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A kinetic model for growth and biosynthesis of medium-chain-length poly-(3-hydroxyalkanoates) in Pseudomonas putida

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A kinetic model is presented giving a mathematical description of batch culture of Pseudomonas putida PGA1 grown using saponified palm kernel oil as carbon source and ammonium as the limiting nutrient. The growth of the micro-organism is
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    ISSN 0104-6632Printed in Brazilwww.abeq.org.br/bjcheVol. 25, No. 02, pp. 217 - 228, April - June, 2008*To whom correspondence should be addressed Brazilian Journalof ChemicalEngineering A KINETIC MODEL FOR GROWTH ANDBIOSYNTHESIS OF MEDIUM-CHAIN-LENGTHPOLY-(3-HYDROXYALKANOATES) IN  Pseudomonas putida M. S. M. Annuar  1* , I. K. P. Tan 1 , S. Ibrahim 2 and K. B. Ramachandran 3Institute of Biological Sciences, University of Malaya, Phone: 603-7967-6740,Fax: 603-7967-4178, Zip Code: 50603, Kuala Lumpur, Malaysia.E-mail: suffian_annuar@um.edu.my 2 Department of Civil Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia. 3 Department of Biotechnology,Indian Institute of Technology (IIT) Madras,Chennai-600036, India. (Received: June 19, 2007 ; Accepted: November 26, 2007) Abstract - A kinetic model is presented giving a mathematical description of batch culture of   Pseudomonas putida PGA1 grown using saponified palm kernel oil as carbon source and ammonium as the limitingnutrient. The growth of the micro-organism is well-described using Tessier-type model which takes intoaccount the inhibitory effect of ammonium at high concentrations. The ammonium consumption rate by thecells is related in proportion to the rate of growth. The intracellular production of medium-chain-length poly-(3-hydroxyalkanoates) (PHA MCL ) by  P. putida PGA1 cells is reasonably modeled by the modified Luedeking-Piret kinetics, which incorporate a function of product synthesis inhibition (or reduction) by ammonium abovea threshold level.  Keywords: Ammonium; Kinetic; Medium-chain-length PHA;  P. putida ; Substrate-inhibition. INTRODUCTION Poly-(3-hydroxyalkanoates) (PHA) are natural polyesters accumulated intracellularly by varioustypes of microorganisms. When nutrient suppliessuch as nitrogen, oxygen, phosphorus, sulfur or magnesium are imbalanced, it is advantageous for  bacteria to store excess carbon by polymerizingsoluble carbon intermediates into water-insolublemolecules like PHA inside their cells (Madison andHuisman, 1999). PHA is classified into two major families, i.e., short-chain-length PHA (PHA SCL ) andmedium-chain-length PHA (PHA MCL ). Typicalexamples of PHA SCL are poly-(3-hydroxybutyrate)(PHB) and poly-(3-hydroxybutyrate- co -3-hydroxyvalerate) (PHBV). A well known producer of PHA SCL is Wautersiaeutropha (formerly knownas  Alcaligenes eutrophus ). The class of PHA MCL ischaracterized by monomers with a carbon atomlength ranging from 6 to 18, and is primarily produced by the fluorescent pseudomonads(Huisman et al . , 1989). More than 100 differentmonomers have been reported to occur in PHA MCL (Steinbuchel and Valentin, 1995). The PHA MCL arealso targeted for specific uses where chirality andelastomeric properties are important. The constituentmonomers that display different functional groups intheir side chain are a valuable source of chiralsynthons yet to be exploited (Kessler et al . , 2001).Only the PHA SCL have been commercially produced up to 500 tons year  -1 , which wasmanufactured by Monsanto (Kellerhals et al., 2000).  218 M. S. M. Annuar, I. K. P. Tan, S. Ibrahimand K. B. Ramachandran  Brazilian Journal of Chemical Engineering  The PHA MCL are yet to make a significant impact asa viable choice due to the fact that it is veryexpensive to produce this polymer in bulk amountseven for material testing purposes. The final PHA MCL yield and content obtained are lower compared tothose of PHA SCL , which hampered development of its applications (Lee et al . , 2000). Much of theresearch effort was directed to improve its yield and productivity using fermentation processes. SeveralPHA MCL production strategies in the bioreactor suchas batch and continuous (Durner et al . , 2001; Jung etal., 2001), fed-batch (Beom, 2002)and