1. Leksawasdi,N., Joachimsthal,E.L., Rogers,P.L. Department of Biotechnology, University of New South Wales, Sydney, NSW, 2052, Australia Abstract The development of a model for the fermentation of mixtures of glucose and xylose by recombinant Zymomonas mobilis strain ZM4(pZB5), containing additional genes for xylose assimilation and metabolism, has been the focus of this study. 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 glucose/xylose media. Introduction Ethanol, produced from renewable resources such as lignocellulosic residues, has the potential to be a cost-effective and environmentally sustainable liquid fuel. 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. Genetic engineering with the ethanologenic Z. mobilis has achieved a recombinant strain able to ferment glucose and xylose (Zhang et al., 1995) and subsequent kinetic analysis (Joachimsthal et al., 1999; Lawford and Rousseau, 1999; Joachimsthal and Rogers, 2000; Lawford and Rousseau, 2000) has confirmed that relatively high ethanol concentrations and productivities can be achieved with high yields. The optimization and industrial application of alcoholic fermentations has required the development of growth and fermentation models. Previous kinetic models for Z. mobilis have been proposed in the literature (Lee and Rogers, 1983; Nipkow et al., 1986; Veermallu and Agrawal, 1990; Garro et al., 1995). These have generally been modifications of the Monod equation (Monod, 1941) and have included substrate inhibition and product inhibition effects. Unstructured models such as these can provide also a fundamental understanding of the microbial metabolic processes involved. The unstructured mathematical model presented in this study is concerned with fermentation of two sugars, glucose and xylose, by recombinant Zymomonas mobilis ZM4(pZB5). Materials & Methods Microorganism and Fermentation Studies Recombinant Zymomonas mobilis ZM4(pZB5) has the pZB5 plasmid transformed into the host strain (conferring xylose assimilation and pentose metabolism) and was made available by Dr. Min Zhang (NREL, Golden, Colorado). Growth media for Z. mobilis: carbon source(s); yeast extract (10 g/L inoculum, 5 g/L fermentation media); KH 2 PO 4 (2 g/L); MgSO 4 ·7H 2 O (1 g/L); (NH 4 ) 2 SO 4 (2 g/L). Selective pressure for recombinants was applied using a medium supplement of 10  g/ml tetracycline. Experiments were conducted in a 2 L LH controlled fermentor using a working volume of 1 L (200 rpm, 30°C, pH 5.0). Biomass determined by optical density (at 660 nm) and dry cell weight measurements. Sugars and ethanol were measured by HPLC with an Aminex HPX-87H column (Bio-Rad). The Program for Modeling and Simulation The design of VBA (Visual Basic for Applications) program codes in Microsoft  EXCEL for modeling was based on the well established Gauss-Newton method for non-linear regression with step size halving (Myers, 1990; Ratkowsky, 1990). The simulation program was designed to achieve the minimal total Residual Sum of Squares (RSS) and acceptable curve fitting of experimental values. (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 ZM4(pZB5) on glucose and xylose as single carbon sources. For glucose: For 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: 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 and 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 and Rousseau, 1999; Lawford and Rousseau, 2000; Lawford et al., 2000). 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: For simplification, j 1 is designated as . The modification of equation (4) to include both glucose and xylose is shown in equation (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. Ethanol Production 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). For glucose: For xylose: 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  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 individual profile errors contributing disproportionately to the RSS total. For this reason, an RRS total was evaluated. The lowest RRS total (the sum of all RRS values), and hence the best fit, was determined to be for  = 0.65. Modeling Continuous Culture of ZM4(pZB5) on Glucose/Xylose The model developed to fit the batch system was adjusted to fit continuous culture experimental data. Equations (12) to (15) are used to simulate the model. The same parameters found for batch culture (Table 1) were used in the model for continuous culture. Separate terms for maintenance energy requirements on glucose and xylose were not included in the model, as the current model based on q s values for glucose and xylose incorporates sugar uptake for both growth and for endogenous metabolism (maintenance). Figure 2 shows the fit of the model to the experimental data. Discussion A model representing glucose/xylose fermentation by Z. mobilis ZM4(pZB5) has been successfully developed for batch and continuous culture. The specific rate of glucose uptake was 65% of its maximum value, while that of xylose was 35% of its maximum value. 