Response Surface Methodology (RSM) and Artificial Neural Network (ANN) based optimization of cellulase production using Aspergillus niger in solid state fermentation of seed pods of Bombax ceiba

Otimização da produção de celulase por Aspergillus niger em fermentação em estado sólido de vagens de Bombax ceiba utilizando Metodologia de Superfície de Resposta (RSM) e Redes Neurais Artificiais (ANN)

Abstract

The bioconversion of lignocellulosic materials into valuable chemicals demands extensive research on production of cellulase from bacterial and fungal sources. Various Aspergillus species are known for cellulase production. The current study aims to the production and optimization of CMCase and FPase using Bombax ceiba as a substrate from Aspergillus niger under solid state fermentation. The response surface methodology using Box-Behnken design (BBD) and Artificial neural network have been employed to maximize the cellulase activity. The BBD utilized three factors including incubation period, moisture content and inoculum size at three levels to explore the enhanced cellulase activity. The maximum CMCase and FPase activities were found to be 84.5 IU/ml/min and 78.89 IU/ml/min respectively. Moreover, 7 days of incubation duration, 2ml inoculum volume and 60% moisture content were found to be as optimal conditions for CMCase activity. On the other hand, optimal moisture content for FPase was 20%.The results showed that model was highly significant with R² values for CMCase and FPase were obtained as 97.27% and 97.54% by RSM analysis respectively.While R² values from ANN were 97.062 and 99.231% for CMCase and FPase respectively. It is evident from the R² values that ANN capture the non linear relationship between variables more efficiently as compare to RSM. The sensitivity analysis predicts that incubation duration is most critical parameter in cellulase production. Overall, the findings support the utilization of agricultural residues for industrial enzyme production, helping to deal both economic feasibility and environmental sustainability.

Keywords
Aspergillus; cellulase; Box-Behnken design; RSM; SSF; ANN

Resumo

A bioconversão de materiais lignocelulósicos em produtos químicos de valor agregado exige pesquisas amplas sobre a produção de celulase a partir de fontes bacterianas e fúngicas. Várias espécies de Aspergillus são conhecidas pela produção de celulase. O presente estudo visa à produção e à otimização das atividade de CMCase e Fpase utilizando vagens de Bombax ceiba como substrato, a partir de Aspergillus niger, em fermentação em estado sólido. A metodologia de superfície de resposta, utilizando o delineamento Box-Behnken (BBD), e as redes neurais artificiais (ANN) foram empregadas para maximizar a atividade da celulase. O BBD utilizou três fatores — período de incubação, teor de umidade e tamanho do inóculo — em três níveis para investigar a maximização da atividade da celulase. As atividades máximas de CMCase e FPase foram de 84,5 UI/ml/min e 78,89 UI/ml/min, respectivamente. Além disso, constatou-se que um período de incubação de 7 dias, volume de inóculo de 2 ml e teor de umidade de 60% constituíam as condições ideais para a atividade de CMCase. Por outro lado, o teor de umidade ideal para a FPase foi de 20%. Os resultados demonstraram que o modelo foi altamente significativo, com valores de R² de 97,27% para CMCase e 97,54% para FPase obtidos pela análise RSM; já os valores de R² obtidos pela ANN foram de 97,062% e 99,231% para CMCase e FPase, respectivamente. Fica evidente, pelos valores de R², que a ANN captura a relação não linear entre as variáveis ​​de forma mais eficiente do que a RSM. A análise de sensibilidade prediz que a duração da incubação é o parâmetro mais crítico na produção de celulase. De modo geral, as descobertas corroboram o aproveitamento de resíduos agrícolas para a produção industrial de enzimas, contribuindo para conciliar viabilidade econômica e sustentabilidade ambiental.

Palavras-chave:
Aspergillus; celulase; delineamento Box-Behnken; fermentação em estado sólido; RSM; ANN

1. Introduction

The demand of energy is rising day by day worldwide and fossil fuels are major source of energy. However, the excessive use of fossil fuels has led to various environmental issues like global warming, energy crisis and pollution (Azni et al., 2023).This issues can only be resolved by shifting towards renewable energy sources as a sustainable alternative(Boondaeng et al., 2024; Pata, 2021).However, there is still the need of extensive research for commercialization of lignocellulosic based biotransformation method (Fatma et al., 2018).

