Mathematical modelling of ethanol production from glucose/xylose mixtures by recombinant Zymomonas mobilis

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1 Biotechnology Letters 23: , Kluwer Academic Publishers. Printed in the Netherlands Mathematical modelling of ethanol production from glucose/xylose mixtures 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: ; 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 Zymomonas mobilis strain ZM4pZB5, containing additional genes for xylose assimilation and metabolism. A two-substrate model based on substrate limitation, substrate inhibition, and product ethanol inhibition was evaluated, and experimental data was compared with model simulations using a Microsoft EXCEL based program and methods of statistical analysis for error minimization. From the results it was established that the model provides good predictions 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 maximum 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 inhibition constant 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 as lignocellulosic residues, has the potential to be a costeffective and environmentally sustainable liquid fuel Zhang et al However the significant concentrations of glucose and xylose, which are present in lignocellulosic hydrolysates, must be fully fermentable for an economically viable process. The aim in recent years has been to develop recombinant strains which can utilize these sugars with reasonable yields and rates Laplace et al. 1995, Olsson et al. 1995, Zhang et al. 1995, Ho et al Genetic engineering with the ethanologenic Zymomonas mobilis has achieved a recombinant strain able to simultaneously ferment glucose and xylose Zhang et al and subsequent kinetic analysis Joachimsthal et al. 1999, Lawford & Rousseau 1999, Joachimsthal & Rogers 2000, Lawford & Rousseau 2000 has confirmed that relatively high ethanol concentrations and productivities can be achieved with high yields. Optimization of ethanol fermentations is based on the development of realistic growth and fermentation models. Previous kinetic models for Z. mobilis have been proposed in the literature Lee & Rogers 1983, Nipkow et al. 1986, Veermallu & Agrawal 1990, Garro et al These have generally been modifications of the Monod equation Monod 1941 and have included substrate inhibition, product inhibition, as well as substrate limitation effects. Unstructured models such as these can also provide a general understanding of the metabolic processes involved as well as the basis for process optimization. The unstructured mathematical model presented in this study is concerned with simultaneous fermentation of two sugars, glucose and xylose, by the recom-

2 1088 binant Zymomonas mobilis ZM4pZB5. There have been previous reports of models for Saccharomyces cerevisiae on mixtures of glucose/maltose Lee et al and glucose/galactose Gadgil et al. 1996, as well as for Z. mobilis on glucose/fructose Lee & Huang Finding a model which simulates the fermentation characteristics of recombinant Z. mobilis ZM4pZB5 was initiated by modelling growth and fermentation on single sugars glucose and xylose. These models for individual sugars were then combined to form a model to simulate the kinetics of glucose/xylose fermentation in batch systems. Materials and methods Microorganism Recombinant Zymomonas mobilis ZM4pZB5 has the pzb5 plasmid transformed into the host strain and was kindly made available by Dr Min Zhang NREL, Golden, CO. The Escherichia coli genes for production of xylose isomerase, xylulokinase, transketolase, and transaldolase have been introduced into the pzb5 plasmid. These confer xylose assimilation and fermentation capability. The strain was maintained as frozen stock culture in growth media see below supplemented with 10 µg ml 1 tetracycline and 10% v/v glycerol at 70 C. Media composition and preparation Growth media for Z. mobilis: carbon sources; yeast extract 10 g l 1 inoculum, 5 g l 1 fermentation media; KH 2 PO 4 2 g l 1 ; mgso 4 7H 2 O1gl 1 ; NH 4 2 SO 4 2 g l 1. Media were sterilized by autoclaving at 121 C for 10 min. Selective pressure for recombinants was applied using a medium supplement of 10 µg ml 1 tetracycline. Fermentation studies All fermentation inocula were prepared in stationary cultivations incubated at 30 C. Fermentations were initiated with a 10% v/v inoculum. Experiments were conducted in a 2-l controlled fermenter using a working volume of 1 l with an agitation rate of 200 rpm, at 30 C, and a ph of 5. Control of ph was provided by the automatic addition of 3 M NaOH. Samples were removed at various times and stored at 20 C until sample analysis. Analytical methods Biomass concentration was determined turbidometrically at 660 nm. Absorbance measurements were made using whole broth samples that were diluted into the linear range of the instrument. A correlation factor 0.23 previously determined for the strain, was used to convert the absorbance values into biomass concentrations. Sample supernatants were analyzed to determine the concentrations of glucose, xylose, and ethanol. Analysis was performed using HPLC with an Aminex HPX-87H column Bio-Rad with 5 mm H 2 SO 4 at 65 C, 0.6 ml min 1 as the mobile phase. Standards containing mixed components were periodically run to verify calibration accuracy. The batch kinetic data for 25/25, 50/50, and 65/65 g l 1 glucose/xylose media using the above analytical methods have been reported previously Joachimsthal & Rogers The program for modelling and simulation The design of VBA Visual Basic for Applications program codes in Microsoft EXCEL for modelling was based on the well established Gauss Newton method for non-linear regression with step size halving Draper & Smith 1981, Bates & Watts 1988, Myers 1990, Ratkowsky The simulation program was designed to achieve the minimal total Residual Sum of Squares RSS and acceptable curve fitting of experimental values. RSS total = RSS x + RSS s1 + RSS s2 + RSS p, 1 where: x = biomass concentration g l 1 ; s 1 = glucose 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, the microbial growth on each sugar is represented by the specific growth rates of recombinant Z. mobilis ZM4pZB5 on glucose and xylose as single carbon sources. The basis for these equations was taken from a previous model development for Z. mobilis ZM4 for growth and fermentation of glucose Lee & Rogers The equations assume Monod kinetics for substrate limitation and ethanol inhibition, with both a

