Kinetic models and parameters estimation study of biomass and ethanol production from inulin by Pichia caribbica ( KC 977491 )

1 Laboratoire de Mycologie, de Biotechnologie et de l'Activité Microbienne (LaMyBAM), Faculté des Sciences de la Nature et de la Vie, Département de Biologie Appliquée, Université Frères Mentouri, Constantine 1-Algeria. 2 Unité de Biotechnologie et Bioprocédés-Service 3BIO -Ecole polytechnique de Bruxelles, Université Libre de Bruxelles (ULB), Belgium. 3 Laboratoire de l'ingénierie des procédés de l'environnement, Faculté de Génie des procédés Université de Constantine 3Algeria.


INTRODUCTION
Bio-ethanol being a clean, safe and renewable resource has been considered as a potential alternative to the ever-decreasing fossil fuels (Martin et al., 2002;Wyman, 1994).Various substrates are available for the ethanol production but their choice depends on the cost and t he production process profitability (Quintero et al., 2015).
Most of the industrial processes are currently based on hexose carbohydrates from starch or sucrose-containing biomass (Kumari and Pramanik, 2012;Duhan et al., 2013).Among these substrates, inulin has rec eived a major interest since it is present as a carbohydrate reserve in a large variety of plant roots and tubers such *Corresponding author.E-mail: kr.mounira@yahoo.fr.Tel: 00213555773223.Fax: 0021331811523.
The bioconversion of biomass to ethanol is executed following two steps: hydrolysis of solid substrate to reducing sugars and t he fermentation by yeast or bacteria to convert fermentable sugars to ethanol (Torget et al., 1991;Kara Ali et al., 2013).The bioprocess which involves microbial cells is complex in nature and is a critical step for better yield achievement (Mahajan et al., 2010).Behavior of the microbial system can be evaluat ed by the development of kinetic models and experimental designs (Voll et al., 2011;Xu et al., 2011).The use of kinetic models is interesting to reduce the number of experiments needed t o assess the extreme operation conditions and for optimization and control (Lin and Tanaka, 2006).Two different categories of mathematical model; the structured and unstructured models, can be considered for modeling a microbial proc ess (Nielsen et al., 1991;Gadjil and Venk atesh, 1997;Murat and Ferda, 1999;Lei et al., 2001).Structured models take into account some basic aspects of cell structure, function and composition.By contrast, in unstructured models, only a global parameter such as cell mass is employed to describe the biological system, cell growth or product formation.Usually, theoretical models have been proposed and used for the elucidation of metabolic steps and for the calculation of kinetic parameters (Ghos h et al., 2012).To our knowledge, this is the first report to study Pichia caribbica (KC977491) growth kinetics and the modeling of ethanol production from inulin by this yeast strain.The main objectives were to: (I) P roduce biomass and ethanol by P. caribbica (KC977491) in a batch system; (II) Propose unstructured models for growth and ethanol production t o predict a process of fermentation by P. caribbica (KC977491); (III) Validate the obtained results between the theoretical unstructured models and experimental data.

Yeast and culture m edia
The yeast P. caribbica (KC977491) used in this w ork w as isolated from ar id soil area and identified previously (Kara Ali et al., 2013).This strain w as grow n in a medium containing 100 ml of Y PD (yeast extract, 10 g/L; peptone, 20 g/L; glucose, 20 g/L), incubated at 30°C for 24 h under agitation of 150 rpm.Cells (11 ml/ DO600 = 9) w ere further transferred into flasks contain ing 100 ml of the fer mentation medium composed of (g/L): inulin 30, yeast extract 4, peptone 4 and initial pH 5. The culture w as incubated at 37°C under agitation of 150 rpm for 5 days.

Fructose and ethanol analysis
After the fermentation period, the biomass w as separated from Ali et al. 125 medium using centrifugation technique at 5,000 rpm and 4°C for 5 min.The supernatant w ere cleaned by cellulose acetate membrane (0.2 μm, Minisart Sartorius), then, the fructose consumption and ethanol production w ere investigated by HPLC under subsequent conditions follow ing the CWBI protocol: Agilent 1110 series (HP Chemstation softw are) w ith a Supelcogel C-610H column preceded by a Supelguard H pre-column (oven temperature 40°C) .0.1% H3 PO4 solution ( in milliQ w ater) w as used as the isocratic mobile phase at a flow rate of 0.5 ml min -1 and a differential refractive index detector ( RID) w as heated at 35°C.The process lasted for 35 min at a maximum pressure of 60 bars.The standard curves w ere prepared using the different concentrations of fructose and ethanol (from 0.125 to 4 g/l) for both of them.