Cellulase is considered as the main class of industrial enzymes due to its applications, acts as biocatalyst for degradation of cellulosic biomass. Cellulase is comprised of three kinds of enzymes that break beta- 1,4 glycosidic bond at different sites and named so, endoglucanase, β- glucosidase and exoglucanase. The complementary action of these three enzymes allows them to hydrolyze the bonds more effectively (Ezea, 2025). One of the limitation in commercialization is the cost of cellulases that is contributing to 50% of cost of hydrolysis. The lower enzyme activity leads to the utilization of large amount of enzymes for extensive degradation of lignocellulosic waste(Zhang et al., 2012).Because of its significance there are different efforts made to maximize its production from various microbial sources. In this case fungi are considered as new strains because of their cellulase production capability. The expense of production and development of newly discovered strains are the limitations for further discoveries. On the other hand, agricultural waste could be used as substrates (cellulose) that is less expensive (Rabby et al., 2022).

Bacteria and fungi are reported as cellulose degrading microorganisms under natural conditions.(Tengku Norsalwani and Nik Norulaini, 2012).The fungal sourced cellulases comprised of all three components of cellulase while bacteria cannot exhibit filter paper activity (FPase)(Parkash et al., 2016).Trichoderma species are efficient producers of commercial cellulases (Bahaman et al., 2021). A.niger is also considered as good producer and gaining attention for further researches (Pham et al., 2010). The synthesis on industrial scale takes place in submerged cultures, though the limitation of high cost stands there. The cellulase enzymes synthesized from Aspergillus niger are produced by using two techniques, one is submerged fermentation and other is solid-state fermentation, but the latter produces high enzyme activity (Kanakaraju et al., 2020a).SSF has an upper hand to SmF because it is cheap, energy efficient and there is less risk of contamination due to the access of fungal hyphae to substrate is in the absence of free water(Sarkar and Aikat, 2012). Fatima et al. (2024)has reported the successful production of cellulases from Trichodermaharziamumunder non-septic conditions of solid state fermentation. Multifactorial system or one-factor at a time is the traditional technique for the optimization of process parameters, this type of method is time intense and does not represent the interactive effects between components(Sarkar and Aikat, 2012).Response surface methodology is a recent tool to overcome the limitations of traditional methods. This tool designs experiments to achieve the optimum conditions of independent factors for different response values. The BBD has been widely used for optimizing the process parameters (Verma and Kumar, 2019).

Optimization of the produced enzymes is also a crucial step like in the study Cellulases from Aspergillus niger are synthesized using grape wastes in solid-state fermentation(Fatima et al., 2024). ManyAspergillus species have been optimized for high cellulase enzyme production (Sher et al., 2017).The current study aims to produce cellulase using Bombax ceiba as a cheap lignocellulosic raw material from Aspergillus niger under solid-state fermentaion. The process parameters are also optimized using statistical approach, the response surface methodology under Box-Behnken design(BBD) using Minitab software v.17 and artificial neural network using MATLAB software R2015a. However, A.niger has been extensively studied but usage of B.ceiba as a substrate has limited studies. Additionaly, the studies on interactive influence of fermentation parameters using robust approach particularly BBD are less. This research addresses this gap by utilizing a new substrate and systemic methodology for optimization of fermentation conditions.

2. Materials and Methods

2.1. Microorganisms

Aspergillus niger spores were collected from naturally contaminated bread in kitchen (Sargodha Punjab, Pakistan) waste adopting standard microbiological procedures. A small quantity of black colored spores was shifted aseptically to potato dextrose agar (PDA) plates. These PDA plates were incubated for 5-7 days at room temperature of 25-30 °C. After the completion of incubation period the characteristic colonies of black color were become visible. The subculturing of fungus was done by taking spores from PDA plates and streaked onto the slants to create large surface area for fungal growth. These slants were incubated again for 5-7 days. After the development of spores, 10ml of sterile distilled water was added to slants by gentle pipetting go make a suspension of spores(Kanakaraju et al., 2020b). These fungal cultures were then utilized in further experimental analysis.

