Biotechnol. Prog. 1993, 9, 54-63
54
Mathematical Modeling of the Production of Cyclosporin A by Tolypocladium inflatum: Effect of L-Valine Spiros N. Agathos*gt*tand Jaegwan Leet*§ Department of Chemical and Biochemical Engineering and Waksman Institute of Microbiology, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08855-0909
A mathematical model was developed t o describe the kinetics of submerged fungal growth, consumption of nutrients, and production of the immunosuppressant drug, cyclosporin A (CyA). Special emphasis was placed on the experimentally observed stimulatory effect of L-valine on CyA production. The proposed model was based on kinetic information and emerging mechanistic data on CyA biosynthesis. It was assumed that L-valine acts as both precursor and inducer of the CyA-synthesizing multienzyme (CyA synthetase), and an unmethylated intermediate of CyA was postulated in the biosynthetic process. The model consisted of two parts: one describing cell growth and substrate consumption and the other addressing the kinetics of internal properties such as endogenous valine, biosynthetic enzyme, CyA intermediate, and CyA. The success of this extensive model was confirmed by its ability t o simulate adequately the kinetic profiles of both external and internal variables. For instance, the model correctly predicted the time course of intracellular L-valine accumulation. In addition, both the optimal level and timing of exogenous L-valine addition could be predicted for maximum drug production. This study suggests rational new ways of improving the fungal production process of this important immunosuppressant.
Introduction Cyclosporin A (CyA), the main product among a spectrum of cyclic 11-membered peptides produced by the filamentous fungus Tolypocladium z'nflatum, is a strong immunosuppressive drug and is widely used in the area of post-transplant surgery management (Borel, 1986). As this commercially important medicinal agent is poised to become generic, it is anticipated that fundamental knowledge of its fermentative production would have a significant impact on improved bioprocess design. The fermentation of cyclosporins follows the general characteristic of "directed biosynthesis" in peptide production (Kobel and Traber, 1982). Thus, the biosynthesis of CyA is critically affected by the addition to the medium of exogenous amino acids which tire members of the c closporin ring (Kobel and Traber, 1982;Traber et al., 19 9; Lee and Agathos, 1989;Issac et al., 1990). It appears that the supplemented amino acids are modifying the endogenous amino acid pool 'of the producer fungus and directing the biosynthesis as precursors (Billich and Zocher, 1987). CyA and its homologues appear to be synthesized via the so-called nonribosomal "thiotemplate mechanism" in a number of catalytic steps mediated by a single multifunctional enzyme, cyclosporin synthetase (Zocher et al., 1986; Billich and Zocher, 1987; Lawen and Zocher, 1990). Cyclosporin synthetase has relatively low substrate specificity, and thus it is able to catalyze the synthesis of over two dozen cyclosporins in vitro and in vivo, depending on the available precursors (Lawen et al., 1989; Traber et al., 1989). L-Valine, a constituent amino acid of the cyclosporin ring, was previously reported to increase CyA production
B
* Author to whom correspondence should be addressed.
