Structured Model for Penicillin Production

The model proposed in this case is a derivative of the morphologically structured model by Nielsen [424] and accounts for effects of dissolved oxygen on cell growth and penicillin production and variations in volume fractions of abiotic and biotic phases due to biomass formation [63]. Penicillin production is considered to occur in the subapical hyphal cell compartment and to be affected by glucose and oxygen.

Morphology and Metamorphosis

The morphological structure of the model is described in detail elsewhere [423, 424]. Each hyphal element is divided into three cell compartments/regions: apical (Za), subapical (Zs) and hyphal (Zh). Branching, tip extension and differentiation are the three metamorphosis processes considered [423]. Let Za, Zs and Z\t denote the mass fractions of apical, subapical and hyphal portions, respectively in the cell population. Both branching and tip extension are considered to be first order processes, viz.

Branching:

Extension:

Differentiation:

Mass Balance Equations

Growth of apical and subapical cells is described by saturation type kinetics including effects of both glucose and oxygen in multiplicative form. The motivation for this is an earlier modeling work on penicillin production by Bajpai and Reuss [36] where growth has been described by Contois kinetics. Here, in order to reduce the model complexity, Monod kinetics has been used for describing the growth as suggested by Nielsen [423].

Zangirolami et al. [685] suggest that hyphal cells may still retain the same metabolic activity and growth ability exhibited in the subapical compartment to some extent and considers a growing fraction (f^) of hyphal cells in their model. On the other hand, Nielsen [423] suggests that hyphal cells have a metabolism completely different from the actively growing apical and subapical cells, and hence, they are believed not to contribute to the overall growth process and assumes fih to be zero. For simplicity, the growth rate of hyphal cells (/x^) is also considered to be trivial based on Nielsen's work [423]. The overall specific growth rate (fi), which is an average of the growth rates of individual compartments, is then obtained as fi = naZa + fisZs. (2.63)

In view of the above, the conservation equations for the three compartments (components) of the cell population can be expressed as (Za+Zs+Zh=l)

= —ui + U2 — U3 + (fj,g — fi)Za subapical cells (2.65)

The terms ¡iZi (i = a, s, h) in Eqs. 2.64, 2.65, and 2.66 account for dilution associated with biomass formation. The random fragmentation at different positions in individual hyphal elements leads to distribution in characteristics of the population such as the mass and numbers of total tips and actively growing tips [423]. Estimation of the average properties of the hyphal elements has been addressed theoretically by Nielsen [423] and experimentally using image analysis by Yang et. al. [674, 675]. In this case, we have made use of this population model based on the average properties of the hyphal elements [423]. In summary,

Hyphal element balance:

where D is the dilution rate. Hyphal mass balance:

Actively growing tips balance:

dn ~dt where <j> (= a2U\, a2 is constant) is the specific branching frequency (1/{g.h}) and is a function of Zs. ip is the specific rate of fragmentation (l/{g.h}) and is assumed to be constant. The number of actively growing tips is less than the total number of tips (ntotai) due to formation of non-growing tips by fragmentation. Two inactive tips are formed as a result of fragmentation resulting in formation of an additional hyphal element. The average number of inactive tips on each element is exactly 2. The total number of tips then is:

The mass of the average hyphal growth unit (fhhgu ) and total hyphal growth unit length (lhgu) &re then obtained as [85]

Mass balances are as follows: For glucose:

dt V Vabiotic ^abiotic dt

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