2.2. Substrate selection

The Bombax cieba, was used as solid substrate for the fungal growth in solid state fermentation. The leaves were collected from University of Sargodha then dried overnight in hot air oven at 60°C.Then they were ground to make a fine powder.

2.3. Media preparation

The salt media was prepared to provide nutrients and moisture level for proper growth of fungal strain. The media components included in g/L [(NH₄)₂SO₄-1.0, MgSO₄-5.0, FeSO₄. 7H₂O-0.005, and KH₂PO₄-5.0](Kumar et al., 2011).

2.4. Enzyme production

To produce enzyme, 5g of fixed substrate B.ceiba was added in different volumes of nutrient media as per experimental design. These experiments were performed in 250mL Erlenmeyer flasks. After soaking the substrate in respective volumes of media, it was autoclaved at 121˚C for 15 minutes. Then production flasks were cooled and inoculated with specific volume of inoculum A.niger spores (dissolved in distilled water) with gentle pipetting in the sterile production media. The inoculum sizes were according to experimental design. The whole process is performed under strict sterile conditions. Based on specific set of combinations of media and inoculum the flasks were incubated for specific incubation periods at room temperature of 30 ˚C as chosen in design.

2.5. Extraction of crude enzyme

According to previously reported methods,the crude enzyme was extracted by adding the distilled water in fermented flasks in proportion (1:5). Then they were incubated for 1h in shaker at 120rpm. After that, the sample was filtered and centrifuged at 10000rpm in centrifuge machine (Verma and Kumar, 2019). In this way the supernatant was collected and stored in plastic bottles, to be used as crude enzyme source in further experimental analysis.

2.6. Cellulase enzyme assay

The cellulase (CMCase and FPase) activities were determined by standard method as followed by multiple researchers(Irfan et al., 2011; Liaqat et al., 2024; Shoukat et al., 2026).According to previous methods, for FPase assay 0.5ml of citrate buffer along with filter paper strips added in test tubes (experimental), on the other hand 0.5ml of CMC solution added in separate test tubes for CMCase assay. Each test tube was then impregnated with 0.5ml of crude enzyme source. After incubating the test tubes for thirty minutes at 50 ˚C in water bath, 1.5ml DNS was introduced to stop the reaction. Then tubes were placed in boiling water for 10minutes. The absorbance was measured at 540nm after cooling the tubes at room temperature. Glucose was used as standard for comparison.

2.7. Box-behnken design experimental design:

To optimize the different production parameters Box-Behnken Design was used. By Minitab software v.17 the BBD tool was used to explore the effect of independent variables and their interaction to determine the optimal conditions for cellulase activity. According to experimental design three variables were selected at three different levels. The independent variables include: incubation duration, volume of inoculum and moisture content. Table 1 shows the three variables and their levels to be optimized by a set of experiments.The CMCase and FPase activities were used as response value. A set of 15 experiments (runs) were run using definite combinations of process parameters.

Table 1
Values and coded levels of variables used in BBD for optimization.

Parameters (Independent Variables)	Units		Coded Level
		-1	0	+1
Incubation Period (M1)	Days	3	5	7
Vol.of inoculum (M2)	ml/5g	1	2	3
Moisture content ( M3)	%	20	40	60

2.8. Artificial Neural Network (ANN)

ANN modeling was performed using Neural Network Toolbox of MATLAB R2015a (The MathWorks Inc., Natick, MA, USA) software for prediction and optimization of CMCase and FPase productions. The neural network architecture included three inputs (Incubation time, Inoculmn size, and Moisture content), hidden layers, and output (enzyme activity) and thus represented a (3–n–1) architecture. The number of hidden layer neurons in the ANN that resulted in minimum root mean square error (RMSE) was optimized through iteration of the process of training many neural networks. Trainlm algorithm was applied for training of the neural network. The data set was divided into training set (70%), validation set (15%), and test set (15%). Performance of the model was measured using coefficient of determination (R2) and RMSE. The architecture of ANN model is depicted in Figure 1.

