Modeling Conidiospore Production of Trichoderma harzianum Using Artificial Neural Networks and Response Surface Methodology

Featured Application

Conidiospores of Trichoderma harzianum can be applied as biocontrols for plant diseases, which are eco-friendly and safe for human health. The best model obtained in this work is used to find the optimal conditions to produce the maximum number of conidiospores.

Abstract

An alternative to facing plagues without affecting ecosystems is the use of biocontrols that keep crops free of harmful organisms. There are some studies showing the use of conidiospores of Trichoderma harzianum as a medium for the biological control of plagues. To find the optimal parameters to maximize the production of conidiospores of Trichoderma harzianum in barley straw, this process is modeled in this work through artificial neural networks and response surface modeling. The data used in this modeling include the amount of conidiospores in grams per milliliter, the culture time from 48 to 136 h in intervals of 8 h, and humidity percentages of 70%, 75%, and 80%. The surface response model presents R² = 0.8284 and an RMSE of 4.6481. On the other hand, the artificial neural network with the best performance shows R² = 0.9952 and RMSE = 0.7725. The modeling through both methodologies can represent the behavior of the Trichoderma harzianum conidiospores growth in barley straw, showing that the artificial neural network has better goodness of fit than the response surface methodology, and it can be used for obtaining the optimal values for producing conidiospores.

1. Introduction

Feeding is essential for humans in the world; consequently, food production is the main industry in all countries. In addition, the food industry is working on the development of products based on natural ingredients, such as plants. Moreover, there are powders and pills based on plant ingredients that are used as food supplements [1]. To optimize the production of plant-based food, the use of fertilizers has increased to 33 million tons in all regions from 2000 to 2019, according to the Food and Agriculture Organization [2].

In the search for larger agricultural production, many plant illnesses are controlled with chemical fungicides, which are applied to leaves, soil, seeds, and fruits [3]. These farming methods have had a negative impact on the environment and human health [4]. Thus, there are many efforts to find biological alternatives to substitute chemical products [5]. Several microorganisms with natural antagonistic activity against pathogenic organisms have been used as biopesticides [6].

Trichoderma is a ubiquitous fungus that has a wide ability to remove other fungi from soil. Its antagonistic mechanisms include antibiosis, micoparasitism, induction of resistance, and potential for secretion [7], which are responsible for its capacity as an agent of biological control, mainly the genus Phytophthora, Rhizoctonia, Sclerotium, Pythium, and Fusarium, among others [8,9]. The production of microorganisms with potential features as biocontrollers has been a high-priority topic lately.

To create more efficient processes for the microorganism culture used as biocontrollers, there have been implemented mathematical and computational methodologies, such as response surface methodology (RSM) and artificial neural networks (ANNs) [10].

These methodologies forecast the behavior of a process or phenomenon caused by the interaction of its variables. This interaction is quantified by gathering the numerical results from a number of lab experiments, which are used to develop the models.

RSM is a methodology that provides good results to represent the relationship between control variables and response variables with the aim of modeling experimental results obtained in a lab [11]. With this tool, a mathematical model $C$ = F(x₁, x₂, …, x_n) can be developed to explain the relationship between different factors (x₁, x₂, …, x_n) and its influence on the value of the response variable ($C$) [12].

On the other hand, ANNs are a computational technique inspired by biological neural networks, and they have been applied for multifactorial analysis. ANNs are composed of nodes distributed in layers interconnected by arcs, where each arc has a numerical value indicating its weight. These nodes represent the artificial neurons, which are processing units and executing nonlinear additive functions [13].

RSM has been utilized to model the Trichoderma culture in tropical waste (cassava peel, banana pseudostem, coconut shell, sugarcane bagasse, and pineapple peels) for optimizing the culture conditions to enhance the spore production efficiency [14]. Furthermore, it has been applied to model mathematically the cellulose production from Trichoderma harzianum, carrying out the necessary simulations to maximize the enzyme production [15].

The performance of L-methioninase isolated from Trichoderma harzianum has been modeled through RSM and ANNs. Moreover, the optimal values to improve its performance were obtained using genetic algorithms [16].