+ Department of
Chemical and Biochemical Engineering. Waksman Institute of Microbiology. 5 Present address: Department of Biotechnology, Choong-Ang University, Seoul, Korea. 8756-7938/93/3009-0054$04.00/0
as well as direct the distribution of cyclosporins to increased titer of cyclosporin D (Kobel and Traber, 1982). We have recently observedthat exogenous L-valine, but not D-vahe, increases remarkably the volumetric and specific productivities of CyA when this amino acid is supplemented to complex or defined fermentation media (Lee and Agathos, 1989). We have further demonstrated a direct link between CyA productivity and the magnitude of the intracellular pool of L-valine (Lee and Agathos, 1991). We now proceed to develop a mathematical description of the kinetics of fungal growth, nutrient utilization, and CyA production, taking into account the influence of L-valine on drug formation. Quantitative representations of the kinetics of filamentous microbial growth and peptide secondary metabolite formation should be illuminated by an appreciation of the mechanisms involved in the biosynthesis of these industrially important products. So far relatively few reports have addressed the mathematical modeling of such systems, and there is a general paucity of physiologically and mechanistically structured models capable of predicting the kinetic behavior of intracellular entities (enzymes, substrates) and their influence on product formation. The critical influence of initial phosphate concentration in the medium on alkaloid production by the fungus Claviceps purpurea has been incorporated in a chemically structured model (Pazoutovl et al., 1981) which is capable of predicting the time course of intracellular phosphate, in addition to the kinetics and maximal accumulation of alkaloids at different initial phosphate levels. In a metabolically and morphologicallystructured model of cephalosporin C formation by the fungus Cephalosporium acremonium (Matsumura et al., 1981), the regulatory effects of methionine and glucose on cell growth and antibiotic production (Matsumura et al., 1980b)were incorporated, resulting in good predictions of the time-dependent trajectory of intracellular methionine
0 1993 American Chemical Society and American Institute of Chemical Engineers
Blofechnol. hog., 1993, Vol. 9, No. 1
and of the cell mass, nutrient, and product kinetics under a variety of initial conditions. In this article, we are investigating the kinetic behavior of endogenous valine and cyclosporin synthetase in the mycelium of T.inflatum, and we perform a kinetic analysis of CyA production by mathematically modeling the putative role of this amino acid as a limiting precursor and an inducedactivator of cyclosporin synthetase.
Materials and Methods Microorganism. The microorganism used was Tolypocladium inflatum (ATCC 349211, sometimes referred to erroneously as Beauueria niuea. The initial culture was adapted to glucose through subculturing in glucosecontaining medium (Lee and Agathos, 1989). Seed stock cultures were prepared in 30% glycerol solution and preserved at -20 "C. Liquid seed cultures were prepared using a seed stock culture at 5% (v/v) inoculum. Chemicals. All chemicals except HPLC solvents were obtained from Sigma (St. Louis, MO). HPLC solvents were from Fisher Scientific (Springfield, NJ). Allmaterials used were of analytical grade, while solvents were of HPLC grade with the exception of n-butyl acetate. Medium. Synthetic medium (SM) contained glucose (30 g/L), ammonium sulfate (10 g/L), KHzPOI (0.75 g/L), and a trace metal solution (1 mL/L), and its pH was adjusted at 5.7 as described previously (Lee and Agathos, 1989). L-Valine was added at levels and times as described in the Results section. Culture Conditions. Seed cultures were grown in this medium in a 500-mL shake flask at 200 rpm for 5 days at 27 "C. Inoculation volume was 5 % of the fermentation media volume. A Model G76 gyratory shaker (New Brunswick Scientific, Edison, NJ) was used for seed culture. A 2-L Multigen fermentor (New Brunswick Scientific) was used in order to obtain the basic kinetics of unsupplemented and L-valine-supplemented (4 g/L) batch fermentation. The working volume was 1.5 L, the inoculum level 10% (v/v), the agitation 400 rpm, and the aeration 1w m (1.5 L of air/min). Foaming was controlled by usingantifoam SAG 471 (Union Carbide, Bound Brook, NJ). The culture pH was controlled a t 5.7 with KOH (5 N) and HzS04(2 N), and the temperature was maintained at 27 "C. The shake-flask cultures designed to test timing and level of L-valine addition were performed in 125-mL flasks containing 40 mL of SM plus L-valine where applicable (see Results). Analyses. Cell Mass. Dry cell weight determinations were carried out as previously described (Lee and Agathos, 1989). Glucose. Glucose analysis was carried out with a YSI Model 27 glucose analyzer (Yellow Springs Instrument Co., Yellow Springs, OH). Phosphate. For the measurement of phosphate, the vanadomolybdophosphoric acid method was used, which is based on a colorimetric determination (Kitson and Mellon, 1944). ~ - V a l i n e .An HPLC method was chosen to analyze this amino acid (Tapuhi et al., 1981), whether L-valine was contained in the medium or in the cells. The specific conditions of the determination and the preparation of cell extracts were reported previously (Lee and Agathos, 1991). Recovery and Analysis of CyA. A 10-mL portion of the culture broth which was kept frozen at -20 "C was extracted with n-butyl acetate and subsequently analyzed by HPLC. The extraction procedure and analysis method are described in previous reports (Lee and Agathos, 1989,
55
72H5 N-
H3C
C-C-N-C-C-N-C
I 0-c I
Fc-7
p
11
lo
FH3
-C-N-C-C-N
/I
-CH2
A
1 I 0
'
ll
p
:
3 1
c-0
I
9
N-CH3
H3C H$-
N
8
7
6
$
N-C-C-N-c
IC-C-
n
i
0
a
i 3
i
H
i 0
i a
-N
-C 3
II 0
I
-C
I
'fh a
3
-C
-N
-c -c
H3CAM,I
%C*Ui,
0
1 CHz
H2CACH2
Figure 1. Molecular structure of CyA.
