Penicillium oxalicum BGPUP-4, an isolate from our laboratory (Punjabi University, Patiala, India), was used for the production of inulinase. The fungal culture was maintained on potato dextrose agar (PDA; HiMedia Laboratories Pvt. Ltd., Mumbai, India) slants as described previously (11).

Inoculum was prepared by growing a stock culture of P. oxalicum BGPUP-4 in Erlenmeyer flasks containing PDA at 30 °C for 5 days. After incubation, fungal spores were harvested and suspended in sterile distilled water containing 0.01% (by volume) Tween 80 (HiMedia Laboratories Pvt. Ltd). The spores were dislodged from the hyphae with the aid of a sterile glass rod. Thereafter, the spore suspension was filtered through a sterile absorbent cotton wool plug to remove any remaining traces of hyphal fragments. The number of spores was counted using a haemocytometer (model BR718920; Sigma-Aldrich, St. Louis, MO, USA) and microscope (model CH20i; Olympus Opta Systems Pvt. Ltd, New Delhi, India). The number of spores in the inoculum was adjusted to 10⁴ spore/mL with presterilized distilled water, under aseptic conditions.

Fresh carrots were procured from the local market, Patiala, India. After thorough washing, they were crushed properly in a juice extraction machine (Philips India Ltd., Gurgaon, India) to obtain juice. Carrot residue obtained after the extraction was pressed and dried in an oven (Narang Scientific Works Pvt. Ltd, New Delhi, India) at 50 °C, until it dehydrated completely. The dried carrot pomace was ground using mortar and pestle to uniform powder and passed through a 150-µm sieve.

Solid-state fermentations (SSF) were carried out in Erlenmeyer flasks (250 mL) containing 10 g of carrot pomace moistened with distilled water containing (in %, mass per volume): inulin 0.5, NaNO₃ 0.2, KH₂PO₄ 0.2, KCl 0.1, MgSO₄·7H₂O 0.05, FeSO₄·7H₂O 0.001 and NH₄H₂PO₄ 0.2 (all from HiMedia Laboratories Pvt. Ltd.). Three variables optimized for inulinase production using statistical experimental model are A: moisture content (70-90%), B: incubation time (4-6 days) and C: pH (5-7), while the other above-mentioned medium constituents were kept constant during the progression of the study. The Erlenmeyer flasks were sealed with hydrophobic cotton and autoclaved at 121 °C for 30 min. Preliminary studies showed no changes in the moisture content of the substrate after autoclaving. After cooling, the flasks were inoculated with previously prepared 2 mL of spore suspension (10⁴ spore/mL) and mixed uniformly with a sterile glass rod, under aseptic conditions. Subsequently, flasks were incubated in an environmental chamber (model CHM-10 Plus; REMI Lab World, Mumbai, India) with temperature and humidity control.

Optimization of fermentation conditions is an important factor in developing feasible bioprocess to obtain desirable product. Optimal processing conditions can be constituted using an efficacious statistical experimental model. Central composite rotatable design (CCRD) used in response surface methodology (RSM) is a collection of several statistical models and has been employed to study the influence of three different variables and their combined interactions on inulinase production by P. oxalicum BGPUP-4. Statistical analysis was carried out using Design expert v. 7.0.0 software package (Stat-Ease Inc., Minniapolis, MN, USA). The variables were optimized using 2³ factorial design. The five coded levels used to study three independent variables were -1.414, -1, 0, 1 and 1.414 (Table 1). CCRD produced a total of 15 combinations which comprised four factorial and six axial points, and five replicates at the centre point. The experimental runs 1, 3-5 and 14 at the centre point were used to find experimental inaccuracy and duplicability of the results. All the experiments were carried out in triplicates. To substantiate the model’s accuracy, validation of experiments was performed to equate predicted and experimental results.

Inulinase production and I/S ratio were the two responses on which the influence of three chosen independent variables was anticipated. A multiple regression analysis of experimental data obtained from an empirical model was accomplished using least square method, to fit into the following second-order polynomial equation:Y=β₀+∑β_iX_i+∑β_iiX_i²+∑ β_ijX_iX_j /1/where Y is measured response, β₀ is the intercept term, β_i is linear coefficient, β_ii is quadratic coefficient, β_ij is an interaction coefficient and X_i and X_j represent coded independent variables. The statistical implication of the model was revealed through analysis of variance (ANOVA) for polynomial model with 95% confidence level. Student’s t-test and Fisher’s F-test were also applied to ascertain statistical significance of regression coefficients and to evaluate significance of second-order model equation and terms. Besides, the excellence of the polynomial model can be exhibited in terms of coefficient of determination (R²), adjusted R² and adequate precision. The value of R² is important to explain the variability in the observed responses with respect to experimental factors and interactions between them. Moreover, 2D contour plots were also analysed to study interaction between each variable and its corresponding effect.