Figure 1
Architecture used for ANN analysis.

3. Results and Discussion

According to most cited researches, the statistical optimization strategy is being employed to determine the operational and much suitable conditions of process parameters. This approach could resolve the limitations of conventional methodologies (OFAT) and got an upper hand in optimization of cellulase production. In this section, response surface methodology is adopted by using Box-Behnken design consisting of 15 runs to evaluate the influence and interaction of three variables including incubation duration, inoculum size and moisture content at three levels as shown in Table 1 for cellulase production under solid state fermentation (Garai and Kumar, 2013; Verma and Kumar, 2019).

The results of BBD, in which CMCase and FPase as response values, are listed in Table 2. And optimization results are illustrated in the contour plots and observed versus predicted plots. According to the results, incubation period (7days), inoculum size (2ml) and volume of media (60%) were observed as most operative and optimal combinations for maximum CMCase activity (84.5 IU/ml/min). While the maximum FPase activity (78.89 IU/ml/min) was observed at incubation duration (7days), inoculum size (2ml) and volume of media (1ml). Almost similar results were reported in previous research, in which the cellulase exhibited maximum activity (1.290 IU/ml) after 6 days of incubation and moisture content of 76% under solid state fermentation utilizing wheat bran as a substrate by A.niger NCIM 777(Verma and Kumar, 2019).

Table 2
BBD results for CMCase and FPase experimental and predicted values (as response values).

Run	Incubation	Inoculum size(ml)	Moisture Content (%)	CMCase Activity	FPase Activity (IU/ml/min)
	time(d)
No.	(M1)	(M2)	(M3)	(IU/ml/min)
				Actual	Predicted	Actual	Predicted
1	7	2	20	78.8	77.89	78.89	75.81
2	5	3	60	53.89	52.37	36	35.13
3	5	2	40	58.7	57.05	48	49.1
4	5	2	40	58	57.05	49	49.1
5	5	2	40	54.47	57.05	50.3	49.1
6	3	3	40	57	57.05	56	53.7
7	7	3	40	64.1	64.4	49	52.0
8	5	1	20	54	55.5	48	48.86
9	7	2	60	84.5	85.65	72	69.85
10	3	2	20	64.47	63.32	59	61.15
11	3	2	60	75	75.90	65	68.07
12	3	1	40	66	65.6	61	57.988
13	5	3	20	40	40.53	33.2	33.2
14	5	1	60	64.57	64.03	48	47.93
15	7	1	40	83.7	83.08	74	76.21

It has been reported that inoculum size of 5-15% was evaluated for CMCase and Fpase (8.89U/g and 3.56 U/g)production and 10% was found to be optimum. Incubation period was also evaluated and 72h time was observed as optimum for maximum cellulase production using coir waste as a substrate under solid-state and submerged fermentation both(Mrudula and Murugammal, 2011).

In accordance with results of statistical design of another research, optimum pH of 4.8, incubation duration 156 h (6.5 days) and 65% moisture content were observed optimum in solid state fermentation with cellulase activity of 10.8 U/g (Kumar et al., 2011). The optimal conditions identified for mutant strain under solid state fermentation, were 20% moisture content, inoculum size of 25% w/w and cultivation time of 4 days utilizing aboria sawdust that was pretreated by ammonia. The p-values were compared by applying ANOVA (Babalola et al., 2015).The enhanced CMCase activity (0.0925 IU/ml) was observed in 96 hours of fermentation period by mutant A.niger utilizing saw dust as a substrate under solid state fermentation(Acharya et al., 2008).

Table 3 shows the results of ANOVA for CMCase activity in which p-value (p=0.000) indicates that this model is highly significant. In this way it is confirmed that there is strong relationship between the chosen process parameters and enzyme activity. In linear terms all three factors incubation period (p=0.000), moisture content (p=0.001) and inoculum size (p=0.000) are significant. Incubation time and inoculum size are equally significant and moisture content is less significant as compared to them. In interaction of the parameters the highly significant interaction is between incubation period and inoculum size (p=0.048).

