Preparative Biochemistry & Biotechnology, 45:158–172, 2015 Copyright # Taylor & Francis Group, LLC ISSN: 1082-6068 print/1532-2297 online DOI: 10.1080/10826068.2014.907177
Optimization and Kinetic Modeling of Cell-Associated Camptothecin Production from an Endophytic Fusarium oxysporum NFX06 Sogra Fathima Musavi, Abhinandan Dhavale, and Raj Mohan Balakrishnan Department of Chemical Engineering, National Institute of Technology, Surathkal, Karnataka, India The production of cell-associated camptothecin (CPT) from an endophytic fungus Fusarium oxysporum NFX06 isolated from Nothapodytes foetida and its kinetics studies were proposed. Response surface methodology (RSM) based on central composite design (CCD) was used to construct a model to describe the effects of substrate concentration. Three independent variables (dextrose, peptone, and MgSO4) were successfully employed to study the yield of CPT under submerged fermentation. The maximum yield of CPT obtained from CCD was about 598.0 ng=g biomass. The model-validated optimum predicted CPT yield and experimental CPT yield from the biomass were found to be 628.08 ng=g and 610.09 ng=g at the concentrations of dextrose 42.64 (g=L), peptone 9.23 (g=L), and MgSO4 0.26 (g=L) respectively. The predicted yield of CPT was 4.90% higher than the value obtained from CCD and 2.85% higher than the value obtained from experiment conducted at optimum conditions. The kinetic parameters, maximum specific growth rate lmax ¼ 1.212 day1, growth-associated CPT production coefficient (a ¼ 29.35 ng=g biomass), and non-growth-associated CPT production coefficient (b ¼ 0.03 ng CPT=g biomass-day) were obtained. The logistic model was found suitable to predict mycelial growth with a high determination coefficient (R2). Luedeking–Piret and modified Luedeking–Piret models were employed to represent the product kinetics and substrate consumption kinetics. A good concurrence was found between the experimental and predicted values, representing that the unstructured models were able to illustrate the fermentation profile effectively. Keywords camptothecin (CPT), Fusarium oxysporum, modeling, Nothapodytes foetida, response surface methodology (RSM)
INTRODUCTION Camptothecin (CPT), a monoterpene indole alkaloid, is a potent natural anticancer drug. It was first isolated from a Chinese deciduous tree Camptotheca acuminate Decne.[1] Later it was isolated from a variety of plant species including Merriliodendron megacarpum, Nothapodytes nimmoniana, Ophirrohiza mungos, Ophirrohiza pumila, Eravatamia heyneana, and Mostuea Address correspondence to Raj Mohan Balakrishnan, Associate Professor, Department of Chemical Engineering, National Institute of Technology, Surathkal–575 025, Karnataka, India. E-mail: [email protected] Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lpbb.
MODELING OF CELL-ASSOCIATED CAMPTOTHECIN PRODUCTION
159
brunonis as reported.[2] Among these, the highest concentration of CPT has been reported from Nothapodytes foetida (Icacinaceae), which inhabits Western Ghats, India.[3] CPT is well known for its pharmacological properties, such as its amazing inhibitory action against tumor cells,[4] and also for its activity against human immunodeficiency virus (HIV).[5] Several attempts have been made to produce CPT from plant cells and tissue cultures but the yield has been found to be low.[6] Moreover, the overexploration of this source led to the plant being an endangered species all over the globe.[7] Hence the production of CPT from endophytes came into existence. Bacon and White[8] described endophytes are microbes that colonize living, internal tissues of plant without causing any immediate, overt negative effect. As reported by various researchers, endophytic fungi represent an important and quantifiable component of fungal diversity, with an estimate of at least 1 million species.[9–11] They are found in nearly all plant families and have been investigated to be a rich resource of novel biological active secondary metabolites such as antibiotics, antimycotics, immunosuppresants, and anticancer compounds.[12] The production of CPT and its analogues isolated from endophytes of the host plant N. foetida have been reported in the literature.[13–16] Developing a process for maximizing the production of CPT by standardization of media components is crucial. Media optimization by classical method is laborious and time-consuming. An alternative and more competent move toward microbial fermentation is the use of statistical methods.[17] Response surface methodology (RSM) is one such method widely used for optimization of medium components in fermentation processes.[18–24] It is also used to explain the mutual effects of all factors in the fermentation process.[25] It combines an experimental approach with mathematical methods and statistical presumption for constructing and exploring functional correlation between response variables and a set of design variables.[26] Several researchers have reported the kinetics of microbial growth and substrate utilization.[27–30] However, there is no report on the growth, substrate utilization, and production kinetics of an endophytic fungus. Hence, the objective of this study is to enhance the production of cell associated CPT by optimization of simple media components using RSM and to study the kinetic modeling of growth, substrate consumption, and product formation by an endophytic fungus, Fusarium oxysporum NFX06.
