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.