1991). Authentic cyclosporin standards were generously provided by Sandoz Corporation (East Hanover, NJ).
Model Development Biochemistryof Cyclosporin Synthesis. The nonribosomal biosynthesis of microbial peptides described by Lipmann (1973) has been accepted for CyA, since much experimental evidence supports the mechanism. CyA is a cyclic peptide consisting of 11amino acids (Figure 1). Several aspects of the biosynthetic mechanism were suggested by Kleinkauf s and Kobel's laboratories (Zocher et al., 1986; Kobel and Traber, 1982; Kobel et al., 1983; Zocher et al., 1984). The following biosynthetic features were proposed and supported by subsequent evidencefrom their research efforts. Methyl groups of the N-methylated amino acids and of the unusual Cg amino acid residue in position 1originate from L-methionine via S-adenosyl-L-methionine (Kobel et al., 1983; Zocher et al., 1984,1986; Billich and Zocher, 1987; Lawen et al., 19891, and the priority of methylation is on the amino groups of the CyA molecule. Bond formation between amino acid residues proceeds after the synthesis of the Cg acid in position 1and after the activation of each constituent amino acid. It appears that N-methylation may be a bottleneck step in the biosynthesis of CyA (Zocher et al., 1986; Lee and Agathos, 1991). Additionally, exogenousL-methionine results in a significant reduction in CyA production (Lee and Agathos, 1989), which is consistent with the facts that the synthetase only activates nonmethylated amino acids and that N-methylation is a result of 5'-adenosyl-L-methionine participation in the post-activation step (Billich and Zocher, 1990). We assumed that the nonmethylated form of CyA is accumulated inside the fungal cell, even though this intermediate is enzyme-bound (Lawen and Zocher, 1990). Additionally, a crucial factor taken into account for the formulation of the kinetic model was the enhancement of CyA production by L-valine (Lee and Agathos, 1989,1991). We also assumed that L-valine, after its transport into the cell and enrichment of an intracellular amino acid pool, acts as an inducer of cyclosporin synthetase and as a precursor of the CyA molecule. The conceptual features of the model are depicted schematically in Figure 2. Model Assumptions. (1)Phosphate was assumed to be a growth-limiting nutrient, on the basis of experimental evidence suggesting that the other components in the fermentation medium are not limiting before phosphate depletion (Lee, 1989). (2) Cell growth obeys simple Monod kinetics. Two forms of cells are assumed. Generally, fungal cell growth follows the life cycle of hyphae to spores. In the model, only hyphae are considered the active form of cell type and spores are assumed to have no metabolic activity. The
Biotechnol. Prog., 1993, Vol. 9, No. 1
56 cell wall
DNA
B
stages of cell development, i.e., hyphae, swollen hyphae, and arthrospores, of C. acremonium were significant in the cephalosporin C fermentation. Similar morphological changes were observed in the culture of 7’.inflatum, but there was no major difference between hyphae and swollen hyphae, so that only two cell types were considered for the CyA fermentation. A mass balance equation describing these two cell types (hyphae and spores) and the total cell mass in a batch culture is expressed as follows:
x = x, + x2
transport of external valine E: synthetase S,:i
Sve
endogenous L-valine
Sve: exogenous L-valine Sint: intermediate complex
CyA: cyclosporin A
Figure 2. Proposed mechanism of the role of L-valine in the enhancement of CyA synthesis.
