaca presents neutralizing properties on various effects caused by ophidian venoms. According to the literature, several other plants have had their antiophidian potential described, such as: Marsypianthes chamaedrys (MAGALHÃES et al., 2011), Plathymenia reticulata (FARRAPO et al., 2011), Hypericum brasiliense (ASSAFIN et al., 2011) among other. These plants presented inhibition statistically satisfactory of some toxic parameter induced by the venom of snakes, however, can be observed many times, the incorrect use of statistical tools, especially for multiple comparisons, for example, use them to test level effects of a quantitative factor, where the correct would be to adjust regression.

According CARDELLINO & SIEWERDT (1992), in a review of the published works in the Revista da Sociedade Brasileira de Zootecnia between the years 1984 and 1989, 260 articles were using some kind of comparison test of means, of these 64.2% were utilized incorrectly. Currently, this is becoming a common practice in areas that have little contact with the theory of statistics.

Thus many scientific papers leave in low priority the statistical rigor in the planning of their experiments, "sinning" in the non use of a range of tools for quantitative analysis or misuse of the same. In this way, a well prepared planning and the correct use of statistical methods applied in the context in question, showing the step by step of its application may assist researchers and students in the biomedical area, especially with regard to statistical analysis.

Based on the importance of statistical rigor and in the correct way of using their tools, the aim of this paper is to present an application of linear and nonlinear regression models to assess the efficiency degree of venom neutralization of Bothropos pauloensis by the aqueous extracts of Hedychium coronarium and Jathropha curcas.

2. Methods

2.1. Crude venom

The crude venom of Bothrops pauloensis was acquired along the Empresa Proteínas Bioativas (Serpentário Bioagents Ltda.), Batatais-SP. After collection, the venom was immediately vacuum desiccated at room temperature and stored at -20 ° C until the moment of use.

2.2. Plant extracts

To obtain the extracts, firstly the leaves of each plant (Hedychium coronarium and Jathropha curcas) were removed, washed with distilled water, triturated in a blender where the mixture filtered and the liquid content were centrifuged at 10.000rpm for 30 minutes. Each supernatant was frozen at - 80 ° C and then lyophilized. The final product dehydrated was hermetically stocked until the moment of use.

2.3. Coagulant activity

The coagulant activity induced by the venom of Bothrops pauloensis was analyzed according to PEREIRA et al., (2010). For inhibition assays of this biochemical parameter were used aqueous extracts of Hedychium coronarium and Jathropha curcas, previously incubated for 30 minutes with 25mg of the aforementioned crude venom the respective extracts in the ratios of 1: 0; 1: 1, 1: 5, 1:10, 1:20, 1:30, 1:40 and 1:50 (m/m; venom/extract), with a Completely Randomized Design (CRD) with 3 repetitions and 8 treatments. The time required for the formation of the fibrin in the form of coagulum was measured in seconds for the two extracts, and the inhibition of activity was observed in accordance with the mean increase of the coagulation time in relation to controls.

2.4. Statistical analysis

The achieved results went through adjustments in regression models between concentration levels of extract (x) and coagulation time (y) (seconds). To the extract Hedychium coronarium, it is observed that the phenomenon under study shows a linear behavior (Figure 1). While for the aqueous extract Jathropha curcas a nonlinear behavior (Figure 2), that is to say, as increasing the concentration of extract, plasma coagulation time becomes longer, but not linear, which justifies the adoption of nonlinear models for the study of coagulation time for different concentrations of aqueous extract of Jathropha curcas.

3. Results

The mean time and standard errors of the plasmatic coagulation induced by the snake venom Bothrops pauloensis and after inhibition of this activity by the aqueous extracts of Hedychium coronarium and Jatropha curcas are shown in Table I. The mean ​​and standard errors results were obtained from 3 tests. In comparison to the positive control (only venom) there was a dose-dependent increase in the time of the plasma coagulation. The positive control was working with plasma and 25mg of crude venom induced the plasma coagulation, whose time was 8.67 seconds, while the negative control containing plasma incubated with 1250mg of each extract kept the plasma incoagulable. For inhibition tests (crude venom + vegetable extract) there was a dose-dependent increase in the time of the plasma coagulation. For the Hedychium coronarium extract as shown in Table I, the variation in coagulation time was negligible in all tested proportions. This behavior can be related to the low concentration of the antiophidian principle of this plant. As for Jatropha curcas extract the coagulation time was higher (Table I), so that from 1:20 ratio (m/m) there was complete inhibition of the coagulation. The sensitivity of the device records the coagulation for 120 seconds, after this period the plasma is considered incoagulable. In cases where the time for clot formation exceeds this time limit, as observed in this study, the crude venom is considered to be inhibited in its entirety. Royston and Pereira et al., observed similar results using extracts of Casearia mariquitensis and Hedychium coronarium respectively.