Both techniques have been used in various fields of research to represent diverse phenomena and analyze the interaction between independent or input variables and the response or output variables. Furthermore, this methodology can also be applied to modeling other biological systems, such as agricultural [17,18,19] ecological systems [20,21,22], among others, where there exists a high correlation between the independent and dependent variables.

Nevertheless, the modeling of the interaction of variables in Trichoderma harzianum conidiospores in barley straw has not been used before. Previous research work related to conidiospore production from Trichoderma harzianum is focused on the production of L-methioninase or cellulase from Trichoderma harzianum but not on conidiospore production. Moreover, the variables considered in this work, such as culture time (h) and humidity percentage (%), were not used in the related papers published previously. Thus, in this research work, both tools are applied to analyze this production process, to model the interaction between the involved variables, and to obtain the optimal conditions for input parameters and the maximum production from different percentages of humidity in the samples and diverse moments in the culture time.

2. Materials and Methods

2.1. Experimental Development

To obtain the experimental values, we used Trichoderma harzianum from the Agrobiotechnology Laboratory of the Universidad Politécnica de Pachuca. The barley straw used for the microorganism growing was harvested from the fields of Zempoala, Hidalgo, México.

Based on the results of previous research [23], the modeling for this research uses straw with mineral salts added, which increases spore production, and straw previously washed. Three different humidity percentages were analyzed (70%, 75%, 80%), and the number of conidiospores was counted every 8 h. The humidity percentage range from 70 to 80 percent was chosen due to previous experiments in the lab showing high performance in spore production, and the range of the number of hours from 48 to 136 h was selected due to the substrates used and the lifecycle of the fungus. The application of RSM and ANN models allows the generalization of this biological phenomenon to replicate its behavior and search for optimal conditions, instead of developing many experiments, which are time-consuming and expensive.

In total, 36 experiments in triplicate were carried out, and the average values for each experiment are shown in

Table 1. Experimental results of the number of conidiospores.

Experiment Number	Culture Time (h)	Humidity Percentage	Amount of Conidiospores
1	48	70	6,750,000
2	48	75	5,500,000
3	48	80	2,750,000
4	56	70	52,500,000
5	56	75	56,000,000
6	56	80	74,250,000
7	64	70	115,500,000
8	64	75	119,000,000
9	64	80	190,000,000
10	72	70	49,500,000
11	72	75	197,500,000
12	72	80	212,000,000
13	80	70	121,500,000
14	80	75	164,000,000
15	80	80	280,000,000
16	88	70	180,000,000
17	88	75	156,000,000
18	88	80	246,000,000
19	96	70	112,500,000
20	96	75	262,500,000
21	96	80	375,000,000
22	104	70	170,000,000
23	104	75	262,500,000
24	104	80	220,000,000
25	112	70	215,000,000
26	112	75	257,500,000
27	112	80	250,000,000
28	120	70	180,000,000
29	120	75	258,000,000
30	120	80	382,500,000
31	128	70	115,500,000
32	128	75	417,500,000
33	128	80	322,500,000
34	136	70	144,000,000
35	136	75	305,000,000
36	136	80	432,500,000

.

2.2. Data Adjustment Techniques

The modeling of collected data is completed by the RSM [24,25] and with ANNs [26,27].

RSM and ANNs have been used to model systems in a wide range of fields. Both techniques have proven to be efficient in the representation of these systems. On one hand, RSM uses linear regression to obtain the mathematical model with the minimum error. On the other hand, ANNs have been adopted as a tool to model complex systems, which learn the behavior of the system through a training phase based on gathered data on the variables of interest.

Nevertheless, these techniques present some disadvantages. In the case of RSM, it is assumed that the relationships in the system can be approximated by polynomial equations, which may not always be true for highly complex or nonlinear systems. The dimensionality is another drawback for RSM models because if the number of variables increases, the number of terms in the equation also increases, creating complex polynomials.

In the case of ANNs, the training can be computationally intensive and time-consuming, requiring powerful hardware to carry out the search for the ANN with the best performance. Moreover, the black box nature of ANNs presents problems such as understanding how the mapping is found by the ANN and how the weights can be interpreted by users.

Despite the disadvantages these techniques can present, they are powerful and versatile tools for modeling systems and making predictions.

