Substrate Inhibition Growth Kinetics for Cutinase Producing Pseudomonas cepacia Using Tomato-peel Extracted Cutin

Cutinase [EC 3.1.1.74] is a key enzyme known to hydrolyze cutin – a water insoluble polymeric network of esterified hydroxyl and epoxy fatty acids (C16 and C18), and the predominant component embedded in plant cuticles1 protecting it from desiccation as well as microbial and insect attack. Cutinase is believed to belong to a group of intermediate enzymes between lipase and esterase, which are able to hydrolyze cutin polymer, soluble esters and emulsified triacylglycerol – as efficiently as pancreatic lipases.2 The absence of any significant structural rearrangements upon binding to a non-hydrolysable substrate analogue represents an important feature of cutinase.3 Because of no or little interfacial activation and being active on both soluble and emulsified triglycerides, this enzyme is gaining more attention over lipases in recent years.1


Introduction
Cutinase [EC 3.1.1.74]is a key enzyme known to hydrolyze cutin -a water insoluble polymeric network of esterified hydroxyl and epoxy fatty acids (C16 and C18), and the predominant component embedded in plant cuticles 1 protecting it from desiccation as well as microbial and insect attack.Cutinase is believed to belong to a group of intermediate enzymes between lipase and esterase, which are able to hydrolyze cutin polymer, soluble esters and emulsified triacylglycerol -as efficiently as pancreatic lipases. 2 The absence of any significant structural rearrangements upon binding to a non-hydrolysable substrate analogue represents an important feature of cutinase. 3Because of no or little interfacial activation and being active on both soluble and emulsified triglycerides, this enzyme is gaining more attention over lipases in recent years. 1 Cutinases have potential use in the dairy industry for hydrolysis of milk fat, oleochemical industry for synthesis of structured triglycerides polymers and surfactants 4 , as ingredients for personal-care products, pharmaceuticals, and in agricultural chem-icals preparation to increase the pharmacological effect. 57][8][9] On the other hand, there are only a few isolated studies on bacterial cutin degradation ability or bacterial cutinase [10][11][12] , which are even better in terms of thermal or pH stability when compared to their fungal counterpart.Unlike fungal cutinase, which loses its activity at 45 °C, bacterial cutinase could be stable at as high as 70 °C. 13Microbial production and specificity of enzymes have been shown to be dependent on the nature and concentration of substrate.
Authors have tried to find a cost-effective cutin substitute to induce cutinase production. 14Recently, Dutta et al. 1 reported efficient induction of bacterial cutinase with cutin hydrolysate.However, the production of cutinase is often highly regulated by the growth conditions. 15Substrate inhibition remains a very general phenomenon in hydrolysis of water-insoluble substrates by extracellular microbial enzyme systems. 16As substrate consumption is coupled to the cell growth and enzyme production, the assessment of a proper substrate inhibition growth model for cutinase producing microbial culture would be an integral and essential roadmap to eval-uate, predict and optimize the biological process system.
In the present work, kinetics of cutinase production using laboratory-isolated cutin from tomato peels as inducer/substrate and carbon source have been studied.At different initial cutin concentrations, cell growth and cutinase production by Pseudomonas cepacia (NRRL B 2320) were measured.Experimental data were analyzed with a set of wellknown substrate inhibition models and the selected models were rigorously compared for their goodness of fit, parameter sensitivity, and different statistical and information content criteria.

Preparation of cutin
Cutin as substrate for cutinase was prepared in the laboratory from fresh tomato peels using the method described by Chen et al. 12 In brief, the tomato peels collected from fresh tomatoes were boiled in oxalic acid/ammonium oxalate buffer for 3-4 h.After cooling to room temperature, the peels were digested with enzymes (cellulase and pectinase) to remove pectin and cellulose, subjected to extensive solvent extraction with methanol-chloroform in soxhlet apparatus to remove the embedded waxes, and then dried in an oven at 40 ºC.These dried peels were ground to powder (< 20 mesh) to obtain cutin.

Microorganism and maintenance
The bacterium used in this study, P. cepacia NRRL B 2320 (also known as Burkholderia cepacia), was procured from Agricultural Research Service (ARS-Culture collection), USDA, Peoria, USA.The organism was grown on nutrient agar medium at 28 °C.