Table I. Inhibition coagulant activity of the bovine plasma citrated plasma
by the Hedychium coronarium andJatropha curcas extracts

: mean time of coagulation; : standard error of the mean time of coagulation.

In the Table II it is presented the variance analysis for the variable “coagulation time” for the aqueous extract Hedychium coronarium.

Table II. ANOVA for the variable answer “coagulation time” (seconds) in
different concentrations of the aqueous extract Hedychium coronarium.

** Significant to 1 % of probability; DF: Degree of Freedom; SS: Sum of Square; MS: Mean Square; F: value of the F statistic.

4. Discussion

At the significance level of 1%, the treatments are significant, i.e, there is a significant difference between extract concentration levels, and coagulation time. From Table III we have the assumptions of the model on CRD (Table II) which are satisfied by the test of Shapiro-Wilk the p-value was greater than 5%, indicating normality. Analogously, there is the p-value from statistic of Levene's test that is greater than 5%, which show that the variance is constant for the prevalence studied. Thus, we have reliable results on the inference made by analysis of variance for the effect of the concentrations of Hedychium coronarium aqueous extract.

Table III. Results of the Shapiro-Wilk test for residuals and Levene for the
model of delineation entirely randomized n = 24. (CRD) (Table I) with n = 24.

In Table IV the decomposition is shown in linear components, quadratic referring to the sum of squares of treatments (concentrations of Hedychium coronarium aqueous extract).

Table IV. ANOVA to the decomposition of the sum of square of
concentrations of Hedychium coronarium aqueous extract.

** Significant to 1 % of probability; NS = non significant.

Each mean square is tested by error and the null hypothesis is that the mean population for comparison is zero. If only the linear effect is significant, it is concluded that the increase in response to successive levels of the factor (concentration of Hedychium coronarium aqueous extract) is constant. Therefore, the analysis shows that the linear effect (or 1st degree) is meant to the extract concentrations. The component of 2nd degree non-significant indicates that it would not bring any improvement to the adjustment. The linear model can explain about 65% of the total variation, which according to Anderson et al., (ANDERSON; SWEENEY; WILLIAMS, 2007), for data in the biological sciences, values equal R² ​​or greater than 0,60 are often considered useful. It can also be seen, Table V, that the confidence intervals for the parameters do not contain zero, which shows their significance.

Table V. Statistics referring to the composition of the regression model in estimated 1st degree.

  (*)x: level or dose of extract concentration; (1) R²: coefficient of determination and (2)Adj. R²: Adjusted coefficient of determination

To check the normality assumptions, homogeneity of variance and independence of residuals for the linear model were made the Shapiro-Wilk test, Levene and Durbin-Watson respectively. The test results are shown in Table VI.

Table VI. Results of the Shapiro-Wilk test, the Durbin-Watson and Levene
for the residue of the regression model of 1st degree with n = 24.

From Table VI, we have that the p-value of the Shapiro-Wilk statistic is greater than 5%, which indicates no rejection of H0, in other words, it is acceptable the normality assumption of the residuals to the model of 1st degree. The same was observed for Levene's test, wherein the p-value was greater than 5%, which indicates no rejection of H0, which means, it is permissible the assumption of the constant variance for all levels of concentration of the extracts. Similarly, through the Durbin-Watson test can be observed the residuals independence (ROYSTON, 1983).

Therefore, the fitted model, Figure 1, to predict the coagulation time depending on the level (or dose) of concentration of the Hedychium coronarium aqueous extract is: Time = 1.8812  Dose + 11.923.

This result differs from that found by (PEREIRA et al., 2010), where it fitted a model of the 2nd degree for the same aqueous extract (Hedychium coronarium), Time = 74,0128 + 24,2132 Dose – 3,3766 Dose2, and yet, it has that the coagulation time observed in the work of Pereira et al. (2010) were much higher than the estimated model in Figure 1. A justification for this sharp decrease in coagulation time was the way how this extract was processed, as in the case of this work was done a scraping on plant leaves, and whit this was eliminated the high power of inhibition of Hedychium coronarium what had been observed by (PEREIRA et al., 2010).