rate of morphogenetic change from hyphae to spores is assumed to be an inverse function of phosphate concentration. (3) The yield coefficients of biomass on glucose and on phosphate, YX/G and Y x ~ pare , constant during the growth phase. Additionally, glucose is consumed for the production of exocellular materials like polysaccharide in the stationary phase. It was observed that most of the polysaccharide-likematerial was produced after cell growth stopped. (4) External L-valine is transported inside the cells by an active transport mechanism (Romano, 1986), and the degradation of L-valine in the medium follows first-order kinetics. (5) Internal L-valine is consumed through the cellular metabolism and the synthesis of an intermediate complex. The degradation rate of internal L-valine is proportional to its concentration. (6) A hypothetical intermediate complex is assumed in the form of nonmethylated CyA. The stoichiometric coefficient, CY,between L-valine and nonmethylated CyA is 0.2149, and the ratio of molecular weight of nonmethylated CyA to that of CyA, 8, is 0.9068. The biosynthesis of the intermediate is proportional to synthetase concentration. The term “synthetase” as used here means the whole enzyme system between starting material (amino acids) and intermediate complex. (7) Synthetase is induced by internal L-valine, and the rate of its appearance can be expressed by a MichaelisMenten type equation. This formalism is one among several other types that have also been proposed for enzyme induction (Yagil and Yagil, 1971; Toda, 1981). The synthetase is deactivated by first-order kinetics. (8) The production rate of CyA is proportional to the concentration of the intermediate (nonmethylated CyA). (9) Finally, internal properties such as concentrations of intracellular L-valine,intermediate, and synthetase are diluted by cell growth, and each component is evenly distributed during the growth phase (Fredrickson, 1976). Development of Model Equations. Extracellular Properties. Cell Growth. Morphological differentiation has been considered to be important for fungal cell growth and production of secondarymetabolites (Campbell,1983). Matsumura et al. (1980a) assumed that three different
(1) where total cell mass (X, in g/L) is the sum of the cell masses of hyphae (XI, in g/L) and spores (X2,in g/L). X is the only experimentally observableparameter, and X1and X2 are obtained by simulating the mass balance equations. Mass balances are formulated as follows: dX1 --px1-dt
--dX2dt
kDKp x, KP + s,
kDKP x, Kp+ S,
(3)
where p is the specific growth rate (in h-l) of hyphae and the second term of the right-hand side of eq 2 is the expression for the degeneration of hyphae to spores. A Monod dependence of specific growth rate is assumed: P=-
PmSp
(4)
KP + s, where S, is the concentration of phosphate in the form of KH2P04. It is assumed that the morphological change of hyphae to spores is controlled by phosphate concentration, as there is no apparent depletion of carbon and nitrogen sources in the fermentation triggering this morphological transition. P m is the maximum specific growth rate of hyphae, and kD is the kinetic constant involved in the morphogenesis of hyphae to spores. In all subsequent notation, the subscript 1 refers to properties of hyphae and the subscript 2 refers to properties of spores. Phosphate Utilization. Phosphate consumption is directly related to the growth of hyphae, on the basis of batch kinetic data (Lee, 1989),through a yield coefficient that is constant during balanced growth
