Rfn VmZhYHG vmZsMg236

in Eq. 2.15 with Yh/g (yield of hyphae based on glucose consumption) and vm being kinetic parameters. For methionine in the abiotic phase, rtrans = + ^ = Umhcf>3(m),

with Umhi Ums■ and Km being the associated kinetic parameters.

Owing to the considerable significance of intracellular methionine in regulating expression of CPC-synthesizing enzymes, conservation equations for methionine in the three cell types are also part of the structured model. Let mih,mis and rriie denote concentrations of methionine inside the hyphae, swollen hyphal fragments, and arthrospores, respectively. The conservation equation for the cell type j (j = h, s, a), which is analogous to that for total cell mass, Eq. 2.11, has the form dXj/dt = {nj - kD)XJ - DXj, j = h,s, a, (2.38)

with the effective specific growth rates and ¡ia being expressed based on Eq. 2.33 as nh = {n'~0), Ps = PZh/Zs - 7, ixa = 1Zs/Za. (2.39)

The conservation equations for an intracellular species in one or more of the cell types can be expressed in a form similar to those in Eqs. 2.13 and 2.14b. For a specie q, the temporal variation in its intracellular concentration in cell type j, q^, can therefore be expressed as dqv/dt = rf<T - r£»"B - Wij, (2.40)

with rfp and r^ans representing the specific rate of net generation of specie q in cell type j and the specific rate of transport of specie q from cells of type j into the abiotic phase [both in units mass (moles) of q /{time, mass of cells of type j}]. For methionine (s = m), these rates have the following forms for the three cell types under consideration [35, 374], rr = - k3hmlh - V^uM9)mh - I3mih, 7fans = -Uh, 7fans = -U„

rfn = - k3srnis - V^Mtims + ¡3mlhZh/Zs - 7mis, r?'1 = -k3amia + mlsZs/Za, rfans = 0. (2.41)

The first terms on the right sides of expressions for rf'm and rfen account for biosynthesis of methionine in hyphae and swollen hyphal fragments, respectively. The terms in the expressions above containing ¡3 and 7 represent (dis)appearance of methionine in a particular cell type population associated with interconversion between two cell types. The presence of glucose in the abiotic medium is considered to increase the rate of methionine utilization for protein synthesis. The estimation of the kinetic parameters in Eq. 2.41 has been based on comparison of the experimentally measured and model predicted values of the average intracellular methionine concentration, (mi)avg, the value predicted by the model being

The kinetic parameters in Eq. 2.41 have been considered to be constant. The rate of synthesis of CPC is considered to depend on activity of enzymes responsible for synthesis of CPC. The conservation equation for this enzyme pool (denoted as e) in swollen hyphal fragments is provided by Eq. 2.40 with qih — eih — e, with rft™ = 0, rS" = (1 IXs){VmEmisXsl{mls + KE})t_tlQ - 7e, Q = {1 + (K/an)g}/{l + (K/a")(l + r))gn} (2.42)

and VmE, Ke, k, ct, n, and 77 being the kinetic parameters. The effect of catabolite repression by glucose is included in Q (n > 1). The subscript (t — tj) denotes evaluation at time t' =t — i/, with tj representing the time lag between induction and gene expression. Finally, the mass balance for the target product (p), cephalosporin C (Cp = p), is expressed as in Eq. 2.15 with rfa = eZs, RfD = -kPDp. (2.43)

The second expression in Eq. 2.43 accounts for degradation of cephalosporin C in the abiotic phase. The magnitudes of various kinetic parameters for the structured model are reported in [35] and [374], The state variables (Eq. 2.1) in this model therefore are x = [X g m Zh Zs m,/, mis mia e p]T for batch and continuous cultures and x = [X g m Zh Zs rriih rrks m-ia e P F]T for a fed-batch culture. The identity Zyi + Zs + Za — 1 implies that only two of the three fractions of the cell population are independent state variables.

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