Figure 1. Observed values and adjust of the linear model between
concentration levels of the Hedychium coronarium plant extract versus coagulation time (in seconds)

Table VII presents the analysis of variance for the variable "coagulation time" for the Jathropha curcas aqueous extract.

Table VII. Analysis of variance for the response variable "coagulation time" (seconds)
at different concentrations of Jathropha curcas aqueous extract.

  ** Significant to 1 % of probability

To the level of significance of 1%, the treatments are significant, i.e., there is a significant difference between the levels of the Jatropha curcas extract concentration and coagulation time. Therefore, the results allow concluding that the level of extract concentration influences the coagulation time.

Table VIII. Estimated values of the evaluators of adjust quality of the exponential
asymptotic models with 2 and 3 parameters for Jathropha curcas extract.

(1) p: number of parameters; (2) Adj. R²: adjusted coefficient of determination;
(3) SRD stantard residual deviation; (4) AIC: Criteria of information of Akaike.

According to the results shown in Table VIII it can be inferred through intermediate of the estimates of evaluators of adjust quality, that the exponential asymptotic model with 3 parameters provided better adjust compared to the model with two parameters, because it has a higher adjusted coefficient of determination and lower standard residual deviation. As for the Akaike Information (AIC), used in selecting the most appropriate model, it allows to affirm, according to the results shown in Table VIII, that the model with 3 parameters is the closest to be considered correct in describing the phenomenon, once that it showed the lowest value for this criterion. In relation to the coefficient of determination it is observed that the model with three parameters can capture 99.24% of the total variation of the coagulation time.

To verify the assumptions of normality and independence of the residuals were made the Shapiro-Wilk test and Durbin-Watson respectively. The test results are shown in Table IX.

Table IX. Statistics associated with the residual analysis of exponential
asymptotic models with 2 and 3 parameters for Jathropha curcas extract.

From Table IX it has that the p-value of the Shapiro-Wilk statistic is greater than 1%, only to the model C, which indicates the non rejection H0, that is, the normality assumption is permissible of the residuals to this model. As for the pattern B the normality assumption of the residuals is not fulfilled, which is also used as a criterion for the rejection of such model. The assumptions of independence and uniformity of residuals have been met by Levene test and Durbin-Watson, respectively, for the two models (ROYSTON, 1983).

Table X.
Estimates of parameters (in brackets the-standard errors) of the exponential asymptotic
models with 2 and 3 parameters to the concentration data of the Jathropha curcas extract and coagulation time.

Figure 2. Values observed and adjust of the exponential asymptotic models with
2 and 3 parameters to the data of concentration levels of Jathropha curcas
plant extract versus coagulation time (in seconds).

Note that all analyses were implemented in the freeware R Development Core Team (2015).

5. Conclusions

The linear model provided a good adjust to the data of concentration levels of Hedychium coronarium plant extract versus coagulation time (in seconds) that according to Anderson et al. (2007), models that can capture 60% of the total variation can be useful. Therefore, the fitted model was Time = 1.8812  Dose + 11.923. As noted it is suggested that the use of this extract should be done without scraping the leaves, because if done the plant loses its main feature which is to inhibit the snake venom.

The asymptotic exponential model with three parameters (model C) showed a best fitted to the data of concentration levels of Jathropha curcas plant extract versus coagulation time (in seconds) according to the evaluators of the quality of adjust. The model in question has captured 99.24% of the total variation of the coagulation time. Therefore, from the model Time = 121.2033 - 115.9683  exp  (-1.5986  Dose) can be obtained good results for predicted values ​​within the range studied.

References

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Acknowledgment

We thank’s Foundation for Research Support of the State of Minas Gerais (FAPEMIG) for financial support for this work develop.

1. Mestranda em Biotecnologia pela Universidade paulista Júlio Mesquita, Campus Araraquara-SP, e-mail: naiani_tartarine@hotmail.com

2. Docente da Faculdade de Matemática da Universidade Federal de Uberlândia-MG, e-mail: janser@famat.ufu.br

3. Docente da Faculdade de Matemática da Universidade Federal de Uberlândia-MG, e-mail: quintiliano@famat.ufu.br

4. Docente do Instituto de Genética e Bioquímica da Universidade Federal de Uberlândia-MG, e-mail: veridiana@ingeb.ufu.br

5. Docente da Faculdade de Medicina da Universidade Federal de Uberlândia-MG, e-mail: luiz.izidoro@ufu.br