A number of researchers have tried to use correlations to relate key
components uptake rates to their concentration in the medium and
consequently simulate the dynamic behaviour of the microorganism
during batch or fed-batch fermentations using genome-scale metabolic
reconstructions. For this aim, some dynamic flux balance modeling
frameworks (combination of steady-state intracellular model of carbon
metabolism with key-components mass-balance-corresponding ODEs via
Michaelis-Menten uptake kinetics) have been developed. For more
information might take a look at the following articles:
Hjersted, J.L., Henson M.A., 2006. Optimization of fed-batch
Saccharomyces cerevisiae fermentation using dynamic flux balance
models. Biotechnol. Progr. 22, 1239–1248.
Hjersted, J.L., Henson, M.A., 2009. Steady-state and dynamic flux
balance analysis of ethanol production by Saccharomyces cerevisiae.
IET Syst. Biol. 3,167-179.
Hjersted, J.L., Henson, M.A., Mahadevan, R., 2007. Genome-scale
analysis of Saccharomyces cerevisiae metabolism and ethanol production
in fed-batch culture. Biotech. Bioeng. 97, 1190-1204.
Eslamloueyan, R., Setoodeh, P., 2011. Optimization of fed-batch
recombinant yeast fermentation for ethanol production using a reduced
dynamic flux balance model based on artificial neural networks. Chem.
Eng. Comm. 198, 1309–1338.
and
Vargas, F.A., Pizarro, F., Pérez-Correa, J.R., Agosin, E., 2011.
Expanding a dynamic flux balance model of yeast fermentation to
genome-scale. BMC Syst. Biol. 5, 75.
It is somehow difficult and not quantitatively accurate. But, you
might use Michaelis-Menten kinetics to correlate carbon-source uptakes
to its concentrations in the medium. Afterwards, you might change the
lower bond value for carbon source uptake (set the lower bond to the
correlated values step-wisely) and determine the corresponding
specific growth rates. Through this way you might do mapping.
Please do not forget that high carbon source concentrations
practically may contribute to inhibition effects on cell growth while
this fact is not considered in steady-state FBA. You might handle the
problem by consideration of the inhibition constants (the optimal
values should be determined) in Michaelis-Menten kinetics.
Good Luck
Payam