As mentioned under model assumption 2 above, the phosphate, glucose,and L-valine consumption contributed by the spore population is neglected (see eqs 5,6, and 8). Glucose Consumption. Glucose consumption is related to cell growth, cell maintenance, and exocellular material production. The mass balance of glucose utilization becomes
(7) where Y X / Gis the cell yield coefficient of hyphae growth on glucose and meis the maintenance coefficientof hyphae. Vl.uti1, a portion of specific glucose consumption, reflects the production of extracellular material during the stationary phase. kgl and kg2 are rate constants related to
Biotechnol. prog., 1993, Vol. 9, No. 1
57
V1.util. The latter is modeled as an inverse function of growth rate on the basis of kinetic patterns observed for extracellular material production from glucose, which peaks in the stationary phase of growth. Exogenous &Valine. Amino acids are generally transported inside the cell by an active transport mechanism, especially in the case of fungal cells (Romano, 1986). The transport rate of external valine (&e) can be written as a Michaelis-Menten type expression because of the involvement of permease enzyme(@ in the transport:
uv= Kuvv1. m+SSv ve e where Uvis the specific rate of L-valine uptake by hyphae. Intracellular Properties. Material Balances of Endogenous Variables. As shown in eq 10, internal L-valine (of concentration Svi)will be consumed through cell growth and biosynthesis of the intermediate complexand supplied by uptake through the cell wall (at a rate Uv)and synthesis through anabolism (at arate Vvi.syn). The close connection between this anabolic synthesis rate and cellular growth is illustrated by eq 13. Mycelial intracellular L-valine (of concentrationSvi.1)may be diluted by the growth of hyphae (eq lo), and the relationship between Svi and Svi.1can be expressed by eq 17. Also,this amino acid can be utilized for cell growth (at a rate Vzl.util) and cell maintenance (at a rate Vz~.~til). An intermediate complex for CyA synthesis can be generated by the consumption of Sd.1, whose rate is expressed by the term aVint.syn. The stoichiometric ratio of L-valine to unmethylated CyA intermediate is expressed by a and that of intermediate to CyA by 8. Mass balances of intracellular L-valine, intermediate (concentrationS i n t ) , and synthetase (concentration E) are given by eqs 10-12, respectively:
dSint -= dt
Vint.syn
- psint - pkCyASint - ki.dSint
(11)
where
(13)
(14)
vzz.util
VE
=
=
kzz
vE.msvi.l Kv4
+ Sn.1
(16)
(18)
where Svi is the concentration of endogenous L-valine per dry cell mass and S ~ .isl the concentration per cell mass of hyphae. Degradation kinetics of intracellular valine is assumed to be proportional to ita concentration (eq 10). The rate of synthesis of cyclosporin synthetase (E) is expressed by induction or activation kinetics, in which endogenous L-valine is assumed to play the role of inducer or activator (eq 18). Cyclosporinsynthetasewill be diluted by cell growth, and ita degradation is assumed to follow fist-order kinetics (eq 12). It is also assumed that L-valine, intermediate complex, and synthetase are localized only in hyphae because of no apparent metabolic activity in spores. Note that in the mass balance equations the amounts of intracellular species are given per unit of biomass rather than given on a volumetric basis. During cell growth, the concept of even distribution of intracellular materials is adopted, as suggested by Fredrickson (1976). Cyclosporin A Synthesis. It is assumed that the rate of CyA formation is proportional to the concentration of its intermediate; in addition, a slow, fmt-order degradation of CyA is assumed:
'2 -
--
kCyASintXl
- kp.dCCyA
where k c y A is the CyA formation rate constant, kp.d is the degradation kinetic constant, and C C ~isAthe volumetric concentration of CyA (mg/L).