MATERIALS AND METHOD Microorganism and Culture Conditions The cell-associated CPT-producing endophytic fungus was isolated from leaves of Nothapodytes foetida. The endophytic fungus F. oxysporum NFX06 was identified based on internal transcribed spacer (ITS) sequence analysis. The nucleotide sequence of NFX06 was submitted in the Genbank with an accession number KC914432. The culture was maintained on potato dextrose agar (PDA) slants and stored at 4 C. The spore suspension was prepared by dispersing (1 cm 1 cm) mycelial agar plug taken from an actively growing colony in a solution containing Tween 80 (0.1% v=v), filtered using Whatmann No. 1 filter paper and counted for number of spores in colony-forming units using a hemocytometer. One hundred microliters of spore suspension was used as inoculum for fermentation under a shake-flask condition.
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Shake-Flask Experiments The preliminary shake-flask studies were carried out in a medium containing (g=L) dextrose, 40.0; peptone, 7.5; KH2PO4, 0.60; MgSO4 7H2O, 0.4; and ZnSO4 7H2O, 0.88, for growthand cell-associated CPT production. The initial pH of the medium was adjusted to pH 5.4. The media and the salts were autoclaved separately at 121 C for 20 min and mixed together after cooling. Fermentation was carried out at 26 2 C, 120 rpm, for a period of 8 days. Response Surface Method: Central Composite Design (CCD) Response surface methodology using central composite design (CCD) was applied to model the cell-associated CPT production. This approach involves full factorial search by investigative instantaneous, methodical, and competent discrepancy of three important parameters. Concentrations of dextrose (X1), peptone (X2), and MgSO4 (X3) were chosen as the independent variables, identifying possible interaction and higher order effect, and determining the optimum operational conditions. A 23 factorial design augmented by 6 axial points (a ¼ 1.682) and 6 replicates at the center point was implemented in series of 20 experiments, wherein the effect of each component on CPT was the dependent response variable. Five level of variation were selected for each variable as shown in Table 1. To simplify the calculation, the independent variable coded as Z was used, Z ¼ ðX X0 Þ=DX
ð1Þ
where X corresponds to natural value, X0 is the natural value in the center of the domain, and DX is the increment of X corresponding to one unit of Z. Experimental data were fitted to a second-order polynomial model as given in Eq. (2) and the coefficients were obtained using multivariant regression analysis: y ¼ A0 þ
3 X
Ai Xi þ
i¼1
3 X i¼1
Aii Xi2 þ
2 3 X X
ð2Þ
Aij Xij
i¼j j¼iþ1
where y ¼ response function, A0 ¼ intercept, Ai, Aii, Aij ¼ coefficients of the linear, quadratic, and interactive terms, respectively, and Xi and Xij are level of independent variables. The model was used to evaluate the response based on the effect of each independent variable. Three additional TABLE 1 Independent Variables and Their Coded and Actual Values Used in the Response Surface Design Actual values Coded values (Z) –1.628 –1 0 1 1.628
X1-Dextrose (g=L)
X2-Peptone (g=L)
X3-MgSO4 (g=L)
23.18 30.0 40.0 50.0 56.83
3.33 5.0 7.5 10.0 11.7
0.07 0.2 0.4 0.6 0.73
MODELING OF CELL-ASSOCIATED CAMPTOTHECIN PRODUCTION
161