Table 3
Significance of model terms for CMCase activity as evaluated by ANOVA.

Source	df	Adj SS	Adj MS	F-value	p-value
Model	9	2113.75	234.86	56.49	0.000*
M1- incubation period(d)	1	295.61	295.61	71.11	0.000*
M2-Inoculum size (ml)	1	354.84	354.84	85.36	0.000*
M3-Moisture Content (ml)	1	206.96	206.96	49.78	0.001*
(M1)2	1	1018.73	1018.73	245.05	0.000*
(M2)2	1	131.47	131.47	31.62	0.002*
(M3)2	1	15.15	15.15	3.64	0.115
M1M2	1	28.09	28.09	6.76	0.048*
M1M3	1	5.83	5.83	1.40	0.289
M2M3	1	2.76	2.76	0.66	0.453
Error	5	20.79	4.16
Lack-of-fit	3	10.51	3.50	0.68	0.641
Pure error	2	10.28	3.50
Total	14	2134.54

• ^*
  statistically significant effects (p < 0.05).

In addition to this, FPase activity was also analyzed by ANOVA and results are shown in Table 4 As per statistical results, the model has p=0.002 (p<0.005) that shows strong influence of selected parameters on FPase production. In terms of interaction, incubation period (M1) and moisture content (M3) shows strong relationship (p=0.035) in FPase production. The overall reliable results indicate the experimental variability.

Table 4
Significance of model terms for FPase activity as evaluated by ANOVA.

Source	df	Adj SS	Adj MS	F-value	p-value
Model	9	2390	265.61	22.06	0.002*
Linear	3
M1- incubation period(d)	1	135.22	135.22	11.23	0.020*
M2-Inoculum size (ml)	1	403.28	403.28	33.50	0.002*
M3-Moisture Content (ml)	1	0.46	0.46	0.04	0.853
(M1)2	1	1355.64	1355.64	112.61	0.000*
(M2)2	1	251.99	251.99	20.93	0.006
(M3)2	1	0.79	0.79	0.07	0.809
M1M2	1	100.00	100.00	8.31	0.035*
M1M3	1	41.54	41.54	3.45	0.122
M2M3	1	1.96	1.96	0.16	0.703
Error	5	60.19	12.04
Lack-of-fit	3	57.53	19.18	14.42	0.066
Pure error	2	2.66	1.33
Total	14	2450.68

• ^*
  Significant.

Figure 2(A) Contour chartsare showing the combined effect of inoculum size and moisture content on CMCase activity at constant incubation duration of 5 days. According to contour plot the maximum CMCase activity (>65 IU/ml/min) is exhibited at higher moisture content (50-60%) alongwith lesser inoculum size (1.3-1.6ml). Then by keeping inoculum size fixed at 2ml the maximum CMCase activity was observed at 5-6^th day of incubation and higher moisture content of 50-60% ml.The interactive effect of incubation duration and inoculum size by holding moisture content at 2ml, at which maximum activity is shown at 6-7^th day of fermentation with 1.2-1.6 ml inoculum size. While the activity is reduced at higher inoculum sizes in increased incubation period could be due to lack of nutrients and metabolic stress.

Figure 2
Contour plots illustrating interactive effect of selected parameters on CMCase (A) and FPase (B) activity.

The combined effect of moisture content and inoculum size on FPase activity is illustrated in figure 2(B) that revealed stronger effect of inoculum size as compared to moisture content as contour chart has vertical lines. The maximum Filter paper activity (>50.0 IU/ml/min) is observed at 1-1.7 ml inoculum volume and 50-60% ml moisture content at 5^th day of fermentation. The increased inoculum volume than 2.0ml resulted in decrement of FPase activity (< 40 IU/ml/min) despite increase in media volume. So, adequate moisture content (media volume) could mitigate this problem. Then maximum FPase activity (>75 IU/ml/min) is determined at longer incubation duration of 6.5-7days and media volume of 2.5-3.0 ml by holding inoculum size constant at 2ml. This contour plot reflects the stronger impact of fermentation period on FPase activity than moisture content. The interactive effect of incubation duration and inoculum size on FPase activity at fixed moisture content of 2ml. The maximum activity (>70 IU/ml/min) is at lower to medium inoculum size of 1.2-1.8 ml and incubation period of 6-7 days.

