4.2 Kinetics of β-carotene synthesis
There are three fermentation forms: I, growth-related type; II, growth
part-related type; III, non-growth-related type. In general, the
formation of weak organic acids, such as citric acid, lactic acid, and
succinic acid, has been well simulated by the Luedeking-Piret model that
consists of a growth-associated part and non-growth-associated part. In
this case, we employed this model to describe the kinetics of β-carotene
production.
\(\frac{\text{dP}}{\text{dt}}=\alpha\frac{\text{dX}}{\text{dt}}+\beta X\)(2)
Where P is the product concentration, X (g/L) is the concentration of
cells, t is the fermentation time, α and β are the coefficients. α
(g/g)
denotes the parameters for product formation constant (associated with
the cell growth rate) and β (g/g) denotes the parameters for product
formation constant (related to the number of cells). As for three
fermentation types: Ⅰ: α ≠ 0, β = 0; II: α ≠ 0, β ≠ 0; III: α = 0, β ≠
0.
Figure 6 depicts the time courses of β-carotene content separately
derived from the model equations and the experiments.
Figure
6a and Figure 6b show the fitting results for the fed-batch fermentation
and DO-stat fed-batch fermentation, respectively. β-carotene synthesis
of engineered Y. lypolitica belongs to a partial coupling with
cell growth (fermentation type II) because the rate of product formation
is related to both the growth rate and the number of cells. A
mathematical model was proposed by Luedeking and Piret, which properly
described the mechanism of β-carotene synthesis.
The simulated kinetic parameters were listed in Table 1. It shows that a
relatively accurate result could be observed between experimental and
simulation data. The value of α was 4.74×10-4 for
fed-batch fermentation and -0.6 for DO-stat fed-batch fermentation. The
value of β was -2.86×10-6 for fed-batch fermentation
and 0.05 for DO-stat fed-batch fermentation.
A higher α value was obtained for the fed-batch fermentation, indicating
the β-carotene synthesis was mainly affected by cell growth rate at
fed-batch fermentation. A higher β value was obtained for DO-stat
fed-batch fermentation, which indicates the β-carotene synthesis was
affected mainly by the number of cells during DO-stat fed-batch
fermentation.
4.3 Kineticsof
glucose consumption
Figure 7a shows the nonlinear fitting of experimental data from DO-stat
fed-batch fermentation substrate consumption. The classical kinetic
model suggested by Luedeking and Piret was chosen to describe the
substrate consumption as follows:
\(-\frac{\text{dS}}{\text{dt}}=\frac{1}{Y_{\frac{X}{S}}}\frac{\text{dX}}{\text{dt}}+\frac{1}{Y_{\frac{P}{S}}}\frac{\text{dP}}{\text{dt}}+mX\)(3)
Where Yx/s (g/g) and Yp/s (g/g)
represent the substrate yield for biomass and product, respectively, and
m represents the maintenance coefficient. The whole formula (3)
represents glucose used to generate biomass, product, and cellular
maintenance energy. The simulated kinetic parameters were listed in
Table 1. The equation fits the experimental data from the consumption of
the substrate with an R2 of 0.9558. The
Yx/s and Yp/s are 0.22 and 0.14,
respectively. It is difficult to fit the data of glucose consumption
during fed-batch fermentation because the change in glucose
concentration was small. The
Yx/sis
0.06 in fed-batch fermentation that directly calculated by
Yx/s= ∆X/∆S. The Yp/s is
2.5×10-4 in fed-batch fermentation solved by
Yp/s= ∆P/∆S. It is evident that the parameter
Yx/s and Yp/s are higher for DO-stat
fed-batch. It demonstrates that DO-stat fed-batch fermentation led to
higher biomass and product yield for the substrate.
Figure 7b depicts the glucose consumption in different growth periods at
fed-batch fermentation and DO-stat fed-batch fermentation. We divided
the glucose consumption into three phases: the lag phase, the
logarithmic phase, and the stationary phase. In the lag phase, 1.5 g of
glucose were consumed in one liter of fermentation broth at both
fermentations. In the logarithmic phase, one liter of fermentation broth
consumed 123.5 g and 262 g of glucose for the fed-batch fermentation and
the DO-stat fed-batch fermentation, respectively. In the stationary
phase, 175 g and 74 g glucose were consumed in one liter of fermentation
broth for the fed-batch fermentation and the DO-stat fed-batch
fermentation, respectively. These results clearly show that more glucose
consumption was achieved in the logarithmic phase when DO-stat fed-batch
fermentation strategy was implemented.