3 1089 threshold level and a maximum inhibitory concentration, 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 For xylose: r x,2 = µ max,2 s 1 K sx,1 + s 1 1 p P ix,1 P mx,1 P ix,1 s 2 K sx,2 + s 2 1 p P ix,2 P mx,2 P ix,2 Kix,1 K ix,1 + s 1 Kix,2 K ix,2 + s The terms used are defined fully in the Nomenclature section, with subscript 1 referring to glucose and subscript 2 to xylose. As growth occurs simultaneously on both glucose and xylose, and competition for uptake occurs between the two sugars, the contribution of glucose and xylose to biomass formation is assumed to be: dx = j 1 r x,1 x + j 2 r x,2 x, 4 where the weighting factor j is dependent on the relative consumption rates of the two sugars. The weighting factors for glucose and xylose uptakes are specified as j 1 and j 2, respectively. An important assumption of the model is that the sum of the weighting factors for glucose and xylose uptake is unity. This is based on the assumption that both glucose and xylose compete for uptake via a common and unchanged sugar transport system in Z. mobilis. This system has been reported previously as the glucose facilitated transport system mediated by the Glf gene DiMarco & Romano 1985, Parker et al. 1995, Weisser et al. 1995, Other authors have reported simultaneous glucose and xylose uptake by recombinant Z. mobilis Zhang et al. 1995, Krishnan et al. 2000, Lawford & Rousseau 1999, 2000, Lawford et al It is evident from our earlier kinetic data also that both glucose 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 designated as α. The modification of Equation 4 to include both glucose and xylose is shown in Equation 6: dx =[ar x,1 + 1 αr x,2 ]x. 6 Glucose and xylose uptake For sugar uptake, glucose and xylose are considered in separate rate equations. The same constraint is placed upon these proportioning factors to indicate an unchanged activity and constant total sugar uptake rate via the Glf diffusion transport protein for glucose/xylose. The glucose and xylose uptakes can be represented by Equations 7 and 8, respectively, ds 1 ds 2 = αq s,max,1 s 1 K ss,1 + s 1 1 p P is,1 P ms,1 P is,1 = 1 αq s,max,2 Ethanol production 1 p P is,2 P ms,2 P is,2 Kis,1 x, 7 K is,1 + s 1 s 2 K ss,2 + s 2 Kis,2 K is,2 + s 2 x. 8 For ethanol production, the rate is given by Equation 9. The rate of ethanol production can be related to the rates of glucose and xylose uptake as shown in Equations 10 and 11. dp =[αr p,1 + 1 αr 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 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 Kip,1 K ip,1 + s 1 Kip,2 K ip,2 + s Parameter values which resulted in minimization of the differences between the simulation and experimental data were calculated using computational strategies outlined in the Materials and methods section.