Seed culture medium
The medium used for the development of seed culture contained (g L -1 ): glucose 6.0, beef extract 3.0, peptone 15.0, urea 6.0, KH 2 PO 4 2.0, KCl 0.5, MgSO 4 • 7H 2 O 5.0 (pH 7.0).The seed culture medium was inoculated with a loop full of pure culture grown on nutrient agar slant.The culture was then incubated for 10 h (to reach culture OD of 0.6~0.8 at 600 nm) at 28 °C and 180 rpm in a shake flask.

Kinetic experiment
The medium for cutinase production contained (g L -1 ): beef extract 4.0, peptone 17.77, urea 5.0, KH 2 PO 4 3.0, KCl 0.635, MgSO 4 • 7H 2 O 5.546 and crude cutin preparation at 2-20 g L -1 , and the initial pH was adjusted at 7.0.A 2 % v/v of inoculum from the seed culture was added to 50 mL of the medium in sets of 250 mL Erlenmeyer flasks.The flasks were incubated in a shaker incubator set at 28 °C and 180 rpm.Samples (culture medium) were withdrawn at regular intervals and measured for cutinase activity.For each initial mass concentration of cutin in batch experiment, the specific growth rate (μ) was calculated from the slope of plot drawn between ln (γ x ) vs time; where, γ x is the dry cell mass obtained at a particular time.The experiments were conducted in duplicate and an enzymatic assay was performed in duplicate for each sample.

Cutinase assay
Samples were centrifuged at 10,000 g for 10 min at 4±1 ºC.The supernatant was separated and used for cutinase assay.The activity was measured by two different sets of assay.Firstly, a non-specific yet simple spectrophotometric assay, which does not distinguish between esterase and cutinase, was used to measure the release of p-nitrophenol (pNP) from p-nitrophenylbutyrate (pNPB). 12The production of cutinase was further confirmed by using cutinase-specific substrate p-nitrophenyl (16 methyl sulphone ester) hexadecanoate (p-NMSH). 17or the nonspecific assay, an aliquot of (20 µL) culture supernatant was added to 980 µL of reaction mixture, which was prepared by adding 1 mL of pNPB solution (23 mmol L -1 in tetrahydrofuran) to 40 mL of potassium phosphate buffer (50 mmol L -1 ) containing sodium deoxycholate (11.5 mol L -1 ).The release of p-nitrophenol was monitored at 410 nm for 15 min at 37 ºC.One unit of enzyme activity was defined as the amount that releases one µmol L -1 of p-NP min -1 under assay conditions.The production of cutinase was confirmed by using cutina sespecific substrate p-NMSH according to Degani et al. 17 with minor modifications (incubation period of 4 h instead of 15 min).

Microbial biomass measurement
Due to the presence of cutin, the cell dryweight concentration could not be measured directly, and therefore, the intracellular protein concentration was measured. 18Briefly, the cell samples were centrifuged at 10,000 g for 10 min at 4 ºC and the pellets were re-suspended with an equal volume of distilled water and again centrifuged.After repeating the washing step two more times, the cells pellet was subjected to alkaline lysis (heating at 100 ºC for 20 min in original volume using 0.4 N NaOH).The total protein content in the samples was determined by Lowry's method 19 using bovine serum albumin (Sigma) as standard.The relationship with cell dry weight and intracellular protein was established as: Substrate inhibition growth models for cutinase production In this particular study, a large set of different widely published substrate inhibition models that have evolved from or are an extension of Monod's kinetics, were used to analyze experimental data (Table 1).The Andrews model explains the inhibitory effects of substrate at higher concentrations, which however, reduces to the conventional Monod's equation when the inhibition constant becomes very high. 20The Luong model is a generalization of Monod's kinetics that includes an addi-tional term to account for complete growth inhibition above a critical substrate concentration.The relation between the specific growth rate and the initial substrate concentration could either be linear (n = 1), a concavity upward (n > 1) or a concavity downward (n < 1) depending on the value of the constant parameter (n). 21The Han and Levenspiel model is an extension of the Monod's model to account for cell, product and substrate inhibition, and is also capable of explaining the type of inhibition as competitive, non-competitive or uncompetitive depending upon the values of the two constant parameters (n, m).This model also assumes a value for critical inhibitory concentration of substrate, above which growth completely ceases. 22The Haldane growth model incorporating both the substrate affinity constant and the substrate-inhibition constant is widely accepted for representing the growth kinetics under inhibitory substrates.The kinetics follows simple Monod's model when the inhibition constant is infinitely large. 23The Moser model is a modified Monod equation with a power function of substrate concentration.The value of the power determines the degree of inhibition.However, it does not indicate critical substrate concentration or inhibition constant. 24The Aiba growth inhibition model depicts a decrease in specific growth rate with an increase in product concentration.The exponential term to take care of the product inhibition could be well replaced with substrate concentration.However, it fails to give the critical value of inhibitory substrate/product concentration. 25he Yano model was originally proposed for the kinetics of amylase production at high sugar concentration. 26The Edward model gives the protective diffusional-limitation of high and inhibitory substrate concentrations. 27The Webb model is the modified Yano model, where (1 + γ s /K) term is present in the numerator rather than the denominator. 28he parameters of different models were estimated from the experimental results using MAT-LAB v.7.1.Since the models had non-linear coefficients, the parameters were estimated iteratively with non-linear least square algorithm.