Results Parameter Estimation and Model Simulation Approach. The model parameters were estimated with NONLIN, a program developed by Metzler et al. (1976) at Upjohn Co. (Kalamazoo, MI). The Gauss-Newton method was used to compute the parameter values through nonlinear regressional analysis of batch fermentation data. The precision factor for the differential equation solver was 0.001, the convergence criterion for the nonlinear regression algorithm was O.OOO1, and the increment for numerical approximation of partial derivatives was set at 0.001. The model was solved using the package IVPRK of the IMSL Math Library (19871, in which RungeKutta formulas of the fifth and sixth orders were implemented. A total of 25 parameters was involved in the model. The equations described above were separated into two groups. The first group (eqs 1-9) consisted of an unstructured model of cell growth and extracellular variables, whereas the second group (eqs 10-19) was more structured metabolically as it described elements of the cellular mechanism of CyA production. To facilitate a numerical solution, external and internal properties were treated separately. In the former group, 11parameters involved in the description of morphology, hyphal growth, and consumption of substrateswere obtained from regressional analysis of kinetic data derived from batch fermentations using SM supplemented with L-valine (4 g/L) in the 2-L bioreactor. The estimated values of these parameters are given in Table I, and the simulated kinetic profiles, along with experimental data, are given in Figure 3a-d. Similarly, in the second set of equations, 14 parameters were estimated using the values obtained from the previous regressional analysis and are given in Table 11. The simulations and kinetic profiles of internal variables are also depicted in Figure 3e-h. The physical/biological significance of each parameter is implied in the format of the equation(s) where it appears (e.g., rate constants, growth-associated terms, etc.). In this context, the magnitude of each parameter is dictated by ita role in the corresponding mass balance equation. For instance: the
Biotechnol. hog., 1993, Vol. 9, No. 1
58
Table I. Estimated Parameter Values in Equations 1-9 (External Properties) uarameter eat value uarameter est value KP 9.88 X lo-' uv.m 1.23 x 10-3 YXJG 0.591" Kvi 5.30X lo-' kv.d 6.96 X lo4 YXJP 10.37" kgl 8.91 X lo4 me 1.01 x 10-4 kgz 6.68 x Pmi 7.18 X kD 1.83 x 10-3
Table 111. Initial Conditions Used for Simulation of Model Equations
a Overall yield coefficients calculated from experimental values at exponential phase are 0.48 and 11.8,respectively.
k the parameter set, and g2j the standard deviation of measurement. Calculations of parameter sensitivity were performed for the batch fermentation (Guttman et al., 1971). To determine the sensitivity of model predictions to parameters, the value of each parameter was increased by 1% , and the relative absolute change in x2 is reported in Table IV. Changes in x2 were less than 2 % This indicates that the model results are not sensitive to the parameter values. In this calculation, six dependent variables were considered: biomass, glucose, phosphate, CyA, external valine, and internal valine. Errors of measurement of cell mass, phosphate, glucose, external valine, and CyA were computed as 0.057,0.031, 0.50,0.084,and 0.049 g/L, respectively, and 0.001 83 glg of dry cell weight (DCW) for internal valine. The biases in the fitting procedure were kept to a minimum by weighting the elements of each observation by a factor of unity (normalizingthe deviation from the experimental data with the highest magnitude). In analyzing the accuracy of measurements, three sets of fermentations carried out under the same conditions were used to calculate the x2of the six dependent variables. Except for the internal valine concentration, which is overestimated by 5-lo%, all of the other dependent variables showed good agreement with simulation values. Verification of the Model over Various Conditions. The mathematical model had to be tested further for ita practicability in simulating various environmental situations. Logistic considerationsprompted the use of shake flasks for generating experimental data under a wide variety of environmental conditions. Even though the fermentation conditions in shake flasks are somewhat different from those in stirred tank reactors in