Functional state modelling approach validation for yeast and bacteria cultivations

Figures & data

Table 1. Functional states interrelationships.

Functional state	Rule
First functional state (FS I) first product synthesis state	S > Scrit and O2 > O2crit
Second functional state (FS II) mixed oxidative state	S ≤ Scrit and O2 ≥ O2crit and P > 0
Third functional state (FS III) complete sugar oxidative state	S ≤ Scrit and O2 ≥ O2crit and P = 0
Fifth functional state (FS V) second product synthesis state	S ≤ Scrit and O2 < O2crit and P > 0

Note: S is the concentration of substrate (g·L⁻¹); O₂ is the dissolved oxygen concentration (%); P is the concentration of the product (g·L⁻¹), which is ethanol in the case of S. cerevisiae cultivation and acetate in the case of E. coli cultivation.

Table 2. Local model parameter functions.

Specific rates	FS I	FS II	FS III	FS V
μ
qS
qP			0

Note: S_crit is the critical level of substrate concentration (g·L⁻¹); O_2crit is the critical level of dissolved oxygen concentration (%); μ_max is the maximum specific growth rate (h⁻¹); Y_i/j is the yield coefficient (g·g⁻¹); k_j is the saturation constant (g·L⁻¹ or %).

Table 3. Conditions of fed-batch cultivations.

Cultivation conditions	S. cerevisiae*	E. coli
Volume (L)	1.5	2.0
Temperature (°C)	30	35
pH	5.7	6.9
Stirrer speed (r·min^−1)	500	900–1800
Sin (g·L^−1)	50	100
Set point (g·L^−1)	0.08/0.05*	0.1

*Two different runs of S. cerevisiae fed-batch cultivation were carried out: the first one at set point 0.08 and the second one at set point 0.05 g·L⁻¹ glucose.

Table 4. Estimated values of local model parameters.

	FS I		FS II		FS V
Parameters	S. cerevisiae	E. coli	S. cerevisiae	E. coli	E. coli
μS (h^−1)	0.24	0.45	0.95	0.58	0.55
μE (h^−1)	–	–	0.34	0.32	–
kS (g·L^−1)	0.28	0.03	0.11	0.04	0.093
kE (g·L^−1)	–	–	5.01	5.44	–
YS/X (g·g^−1)	0.09	0.46	0.45	0.49	0.33
YP/S (g·g^−1)	1.48	0.045	0.67	0.22	5.26
kLa (h^−1)	80	52.49	98.27	87.27	30.54
(g·g^−1)	0.001	0.096	–	–	0.063
(g·g^−1)	–	–	0.001	14.58	–
(g·g^−1)	–	–	0.0013	26.09	–
(g·L^−1)	–	–	–	–	0.028

Figure 1. Comparison between a simulated and a real fed-batch S. cerevisiae cultivation process (run I).

Figure 2. Comparison between a simulated and a real fed-batch S. cerevisiae cultivation process (run II).

Figure 3. Comparison between a simulated and a real fed-batch E. coli cultivation process.