high-cell-density processes (Lee et al., 2000) under variouscultivation conditions have been described.For the production of PHA MCL , one of the most preferred feedstocks is highly reduced and longcarbon chain molecules such as animal or vegetableoils or their free fatty acids. These substrates havehigh energy content, which is excellent for good cellgrowth and energy metabolism. It is suggested thatthese oils in the semi-purified form can be a cheaper substrate for PHA MCL fermentation as compared tothe purified, single-type fatty acids. However, mostof the studies on PHA MCL fermentation employed thelatter as the carbon source, which gives more definedfermentation components. Relatively high yield and productivity have been reported for the use of pure,single type fatty acids as the fermentation feedstock (Durner et al., 2001). The usage of crude fatty acidmixtures or their oils, however, has not been a popular choice.One of the pioneering studies on the utilization of crude mixture of fatty acids from plant oils for microbial PHA MCL production was reported by Tanet al. (1997). Using ammonium-limited culture of   Pseudomonas putida PGA1 in shake-flasks, theyhave shown that saponified palm kernel oil (SPKO)and its major free fatty acids, when used as the solecarbon and energy source in the fermentation, gavegood biomass growth and PHA MCL yield.Subsequently, kinetics of ammonium uptake andgrowth of   P. putida PGA1 using SPKO as the solecarbon and energy source with ammonium as thelimiting nutrient was studied by Annuar et al. (2006).They reported that the ammonium uptake by  P. putida PGA1 cells can be described using a first-order kinetic model, indicating that the micro-organism’s specific uptake rate of ammonium and itsgrowth should increase as the ammonium ionconcentrations become higher (  0.1-0.2 gL -1 ).Further increase in the ammonium ion concentrationabove 0.2 g L -1 resulted in slightly lower specificgrowth rates of   P. putida PGA1 (Annuar et al . , 2006,2007).In cultivations using an automated bioreactor,PHA MCL accumulation by  P. putida PGA1 isencouraged under ammonium-limited conditionswith SPKO as the sole carbon and energy source(Annuar et al., 2007). The amount of PHA MCL accumulated and its specific production rate, q PHA ,were influenced by the residual ammoniumconcentration level in the culture medium. It wasobserved in both batch and fed-batch fermentationsthat when the residual ammonium becomesexhausted (<0.05 g L -1 ), the PHA MCL accumulationand q PHA were significantly reduced (Annuar et al.,2007). However, this effect can be reversed byfeeding low amount of ammonium to the culture,resulting in significantly improved PHA MCL yieldand productivity. It is concluded that the feeding of residual ammonium concentration in the culturemedium during the PHA MCL accumulation has a positive effect on sustaining the PHA MCL  biosynthetic capability of the organism. Uptake of SPKO by the micro-organism follows zero-order kinetics, indicating a mass transfer limitation of thefree fatty acids by the  P. putida PGA1 cells (Annuar et al., 2007).Several kinetic models have been proposed for the growth and PHA SCL production by strains of  W.eutropha under chemolithoautotrophic andheterotrophic growth conditions using laboratory-scale automated bioreactor (Heinzle and Lafferty,1980; Mulchandani et al., 1989; Belfares et al.,1995). On the other hand, no formal kinetic modelshave been reported for growth and PHA MCL  production by microorganisms, especially by themain producer of PHA MCL , i.e.,  Pseudomonas sp.In this short communication, a kinetic model for growth and PHA MCL production by  P. putida PGA1is presented which complements the earlier studiesof Annuar et al. (2007). The present study evaluatedseveral kinetic models for growth of   P. putida PGA1on SPKO with ammonium as a limiting nutrient.Two classes of growth models were tested on published experimental data of Annuar et al. (2006),i.e., models incorporating a substrate inhibition parameter and models that consist of only growth parameters. This was followed by the developmentof a simple mathematical model via partial adoptionof a published model of Heinzle and Lafferty (1980),which reasonably describes the limiting substrateconsumption (i.e., ammonium) and PHA MCL  production in  P. putida PGA1 in a batch fermentation.The simulation results for growth, ammoniumconsumption and PHA MCL biosynthesis in  P. putida PGA1 were compared with the publishedexperimental data (Annuar et al., 2007).  