These optimized activities of FPase and CMCase validate the experimental design and response surface methodology. In addition to this the independent parameters and response relationship is also confirmed by the plots.

The maximum CMCase activity (0.20 U/g/min) by A. Tubingensiswas observedat 6^th day of submerged fermentation and 9^th day in case of SSF utilizing rice straw waste as substrate(El-Nahrawy et al., 2017). The maximum endoglucanase activity(4.47 U/ml) by A. niger ASP2 (isolated from date by-products) was determined after 96h incubation time(Bellaouchi et al., 2021).Similar results were reported by Kang et al. (2004) by A.niger KK2 utilizing lignocellulosic waste. Purpureocillium lilacinum yielded highest cellulase production(1.14 U/ml FPase and 1.77 IU/ml CMCase) after 7 days of fermentation period and 2x10⁶inoculum volume under solid state fermentation(Srilakshmi et al., 2017).

Figure 3, illustrates the desirability plot of CMCase and FPase activities (IU/ml/min). At optimum conditions, achieving maximum predicted activity of CMCase as 88.66 IU/ml/min that is very close to observed value (84.5 IU/ml/min). This plot indicates the ideal response of optimization. The optimal conditions are 7 days of incubation period, 1.28ml inoculum size and 3ml moisture content for ideal CMCase activity in account of investigated parameters. The activity of CMCase shows decrement at 3 days of incubation period, lower moisture content of 1ml and reduced inoculum size than 1.288ml.

Figure 3
Desireability plot for CMCase and FPaseactivity (IU/ml/min).

While the desirability value of 1.000 for FPase activity revealed the significant quadratic impact of all the three parameters. The predicted value of 80.77 IU/ml/min lies in close proximity to observed activity (78.5 IU/ml/min). It shows almost the same optimal values of incubation period and inoculum size. While moisture content of 1ml has shown ideal FPase activity. Overall the desirability charts confirm the reliability of the model to corresponding optimized conditions for CMCase and FPase activities.

The optimization of FPase as 7.22 IU/ml/min by increasing fermentation period to 7 days at 3% cellulose mixture and 0.35% nitrogen source ammonium sulphate(Zohri et al., 2022). The effect of different moisture levels ranging from 1:1- 1:5 on CMCase as response value on A.niger BK01 were explored. The maximum activity is reported as 10.98 U/gds at 1:2 moisture level(Aggarwal et al., 2017). The most substantial factor in solid-state fermentation is moisture content. The adequate moisture level is responsible efficient mass transfer(Liu and Yang, 2007). As high moisture level could decrease oxygen penetration while the lower level results in reduced microbial growth and accessibility to nutrients (Vu et al., 2010). The optimal levels of moisture are reported as 40-60%(Narasimha et al., 2006). Aspergillus sp. SU14 demonstrated enhanced CMCase yield at 50% moisture content utilizing wheat bran under static fermentation (Vu et al., 2011). According to another study A.niger showed maximum CMCase activity at 70% moisture level in 96h. The fungus was grown on Vigna mungo under solid state fermentation (Umbrin Ilyas et al., 2011).

The actual values of CMCase and FPase are very close to predicted ones this depicts the strong correlation of all the parameters. The graphical illustration of comparison in actual and predicted values of both CMCase and FPase activities is given in figure 4.

Figure 4
Actual versus predicted values plots for CMCase and FPase.

In this study, another statistical approach was employed named as ANN (Artificial neural network).

ANN is a computational model developed as per structure and function of human neural networks. It works by altering or learning the input and output, the dataset that passes through network alters the structure of ANN. ANN is a statistical tool that has capability of describing complex interactions between inputs and outputs. It can assess non-linear relations to discover patterns. ANN is also named as a neural network design (Qamar and Zardari, 2023). A neural network that is trained for specific dataset is considered as an expert to assess that category of information (Fan et al., 2021).