Statistical comparison of model for acceptability
The various substrate inhibition models chosen for this study were different in terms of complexity (degree of freedom).Therefore, it was essential to test whether experimental data could be more consistent with one mechanism (model) than with the other.Kinetic models, where improved fitting (lower model sum of square or highest regression coefficient) comes at the cost of increasing complexity, must be compared either using the extra sum-ofsquare F test 29 for nested models or Akaike information criterion (AIC) for both nested and non-nest-Ta b l e 1 -List of substrate inhibition models initially selected for this study Haldane 1] In our study, the best-fit 3-parameter and 4-parameter models were compared using both F test and AIC.
The extra sum-of-square F test, as an alternate view for ANOVA analysis, assumes the simpler model to be correct (null hypothesis) if the relative increase in the model sum of squares and in the degree of freedom are approximately equal.Otherwise, if the relative increase in the model sum of squares largely exceeds the relative increase in the degree of freedom, the complex model (alternate hypothesis) is justified.The F ratio is given by Eq. 2. Where, "SS" represents the sum of square differences between experimental and model data, and "df" represents their degree of freedom.Subscripts "simple" and "alternate" represent the two models of different complexity.The probability value for the F distribution is compared with the confidence level cutoff probability.
The Akaike information criterion (AIC) is defined by the following equation: Where, "p" is the number of data points, "b" is the number of parameters "prm" to be fitted by the regression plus one (b = prm + 1).When there are few data points, the corrected AIC (AIC c ) is used.
The model with lower AIC c value is more likely to be correct and the probability (pAIC) that the more complex model is correct is given by Where, ΔAIC c is the difference between AIC c values of the complex and simple models.

Growth and enzyme activity profiles at varying substrate concentrations
The growth profiles of P. cepacia at different initial substrate concentrations are shown in Fig. 1.It was observed that the growth of P. cepacia was very low at the initial cutin concentration of 2 g L -1 , but continued to improve up to an initial substrate concentration of 10 g L -1 .Irrespective of initial cutin concentrations in different sets, there was a consistent lag period of about 4 h before the onset of logarithmic growth, and the stationary phase was reached at about 96 h.
Extracellular enzyme activity measured at different time intervals from batch experiments with varying initial substrate concentrations is presented in Fig. 2. The culture enzyme activity continues to increase until 96 h, when the highest enzyme activity was recorded (344 U mL -1 ) with initial substrate, cutin concentration of 10 g L -1 .The activity was 3.1 U mL -1 with p-NMSH assay.This observation suggested the possibility of substrate inhibition when cutin concentration increased above 10 g L -1 .However, there is no available report that quantitatively relates cutinase production to cutin as the sole carbon source.Fett et al. 10 have observed that cutin hydrolysate failed to induce cutinase production with T. fusca, and higher concentrations of cutin hydrolysate were inhibitory towards microbial F i g . 1 -Growth profile of P. cepacia at different initial substrate concentrations

-Enzyme activity profile obtained at different initial substrate concentrations
growth.A very logical reasoning could be that, at low concentrations, the effect of the nutrient was negligible on gross measures of metabolic activity, such as specific growth rate, respiration rate and rate of protein/enzyme synthesis, etc.However, at higher concentrations of cutin, the mass and oxygen transfer in the media had been hindered due to the insoluble nature of cutin, thus, cell growth as well as enzyme production had decreased.It was observed that the same cutin concentration (>10 g L -1 ) was responsible for attenuation of the specific growth rate as well as enzyme production.At this point, either some other environmental factor was limiting the nutrient supply or the cells themselves had reached their own limit for the cultural conditions.