Cell mass analysis
The biomass concentration of P. caribbica w as deter mined by the dry w eight method (Buono and Er ickson, 1985).The cells obtained as mentioned previously w ere washed tw ice w ith w ater and dried by incubation at 105°C until constant w eight.

Kinetic models
A mathematical model is a collection of mathematical relationships which describe a process.Practically in each model, a simplification of the real process is made.Mathematical models have proven to be very useful in gaining ins ight in processes ( Philippidis et al.,1992;Santos et al., 2012) for instance by comparing different models and their ability to describe experimental data (Auer and Thyrion, 2002;A mribt et al., 2013).Further more, models have been successfully used for optimization or control of processes (Yip and Marlin, 2004).Different types of models can be distinguished for the different goals and depending on the available infor mation.Some characteristics w hich are of interest for modeling bioprocesses are illustrated in Table 1.

M icrobial growth kinetics
The logistic equation is a very common unstructured model in macroscopic description of cell grow th processes ( Parente and Hill, 1992).It accounts for the inhibition of grow th which occurs in many batch processes (Benkortbi et al., 2007).In this study, the logistic equation w as adapted to investigate P. caribbica (KC977491) grow th.It can be described as follow s: Where X is the biomass concentration (g/L), Xm is the maximum biomass concentration (g/L), μm is the maximum gr ow th rate (h -1 ) and t is the time (h).The integration of the biomass production rate w ith the use of the initial condition (at t = 0, X = X0) gives a sigmoidal var iation of X as a function of t w hich may r epresent both an exponential and a stationary phase (Equation 2): (2)

Ethanol production kinetics
The kinetic of product for mation w as based on the Luedeking-Piret model, initially developed for the fer mentation of gluconic acid by different types of microorganisms (Luedeking and Piret, 1959).It is is the substrate inhibition constant (g/L) is the maximum inhibitory lactate concentration (g/L) : is the threshold level of lactate before an inhibitory effect (g/L) is a parameter related to the toxic power for biomass h: is a parameter related to the inhibitory product Altiok et al. (2006) an unstructured model, w hich combines grow th and non-grow th associated contribution tow ards product formation.Thus, the product for mation depends upon the gr ow th rate (dX/dt) and instantaneous biomass concentration (X) (Equation 3). (3) Where " P" is the product concentration (g/L), " m" (g/g) and "n" (1/h) are the Luedeking-Piret equation parameters for grow th and nongrow th associated product for mation respectively.A carbon substrate is used to form cellular material and metabolic products as w ell as for the cellular maintenance.
The product formation rate equation ( Equation 4) can be expressed by integr ating Equation 3 using Equation 2 w ith the initial conditions P = 0 at t = 0:

Substrate consumption kinetics
Kinetics substrate consumption can be described as follow s: (5) Where, p= 1/YX/S (g/g) and q is maintenance coefficient (1/h).Equation ( 5) is rearranged as follow s: Substituting Equation 2in Equation 6 and integrating w ith initial conditions ( ; t = 0) give the follow ing equation:

Model of param eters estim ation
Kinetic models w hich describe the microbial process on a particular substrate are nonlinear w hich in turn makes parameter estimation relatively difficult.Tho ugh few models can be linear, their utilization is limited because of the error associated w ith the transformation of dependent variable and therefore resulted in inaccurate parameter estimations.Hence, the nonlinear least-squares regression is often used to estimate kinetic par ameters from nonlinear expressions.The parameter estimation obtained from the linear kinetics expressions can be used as initial estimation in the iterative nonlinear least-squares regression using the least square curve fit in order to fit the models developed and to estimate the parameters (substrate consumption, biomass and product formation).
Fitting pr ocedures and parametric estimations calculated from the results w ere carried out by minimization of the sum of quadratic differences betw een experimental and model-predicted values, using the nonlinear least-squares Levenberg-Marquardt method (Marquardt, 1961) w ith a developed Mathcad program.The coefficient of deter mination R 2 w as estimated to assess the accuracy of the estimated parameters achieved by fitting the experimental values to the proposed mathematical models.If R 2 approximate to 1, this coefficient justifies an excellent consistency of these equations (Annuar et al., 2008).Furthermore, the ANOVA

RESULTS AND DISCUSSION
Many researchers have attempted to model yeast fermentation and different approaches have been considered (Aiba et al., 1968;Ghose and Tyagi, 1979;Hoppe and Hansford, 1982).However, it is not easy to choose a single best fitting.In order to choose the best model it is import ant to consider how well it describes the transition from ex ponential t o stationary phase of t he process model (Kostov et al., 2012).