Fitness of training (a), validation, test and all data sets in ANN model for CMCase optimization, (b) Error histogram and Training stat plot (c) are shown in Figure 5. (a) Fitness of training, validation, test and all data sets in ANN model for FPase optimization, (b) Error histogram and (c) Training stat plot are shown in Figure 6. The histogram of error shows that most of the prediction errors fall near zero, which indicates good accuracy of the predictions and low bias in the output of the model. Similarly, coefficient of determination (R²=97.062%) and (R²=99.231%) for CMCase and FPase respectively and Training, validation and testing values of CMCase are 99.129%, 1% and 1% and for FPase are 99.33%, 1% and 1% respectively. Low RMSE values also indicate the good predictive ability of the model. It indicates that 70% of CCD data used for training the model have been able to train the model very well. At the same time, 15% of CCD data used for testing purpose have been able to produce optimized results. This is because on the basis of trained data, the model tests 15% data.

Figure 5
Fitness of training, validation, test and all datasets in ANN model CMCase optimization, (b) Error histogram, (c) Training state plot (CMCase IU/ml/min).

Figure 6
Fitness of training, validation, test and all datasets in ANN model FPase optimization, (b) Error histogram, (c) Training state plot (FPase IU/ml/min).

Sensitivity analysis of CMCase with respect to Moisture content levels are shown in figure 7. According to Figure, CMCase sensitivity is higher for Incubation period and moisture content, but it is lower for inoculmn size. Sensitivity analysis of FPase with respect to Moisture content levels are shown in figure 8. In the case of FPase, Sensitivity of FPase is higher for Incubation period and lower for moisture content. Similar interpretation style will be used for remaining plots. In general, the sensitivity analysis reveals that CMCase production was affected mostly by the Incubation period and moisture content, while the FPase production was largely determined by the level of Incubation period. The difference may be associated with different sensitivity of the enzymes to nutrients, and hence, the necessity to optimize their production separately. Numerical record of both CMCase and FPase of neural network which shows Quantities, Training MSE, Validation MSE, Testing MSE, Training Time, Gradient, Performance Mu ,Epoch , RMSE and R2 given in Table 5. Table 5 is showing performance statistics of ANN model in which higher R² values for both CMCase and FPase validating that ANN better assess non-linear relationships between variables.

Figure 7
Sensitivity analysis (a,b,c) for CMCase production with varied moisture content (-1,0,+1), incubation period (-1,0,+1) and fixed inoculum size (0).

Figure 8
Sensitivity analysis (a,b,c) for FPase production with varied moisture content(-1,0,+1), incubation period(-1,+1,0) and fixed inoculum size (0).

Table 5
ANN performance statistics for CMCase and FPase activity prediction.

Quantities	Training MSE	Validation MSE	Testing MSE	Training Time	Gradient	Performance	Mu	Epoch	RMSE	R2
CMCase (IU)	5.433897e-03	1.195584e-02	1.019418e-01	0.3590	1.384320e-02	3.540925e-03	1.000000e-04	22	3.0807	97.062%
FPase (IU)	1.225445e-02	7.448104e-02	3.954831e-02	0.2300	1.592095e-11	1.471912e-04	1.000000e-04	4	3.5532	99.231%

3.1. Sensitivity analysis

In this X= incubation period, Y= Inoculum size and Z= Moisture Content. Sensitivity analysis performed by taking derivatives of the coded coefficients of variables. Coefficients which have p value 0.05 or lower are significant and used for the sensitivity analysis. So, this analysis required coded coefficient values with significant p values which are calculated using Minitab software. Sensitivity plots indicate the maximum influence of incubation period on CMCase and FPaseproduction. The inoculum size has negative impact on both FPase and CMCase production due to competition and reduced nutrients with time.