After successful fermentations, the extracellular enzyme was extracted by adding 100 mL of sodium acetate buffer (0.1 M, pH=5.0; HiMedia Laboratories Pvt. Ltd) to the fermented substrate in Erlenmeyer flasks. The content of each flask was kept under agitation (150 rpm) on a rotary incubator shaker (model CIS-24 BL; REMI Lab World) for 2 h at 30 °C for enzyme extraction. Thereafter, the extract was filtered through Whatman No. 1 filter paper and centrifuged at 3000×g (model REMI CPR-30 Plus; REMI Elektrotechnik Ltd., Mumbai, India) for 10 min at 4 °C. Supernatant was collected as crude inulinase produced by SSF. It was then analysed for inulinase and invertase activities. Inulinase/invertase activity ratio (I/S) was also calculated.

Moisture content, incubation time and pH were considered as significant variables for statistical optimization of inulinase production from carrot pomace in SSF. The experimental design matrix was calculated using CCRD. Linear, 2F1, quadratic and cubic models were analysed to find the regression equation of the experimental data. The experimental design and the results obtained after statistical optimization of the two responses, i.e. inulinase production and I/S ratio are shown in Table 2. A suitable model, i.e. quadratic model chosen because of high F value, was assessed on the basis of sequential sum of squares and analysis of variance (ANOVA) results. The F value is the ratio of the mean squares of the regression and the mean squares of the error, which specifies the significance of each factor in the model (13). The higher F values of 1173.87 and 104.75 for inulinase production and I/S ratio, respectively, justify the significance of the model. The experimental results corresponded with a second order polynomial equation. The values of regression coefficients were calculated and the fitted equations (in terms of coded values) for predicting inulinase production and I/S ratio, regardless of the coefficient significance were as given below:Inulinase production=+274.81+1.59·A–11.14·B+0.035·C–12.21·A·B+1.21·A·C–4.11·B·C+4.54·A²+9.59·B²+2.84·C² /2/ I/S=+4.08–0.19·A–0.046·B–0.088·C–0.22·A·B–0.30·A·C–0.24·B·C–0.21·A²–0.25·B²– 0.18·C² /3/ Table 2

Run	Factor*			Experimental results		Predicted results
	A	B	C	Inulinase productionIU/g	I/S	Inulinase productionIU/g	I/S
1	80.00	5.0	6.0	275.00	4.09	274.55	4.11
2	80.00	3.6	6.0	309.80	3.63	310.25	3.39
3	80.00	5.0	6.0	274.00	4.04	274.55	4.11
4	80.00	5.0	6.0	275.30	3.94	274.55	4.11
5	80.00	5.0	6.0	275.20	4.11	274.55	4.11
6	90.00	4.0	7.0	322.10	3.38	321.61	3.33
7	80.00	5.0	7.4	280.60	3.68	281.18	3.54
8	80.00	5.0	4.6	279.50	3.83	280.08	3.42
9	70.00	6.0	7.0	291.80	3.94	291.13	4.35
10	90.00	6.0	5.0	272.70	3.74	272.03	4.27
11	70.00	4.0	5.0	286.20	3.03	285.71	3.24
12	65.86	5.0	6.0	281.70	3.92	282.28	4.11
13	80.00	6.4	6.0	278.30	5.63	279.01	4.84
14	80.00	5.0	6.0	274.40	4.08	274.55	4.11
15	94.14	5.0	6.0	286.20	4.11	286.78	4.11

*Symbols A, B and C are the same as in Table 1

The statistical relevance of Eqs. 2 and 3 for response surface quadratic model was established by ANOVA. Statistical data given in Table 3 indicate that the model is highly significant. Fisher’s F-test and student’s t-test were used to determine significance of the coefficients of the independent variables. Higher F value and smaller probability>F value confirm the significance of the corresponding coefficient term. The probability>F value less than 0.05 suggests the significance of each coefficient. It is necessary to define the pattern of interaction between the two coefficients (Table 4). The smaller the probability>F value, the more significant the corresponding coefficient (14-17). A, B, C, AB, AC, BC, A², B² and C² are the significant model terms for inulinase production. Amongst them, B, AB, BC, A², B² and C² were extremely significant (p>0.0001). For I/S ratio, A, B, C, AB, AC, BC, A², B² and C² were also significant, but A², B² and C² were the most significant terms (p>0.0001). The degree of freedom for pure error for both, inulinase production and I/S ratio, was 4, which once more manifests the authenticity of the models. Probability>F and F values of the lack-of-fit for inulinase production were 0.7075 and 0.16, while for I/S ratio they were 0.2441 and 1.86, respectively. This implies that the lack-of-fit is not significant compared to the pure error, which justifies the fitness of the quadratic model for the present study.

The goodness of fit of the model is shown in Table 5. Multiple correlation coefficient R is a scalar, which is used to define the correlation between the actual and predicted values of the variable. The higher R values of 0.9995 and 0.9947 for inulinase production and I/S ratio, respectively, showed good agreement between actual and predicted values. The adjusted R² and predicted R² were 0.9987 and 0.9973 for inulinase production, and 0.9852 and 0.8134 for I/S ratio, respectively. A minute difference between the adjusted R² and predicted R² showed reasonable agreement between the two values. Adequate precision measures the signal to noise ratio. A ratio greater than 4 is advisable, therefore, the ratio of 118.71 and 32.61 for inulinase production and I/S ratio, respectively, indicates an adequate signal for the present model and suggests that the model can be used to navigate the design space.