confirmation experiments were conducted to verify the validity of the statistical experimental strategies. Statistical Analysis Design-Expert software (version 8.0.7.1 Stat-Ease, Inc., Minneapolis, MN) was used to analyze the experimental data. The significance of each coefficient was determined using the F-test and p value; p < 0.05 was considered to be statistically significant. Extraction of Cell-Associated Camptothecin Extraction of cell-associated CPT from mycelium was carried out with some modifications.[31] The mycelia were dried at 60 C in a hot-air oven until they attained constant moisture content within 24 hr of the drying period. The dried samples were ground to fine powder using pestle and mortar. About 1 g of fine tissue powder from each of the samples was extracted with 61% of ethanol at 60 C in a shaking water bath. After cooling to room temperature, the extract was concentrated using a rotary vacuum evaporator (Superfit, India). The milky residue obtained was again extracted thrice with 4:1 ratio of chloroform and methanol. It was then concentrated and centrifuged at 10,000 rpm for 10 min at 10 C. The supernatant was then passed through a 0.22-mm filter (Tarsons, India) and analyzed for the presence of CPT using a Perkin Elmer (USA) LS55 fluorescence spectrophotometer. Determination of Camptothecin An initial analysis was carried out to determine the wavelengths at which maximum intensity is exhibited by the pure CPT (Sigma Aldrich, India). The standard was prepared and 10 ng=mL of pure CPT was scanned spectrofluorimetrically to obtain the excitation and emission wavelengths.[32] The kmax (370 nm) shown by pure CPT has an excitation at 369 nm and emission at 423 nm. A stock solution of CPT was prepared by dissolving 1 mg of standard CPT in 4:1 ratio of chloroform and methanol, and further dilutions were made using methanol to prepare the working solution of 2–10 ng=mL. A calibration curve between concentration of standard CPT and the intensity of fluorescence was plotted and the concentration of cell associated CPT in the sample was determined using the regression equation of Eq. (3): Y ¼ 34:272 X 38:057
ð3Þ
RESULTS Experimental Design Model Fitting and Analysis of Response for Optimization of CPT Production RSM is a sequential procedure for efficient and rapid determination of optimum value of any process parameter.[33] It is also determines statistically the importance of individual factors,
162
MUSAVI ET AL.
appropriateness of the functional form and sensitivity of response on each factor.[34] The range and levels of experimental variables investigated in this study were presented in Table 1. The central values (zero level) chosen for experimental design were X1-dextrose 40 (g=L), X2peptone 7.5 (g=L), and X3-MgSO4 0.6 (g=L). The results of CCD experiments for studying the effects of three independent variables, namely, dextrose, peptone, and MgSO4, on cell-associated CPT production are presented in Table 2 along with the predicted and actual responses. The application of RSM yielded the following regression equation: CPT ¼ þ597:52 þ 72:75X1 þ 35:06X2 53:54X3 0:25X1 X2 18:75X1 X3 14:25X2 X3 58:53X21 65:08X22 51:99X23
ð4Þ
where Y is CPT yield, and X1, X2, and X3 are the coded values of dextrose, peptone, and MgSO4, respectively. Statistical testing of the model was done by Fisher’s statistical test for analysis of variance (ANOVA) and the results are shown in Table 3. The calculation of regression analysis gave the value of the determination coefficient (R2 ¼ 0.9628). This implies that 96.28% of the experimental data of the CPT production was compatible with the data predicted by the model and only 3.72% of the total variations are not explained by the model. The value of the adjusted determination coefficient (Adj R2 ¼ 0.9256) was also high to advocate for a high significance of the model with F-value of 259.55. In this case the Adj R2 value was 92.56% which was lesser than the R2 value of 96.28%. The predicted R2 of 61.76% was in reasonable agreement with the Adj R2 of 92.56%. TABLE 2 Central Composite Design Matrix for Independent Variables in Uncoded Units Along with Experimental and Predicted Values of CPT Run order 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
X1
X2
X3
CPT(ng=g) actual
CPT(ng=g) predicted
Residual
40.00 40.00 40.00 40.00 30.00 30.00 30.00 50.00 30.00 50.00 50.00 50.00 40.00 23.18 56.81 40.00 40.00 40.00 40.00 40.00