terms of shear and gas transfer, it was expected that, overall, the fermentation kinetics in shake flasks would follow a pattern similar to that in a stirred tank bioreactor. Simulation of the Effect of Addition Time of L- Valine. Figure 5 shows the comparison between final titers of CyA in shake flask fermentations and model simulation results. Cells were grown in SM medium, and 4 g/L L-valine was added at the specified time. Early additions of the amino acid result in high CyA titers, whereas later additions are not effective. The simulated curve shows a displacement along the time axis, but the qualitative trends of the final titers enhanced by L-valine during the fermentation period can be predicted reasonably well by the kinetic model. The reason for the displacement may be due to the different environmental conditions between shake flasks and the stirred tank reactor as mentioned above. To integrate the model equations, the initial conditions shown in Table I11 were used. The initial value of Sa was glg of cell (Le., within the order of chosen as 2.0 X magnitude of intracellular amino acid concentrations), as the simulation results were little affected by this initial condition. The time courses of internal valine and CyA were simulated and are presented in Figure 6a,b. Up to the 150th hour of the batch, the addition of 4 g/L L-valine shows similar trends in both Sa and CQA,and specifically, it does not affect significantly the final CyA titer. This
Table 11. Estimated Parameter Values in Equations 10-19 (Internal Properties) eat value 1.02 x 10-3 7.57 x 10-6 1.19 x 102 9.50X lo4 1.06 x 10-2 1.01 x 10-3 2.29 x
est value 4.83 X 2.79 X 10" 1.51 X lo-' 1.59 X 3.48 x 10-3 3.64 x 7.10 x 10-i
magnitude of the rate constant k2l.util as given in Table I1 (1.19 X lo2) is justified by the fact that this constant is proportional to the substantial growth-related rate of L-valine utilization, V21.utilt in contrast to constants like k22 and k23 that are featured in the much smaller nongrowth-associated rate of L-valine consumption, V22.util. L-Valine-SupplementedBatch Culture. As can be seen from the different panels of Figure 3, the experimental kinetic data from the L-valine-supplemented bioreactor run were in good agreement with model predictions. Notably, the internal L-valine concentration profile (Figure 3e) was correctly simulated as predicted by eq 10. The transitory increase in intracellular L-valine is very prominent, and the persistence of high-level CyA production over amajor portion of the stationaryphase (mixedgrowthassociated production kinetics) is clearly evident (Lee and Agathos, 1991). Note also the close agreement between estimated and experimentally measured cellular yields (Table I). Batch Culture without L-Valine. To evaluate the enhancing effect of L-valine on CyA production, a control batch reactor run without exogenousL-valine addition was carried out, and fermentation variables were analyzed. As shown in Figure 4,cell growth and substrate consumption profiles were similar to those of L-valine-supplemented culture (Figure3). However, the time courses and absolute values of CyA and of internal L-valine were dramatically different from the corresponding kinetics in L-valinesupplemented culture. In this control fermentation, the pattern of CyA production was more growth-associated, and the lower titers kept pace with the low and even profile of intracellular L-valine (Lee and Agathos, 1991). Again, the experimental data from the nonsupplemented case were adequately simulated using the model and parameters estimated from L-valine-supplemented fermentation. Analysis of Parameter Sensitivity. Deviation between experimental data and model simulation was analyzed by calculating x2,as there was a sufficient number of available data (>30)(Guttman et al., 1971):
22
b. - Yj,i(Xi,k)I2
x2
=
J=1
'
I,'
2
(20)
" j
where m is the number of dependent variables, n the number of experimental data for each dependent variable, Yji(xi,k)the model prediction, x i the independent variable,
variable
initial value
Xi
0.57 (g/L)
Sp
0.0 (g/L) 0.75 (g/L)
Sg
30.0 (g/L) as indicated (g/L)
xz Sve
variable
initial value
Sa Sbt
2.0 x (g/g of cell) 0.0 (g/g of cell) 0.0 (unit/g of cell)
E CCyA
0.0
.
(g/L)
Bbtechnd. Rog..,1993, Vol. 9, No. 1
0
0 0
200
100
300
0
200
100
tlme (h)
300
time (h)
b 401
time (h)
c
-
0.8
0.6
2ol
H
0.4
(Y
r
Y
0.2
0.0 0
200
100
300
time (h)
--'..