4 1090 Fig. 1. Simulation of the mixed sugar system and experimental data for ZM4pZB5 on 25 g l 1 glucose and 25 g l 1 xylose medium.,glucose;, xylose;, ethanol;, biomass. Fig. 2. Simulation of the mixed sugar system and experimental data for ZM4pZB5 on 50 g l 1 glucose and 50 g l 1 xylose medium.,glucose;, xylose;, ethanol;, biomass. Glucose/xylose fermentation simulation Simplification of the derived model and determination of optimal parameter values Conditions were imposed upon the parameters to relate to their microbial/biochemical relevance. These conditions are listed in Table 1. Initial parameter values used to define local search region were determined from previously published values Joachimsthal & Rogers Simulation of the batch glucose/xylose fermentations The initial concentration values of each component Table 2a and the values of the kinetic parameters Table 2b which resulted in the minimization process of RSS total value were determined and the fit of the model to the experimental data calculated. The RSS total and correlation coefficient R 2 values were used to assess the fit of the model to the experimental data. As shown in Figures 1 3, the glucose/xylose model demonstrates excellent simulation of the experimental data for glucose and xylose media containing 25/25, 50/50, and 65/65 g l 1 of each sugar. Sensitivity analysis The model for the fermentation of glucose/xylose in a batch system was examined for its sensitivity to changes in the value of α with all other initial and parameter values being allowed to float within previously defined limits. RSS total was not considered to be the best indicator for sensitivity analysis because it measures fitting only in absolute terms, with the Fig. 3. Simulation of the mixed sugar system and experimental data for ZM4pZB5 on 65 g l 1 glucose and 65 g l 1 xylose medium.,glucose;, xylose;, ethanol;, biomass. individual profile errors contributing disproportionately to the RSS total. For this reason, an RRS total was evaluated. The RRS total was determined using the following equation. RRS total = RRS x + RRS s1 RRS s2 RRS p 12 where N RRS m = 1 i predicted, n=1 i exp i predicted = predicted value; i exp = experimental value; m = x, s 1, s 2, or p designated variable in each data set; N = total number of data points in each experiment; n = 1toN. 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.

5 1091 Table 1. Conditions used for initial model parameter simplification based on microbial/biochemical relevance. Condition Assumption 1 q p,max,1 < 0.51q s,max,1 Based on theoretical yields of ethanol from glucose and xylose q p,max,2 < 0.53q s,max,2 2 K ss,1 = K sp,1 When sugar uptake is affected by low sugar concentrations the K ss,2 = K sp,2 ethanol production rate is affected in the same way 3 P ms,1 = P mp,1 When sugar uptake is inhibited completely by ethanol no further P ms,2 = P mp,2 ethanol can be produced 4 P is,1 = P ip,1 The ethanol concentration that begins to inhibit sugar uptake also P is,2 = P ip,2 begins to inhibit ethanol production 5 K is,1 = K ip,1 When sugar uptake is limited by the concentration of sugar, K is,2 = K ip,2 ethanol production is limited in the same way Discussion A model representing fermentation of glucose and xylose by the recombinant Z. mobilis ZM4pZB5 has been successfully developed. As seen from Figures 1 3, the predicted results are in good agreement with the experimental batch culture data. The parameters estimated in the simulation can be related to sensible microbial/biochemical values. The model describes the high ethanol production rate during the initial phase of primary glucose/xylose fermentation, followed by the slower production rate from xylose after glucose is consumed. The model also accommodates the experimentally observed simultaneous utilization of glucose and xylose in batch culture. From an evaluation of the parameter values determined using the minimization routine, some conclusions may be drawn. In the present model for example, the substrate limitation Monod or saturation constant for biomass production by xylose K sx,2 was approximately 3 times that of glucose K sx,1 indicating a higher affinity for glucose than xylose at substrate limiting levels. Other reports comparing the glucose and xylose saturation constants for organisms such as Saccharomyces cerevisiae Krishnan et al and Klebsiella oxytoca Turner et al relate a similar result with the K sx value for xylose being 3 6 times that of glucose. This study incorporated weighting factors to represent the relative preference for sugar utilization and the production of ethanol and biomass from either glucose or xylose. Assuming direct competition between glucose and xylose for the transport system in Z. mobilis, this parameter designated α showed that the specific rate of glucose uptake was 65% of its maximum value, while that of xylose was 35% of its maximum value when the two sugars were present initially in a 1:1 ratio. These values were found to give the best fit, as was determined by sensitivity analysis. From the model parameter values, ethanol would become inhibitory to growth from glucose and xylose above a threshold level of approximately gl 1 P ix,1, P ix,2. Threshold ethanol concentrations of 42.6 g l 1 P ip,1 and 53.1 g l 1 P ip,2 were determined for glucose and xylose uptake respectively. In general, growth would be subject to complete ethanol inhibition at a lower ethanol concentration than for sugar uptake. The maximum inhibitory ethanol concentration for growth on glucose P mx,1 = 57.2gl 1 was similar to that for growth on xylose P mx,2 = 56.3gl 1. The maximum inhibitory ethanol concentration for glucose uptake P ms,1 = 75.4 gl 1 was slightly lower than that for xylose uptake P ms,2 = 81.2 gl 1. The model parameter values indicate that biomass production from glucose or xylose was more sensitive to ethanol inhibition, than sugar uptake and subsequent ethanol production. The model parameter values indicate that significant glucose inhibition of the rate of growth would occur at concentrations above 200 g l 1 K ix,1, which is lower than the concentration above which xylose inhibits biomass production K ix,2 = 600gl 1. Glucose would become significantly inhibitory to ethanol production at concentrations above 186 g l 1 K ip,1, whereas xylose inhibition effects on ethanol production are insignificant at xylose levels used in the

