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Mathematical Modelling of Ethanol Production From Glucosexylose

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Mathematical Modelling of Ethanol Production From Glucosexylose
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   Biotechnology Letters  23:  1087–1093, 2001.© 2001  Kluwer Academic Publishers. Printed in the Netherlands.  1087 Mathematical modelling of ethanol production from glucose/xylosemixtures by recombinant  Zymomonas mobilis Noppol Leksawasdi, Eva L. Joachimsthal & Peter L. Rogers ∗  Department of Biotechnology, University of New South Wales, Sydney, NSW 2052, Australia ∗  Author for correspondence (Fax: +61 2 9313-6710;E-mail: p.rogers@unsw.edu.au) Received 16 March 2001; Revisions requested 10 April 2001; Revisions received 9 May 2001; Accepted 9 May 2001 Key words:  ethanol, modelling, recombinant  Zymomonas mobilis Abstract A model has been developed for the fermentation of mixtures of glucose and xylose by recombinant  Zymomonasmobilis  strain ZM4(pZB5), containing additional genes for xylose assimilation and metabolism. A two-substratemodel based on substrate limitation, substrate inhibition, and product (ethanol) inhibition was evaluated, andexperimental data was compared with model simulations using a Microsoft EXCEL based program and methodsof statistical analysis for error minimization. From the results it was established that the model provides goodpredictions of experimental batch culture data for 25/25, 50/50, and 65/65 g l − 1 glucose/xylose media.  Nomenclature:  1 – glucose; 2 – xylose;  x  – biomass concentration (g l − 1 );  s  – substrate concentration (g l − 1 ); p  – ethanol concentration (g l − 1 );  µ max  – maximum overall specific growth rate (1 h − 1 );  q s, max  – overall max-imum specific substrate utilization rate (g g − 1 h − 1 ); q p, max  – overall maximum specific ethanol production rate(g g − 1 h − 1 );  α  – weighting factor for glucose consumption;  P  m  – maximum ethanol concentration (g l − 1 );  P  i – threshold ethanol concentration (g l − 1 );  K s  – substrate limitation constant (g l − 1 );  K i  – substrate inhibitionconstant (g l − 1 );  R 2 – correlation coefficient; RSS – residual sum of squares; RRS – relative residual summation;RRS total  – sum of all RRS values. Introduction Ethanol, produced from renewable resources such aslignocellulosic residues, has the potential to be a cost-effective and environmentally sustainable liquid fuel(Zhang  et al.  1995). However the significant con-centrations of glucose and xylose, which are presentin lignocellulosic hydrolysates, must be fully fer-mentable for an economically viable process. The aiminrecentyearshasbeentodeveloprecombinantstrainswhich can utilize these sugars with reasonable yieldsand rates (Laplace  et al.  1995, Olsson  et al.  1995,Zhang  et al.  1995, Ho  et al.  1996). Genetic engi-neering with the ethanologenic  Zymomonas mobilis has achieved a recombinant strain able to simultane-ously ferment glucose and xylose (Zhang  et al.  1995)and subsequent kinetic analysis (Joachimsthal  et al. 1999, Lawford & Rousseau 1999, Joachimsthal &Rogers 2000, Lawford & Rousseau 2000) has con-firmed that relatively high ethanol concentrations andproductivities can be achieved with high yields.Optimization of ethanol fermentations is based onthe development of realistic growth and fermentationmodels. Previous kinetic models for  Z. mobilis  havebeen proposed in the literature (Lee & Rogers 1983,Nipkow  et al.  1986, Veermallu & Agrawal 1990,Garro  et al.  1995). These have generally been mod-ifications of the Monod equation (Monod 1941) andhave included substrate inhibition, product inhibition,as well as substrate limitation effects. Unstructuredmodels such as these can also providea generalunder-standingofthemetabolicprocessesinvolvedaswellasthe basis for process optimization.The unstructuredmathematical model presented inthis study is concerned with simultaneous fermenta-tion of two sugars, glucose and xylose, by the recom-  1088binant  Zymomonas mobilis  ZM4(pZB5). There havebeen previous reports of models for  Saccharomycescerevisiae  on mixtures of glucose/maltose (Lee  et al. 1995) and glucose/galactose (Gadgil  et al.  1996), aswell as for  Z. mobilis  on glucose/fructose (Lee &Huang 2000). Finding a model which simulates thefermentation characteristics of recombinant  Z. mobilis ZM4(pZB5) was initiated by modelling growth andfermentation on single sugars (glucose and xylose).These models for individual sugars were then com-bined to form a model to simulate the kinetics of glucose/xylose fermentation in batch systems. Materials and methods  Microorganism Recombinant  Zymomonasmobilis ZM4(pZB5)hasthepZB5 plasmid transformed into the host strain andwas kindly made available by Dr Min Zhang (NREL,Golden, CO). The  Escherichia coli  genes for produc-tion of xylose isomerase, xylulokinase, transketolase,and transaldolase have been introduced into the pZB5plasmid.Theseconferxyloseassimilationandfermen-tation capability. The strain was maintained as frozenstock culture in growth media (see below) supple-mented with 10  µ g ml − 1 tetracycline and 10% (v/v)glycerol at – 70  ◦ C.  