Kinetic Model for Growth and PHA MCL Production 219  Brazilian Journal of Chemical Engineering Vol. 25, No. 02, pp. 217 - 228, April - June, 2008 MATERIALS AND METHODSMicroorganism  Pseudomonas putida PGA1 strain was a gift fromProfessor G. Eggink of the AgrotechnologicalResearch Institute, Wageningen, The Netherlands. Medium Composition In all studies, a defined mineral medium was usedwith NaNH 4 HPO 4 .H 2 O providing the limitingammonium nutrient. SPKO was supplied as the solecarbon and energy source. The exact composition of the mineral medium and trace elements used wasdetailed in Annuar et al. (2007). Saponification of  palm kernel oil (PKO) was carried out according toTan et al  . (1997). PKO is the extract from the nut of the oil palm (  Elaeis guineensis Jacq .) fruit. The oilconsists of a mixture of C6–C18:2 fatty acids withapproximately 82% saturated fatty acids and 18%unsaturated fractions. Detailed fatty acidcomposition of palm kernel oil was reported byElson (1992). Shake-Flasks Studies The different growth models for   P. putida PGA1were evaluated using experimental data obtainedfrom shake-flasks cultivation. The correspondingdata and details of the experimental conditions for this cultivation which include the cultivationconditions, growth and ammonium assays, dataanalyses and numerical calculations have beendescribed elsewhere (Annuar et al., 2006). Bioreactor Studies Experimental data for comparison with simulationresults were obtained from published work of Annuar  et al  . (2007), which also elaborated on the bioreactor specifications and experimental conditions (fatty acidcompositions of SPKO, cultivation conditions,analytical methods, data analyses and calculations).Data from batch fermentation was used for comparisonwith the simulation results. The main geometriccharacteristics of the stirred tank bioreactor and theinitial conditions of the experiment are reproduced inTables 1 and 2, respectively. In the bioreactor studies,the temperature and the pH were maintained at 30( r 0.5) q C and 7.0 ( r 0.05), respectively, with anagitation rate of 600 rpm and an aeration rate of 0.5vvm of filtered air. Silicone anti-foaming agent (BDH)was included in the aqueous medium at 1.0 g L -1 . Experimental Data Regression and Estimation of Growth Model Kinetic Parameters Mathematical models describing growth only andthose that incorporated growth inhibitions by thesubstrate were fitted to the shake-flask cultivationdata using non-linear regression function of Polymath 6.0 software. The program uses theLevenberg-Marquardt (LM) algorithm, a techniquethat uses an iterative solution method to calculate thekinetic parameter values. Table 1: Dimensions of the stirred tank bioreactor (Biostat  B 3-liter fermenter,B. Braun Biotech International) and its components. Design parameters Specifications Total volume 3 litresDiameter of inner tank 130 mmHeight of tank 240 mm Number of baffles 4Baffle width 10.5 mmType of impellers Rushton disc turbine Number of impellers 2Distance between impellers 79.5 mmDistance of lower impeller from bottom plate 25 mmImpeller diameter of disc 53 mm Number of blades 6Impeller blade width 10.5 mmImpeller blade length 14.5 mmDiameter of single ring sparger 48 mm Number of holes 14Distance of ring sparger from bottom plate 20 mmDiameter of oxygen electrode 12 mm  220 M. S. M. Annuar, I. K. P. Tan, S. Ibrahimand K. B. Ramachandran  Brazilian Journal of Chemical Engineering  Table 2: Initial conditions for the batch fermentation of   P. putida PGA1 in a stirred tank bioreactor. FermentationmodeWorking volume(L)Initial SPKOconcentration(g L -1 )Initial ammonium(S) concentration(g L -1 )Initial totalbiomass (X)concentration(g L -1 )Initial residualbiomass (R)concentration(g L -1 )Initial PHA MCL (P) concentration(g L -1 ) Batch 1.2 6.8 0.40.115( r 0.050) 0.11 ( r 0.04) 0.009( r 0.002) Simulation of Batch Fermentation Simulation of the batch fermentation in the bioreactor was performed using the differentialequations solver of Polymath 6.0 software. A set of