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. Xylose substrate inhibition effects are less significant than those of glucose for both growth and ethanol production. This forms a basis for predictions of optimal dilution rates and maximum productivities for various conditions and sugar concentrations. Nomenclature 1 = Glucose, 2 = Xylose, x = Biomass (g/L),  max = Maximum specific growth rate (1/h), s = Substrate (g/L), q s,max = Maximum specific substrate utilization rate (g/(g·h)), p = Ethanol (g/L), q p,max = Maximum specific ethanol production rate (g/(g·h)),  = Weighting factor for glucose consumption, P m = Maximum ethanol concentration (g/L), P i = Threshold ethanol concentration (g/L), K s = Substrate limitation constant (g/L), K i = Substrate inhibition constant (g/L), RSS = Residual sum of squares, RRS = Relative residual summation References Myers,R.H. (1990). Classical and Modern Regression with Applications, 2 nd Edition. Duxbury Press, Belmont. Nipkow,A., Sonnleitner,B., Fiechter,A. (1986). J. Microbiol., 4: 35–47. Parker,C., Barnell,W., Snoep,J., Ingram,L., Conway,T. (1995). Molec. Microbiol., 15: 795–802. Ratkowsky,D.A. (1990). Handbook of Nonlinear Regression Models. Marcel Dekker, New York. Veermallu,U., Agrawal,P. (1990). Biotechnol. Bioeng., 36: 694–704. Weisser,P., Krämer,R., Sahm,H., Sprenger,G.A. (1995). J. Bacteriol., 177: 3351–3354. Zhang,M., Eddy,C., Deanda,K., Finkelstein,M., Picataggio,S. (1995). Science, 267: 240–243. Acknowledgements The financial support of NREL (National Renewable Energy Laboratories, U.S.A) and the Thai Government (N. Leksawasdi) is gratefully acknowledged. The project is funded partially under the U.S Department of Energy Sub Contract XDH-9-29055-01. The values of the kinetic parameters (Table 1) 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 Figure 1, the glucose/xylose model demonstrates excellent simulation of the experimental data for glucose and xylose media containing 50/50 g/L of each sugar. Note: All of the R 2 values of the three concentrations (25/25, 50/50, and 65/65 g/L) were greater than 0.998. The RSS total for individual concentrations were 15.9, 48.1, and 156 for 25/25, 50/50, and 65/65 g/L respectively. Table 1Optimal kinetic parameters for all data sets with  = 0.65 0 10 20 30 40 50 60 05101520253035404550 Time (h) Glucose, Xylose, Ethanol (g/L) 0 1 2 3 4 5 6 Biomass (g/L) Figure 1. Simulation of the mixed sugar system and experimental batch culture data for ZM4(pZB5) on 50 g/L glucose and 50 g/L xylose medium. Dots represent experimental data, lines represent simulated curve. 0 5 10 15 20 25 30 35 40 45 0.060.080.100.120.140.16 Dilution Rate (1/h) Glucose, Xylose, Ethanol (g/L) 0 1 2 3 4 5 6 7 8 9 Biomass (g/L) Figure 2. Simulation of the mixed sugar system and experimental continuous culture data for ZM4(pZB5) on 40 g/L glucose and 40 g/L xylose medium. Dots represent experimental data, lines represent simulated curve. Glucose/Xylose Fermentation Simulation Simulation of the Batch Glucose/Xylose Fermentations (2) (3) (4) (5) (6) _ (7) (8) (9)(10)(11) (12) (13) (14) (15) References DiMarco,A., Romano,A. (1985). Appl. Env. Microbiol., 49: 151–157. Garro,O.A., Rodrigues,E., Unda,R.P., Callieri,D.A.S. (1995). J. Chem. Technol. Biotechnol., 63: 367–373. Joachimsthal,E.L., Haggett,K.D., Rogers,P.L. (1999). Appl. Biochem. Biotechnol., 77-79: 147–157. Joachimsthal,E.L., Rogers,P.L. (2000). Appl. Biochem. Biotechnol., 84–86: 343–356. Krishnan,M.S., Blanco,M., Shattuck,C.K., Ngheim,N.P., Davidson,B.H.. (2000). Appl. Biochem. Biotechnol., 84–86: 525–541. Lawford,H.G., Rousseau,J.D, Tolan,J.S. (2000). 22 nd Symposium on Biotechnology for Fuels and Chemicals, Gatlinburg, Tennessee, U.S.A., May 7–11, 2000. Lawford,H.G., Rousseau,J.D. (1999). Appl. Biochem. Biotechnol., 77-79: 235–249. Lawford,H.G., Rousseau,J.D. (2000). Appl. Biochem. Biotechnol., 84-86: 277–293. Lee,K.J., Rogers,P.L. (1983). Chem. Eng. Journal, 27: B31–B38. Monod,J. (1941). Recherches sur la Croissance Bacteriennes. Masson, Paris. Glucose Xylose Ethanol Biomass Glucose Xylose Ethanol Biomass