Microbial growth
The logistic equation of biomass growth (Equation 2) is used to fit the batch fermentation growth data.Figure 1 compares the predictive model related to cell growth with the experimental data recorded during batch fermentation of P. caribbica (KC977491).The maximum biomass concentration (1.2 g/ L) was obtained after 96 h of fermentation and a complete depletion of fructose in the medium.In addition, a Levenberg-Maquardt method is used in Mathcad to obtain µ max by minimizing the differenc e between experimental growth and calculat ed one using Equation 2. The program gives the value of µ max = 0.052 h -1 . This value is relatively low compared to those reported in several studies.Indeed, the µ max value from Saccharomyces diastaticus (strain LORRE316) was in the interval of 0.1 and 2 h -1 with optimum of 0.9 h -1 (Wang and Sheu, 2000).Otherwise, the production of ethanol using Saccharomyces cerevisiae (A TCC4126) has showed a µ max of 0.28 h -1 (Bazua and Wilke, 1977).
Moreover, the µ max related to S. cerevisiae ITD00196 reached 0.58 h -1 in a batch system (Jiménez-Islas et al., 2014).The variation of this parameter may be explained by the type of microorganisms, the substrate consumption and the environmental conditions.
The analysis of Figure 1 shows that there is an adequacy between the experimental data and those predicted (R 2 = 0.91).Also, the analysis of variance (ANOVA ) results for the growth model are presented in the Table 2. F-value (101.694608) is greater than critical F value (5.11735501), whic h proved the acceptance of this test.On the basis of the obtained res ults, a good correlation coefficient (R 2 = 0.91) and a significant ANOVA test shows that the proposed logistic model is adequate to explain the sigmoidal profile of the yeast growth.According to the literature, the study proposed by Dodic et al. (2012), was carried out used logistic empirical kinetic model to describe batch fermentation of raw juice.The results show a good agreement with experimental data (R 2 = 0.99), thus, the logistic equation was found to be an appropriate kinetic model for successfully describing yeast cell growt h in batch fermentation of raw juice system.

Ethanol production
The Equation 4 is applied to simulat e the product formation, thus, Figure 2 shows the comparison of predicted model and experimental data for ethanol production by P. caribbica.The ethanol concentration reached its highest values in 96 h (6.2 g/L) from experimental data.Using the same procedure as above, the programs returns the values of 7.725 g/g for the growth associated rate constant "m" and -0.088 1/ h for the non-growth associated rate constant "n".
These results show that the degree of growth associated constant rate "m" is much greater than the non-growth associated rate constant "n".Similar results were achieved by Jiménez-islas et al. (2014).The simultaneous cell growth and ethanol production suggest that it is a growth-associated product.This result is in accordance with that of Thatipamala et al. (1992) who found that when using glucose as substrate, ethanol and biomass were produced simultaneously.In contrast, Ahmad et al. (2011) performed a series of experiments to show that ethanol batch fermentation is a non-growt hassociated process that uses glucose.However, these authors used a forced aeration of 0.075 vvm in the culture medium and an agitation speed of 75 rpm, whereas, in our experiments, air was only trans ferred naturally from air phase to liquid phas e.This discrepancy can be explained by the fact that when oxygen is absent, S. cerevisiae produces ethanol in order to reoxidize NADH + to NAD + ; however, in presence of oxygen, it acts as a final electron acceptor.
Moreover, the analysis of Figure 2 shows that there is a good agreement between model predictions and experimental data, effectively a correlation coefficient (R 2 ) value for et hanol production was 0.96.The analysis of variance (A NOVA) results for the ethanol production model are presented in the Table 3.
ANOVA of the regression model (Table 3) demonstrates the fitness of this model due to the F-value of 95.485816 greater than critical F value (4.4589701).
A good R 2 (0.96) for ethanol production and a significant ANOVA test confirmed that the model provides the relevant prediction The same results were obtained in several researches using the same model (Annuar et al., 2008).In addition, Jiménez-Islas et al. ( 2014) found the effects of pH and temperature on ethanol production from red beet juice by t wo strains: S. cerevisiae ITD00196 and S. cerevisiae A TCC 9763.This study was predicted by using the Luedek ing-Piret model for ethanol production and validated only by a correlation coefficient (R 2 ).The authors concluded that this model was found to describe quantitatively this study due to a high level of correlation (R 2 = 0.97).

