Fig 1.
The metabolic pathway of Clostridium acetobutylicum (adopted from [25]).
Table 1.
The mass balance equations for all metabolites in the continuous C. acetobutylicum culture (see Fig 1).
In all equations, [ ] denotes metabolite concentration (mM), R refers to rate equations (mM h−1), r is the base enzyme production rate during acidogenesis (mM h−1), r+ is the upregulated enzyme production rate during solventogenesis (mM h−1), H is defined in Eq (3), D is the dilution rate (h−1), and [Gin] is the inlet glucose concentration (mM). The rate equations are given in Table 2.
Table 2.
The reaction rates in the metabolites’ mass balance equations listed in Table 1.
F describes the effect of glucose inhibition (see Eq (2)). In all equations, V is the maximum reaction rate (mM h−1), K is the Michaelis constant (mM), α is the kinetic parameter described by Eq (4), kd is the first order biomass death constant (h−1), and μ is the specific biomass growth rate (h−1).
Table 3.
The estimated kinetic parameters and their 95% confidence intervals.
Fig 2.
Comparison between model predictions and experimental time-course data (from [44]) for the key metabolites in continuous C. acetobutylicum culture.
Fig 3.
Biomass concentration profiles during the two metabolic phases of fermentation.
The pH level 4.5 corresponds to the stationary biomass concentration during solventogenesis, while the pH level 6.0 corresponds to the exponential biomass growth during acidogenesis.
Fig 4.
Butanol and butyrate concentration profiles for different inlet glucose concentration levels.
Due to the product inhibition effect, the concentration of butanol and butyrate asymptotically reaches a maximum level as the inlet glucose concentration increases.
Fig 5.
Concentration profiles for ABE solvents and acids at acidogenic pH (6.0) and solventogenic pH (4.5).
At time 500 hr the culture pH is switched from 6.0 to 4.5 to demonstrate the shift from acidogenesis to solventogenesis.
Fig 6.
The effect of dilution rate and culture pH on steady-state butanol productivity.
Fig 7.
Steady-state butanol productivity as a function of dilution rate and culture pH.
Fig 8.
Normalized dynamic sensitivity of acetone, butanol, and ethanol concentration to the enzyme production rates.
Fig 9.
Normalized steady-state sensitivity of acetone, butanol, and ethanol concentration to different reaction kinetics along the metabolic pathway.
Fig 10.
Normalized dynamic sensitivity of butanol concentration to the most sensitive reaction kinetics.