2.2.1. Surface Response Methodology

The results of the 36 experiments are used to create a model through RSM, in order to identify the relationship between the conidiospores production and the two control variables (percentage of straw humidity and the culture time).

The data are fitted using the command rstool from the statistic toolbox of Matlab^® 8.1 version (MathWorks^®, Natick, MA, USA). The response variable, representing the amount of produced conidiospores, is expressed as an equation that depends on the values of each factor that contributes to the process. The resulting equation is based on the quadratic model of the surface response (Equation (1)).

$$C={\beta }_0+\sum _{i=1}^k{\beta }_i{x}_i+\sum _{j=2}^k\sum _{i=1}^{j-1}{\beta }_{ij}{x}_i{x}_j+\sum _{i=1}^k{\beta }_{ii}{x}^2+e$$

(1)

where $C$ represents the number of conidiospores, ${\beta }_0$ is the constant term in the equation, ${\beta }_i$ is the coefficient of the linear term, ${\beta }_{ij}$ is the coefficient of the interaction variables term, ${\beta }_{ii}$ corresponds to the coefficient of the quadratic term, $x_i$ and $x_j$ are independent variables, and $e$ denotes the observed error in the response model.

An analysis of variance (ANOVA) is utilized to validate the fitting of the obtained RSM model and the statistical significance of the regression coefficients. The interaction between independent and response variables is analyzed through a contour graphic of the RSM.

2.2.2. Artificial Neural Networks

An ANN is developed to replicate the interaction between the two influencing factors in the Trichoderma harzianum production, the culture time, and the humidity percentage used. The ANN input layer is composed of two neurons, which represent the two independent variables. The output layer just contains one neuron, which represents the amount of conidiospores produced, as a response variable, similar to the RSM model. The data are analyzed with the ANNs toolbox from Matlab^® 8.1. The hyperbolic tangent sigmoid transfer function is used as an activation function for each hidden layer, and the linear transfer function is applied in the output layer.

The experimental response values are used to identify the most appropriate ANN model to recreate this biotechnological process. Furthermore, one objective is to identify the combination between the input values to obtain the maximum amount of Trichoderma harzianum spores. Thus, a Matlab^® script is implemented to find the ANN with the lowest quadratic error. The script can generate ANN models, starting with a 3-layer model, where the first layer (the input layer) contains 2 neurons (culture time and humidity percentage); the midterm layer is the hidden layer, and its number of neurons is changed from one to ten neurons; and the output layer consists of only one neuron, representing the amount of the conidiospores.

A random selection from around 70% of the experiments (26 samples) is chosen to train the ANN. A total of 15% of the experiments (5 samples) are used to validate the model. Lastly, the other 15% (5 samples) are used for the test phase [28]. The training set achieves an R² very close to 1; however, the test and validation sets obtain an R² smaller because these records were not used in the training phase. Finally, considering the whole dataset, the R² obtained is 0.9952.

The ANNs are trained with the retropropagation Levenberg–Marquardt algorithm [29]. Each ANN contains from 1 to 4 hidden layers, and each hidden layer contains from 1 to 10 neurons.

Due to the combination of the number of neurons in one to four hidden layers, a total of 10,000 ANNs were trained. In the search for the ANN with the best performance, at every iteration, the new ANN was compared with the best ANN found until that moment, keeping the best one for the next comparisons. During the 10,000 iterations, 33 times the best ANN was updated. The behavior of R² (Figure 1a), RMSE (Figure 1b), and ADD (Figure 1c) for these 33 ANNs denotes how the R² is moving to one and the RMSE and the AAD are approaching zero.

The network that performs better has an input layer with 2 neurons, an output layer with one neuron, and 4 hidden layers, with 9, 5, 3, and 9 neurons, respectively, with a determination coefficient R² = 0.9952 (Figure 2).

3. Results and Discussion

3.1. Experimental Results

From the utilization of different humidity percentages, and distinct culture times [23], a number of conidiospores are generated (Table 1). The smallest amount obtained is 2.5 million conidiospores (experiment 3), while the largest amount obtained is 432.5 million conidiospores (experiment 36), demonstrating the influence of the independent variables over the response variable.