ordinary differential equations (ODE) (eqs. 1, 8 and9, see Results and Discussion section) was solvedusing the Runge-Kutta-Fehlberg (RKF45) algorithm. RESULTS AND DISCUSSION Simple models are necessary in order to have asolid basis for the design of fermentation processes,for economic calculations, and for the controlof fermentation processes. Modeling requiressimplifications of the complex biological system,which are at the same time a major goal of modeling.In this study, a semi-empirical model proposed on the basis of a simple mechanistic description from the work of Heinzle and Lafferty (1980) was partially adopted.They presented a structured model describing batchculture of  Wautersia eutropha strain H16 (formerlyclassified as  Alcaligenes eutrophus H16) under chemolithoautotrophic growth conditions. In their work, growth and storage of poly-  E  -hydroxybutyrate(PHB), i.e., PHA SCL are described as a function of thelimiting substrate S (i.e., ammonium), the residual biomass R (i.e., PHA-free biomass), and the product P(PHB). Their bacterial ammonium consumption andPHA SCL biosynthesis models were fitted to theexperimental data obtained from the reported work of Annuar  et al. (2007); which details the dynamics of thePHA MCL fermentation of   P. putida PGA1 grown on 6.8g L -1 SPKO and 0.4 g L -1 ammonium as carbon andnitrogen sources, respectively. The growth, ammoniumconsumption, and PHA MCL production profiles arereproduced in Figure 1. 00.10.20.30.40.50.60.70.80.910 5 10 15 t (h)    C  o  n  c  e  n   t  r  a   t   i  o  n  s   (  g   /   L   ) Total biomass[X]Ammonium [S]mcl-PHA [P] Figure 1: Growth and accumulation of PHA MCL in  Pseudomonas putida PGA1 in batchfermentation under ammonium-limitation with SPKO as sole carbon and energy source.  Kinetic Model for Growth and PHA MCL Production 221  Brazilian Journal of Chemical Engineering Vol. 25, No. 02, pp. 217 - 228, April - June, 2008 Rate of Cell Growth ( r  R  ) The total dry biomass (X) of   P. putida PGA1consists of two parts, namely PHA MCL (P) andresidual biomass (R), where R is calculated as thedifference between the total dry biomass andPHA MCL concentration (X=R+P). R is thecatalytically active fraction of biomass, whichincludes proteins and nucleic acid.The limiting substrate ammonium (S) is essentialto produce R and limits its synthesis at lowconcentrations. The synthesis of R is described asfollows,dR/dt = r  R  = P .R (1)where r  R  is the rate of synthesis of R and P  is thespecific rate of synthesis of R.The maintenance requirement for the limitingsubstrate is assumed to be small enough to beneglected. Several growth models were tested todescribe the specific growth rate of   P. putida PGA1(Table 3). The growth models were divided into thosethat incorporate limiting substrate-inhibition kineticsand those that contained only growth kinetic parameters. All the models were fitted to theexperimental data from shake-flask culture withvarying initial ammonium concentrations (Annuar etal., 2006). The estimated values for the model kinetic parameters and fitting constant as returned by the fittingalgorithm are shown in Table 3, along with the post-regression statistics. It is clear that growth models thatincorporate the substrate inhibition parameter (  R 2 :0.9867-0.9955) gave better fits to the experimental datacompared to the models with only growth parameters(  R 2 : 0.9094-0.9569). Among the three models that takeinto account the substrate inhibition factor, the Tessier-type model showed the best fit of the experimental data(  R 2 : 0.9955), as compared to the Andrews (  R 2 : 0.9901)and Aiba (  R 2 :0.9867) models. The graphical outputsshowing the fits of the experimental data by the modelswith growth kinetic parameters only and by the growthmodels incorporating the substrate-inhibition kineticare shown in Figure 2(a) and 2(b), respectively. 00.020.040.060.080.10.120.140.160.180.20 0.2 0.4 0.6 0.8 1 Ammonium concentration (g/L)    S  p  e  c   i   f   i  c  g  r  o  w   t   h  r  a   t  e ,  u   (   1   /   h   ) Experimental dataMonod modelMoser modelTessier model Figure 2a): Fitting of the experimental data with growth models (Monod, Moser and Tessier)without substrate inhibition kinetics.
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