Dynamic flux balance analysis (DFBA) enables the use of detailed intracellular metabolic models for prediction of cellular growth and product formation in batch and fed-batch cultures. The DFBA framework couples stoichiometric balances on intracellular metabolites with extracellular balances on biomass, substrates, and metabolic byproducts under the reasonable assumption that the intracellular dynamics are fast compared to the extracellular dynamics. The distribution of fluxes through the metabolic network is resolved by solution of a linear programming problem with an assumed cellular objective of growth rate maximization. Kinetic expressions for substrate uptakes serve as constraints on the intracellular model, and integration of the extracellular balances using the resolved intracellular fluxes yields predictions of the growth and product formation rates. Our previous work on DFBA has focused on developing optimal operating policies (Hjersted & Henson, 2006) and identifying genetic manipulation targets (Hjersted et al., 2007) for enhanced ethanol production in fed-batch culture. These modeling studies did not include the possible effects of genetic regulation or direct comparisons to cell culture data. In this study we consider the effects of genetic regulatory constraints on DFBA predictions, present experimental validation of the model predictions, and demonstrate enhanced fed-batch ethanol production from experimental implementation of an optimal model-based operating policy.

Regulation of intracellular fluxes by differential gene expression plays an important role in cellular adaptation to stresses encountered in uncertain extracellular environments. Gene expression data obtained from DNA or oligonucleotide microarrays can be used to place additional constraints on fluxes in a metabolic network model (Covert et al., 2001, Åkesson et al., 2004). A previous study by Åkesson and co-workers (2004) showed that improved quantitative agreement between experiments and steady-state flux balance model predictions could be obtained by zeroing model fluxes associated with genes negligibly expressed in experiments. We used gene expression data from the Akesson study to assess the effects of unmodeled regulatory mechanisms on dynamic flux balance model predictions for anaerobic and aerobic growth conditions. Our results showed that the assumed cellular objective of growth rate maximization and the kinetic constraints placed on the limiting substrates were sufficient for obtaining quantitatively accurate predictions of biomass production and ethanol secretion in batch and fed-batch culture.

The regulated fluxes were shown to belong to three groups: (1) most fluxes were already zeroed by the flux balance model through the assumption of growth rate maximization; (2) a small number of non-zero fluxes had no effect on the biomass and ethanol production rates when they were constrained to be identically zero; and (3) a single non-zero flux produced a false non-viable prediction when it was constrained to zero. Therefore, we concluded that accurate dynamic flux balance model predictions can be obtained in the absence of detailed gene expression data.

To further evaluate the predictive capability of the dynamic flux balance model, a series of Saccharomyces cerevisiae batch culture experiments were conducted. On-line measurements of the glucose, ethanol and dissolved oxygen concentrations and off-line measurements of biomass dry weight were used for dynamic flux balance model validation and parameter estimation. Glucose and oxygen uptake parameters and intracellular stoichiometric coefficients for cellular energy requirements were estimated from anaerobic and aerobic batch culture data by nonlinear least squares optimization. The parameterized dynamic flux balance model was used to compute an optimal fed-batch operating policy for maximal ethanol production. Experimental implementation of the optimal policy was shown to enhance fed-batch ethanol production as compared to alternative policies. We believe that these experimental results further motivate the development of an integrated optimization framework that simultaneously identifies promising genetic manipulations and favorable dynamic process operating policies.

References

Åkesson, M., Forster, J. and Nielsen, J., “Integration of gene expression data into genome-scale metabolic models,” Metabolic Engineering, 6:285–293 (2004).

Covert M. W., Schilling, C. H. and Palsson, B. O., “Regulation of gene expression in flux balance models of metabolism,” Journal of Theoretical Biology, 213:73–88 (2001).

Hjersted, J. and M. A. Henson, “Optimization of Fed-Batch Yeast Fermentation using Dynamic Flux Balance Models,” Biotechnology Progress, 22, 1239-1248 (2006).

Hjersted, J., Henson, M. A. and Mahadevan, R., “Genome-Scale Analysis of Saccharomyces cerevisiae Metabolism and Ethanol Production in Fed-Batch Culture,'' Biotechnology and Bioengineering, accepted for publication (2007).