Bioprospecting of Microorganism-Based Industrial Molecules. Группа авторов

Figure 2.10 Kinetics for sophorolipid production (black) and substrates (○, □) uptake in SSF.

Figure 2.10 shows the consumption of hydrophilic and lipophilic substrates over time. Glucose consumption is recorded around the fifth day of cultivation; at this point, the consumption of the lipophilic substrate is around 65%. However, the lipophilic substrate is still consumed until the end of incubation, where consumption of around 90% was observed. It seems that lipophilic substrate remains as the only carbon source available and is used to obtain energy, which is reflected in the low increase in BS production registered from fifth day of incubation.

      It is important to mention that the decrease in the production of BS could be correlated with the decrease in CDPR observed by respirometry (Figure 2.10). In this case, CDPR is a variable of the process determining the time of the maximum production of BS according to the physiological state of the yeasts in the SSF.

      From the analysis of the experimental data, three balance equations for the substrate’s consumption are proposed based on modified first‐order decay kinetics. These three equations are coupled to the formation of BS through the conversion yields, corresponding consumption of glucose, and oil in the formation of BS. The set of ordinary differential equations (ODE) corresponds to initial value problems and are shown below:

      (2.1)

      (2.2)

      (2.3)

Where Gluc and Gluc₀ are the glucose concentration at any time, and the initial glucose concentration expressed in g/kg _{dry mass}; Oil and Oil₀ are the oil concentration at any time and the initial oil concentration expressed in g/kg_{dry mass}; SL and SL₀ are the sophorolipid concentrations at any time and the initial sophorolipid concentration expressed in g/kg_{dry mass}, respectively. The first‐order reaction constants correspond to k₁ and k₂ (h⁻¹) for the consumption of glucose and oil, respectively. The constants B and C correspond to the residual concentrations of glucose and oil, respectively. The parameters Y₁ and Y₂ correspond to the yield coefficients of glucose and oil in BS, respectively. The ODE was solved with the Berkeley – Madonna program, integrating with the Runge–Kutta method to solve the ODE, and also comparing the experimental values with those calculated by the model. Parameter estimation was carried out using the deepest descent methodology proposed by Marquardt in 1963 [102]; this technique minimizes the difference of the sum of squares between the experimental data and those calculated by the model. Table 2.4 shows the parameters estimated by the program. The estimation of the initial and final values of the three variables are similar to experimental data. However, the conversion yield estimation (Y₁ and Y₂) does not reflect the global yield of raw materials.

Figure 2.10 presents the results of the model simulation (lines) compared to the experimental data. Calculated values for substrate consumption fit well to those obtained experimentally. Glucose and oil consumption have a classic descending behavior of first‐order kinetics. However, the pattern of the BS formation, the most important variable of the process, does not fit correctly to experimental data, particularly during the first 3 days of culture. The curve calculated by the model is not sigmoidal; this latter is a typical pattern for microbial fermentations. Levenspiel [103] pointed out that the kinetics of the formation of the product of interest (sophorolipid in this case) is the basis for obtaining the design equations of ideal reactors. This is done by plotting the inverse of the product formation rate against the sophorolipid concentration (Figure 2.11).

Using this plot, the size of the batch reactor will be proportional to the area under the curve of the inverse of the reaction rate, evaluated between the limits of product formation (0–100 g/kg_{dry mass}). On the other hand, in the case of continuous culture of SSF, the size of the bioreactor will be proportional to a rectangle whose base is the increase in product formation (0–100 g/kg_{dry mass}) and the height of the rectangle is the value of the inverse of the reaction rate (1/r_SL) evaluated at the point of discharge (~ 100 g/kg_{dry mass}). A comparison of these two types of bioreactor systems indicates that the batch reactor is much smaller than the continuous culture reactor; therefore, up to this level of analysis, the batch reactor is the most suitable type of reactor to produce the sophorolipid by SSF. However, it is necessary to deepen the analysis of the concavity of the sophorolipid production curve to have a model that better represents the behavior of the production of BS in SSF.

Table 2.4 Estimated parameters to characterize the kinetics of the production of sophorolipids by SSF. The Runge–Kutta method of 4 order was used, in a time interval of 0–360 hours with an increase in time step of 0.05 hours.

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Parameters		Units	Parameter value
First‐order constant rate	k 1	h−1	0.01784
First‐order constant rate	k 2	h−1	0.00771
Yield of glucose to sophorolipids	Y 1	g SL/g Glucose	3.99 × 10−5
Yield of oil to sophorolipids	Y 2	g SL/g oil	0.69998
Residual glucose constant	B	g/kg dry mass	0.06616
Residual oil	C	g/kg dry mass	0.15279
Initial glucose	G 0	g/kg dry mass	251.20
Initial oil	Oil 0	g/kg dry mass	153.20
Initial sophorolipid	SL 0