7.50 7.50 7.50 7.50 10.0 10.0 5.00 10.0 5.00 10.0 5.00 5.00 7.50 7.50 7.50 7.50 3.29 11.70 7.50 7.50
0.400 0.400 0.400 0.400 0.200 0.600 0.200 0.600 0.600 0.200 0.600 0.200 0.400 0.400 0.400 0.063 0.400 0.400 0.730 0.400
598.00 593.14 596.07 596.25 408.17 322.04 337.22 424.13 325.26 568.10 411.11 515.15 594.48 302.08 580.00 574.13 320.22 525.26 345.23 595.12
591.48 591.48 591.45 591.48 427.47 329.40 328.36 436.90 287.23 609.97 395.79 511.80 603.54 315.00 560.33 546.50 360.53 478.44 366.45 603.55
6.52 1.66 4.62 4.77 –19.30 –7.36 8.86 –12.77 38.03 –41.87 15.32 3.35 –9.06 –12.92 19.67 27.63 –40.31 46.82 –21.22 –8.43
MODELING OF CELL-ASSOCIATED CAMPTOTHECIN PRODUCTION
163
TABLE 3 Analysis of Variance (ANOVA) for Quadratic Model Source Model X1 X2 X3 X1X2 X1X3 X2X3 X21 X22 X23 Residual Lack of fit Pure error
Sum of square
Degree of freedom
Mean square
F Value
p Value
2.57 72280.08 16784.12 16784.12 0.50 2812.50 2812.50 49338.70 60981.10 38928.40 9947.68 9934.43 13.25
9 1 1 1 1 1 1 1 1 1 1 5
28595.5 72280.1 16784.1 39141.7 0.5 2812.5 1624.5 49338.7 60981.1 38928.4 1105.3 1986.2
25.87 65.39 15.19 35.41 4.524 2.54 1.47 44.64 55.17 35.22
Optimization and Kinetic Modeling of Cell-Associated Camptothecin Production from an Endophytic Fusarium oxysporum NFX06 Sogra Fathima Musavi, Abhinandan Dhavale, and Raj Mohan Balakrishnan Department of Chemical Engineering, National Institute of Technology, Surathkal, Karnataka, India The production of cell-associated camptothecin (CPT) from an endophytic fungus Fusarium oxysporum NFX06 isolated from Nothapodytes foetida and its kinetics studies were proposed. Response surface methodology (RSM) based on central composite design (CCD) was used to construct a model to describe the effects of substrate concentration. Three independent variables (dextrose, peptone, and MgSO4) were successfully employed to study the yield of CPT under submerged fermentation. The maximum yield of CPT obtained from CCD was about 598.0 ng=g biomass. The model-validated optimum predicted CPT yield and experimental CPT yield from the biomass were found to be 628.08 ng=g and 610.09 ng=g at the concentrations of dextrose 42.64 (g=L), peptone 9.23 (g=L), and MgSO4 0.26 (g=L) respectively. The predicted yield of CPT was 4.90% higher than the value obtained from CCD and 2.85% higher than the value obtained from experiment conducted at optimum conditions. The kinetic parameters, maximum specific growth rate lmax ¼ 1.212 day1, growth-associated CPT production coefficient (a ¼ 29.35 ng=g biomass), and non-growth-associated CPT production coefficient (b ¼ 0.03 ng CPT=g biomass-day) were obtained. The logistic model was found suitable to predict mycelial growth with a high determination coefficient (R2). Luedeking–Piret and modified Luedeking–Piret models were employed to represent the product kinetics and substrate consumption kinetics. A good concurrence was found between the experimental and predicted values, representing that the unstructured models were able to illustrate the fermentation profile effectively. Keywords camptothecin (CPT), Fusarium oxysporum, modeling, Nothapodytes foetida, response surface methodology (RSM)
INTRODUCTION Camptothecin (CPT), a monoterpene indole alkaloid, is a potent natural anticancer drug. It was first isolated from a Chinese deciduous tree Camptotheca acuminate Decne.[1] Later it was isolated from a variety of plant species including Merriliodendron megacarpum, Nothapodytes nimmoniana, Ophirrohiza mungos, Ophirrohiza pumila, Eravatamia heyneana, and Mostuea Address correspondence to Raj Mohan Balakrishnan, Associate Professor, Department of Chemical Engineering, National Institute of Technology, Surathkal–575 025, Karnataka, India. E-mail: [email protected] Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lpbb.