Specific growth rate and enzyme activity at different substrate concentrations
The cell growth increase with increasing concentration of cutin, the specific growth rate and maximum enzyme activity as a function of initial substrate concentration are presented in Fig. 3.The specific growth rate increased from 0.11 h -1 to 0.21 h -1 before dropping down again to 0.17 h -1 at a substrate concentration of 20 g L -1 .The decrease in specific growth rate (µ) and enzyme activity at and above initial substrate concentration of 10 g L -1 was due to the presence of substrate inhibition kinetics.In fact, the maximum specific growth rate and the maximum enzyme activity measures were highly correlated with Pearson product moment correlation of 0.94 (P < 0.001), suggesting cutinase production to be highly growth-associated.A similar observation has also been reported by Calado et al. 32 , where cutinase production was highly growth-associated while using galactose (10-40 g L -1 ) as the sole carbon source.Characterization of crude and purified cutinase from P. cepacia NRRL B 2320 has been described elsewhere. 33ploration of kinetic models for growth of P. cepacia Even if the patterns of microbial growth throughout the experimental period were similar to each other irrespective of initial cutin concentration, the variation in the experimental specific growth rate for P. cepacia was dependent on the initial substrate concentration.Similar results were reported by Agarwal et al. 18 , where they found that for all initial concentrations of cellulose in shake flask there was a lag of about 2 h, but the time to reach stationary phase increased with increasing initial cellulose concentration.The authors have noted a decreasing trend in the specific growth rate at higher substrate concentration, indicating substrate inhibition.The variation in adaptation of the culture at different initial substrate concentrations due to high substrate concentrations is most probably tolerated by a development of cell adaptation mechanisms during the lag and early exponential growth phases of a batch culture.The substrate inhibition models chosen in this study were regressed with the experimental data, and the model predicted values by MATLAB v.7.1 are presented in Fig. 4. It can be observed that, except the Haldane and Moser's models, most of the other kinetic models had very closely resembling experimental and predicted specific growth rate profiles in the substrate concentration regime.The parameters were estimated using the non-liner regression of various models as presented in Table 2.Among the several models used to fit the present experimental data for specific growth rates, it was observed that the Webb model had the highest R 2 value of 0.933, followed by the Andrews model (R 2 = 0.92), the Aiba model (R 2 = 0.91), and Luong model (R 2 = 0.90) showing an apparent good fit between experimental and model predicted values.The root mean square errors (RMSE) between experimental and model pre- dicted values were 0.0097, 0.0096, 0.010, and 0.01, respectively, for the four different models.Due to its simpler formulation compared to other Monod model derivatives, the Andrews equation remains the most widely used. 34In this study, the Andrews model predicted the substrate inhibition to start at cutin concentration 10 g L -1 , whereas the Webb model predicted the value to be 11.28 g L -1 .The close resemblance of predicted values between the two models is logical because for high value of constant 'K' the Webb model reduces into the Andrews model.The highest maximum specific growth rate (µ max ) was predicted by the Andrews model (0.72 h -1 ), followed by the Webb model (0.518 h -1 ), the Luong and Aiba models (0.44 h -1 ).The predicted µ max by all other models, particularly the Moser and Edward models were much lower and certainly insensible.By modeling growth of Cellulomonas cellulans during production of cellulase using water-insoluble substrate cellulose, Agarwal et al. 18