3.1.1. CMCase sensitivity

The mathematical form of regression model can be defined as Equation 1:

$\begin{array}{c}\text{CMCase}={\beta }_0+{\beta }_1\text{*X}+{\beta }_2\text{*Y}+{\beta }_3\text{*Z}+{\beta }_4\text{*X*X}+\\ {\beta }_5\text{*Y*Y}+{\beta }_6\text{*Z*Z}+{\beta }_7\text{*X*Y}+{\beta }_8\text{*X*Z}+{\beta }_9\text{*Y*Z}\end{array}$ (1)

Based on P-Value, we can write the expression of regression as Equation 2:

$\begin{array}{c}\text{CMCase}=57.06+6.079\text{*X}-6.660\text{*Y}+\\ 5.086\text{*Z}+16.61\text{*X*X}-5.97\text{*Y*Y}-2.65\text{*X*Y}\end{array}$ (2)

The sensitivity analysis can be calculated by taking derivatives of above expression as Equations 3, 4 and 5:

$\frac{\partial \left(\text{CMCase}\right)}{\partial X}=6.079\text{X}+33.22\text{X}-2.65\text{Y}$ (3)

$\frac{\partial \left(\text{CMCase}\right)}{\partial Y}=-6.660\text{Y}-11.94\text{Y}-2.65\text{X}$ (4)

$\frac{\partial \left(\text{CMCase}\right)}{\partial Z}=5.086\text{Z}$ (5)

3.1.2. FPase sensitivity

The mathematical form of regression model can be defined as Equation 6:

$\begin{array}{c}\text{FPase}={\beta }_0+{\beta }_1\text{*X}+{\beta }_2\text{*Y}+{\beta }_3\text{*Z}+{\beta }_4\text{*X*X}+\\ {\beta }_5\text{*Y*Y}+{\beta }_6\text{*Z*Z}+{\beta }_7\text{*X*Y}+{\beta }_8\text{*X*Z}+{\beta }_9\text{*Y*Z}\end{array}$ (6)

Based on P-Value, we can write the expression of regression as Equation 7:

$\begin{array}{c}\text{FPase}=49.10+4.11\text{*X}+-7.10\text{*Y}+\\ 19.16\text{*X*X}-8.26\text{*Y*Y}-5.00\text{*X*Y}\end{array}$ (7)

The sensitivity analysis can be calculated by taking derivatives of above expression as Equations 8 and 9

$\frac{\partial \left(\text{FPase}\right)}{\partial X}=4.11\text{X}+38.32\text{X}-5.00\text{Y}$ (8)

$\frac{\partial \left(\text{FPase}\right)}{\partial Y}=-7.10\text{Y}-16.52\text{Y}-5.00\text{X}$ (9)

4. Conclusion

In conclusion, the recent study effectively revealed the capability of Bombax ceiba as a potent and economically feasible raw material for enhanced cellulase production from Aspergillus niger. The statistical tool (Box-Behnken design) demonstrated as a robust technique to achieve the optimized levels of process parameters for improved FPase and CMCase activities in short time and experimental runs. ANN is found to be the most advanced tool for determination of optimized conditions with more precision and accuracy. Results showed that model was highly significant with R² values for CMCase and FPase were obtained as 97.27% and 97.54% by RSM analysis respectively.While R² values from ANN were 97.062 and 99.231% for CMCase and FPase respectively. So, It is clear from the coefficient of determination R² values that ANN capture the non linear relationship between variables more efficiently and effectively as compare to RSM. The optimized conditions and combined effects ensure the validity and reproducibility of the model. Taken together, the findings of investigation provided valuable information on utilization of agricultural raw material and strong basis for further industrial applications of cellulases in bioprocesses. As, the maximum CMCase and FPase activities were found to be 84.5 IU/ml/min and 78.89 IU/ml/min respectively. Moreover, 7 days of incubation duration, 2ml inoculum volume and 60% moisture content were found to be as optimal conditions for CMCase activity. Future studies should focus on pilot-scale fermentation, purification and biochemical characterization of cellulases, long-term stability assessment, techno-economic analysis, and evaluation of enzyme performance in industrial bioprocesses.

Data Availability Statement

The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.

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*

e-mail: [e-mail]; [e-mail]

Editor:

Takako Matsumura Tundisi

Publication Dates

• Publication in this collection
  25 Sept 2026
• Date of issue
  2026

History

• Received
  29 May 2026
• Accepted
  17 Aug 2026