Media composition and preparation Growth media for  Z. mobilis : carbon source(s); yeastextract (10 g l − 1 inoculum, 5 g l − 1 fermentation me-dia); KH 2 PO 4  (2 g l − 1 ); mgSO 4  ·  7H 2 O (1 g l − 1 );(NH 4 ) 2 SO 4  (2 g l − 1 ). Media were sterilized by au-toclaving at 121  ◦ C for 10 min. Selective pressure forrecombinantswas appliedusinga mediumsupplementof 10  µ g ml − 1 tetracycline. Fermentation studies All fermentation inocula were prepared in stationarycultivations incubated at 30  ◦ C. Fermentations wereinitiated with a 10% (v/v) inoculum. Experimentswere conducted in a 2-l controlled fermenter usinga working volume of 1 l with an agitation rate of 200 rpm, at 30  ◦ C, and a pH of 5. Control of pHwas providedby the automaticaddition of 3 M NaOH.Samples were removed at various times and stored at − 20  ◦ C until sample analysis.  Analytical methods Biomass concentration was determined turbidometri-cally (at 660 nm). Absorbance measurements weremade usingwhole brothsamples that were dilutedintothe linear range of the instrument. A correlation fac-tor (0.23) previously determined for the strain, wasused to convert the absorbance values into biomassconcentrations.Sample supernatants were analyzed to determinethe concentrations of glucose, xylose, and ethanol.Analysis was performed using HPLC with an AminexHPX-87H column (Bio-Rad) with 5 mm H 2 SO 4  (at65  ◦ C, 0.6 ml min − 1 ) as the mobile phase. Standardscontainingmixedcomponentswere periodicallyruntoverify calibration accuracy.The batch kinetic data for 25/25, 50/50, and65/65 g l − 1 glucose/xylose media using the aboveanalytical methods have been reported previously(Joachimsthal & Rogers 2000). The program for modelling and simulation The design of VBA (Visual Basic for Applications)program codes in Microsoft EXCEL for modellingwas based on the well established Gauss–Newtonmethod for non-linear regression with step size halv-ing (Draper & Smith 1981, Bates & Watts 1988, My-ers 1990, Ratkowsky 1990). The simulation programwas designed to achieve the minimal total ResidualSum of Squares (RSS) and acceptable curve fitting of experimental values.RSS total  =  RSS x  +  RSS s 1  +  RSS s 2  +  RSS p ,  (1)where:  x  =  biomass concentration (g l − 1 );  s 1  =  glu-cose concentration (g l − 1 );  s 2  =  xylose concentration(g l − 1 );  p  =  ethanol concentration (g l − 1 ). Development of a double substrate model  Microbial growth For formulation of the double substrate model, themicrobial growth on each sugar is represented bythe specific growth rates of recombinant  Z. mobilis ZM4(pZB5) on glucose and xylose as single carbonsources. The basis for these equations was taken froma previous model development for  Z. mobilis  ZM4 forgrowth and fermentation of glucose (Lee & Rogers1983). The equations assume Monod kinetics for sub-strate limitation and ethanol inhibition, with both a  1089threshold level and a maximum inhibitory concentra-tion, as well as a typical substrate inhibition term.These relationships are represented by Equations (2)and (3).For glucose: r x, 1  =  µ max , 1   s 1 K sx, 1  +  s 1  ×  1  − p  −  P  ix, 1 P  mx, 1  −  P  ix, 1   K ix, 1 K ix, 1  +  s 1  .  (2)For xylose: r x, 2  =  µ max , 2   s 2 K sx, 2  +  s 2  ×  1  − p  −  P  ix, 2 P  mx, 2  −  P  ix, 2   K ix, 2 K ix, 2  +  s 2  .  (3)The terms used are defined fully in the Nomencla-ture section, with subscript 1 referring to glucose andsubscript 2 to xylose.As growth occurs simultaneously on both glucoseand xylose, and competition for uptake occurs be-tween the two sugars, the contribution of glucose andxylose to biomass formation is assumed to be:d x d t  =  j  1 r x, 1 x  +  j  2 r x, 2 x,  (4)where the weighting factor  j  is dependent on therelative consumption rates of the two sugars. Theweighting factors for glucose and xylose uptakes arespecified as  j 1  and  j 2 , respectively. An important as-sumptionof the model is that the sum of the weightingfactors for glucose and xylose uptake is unity. Thisis based on the assumption that both glucose and xy-lose compete for uptake via a commonand unchangedsugar transport system in  Z. mobilis . This system hasbeen reported previously as the glucose facilitatedtransport system (mediated by the  Glf   gene) (DiMarco& Romano 1985, Parker  et al.  1995, Weisser  et al. 1995, 1996). Other authors have reported simulta-neous glucose and xylose uptake by recombinant  Z.mobilis  (Zhang et al.  1995,Krishnan  et al.  2000, Law-ford & Rousseau 1999, 2000, Lawford  et al.  2000). Itis evident from our earlier kinetic data also that bothglucose and xylose can be taken up simultaneously,with xylose at a considerably slower rate.As a result of this assumption, we can write: j  1  +  j  2  =  1  ⇒  j  2  =  1  −  j  1 .  (5)For simplification,  j 1  is designatedas  α . The modifica-tionofEquation(4)toincludebothglucoseandxyloseis shown in Equation (6):d x d t  = [ ar x, 1  +  ( 1  −  α)r x, 2 ] x.  (6) Glucose and xylose uptake For sugar uptake, glucose and xylose are consideredin separate rate equations. The same constraint isplaced upon these proportioning factors to indicatean unchanged activity and constant total sugar uptakerate via the  Glf   diffusion transport protein for glu-cose/xylose. The glucose and xylose uptakes can berepresented by Equations (7) and (8), respectively,d s 1 d t  = − αq s, max , 1   s 1 K ss, 1  +  s 1  ×  1  − p  −  P  is, 1 P  ms, 1  −  P  is, 1   K is, 1 K is, 1  +  s 1  x,  (7)d s 2 d t  = − ( 1  −  α)q s, max , 2   s 2 K ss, 2  +  s 2  ×  1  − p  −  P  is, 2 P  ms, 2  −  P  is, 2   K is, 2 K is, 2  +  s 2  x.  (8)  Ethanol production For ethanol production, the rate is given by Equation(9). The rate of ethanol production can be related tothe rates of glucose and xylose uptake as shown inEquations (10) and (11).d p d t  = [ αr p, 1  +  ( 1  −  α)r p, 2 ] x  (9)For glucose: r p, 1  =  q p, max , 1   s 1 K sp, 1  +  s 1  ×  1  − p  −  P  ip, 1 P  mp, 1  −  P  ip, 1   K ip, 1 K ip, 1  +  s 1  . (10)For xylose: r p, 2  =  q p, max , 2   s 2 K sp, 2  +  s 2  ×  1  − p  −  P  ip, 2 P  mp, 2  −  P  ip, 2   K ip, 2 K ip, 2  +  s 2  . (11)Parameter values which resulted in minimization of thedifferencesbetweenthesimulationandexperimen-tal data were calculated usingcomputationalstrategiesoutlined in the Materials and methods section.  1090 Fig. 1.  Simulation of the mixed sugar system and experimental datafor ZM4(pZB5) on 25 g l − 1 glucose and 25 g l − 1 xylose medium.  , Glucose;  , xylose;  , ethanol;  ã , biomass. Glucose/xylose fermentation simulation Simplification of the derived model and determinationof optimal parameter values Conditions were imposed upon the parameters to re-late to their microbial/biochemical relevance. Theseconditions are listed in Table 1. Initial parametervalues used to define ‘local search region’ were deter-minedfrompreviouslypublishedvalues(Joachimsthal& Rogers 2000). Simulation of the batch glucose/xylose fermentations The initial concentration values of each component(Table2a)andthevaluesofthekineticparameters(Ta-ble 2b) which resulted in the minimization process of RSS total  valueweredeterminedandthefit ofthemodelto the experimental data calculated. The RSS total  andcorrelation coefficient ( R 2 ) values were used to assessthe fit of the model to the experimental data.As shown in Figures 1–3, the glucose/xylosemodel demonstrates excellent simulation of the exper-imental data for glucose and xylose media containing25/25, 50/50, and 65/65 g l − 1 of each sugar. Sensitivity analysis The model for the fermentation of glucose/xylose ina batch system was examined for its sensitivity tochanges in the value of   α  with all other initial andparameter values being allowed to float within previ-ously defined limits. RSS total  was not considered tobe the best indicator for sensitivity analysis becauseit measures fitting only in ‘absolute terms’, with the Fig. 2.  Simulation of the mixed sugar system and experimental datafor ZM4(pZB5) on 50 g l − 1 glucose and 50 g l − 1 xylose medium.  , Glucose;  , xylose;  , ethanol;  ã , biomass. Fig. 3.  Simulation of the mixed sugar system and experimental datafor ZM4(pZB5) on 65 g l − 1 glucose and 65 g l − 1 xylose medium.  , Glucose;  , xylose;  , ethanol;  ã , biomass. individual profile errors contributing disproportion-ately to the RSS total . For this reason, an RRS total  wasevaluated.The RRS total  was determined using the followingequation.RRS total  =  RRS x  +  RRS s 1  RRS s 2  RRS p  (12)whereRRS m  = N   n = 1  1  − i predicted i exp  ,i predicted  =  predicted value;  i exp  =  experimental value; m  =  x ,  s 1 ,  s 2 , or  p  (designated variable in eachdata set);  N   =  total number of data points in eachexperiment;  n  =  1 to  N  .The lowest RRS total  (the sum of all RRS values),and hence the best fit, was determined to be for  α  =0.65 (Table 3).
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