Sensitivity analysis of estimated kinetic parameters
Sensitivity analysis, using the methodology described by Sobie 37 , was performed to evaluate how the change in model parameter estimate would affect the model regression coefficients.In this study, a set of input parameters for both the Webb and Andrews models were varied within ±50 % of their estimates, while keeping all other parameters "on hold".The sensitivity analysis results for all the parameters are presented in Fig. 5.It is apparent from the figure, that the maximum specific growth rate (µ max ) was the most sensitive parameter for both the models.Any variation of µmax (increase or decrease) severely compromised the regression coefficient for the Andrews model (R 2 < -10) or the Webb model (R 2 < -50), particularly with higher end values of µmax.The very high sensitivity of maximum specific growth rate suggests requirement of its precise measurement/estimate for further predictability of the model. 38For any downward change in K I or upward change in K S from their respective optimal estimates, sensitivity profiles for both the models were nearly identical.However, the Andrews model quickly turned out to be more sensitive than the Webb model for any upside variations in K I values or downside variations in KS values from their standard estimate.It was apparent from the figure that the regression coefficient of the Webb model was least sensitive to the Webb constant (K), and in such a situation, inference of its meaningful estimate would be hard or even impossible. 39While measuring parameter sensitivity using change for initial guess, Banerjee and Ghoshal 40 have reported the poor repeatability Webb model fitting to substrate (phenol) inhibition kinetics.This could be due to the exorbitantly high absolute value of the estimated parameter (more than two orders of magnitude) compared to experimental substrate concentration.

Comparison of model for acceptability
The best-fit 3-parameter, 4-parameter, and only one 5-parameter models had regression coefficients of 0.92, 0.933 and 0.73, respectively.The more complex Webb model had better fits than the simpler Andrews (3-parameter) model.Using the extra sum of square F test or Akaike's information content criteria, the two models were compared.The results are presented in Table 3.As the probability value for the extra-sum-square F test was > 0.05, at 95 % confidence we could not reject the null hy-pothesis (simpler model) in favor of the alternative that the more complicated model would be correct.In other words, there was no evidence supporting the alternate model, so the simpler model was accepted.In the AIC-based comparison as the ∆AIC c was positive, we concluded that the change in SSE would not been as large as expected from a change in the number of parameters.The probability for choosing the correct model was > 99 % (here the simpler Andrews model), and associated with an overwhelming evidence ration of 190.65.

Conclusion
P. cepacia can utilize cutin in the range of 2 to 20 g L -1 as a sole carbon source for the production of cutinase.However, substrate inhibition was evident in the growth of P. cepacia.The 4-parameter Webb model and the 3-parameter Andrews model were the best fit among the different models tested.However, AIC and F-test analysis finally favored the acceptance of the 3-parameter Andrews model.Fed-batch culture strategy can be adopted to overcome substrate inhibition through intermittent addition of the substrate which maintains a substrate concentration at a low level or less than inhibitory level.-Specific growth rate, h -1 μ max -Maximum specific growth rate, h -1

F i g . 3 -
Specific growth rate and maximum enzyme activity as a function of initial substrate (cutin) concentrationF i g .4 -Experimental and the various substrate inhibition models predicted specific growth rate profiles as a function of initial substrate (cutin) concentration

F i g . 5 -
Sensitivity analysis of a) maximum specific growth rate, b) substrate inhibition constant, c) Monod half saturation constant and d) Webb constant (only for Webb model) as estimated from the Andrews and Webb models toward model regression coefficients Ta b l e 3 -Summary of model discrimination using Akaike's information criterion methodology and extra sum-of-square F test Models Model specific information Akaike's information criterion Extra sum-of-square F test prm p SS (• 10

*-
L i s t o f s y m b o l s b -Variable of AIC analysis (number of parameters plus one) C -Cell concentration in Han-Levenspiel model, g L -1 df -Degree of freedom for a model with experimen-tal data K -Webb constant, g L -1 K I -Inhibition constant for cutin, g L -1 K M -Monod's constant, g L -1 K s -Half-saturation constant for cutin, g L -1 n,m -Constant parameters p -Number of experimental data points p AIC -Probability that model with given AICc value is correct prm -Number of parameters to be estimated in a model r -Cell growth rate, g L -1 h -1 Δ AICc -Difference in AIC c value between two models SSE -Sum of square of errors G r e e k l e t t e r s γ s -Initial cutin concentration, g L -1 γ s Critical cutin concentration, g L -1 μ