MODELING OF CELL-ASSOCIATED CAMPTOTHECIN PRODUCTION
159
brunonis as reported.[2] Among these, the highest concentration of CPT has been reported from Nothapodytes foetida (Icacinaceae), which inhabits Western Ghats, India.[3] CPT is well known for its pharmacological properties, such as its amazing inhibitory action against tumor cells,[4] and also for its activity against human immunodeficiency virus (HIV).[5] Several attempts have been made to produce CPT from plant cells and tissue cultures but the yield has been found to be low.[6] Moreover, the overexploration of this source led to the plant being an endangered species all over the globe.[7] Hence the production of CPT from endophytes came into existence. Bacon and White[8] described endophytes are microbes that colonize living, internal tissues of plant without causing any immediate, overt negative effect. As reported by various researchers, endophytic fungi represent an important and quantifiable component of fungal diversity, with an estimate of at least 1 million species.[9–11] They are found in nearly all plant families and have been investigated to be a rich resource of novel biological active secondary metabolites such as antibiotics, antimycotics, immunosuppresants, and anticancer compounds.[12] The production of CPT and its analogues isolated from endophytes of the host plant N. foetida have been reported in the literature.[13–16] Developing a process for maximizing the production of CPT by standardization of media components is crucial. Media optimization by classical method is laborious and time-consuming. An alternative and more competent move toward microbial fermentation is the use of statistical methods.[17] Response surface methodology (RSM) is one such method widely used for optimization of medium components in fermentation processes.[18–24] It is also used to explain the mutual effects of all factors in the fermentation process.[25] It combines an experimental approach with mathematical methods and statistical presumption for constructing and exploring functional correlation between response variables and a set of design variables.[26] Several researchers have reported the kinetics of microbial growth and substrate utilization.[27–30] However, there is no report on the growth, substrate utilization, and production kinetics of an endophytic fungus. Hence, the objective of this study is to enhance the production of cell associated CPT by optimization of simple media components using RSM and to study the kinetic modeling of growth, substrate consumption, and product formation by an endophytic fungus, Fusarium oxysporum NFX06.
MATERIALS AND METHOD Microorganism and Culture Conditions The cell-associated CPT-producing endophytic fungus was isolated from leaves of Nothapodytes foetida. The endophytic fungus F. oxysporum NFX06 was identified based on internal transcribed spacer (ITS) sequence analysis. The nucleotide sequence of NFX06 was submitted in the Genbank with an accession number KC914432. The culture was maintained on potato dextrose agar (PDA) slants and stored at 4 C. The spore suspension was prepared by dispersing (1 cm 1 cm) mycelial agar plug taken from an actively growing colony in a solution containing Tween 80 (0.1% v=v), filtered using Whatmann No. 1 filter paper and counted for number of spores in colony-forming units using a hemocytometer. One hundred microliters of spore suspension was used as inoculum for fermentation under a shake-flask condition.
160
MUSAVI ET AL.
