The last term in Eqs. 2.72, 2.74 and 2.76 is due to volume correction that is applied to glucose, penicillin and oxygen concentrations since these are based on liquid volume (Vabiotic)- Biomass concentration, X (= me , e = number of elements per culture volume, and m = average mass per element) is on the other hand based on culture volume (V).

In Eq. 2.73, ms and ep are the maintenance on glucose and the specific rate of product formation, respectively and aa and as are the stoichiometric biomass yield coefficients for apical and subapical cell compartments, respectively. The last term on the right hand side of as (Eq. 2.73) reflects the fact that the target antibiotic is synthesized only by subapical cells. The dissolved oxygen balance (Eq. 2.74) can similarly be expressed after accounting for oxygen consumption due to cell growth, cell maintenance and product formation and m0 is the maintenance on oxygen in Eq. 2.75. The mass balance for penicillin in Eq. 2.76 accounts for hydrolysis/degradation for the antibiotic with K being the degradation/hydrolysis coefficient. The form of sp in Eq. 2.77 is chosen so as to reflect the inhibitory effects observed at high biomass and glucose concentrations.

These balances [Eqs. 2.72, 2.74 and 2.76] reduce to standard balances without volume correction when X « 1/Vbiotic, since Vabiotic = V in that case.

Simulation Results of the Structured Model

For simplicity, at all times, all the hyphal elements were assumed to have the same composition of the three compartments with the same number of actively growing tips and mass. The model parameters are presented in Table 2.5. Parameters related to growth and substrate consumption were taken from Nielsen [423]. Again for simplicity, the growth kinetics of apical and subapical compartments are assumed to be the same resulting in the same stoichiometric yield coefficients for the two compartments and the same maximum specific growth rates (ka = ks).

In all simulations, a batch operation is considered to be followed by a fed-batch operation. The transition from batch culture to fed-batch culture occurs when the level of glucose concentration reaches a threshold value (10 g/L); such threshold values are commonly used in industrial scale penicillin production. The predictions of the model presented here under different operating conditions were compared with various experimental data. Note that most of the parameters are specific to the strain employed, substrate used and culture parameters such as pH, and temperature. Hence, this work focuses on capturing the general dynamic behavior of penicillin production rather than concentrating on strain or medium specific conditions. A set of simulation results are illustrated through Figures 2.7 and 2.13. Similar to the unstructured model, it is obvious from the simulated results that there are four distinct phases based on growth and are shown in Figures 2.7 through 2.13.

Figure 2.7. Time course of the apical fraction of the cells based on the structured model.

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