Substrate consumption
In this study, Equation 7 is applied to predict the consumption of the fructose substrate.However, P. caribbica is able to convert inulin to fructose, which was converted, after that, to ethanol.The hydrolysis of inulin in fructose by inulinase enzyme secreted by this yeast     Ali et al., 2016).
The comparis on of predicted model and experimental data for substrate cons umption modeling during batch fermentation by P. caribbica is shown in Figure 3.
In the beginning, the initial fructose concentration was 8 g/L after 12 h (c onversion inulin into fructose by P. caribbica).Biomass concentration and ethanol production (Figures 1 and 2) increased with a decrease in the fructose level (Figure 3).Fructose consumption had been gradually reduced from the beginning of the fermentation until t 120h when it ran out.In addition, the program used in this study, gives the values of p =14.735 g/g and q = -0.0771/h, these values were calculated in another kinetic study (Pazouki et al., 2008).Thus, the bio-dec olorization of distillery effluent in a batch culture was conducted using Aspergillus fumigatus.A simple model was proposed using the Leudek ing-Piret kinetics for substrate utilization, the equation coefficients calculated were p = 1.41 (g/g) and q = 0.0007 (1/h).The difference bet ween these values may be explained by the types of microorganism, fermentation period and the rate of substrate consumption to obtain the energy necessary for the maintenance of the cells in stationary phase.
It can be observed from Figure 3 that there is a good adequacy between model prediction and experimental data (R 2 = 0.95).The analysis of variance (ANOVA) results for the et hanol production model are presented in the Table 4.The F value (91.2945575) is larger than critical F value (4.45897011); this result clearly shown that, this model was applicable to this particular system (a good correlation coefficient R 2 and a significant ANOVA test).The experimental data reported by Oghome and Kamalu (2012), using modified Leudeking-Piret model, were also studied; the correlation coefficients, R 2 and adjusted R 2 are 0.6849 and 0.9827 respectively, which indicates that this model fits the experimental data very well.

Conclusion
Microbial fermentation is complex and it is quite difficult to understand the complete details process.The model proposed in this study appears relevant to describe the biomass, ethanol production and substrat e consumption versus fermentation time.The growt h pattern followed the logistic model and the parameters were proved.Ethanol production was represented by Luedek ing-Piret model; it was noticed that ethanol production by P. caribbica (KC977491) was growt h associated.High significance of coefficient of determination (R 2 ) was observed with the experimental and predicted results.The statistical analyses using A NOVA were done by means of statistical F-value test which indicates the sufficiency of t he regression models.Therefore, the models developed may be useful for controlling the growth, ethanol production and substrate consumption kinetics at large fermentation scale using this strain.

Figure 1 .
Figure 1.Comparison betw een predicted and experimental grow th kinetics.

Figure 2 .
Figure 2. Comparison betw een predicted and experimental ethanol formation kinetics.

Figure 3 .
Figure 3.Comparison betw een predicted and experimental fructose consumption kinetics.

Table 1 .
Some grow th models reported in the literature.

Table 2 .
Analysis of variance for the grow th model.

of variation Sum of squares (SS) Degree of freedom (DF) Mean square (MS
test w as also carried out to evaluate the accuracy of the models.The tw o basic data measures of variation sources are: Variation due to the regression and variation due to residuals.The statistical F-value is a ratio of the relative regression var iation/relative res idual variation.Thus, if F value is significantly greater than critical F value, this indicates that the regression model is accepted.

Table 3 .
Analysis of variance (ANOVA) for the ethanol production model.

Table 4 .
Analysis of variance (ANOVA) for the substrate consumption model.