3.2. Response Surface Methodology

The RSM model is developed using a quadratic model [30] with two axes for the variables of the process, where x₁ represents the culture time and variable x₂ indicates the culture humidity percentage. Equation (2) is obtained with a statistical confidence level of 95%.

$$\begin{array}{c}C\left(x_1,x_2\right)=-4183.487-7.400x_1+110.482x_2+0.219x_1{x}_2-0.033{x_1}^2\\ -0.786{x_2}^2\end{array}$$

(2)

where $C\left(x_1,x_2\right)$ indicates the amount of conidiospores produced in millions of units.

The influence of the two independent variables $(x_1,x_2)$ over the response variable $C$ is shown in

Table 2. ANOVA from the quadratic model of the RSM for the conidiospores production.

	Sum of Squares	Degrees of Freedom (df)	Mean Square	F-Value	p-Value
Model	3.7556 × 105	5	75,111	29.041	<0.0001
Linear	3.3242 × 105	2	1.6621 × 105	64.262	<0.0001
Nonlinear	43,140	3	14,380	5.5598	<0.0001
Residual	77,592	30	2586.4
Total	4.5315 × 105	35	12,947

, which represents the calculation of the ANOVA [31] from the quadratic model of the surface response. A Fisher value of 29.041 is obtained, and a probability value of p < 0.05 is obtained. The determination coefficient (R²) from the experimental data and the forecasted values with the RSM model is 0.8284 (Figure 3), which indicates that this model describes the data with a precision of 82.84%

The regression analysis [32] for the quadratic equation (

Table 3. Regression analysis for the quadratic model.

Model Term	Coefficient Estimate	Standard Error	F-Value	p-Value
Constant	−4183.5	4071.1	−1.0276	0.31235
A	−7.3998	6.1014	−1.2128	0.23467
B	110.48	108.13	1.0218	0.31505
AB	0.21915	0.075181	2.915	0.0066662
A2	−0.033194	0.012558	−2.6433	0.012927
B2	−0.78625	0.71922	−1.0932	0.28301

) reveals that the interaction between the independent variables presents a bigger effect on the response variable. Nevertheless, none of these terms can be considered meaningful because the p-value is bigger than 0.05.

The contour graph [33] in Figure 4 shows the interaction between the independent variables and their effects on the conidiospores production. These graphs are three-dimensional representations of the surface response as a function of the two independent variables, where the maximum amount of conidiospores is obtained when the culture time increases as well as the humidity percentage current in the sample. Both input variables are directly proportional to the amount of produced conidiospores.

3.3. Artificial Neural Network

The goodness of fit between the experimental data and the responses obtained with the ANN model with the best performance has a high correlation (Figure 5), presenting a determination coefficient close to 1 (R² = 0.9952), which means that the ANN model obtained replicates with a higher certainty level the number of conidiospores produced using the variables of the culture hours and the humidity percentage of the samples.

Figure 6 shows the surface plot of the ANN obtained. The yellow part of the graph indicates the higher number of conidiospores; some of them are located close to 100 h, and some others are between 125 and 140 h. However, the highest value is located near 100 h and 80% of humidity.

This result is validated with the contour graph (Figure 7). Indeed, the highest contour line is marked with 450 million conidiospores in the range from 95 to 101 h. There is another contour line with 450 million conidiospores.

3.4. Comparison of the RSM and ANN Models

The performance of these models is analyzed statistically with the root mean square error (RMSE), determination coefficient (R²), and the absolute average deviation (AAD), based on the following equations: [34]

$$RMSE=\sqrt{\frac{1}{n}\sum _{i=1}^n{\left(F_i-A_i\right)}^2}$$

(3)

$$R^2=\frac{{\left(\sum _{i=1}^n\left(A_i-\overline{A_i}\right)\left(F_i-\overline{F_i}\right)\right)}^2}{\sum _{i=1}^n{\left(A_i-\overline{A_i}\right)}^2{\left(F_i-\overline{F_i}\right)}^2}$$

(4)

$$AAD=\left|\left(\frac{1}{n}\sum _{i=1}^n\left(\frac{F_i-A_i}{A_i}\right)\right)\right|\times 100$$

(5)

where n is the number of points, $F_i$ is the value obtained from the forecast with the RSM or ANN model, $A_i$ is the value obtained experimentally, and $\overline{F_i}$ indicates the average of the equation located under the symbol.