The quadratic models in Eqs. 2 and 3 have nine terms comprising three linear terms, three quadratic terms and three two-factorial interactions. Out of these terms, the insignificant terms (p>0.05) were found only in Eq. 2, which were neglected, resulting in the following equation:

The effect of three independent variables on inulinase production and I/S ratio was studied. Fig. 1 and Fig. 2 show response surface contour plots of the two responses. These plots demonstrate pairwise combination of factors, while keeping the third one at its optimal level. Moreover, they also highlight the role of each factor. The effects of different combinations of the three variables were interpreted. It is apparent from the plots that moisture content has a profound effect on inulinase production, which increases with the increase in moisture content. Maximum inulinase production was obtained at moisture level of 90%, while at its further increase, decrease in inulinase production was observed (Figs. 1a and 1b). Similar response of moisture content on inulinase production by Pichia guilliermondii in SSF has also been reported (18). Nuñez-Gaona et al. (19) also reported that only a certain level of moisture is enough to accelerate nutrient absorption, normal metabolic function and fungal conidial production. Requirement of moisture content can vary from species to species. Generally, minimum of 20% of moisture level is essential for fungal growth, while very high moisture content may retard conidial induction (19). The increase in pH up to 7.0 has also shown a significant influence on inulinase production. However, further increase in pH decreased the inulinase production (Figs. 1b and 1c). A small change in ion balance can instantly affect fungal growth by creating alterations in its cell surface, which concatenates enzyme production or reduction. Our findings are in abidance with the results obtained with Pichia guilliermondii (18), A. niger (20) and Kluyveromyces marxianus (21), where maximum inulinase production was reported at pH close to 7.0. Incubation time is also a pivotal factor for enzyme production. It has been reported that incubation period influences pH of the medium. With extended incubation period, CO₂ or acidic metabolites released by aerobic microbial cells accumulate in the medium, which makes it slightly acidified (22). P. oxalicum BGPUP-4 produced maximum inulinase after 4 days of incubation. After 4 days of fermentation, a slight decrease in inulinase production was observed, which may be attributed to secretion of proteases into the medium that denature the enzyme by hydrolysing peptide bonds between amino acids. Additionally, change in medium optimal conditions with incubation time may also have contributed to inulinase inhibition. Our results corroborate the findings on inulinase production by Bacillus safensis (23) and Penicillium funiculosum (24).

Many microbial sources have been reported to possess remarkable invertase activity along with inulinase activity. This mainly occurs due to the specificity of single active site of an enzyme for both inulin and sucrose as substrates. Hence, I/S ratio is used to distinguish the catalytic activity of the enzyme and to determine its inulinase or invertase activity. I/S ratio greater than 10^-2 determines inulinase activity, while ratio lower than 10^-4 demonstrates invertase activity (25). In the present study, maximum inulinase was produced at I/S ratio of 3.38. High I/S ratio confirmed the inulolytic nature of the produced enzyme. Moreover, I/S ratio obtained from all 15 experimental combinations was also very high, which confirms the conformational specificity of the enzyme active site for inulin only. Other fungal sources such as Aspergillus parasiticus, P. spinulosum and Trichoderma viride have also been reported to show high I/S ratio, i.e. 1.61, 1.79 and 2.6, respectively (26), which however, is lower than the ratio obtained in the present work.

The interactive effect of moisture content and pH on inulinase production and I/S ratio is shown in Figs. 1b and 2b. At pH=7.0 and moisture content of 90%, maximum inulinase production was obtained, while at very low and high pH and moisture content, a reduction in inulinase production was observed. Our results are in accordance with the fact that most of the fungi show optimal growth in slightly acidic or neutral environment. Moreover, extremely high or low moisture content do not induce proper fungal growth, which further pronouncedly reduces metabolite production. Interaction of fermentation time with moisture content and pH also showed a significant effect on inulinase production and I/S ratio (Figs. 1a, 1c, 2a and 2c). Fermentation time of 4 days, moisture content of 90% and pH=7.0 were observed to be optimal for inulinase production. However, fermentation time beyond 4 days decreased the inulinase yield from 322.10 to 272.70 IU per g of dry substrate. This may be attributed to protease secretion into the medium, diminution of important medium constituents or accumulation of secondary metabolites. Decrease in inulinase production also showed a significant effect on I/S ratio.

The predicted values of inulinase production and I/S ratio obtained from the designed model at optimized conditions (moisture content 90%, incubation time 4 days and pH=7.0) were 321.61 IU per g of dry substrate and 3.33, respectively. To testify the validation of the model for predicting inulinase production and I/S ratio, experimental trial was conducted in triplicates using optimized conditions. The performed experiments yielded 322.10 IU per g of dry substrate and 3.38 for inulinase production and the corresponding I/S ratio, respectively. Comparison between these values indicates good agreement between experimental and predicted data, which verifies the validity of current model and existence of an optimal point.