Shake-Flask Experiments The preliminary shake-flask studies were carried out in a medium containing (g=L) dextrose, 40.0; peptone, 7.5; KH2PO4, 0.60; MgSO4 7H2O, 0.4; and ZnSO4 7H2O, 0.88, for growthand cell-associated CPT production. The initial pH of the medium was adjusted to pH 5.4. The media and the salts were autoclaved separately at 121 C for 20 min and mixed together after cooling. Fermentation was carried out at 26 2 C, 120 rpm, for a period of 8 days. Response Surface Method: Central Composite Design (CCD) Response surface methodology using central composite design (CCD) was applied to model the cell-associated CPT production. This approach involves full factorial search by investigative instantaneous, methodical, and competent discrepancy of three important parameters. Concentrations of dextrose (X1), peptone (X2), and MgSO4 (X3) were chosen as the independent variables, identifying possible interaction and higher order effect, and determining the optimum operational conditions. A 23 factorial design augmented by 6 axial points (a ¼ 1.682) and 6 replicates at the center point was implemented in series of 20 experiments, wherein the effect of each component on CPT was the dependent response variable. Five level of variation were selected for each variable as shown in Table 1. To simplify the calculation, the independent variable coded as Z was used, Z ¼ ðX X0 Þ=DX
ð1Þ
where X corresponds to natural value, X0 is the natural value in the center of the domain, and DX is the increment of X corresponding to one unit of Z. Experimental data were fitted to a second-order polynomial model as given in Eq. (2) and the coefficients were obtained using multivariant regression analysis: y ¼ A0 þ
3 X
Ai Xi þ
i¼1
3 X i¼1
Aii Xi2 þ
2 3 X X
ð2Þ
Aij Xij
i¼j j¼iþ1
where y ¼ response function, A0 ¼ intercept, Ai, Aii, Aij ¼ coefficients of the linear, quadratic, and interactive terms, respectively, and Xi and Xij are level of independent variables. The model was used to evaluate the response based on the effect of each independent variable. Three additional TABLE 1 Independent Variables and Their Coded and Actual Values Used in the Response Surface Design Actual values Coded values (Z) –1.628 –1 0 1 1.628
X1-Dextrose (g=L)
X2-Peptone (g=L)
X3-MgSO4 (g=L)
23.18 30.0 40.0 50.0 56.83
3.33 5.0 7.5 10.0 11.7
0.07 0.2 0.4 0.6 0.73
MODELING OF CELL-ASSOCIATED CAMPTOTHECIN PRODUCTION
161
confirmation experiments were conducted to verify the validity of the statistical experimental strategies. Statistical Analysis Design-Expert software (version 8.0.7.1 Stat-Ease, Inc., Minneapolis, MN) was used to analyze the experimental data. The significance of each coefficient was determined using the F-test and p value; p < 0.05 was considered to be statistically significant. Extraction of Cell-Associated Camptothecin Extraction of cell-associated CPT from mycelium was carried out with some modifications.[31] The mycelia were dried at 60 C in a hot-air oven until they attained constant moisture content within 24 hr of the drying period. The dried samples were ground to fine powder using pestle and mortar. About 1 g of fine tissue powder from each of the samples was extracted with 61% of ethanol at 60 C in a shaking water bath. After cooling to room temperature, the extract was concentrated using a rotary vacuum evaporator (Superfit, India). The milky residue obtained was again extracted thrice with 4:1 ratio of chloroform and methanol. It was then concentrated and centrifuged at 10,000 rpm for 10 min at 10 C. The supernatant was then passed through a 0.22-mm filter (Tarsons, India) and analyzed for the presence of CPT using a Perkin Elmer (USA) LS55 fluorescence spectrophotometer. Determination of Camptothecin An initial analysis was carried out to determine the wavelengths at which maximum intensity is exhibited by the pure CPT (Sigma Aldrich, India). The standard was prepared and 10 ng=mL of pure CPT was scanned spectrofluorimetrically to obtain the excitation and emission wavelengths.[32] The kmax (370 nm) shown by pure CPT has an excitation at 369 nm and emission at 423 nm. A stock solution of CPT was prepared by dissolving 1 mg of standard CPT in 4:1 ratio of chloroform and methanol, and further dilutions were made using methanol to prepare the working solution of 2–10 ng=mL. A calibration curve between concentration of standard CPT and the intensity of fluorescence was plotted and the concentration of cell associated CPT in the sample was determined using the regression equation of Eq. (3): Y ¼ 34:272 X 38:057
ð3Þ
RESULTS Experimental Design Model Fitting and Analysis of Response for Optimization of CPT Production RSM is a sequential procedure for efficient and rapid determination of optimum value of any process parameter.[33] It is also determines statistically the importance of individual factors,
162
MUSAVI ET AL.