The values forecasted by both models are close to experimental values, but the determination coefficient value closer to 1 corresponds to the ANN model, which indicates a better fit of the ANN against the one presented by the RSM. Moreover, the RMSE and the ADD values are smaller in the ANN prediction. The results of the error calculation for both models are shown in

Table 4. Comparative metrics of RSM and ANN models.

	RSM	ANN
RMSE	46.4257	7.7249
R2	0.8284	0.9952
AAD	48.9307	10.8791

.

The R-squared values obtained for the RSM and ANN models are 0.8284 and 0.9952, respectively. The ANN represents 99.52% of the data. The closest model is the ANN developed for modeling the yielding L-methioninase from Trichoderma harzianum with a determination coefficient (R²) equal to 0.9950 [16]. The RSM model proposed to represent the mass production of Trichoderma Brev T069 shows an R² equal to 0.9763 [14], and the authors did not propose an ANN model.

The RSM and ANN techniques have been used to model biotechnology processes satisfactorily [35,36]. Similarly to the results presented in this paper, other publications have proven that ANNs denote better performance than RSM models. For example. in the study carried out by the authors of [30], they observed a better modeling ability of the ANN over the modeling performed with RSM. The strength of the ANN for making generalizations of the modeled data could be due to its ability to model nonlinear systems, unlike RSM, which is limited to polynomial models.

The main importance of using ANN in biologically driven systems is that they do not require a full understanding of the relationships between all the factors that influence the outcome. Moreover, an ANN can represent different signal characteristics from the input information, even implicitly combining factors with no “a priori” well-defined relationship [37]. In addition, one of the primary strengths of ANNs is their remarkable ability to learn patterns and relationships from data and carry out functions such as classification, generalization, and prediction [38,39].

Thus, the variables involved in the process of conidiospore production can be modeled and analyzed through ANNs. The ANN with the best performance is used for obtaining the best conditions to maximize the number of conidiospores, and it will increase the production of conidiospores under optimal conditions.

3.5. Setting the Optimal Conditions

The ANN with the best performance has been used for the optimization of the conidiospore production. In the work of Shariati et al. [40], the authors developed a hybrid ANN algorithm with particle swarms for modeling and optimizing the behavior of channel shear connectors in a concrete block machine.

In this research work, the model with the best performance is the ANN with four hidden layers and nine, five, three, and nine neurons on each hidden layer, respectively. This ANN is used to carry out an exhaustive search of the optimum conditions to obtain the largest amount of Trichoderma harzianum conidiospores.

A Matlab^® script is implemented, considering the limit values of each variable. The culture time initiates with 48 h until it reaches the maximum limit of 136 h, with increases of 1 h. In the case of the humidity percentage, the search starts from 70% to 80%, with increases of 1%.

With this strategy, the ANN presents as a result that at 99 h, with 80% humidity, 514 million spores (5.14681 × 10⁸ spores) are produced.

4. Conclusions

The use of biocontrols is an alternative for fighting plagues instead of pesticides that affect nature, crops, and consequently, human health. Therefore, it is important to investigate which organisms can be used as biopesticides. The modeling of the production of these organisms allows for finding the optimal conditions to maximize their production.

In this study, the efficiencies of the ANNs and RSM in the modeling of conidiospore production of Trichoderma harzianum are analyzed. The ANN model shows a better performance with an R² of 0.9952 against an RSM model with an R² of 0.8284.

The best ANN is composed of four hidden layers, with nine, five, three, and nine neurons, respectively, on each hidden layer. This ANN is used to find the appropriate conditions to generate the maximum production of Trichoderma harzianum conidiospores, obtaining around 514 million (5.14681 × 10⁸) conidiospores.

Several organisms can be used as biocontrollers. Thus, for future research, the implementation of these techniques will be used for organism production. This methodology will be used with substrates with better yields in spore production, and we will be looking for the best conditions to maximize the number of spores. Furthermore, a campaign to publicize the benefits of using conidiospores as biocontrol in crops will be carried out.