6 1092 Table 2. a. Initial values for the batch fermentation of ZM4pZB5 on various glucose/xylose media with α = Glucose/xylose 25/25 50/50 65/65 g l 1 x s s p b. Optimal kinetic parameters for all data sets with α = Glucose Biomass production model Xylose µ max, µ max,2 0.1 K sx, K sx, P mx, P mx, K ix,1 200 K ix,2 600 P ix, P ix, Glucose and xylose consumption model q s,max, q s,max, K ss, K ss, P ms, P ms, K is,1 186 K is,2 600 P is, P is, Ethanol production model q p,max, q p,max, K sp, K sp, P mp, P mp, K ip,1 186 K ip,2 600 P ip, P ip, Note: All of the R 2 values of the three concentrations 25/25, 50/50, and 65/65 g l 1 were greater than The RSS total for individual concentrations were 15.9, 48.1, and 156 for 25/25, 50/50, and 65/65 g l 1 respectively. present experiments K ip,2 = 600 g l 1. This indicates that xylose substrate inhibition effects are less significant than those of glucose for both growth and ethanol production. In conclusion, it is evident that a modelling approach can provide increased insight into the various factors influencing the fermentation kinetics of a recombinant strain of Z. mobilis on glucose/xylose media. It provides also a basis for its extension to continuous culture data and to predictions of optimal dilution rates and maximum productivities for various conditions and sugar concentrations. Table 3. Sensitivity of the mixed sugar model to weighting factor for glucose consumption α. α Acknowledgements RRS total The financial support of NREL National Renewable Energy Laboratory, USA and the Thai Government N. Leksawasdi is gratefully acknowledged. The project is funded partially under the US Department of Energy Sub Contract XDH References Bates DM, Watts DG 1988 Nonlinear Regression Analysis and its Applications. New York: J. Wiley, 123 pp. DiMarco A, Romano A 1985 Appl. Env. Microbiol. 49: Draper NR, Smith H 1981 In: Applied Regression Analysis, 2nd edn. New York: J. Wiley, pp Gadgil CJ, Bhat PJ, Venkatesh KV 1996 Biotechnol. Prog. 12: Garro OA, Rodriguez E, Unda RP, Callieri DAS 1995 J. Chem. Technol. Biotechnol. 63: Ho NWY, Toon S, Chen ZD, Brainard A, Lumpkin RE, Riley CJ, Philippidis GP th Symposium on Biotechnology for Fuels and Chemicals, Gatlinburg, TN, May 5 9, Joachimsthal EL, Rogers PL 2000 Appl. Biochem. Biotechnol : Joachimsthal EL, Haggett KD, Rogers PL 1999 Appl. Biochem. Biotechnol : Krishnan MS, Blanco M, Shattuck CK, Ngheim NP, Davidson BH 2000 Appl. Biochem. Biotechnol : Krishnan MS, Ho NWWY, Tsao GT 1999 Appl. Biochem. Biotechnol : Laplace JM, Delgenes JP, Moletta R, Navarro JM 1995 Appl. Microbiol. Biotechnol. 36: Lawford HG, Rousseau JD 1999 Appl. Biochem. Biotechnol : Lawford HG, Rousseau JD 2000 Appl. Biochem. Biotechnol : Lawford HG, Rousseau JD, Tolan JS nd Symposium on Biotechnology for Fuels and Chemicals, Gatlinburg, TN, May 7 11, 2000.

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