appropriateness of the functional form and sensitivity of response on each factor.[34] The range and levels of experimental variables investigated in this study were presented in Table 1. The central values (zero level) chosen for experimental design were X1-dextrose 40 (g=L), X2peptone 7.5 (g=L), and X3-MgSO4 0.6 (g=L). The results of CCD experiments for studying the effects of three independent variables, namely, dextrose, peptone, and MgSO4, on cell-associated CPT production are presented in Table 2 along with the predicted and actual responses. The application of RSM yielded the following regression equation: CPT ¼ þ597:52 þ 72:75X1 þ 35:06X2 53:54X3 0:25X1 X2 18:75X1 X3 14:25X2 X3 58:53X21 65:08X22 51:99X23
ð4Þ
where Y is CPT yield, and X1, X2, and X3 are the coded values of dextrose, peptone, and MgSO4, respectively. Statistical testing of the model was done by Fisher’s statistical test for analysis of variance (ANOVA) and the results are shown in Table 3. The calculation of regression analysis gave the value of the determination coefficient (R2 ¼ 0.9628). This implies that 96.28% of the experimental data of the CPT production was compatible with the data predicted by the model and only 3.72% of the total variations are not explained by the model. The value of the adjusted determination coefficient (Adj R2 ¼ 0.9256) was also high to advocate for a high significance of the model with F-value of 259.55. In this case the Adj R2 value was 92.56% which was lesser than the R2 value of 96.28%. The predicted R2 of 61.76% was in reasonable agreement with the Adj R2 of 92.56%. TABLE 2 Central Composite Design Matrix for Independent Variables in Uncoded Units Along with Experimental and Predicted Values of CPT Run order 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
X1
X2
X3
CPT(ng=g) actual
CPT(ng=g) predicted
Residual
40.00 40.00 40.00 40.00 30.00 30.00 30.00 50.00 30.00 50.00 50.00 50.00 40.00 23.18 56.81 40.00 40.00 40.00 40.00 40.00
7.50 7.50 7.50 7.50 10.0 10.0 5.00 10.0 5.00 10.0 5.00 5.00 7.50 7.50 7.50 7.50 3.29 11.70 7.50 7.50
0.400 0.400 0.400 0.400 0.200 0.600 0.200 0.600 0.600 0.200 0.600 0.200 0.400 0.400 0.400 0.063 0.400 0.400 0.730 0.400
598.00 593.14 596.07 596.25 408.17 322.04 337.22 424.13 325.26 568.10 411.11 515.15 594.48 302.08 580.00 574.13 320.22 525.26 345.23 595.12
591.48 591.48 591.45 591.48 427.47 329.40 328.36 436.90 287.23 609.97 395.79 511.80 603.54 315.00 560.33 546.50 360.53 478.44 366.45 603.55
6.52 1.66 4.62 4.77 –19.30 –7.36 8.86 –12.77 38.03 –41.87 15.32 3.35 –9.06 –12.92 19.67 27.63 –40.31 46.82 –21.22 –8.43
MODELING OF CELL-ASSOCIATED CAMPTOTHECIN PRODUCTION
163
TABLE 3 Analysis of Variance (ANOVA) for Quadratic Model Source Model X1 X2 X3 X1X2 X1X3 X2X3 X21 X22 X23 Residual Lack of fit Pure error
Sum of square
Degree of freedom
Mean square
F Value
p Value
2.57 72280.08 16784.12 16784.12 0.50 2812.50 2812.50 49338.70 60981.10 38928.40 9947.68 9934.43 13.25
9 1 1 1 1 1 1 1 1 1 1 5
28595.5 72280.1 16784.1 39141.7 0.5 2812.5 1624.5 49338.7 60981.1 38928.4 1105.3 1986.2
25.87 65.39 15.19 35.41 4.524 2.54 1.47 44.64 55.17 35.22