..
intermediate
CIA
rynthetare
________
/"..--.-
_,
04 0
100
200 time (h)
300
0
100
200
300
time (h)
Figure 3. Model simulation (solid line) and experimental data (symbol) of L-valine-supplementedbatch fermentation kinetics (data from Lee and Agathos, 1991).
Biotechnol. Prog., 1993, Vol. 9, No. 1
60
e
I
z
3-
.
(D
-.-.-.Q.”
e
I ,
\
a
2 - 1 0
m U @
1-
100
200
-
- - - -
07
0
300
time (h)
d
800
600
+
-e
400
5 0 200 ~”
*
_..I’
200
100
0
300
0
100
time (h)
*........
200
L
!._....t
300
time (h)
Figure 4. Model simulation (solid line) and experimental data (symbol)of batch fermentation kinetics without initial L-valine (data from Lee and Agathos, 1991). Table IV. Sensitivity of Fitted Model Parameters
absolute % change in x2 from 1 % increase Darameter in value 0.001 1.4 2.9
0.8 0.7 0.1
absolute % change in x2 from 1 % increase parameter in value
experiment
0.001 O.OO0 0.001 0.001 O.OO0
0.8
O.OO0 O.OO0
O.OO0
0.001
O.OO0
O.OO0
0.007
O.OO0
1.18
O.OO0
0.001 O.OO0
O.OO0
is closely related to the transitory increase of internal L-valine seen in L-valine-supplemented culture (Figure 3). Additions of this amino acid at progressively later times result in delayed and lower level rises in intracellular L-valine, which translate into commensurately lower CyA production. Thus, the model equations can be used to predict the most effective addition time of L-valine during the fermentation. Simulation of the Effect o f Initial L- Valine Concentration. In order to test further the model’s validity over a variety of conditions, the initial concentration of
slmuiatlon
200
-
0
1
0
50
100
150
200
addition time (h)
Figure 5. Influence of addition time of exogenous L-valine (4
g/L) on CyA production. The solid line represents model simulation and the symbolsare for experimental data (datafrom Lee and Agathos, 1989). exogenous L-valine (i.e., L-valine included in the medium from the start of the batch) was varied under previously described experimentalconditions (Leeand Agathos, 1989, 1991). These fermentationswere also carried out in shake flasks. As shown in Figure 7, the titers of CyA at 240 h
Biotechnol. Rag.., 1993, Vol. 9,No. 1
a
61
1
6o01
experhnent
1
1
0
100
200
300
Figure 7. Simulationof the effect of initialL-valineconcentration on CyA production. The solid line represents model prediction
lime (h)
and the open circles are for experimental data (data from Lee and Agathos, 1989).
........... .........
0
g/L
llllll..l..l.,l..lllI.
l8
o
12 ,J/L
6-
0
100
200
a
.,.--'. 'r
z
300
time (h)
Figure 6. Simulationof the effect of addition time of exogenous L-valine (4 g/L) on time courses of (a) internal L-valine concentration and (b) CyA production.
0
200
300
time (h)
b
were compared with the simulated results using the model, and a good agreement was obtained. Thus, there was an apparent saturation effect at about 6 g/L L-valine upon CyA titer. As shown in Figure 8a, maximum concentration and peak time of internal L-valine are strong functions of initial external L-valine concentration. The same was also found for CyA production (Figure 8b). The initial conditions used for simulating this situation were the same as those in the previous case of variable timing of amino acid addition (Table 111), except for the initial L-valine concentration which was as specified. Again, for batches of a typical length of about 240 h, there was no significant advantage in adding more than 6 g/L L-valine, as gauged by final CyA titer.
100
1200
-
0 g/L
.......
...........
6 g/L
.........
12 g/L
4,
0
Discussion In this study, several intracellular properties were mathematically investigated in detail, and the role of intracellular valine was successfully expressed as a precursor and inducedactivator of CyA synthetase. In the respect of regulatory interactions between external and internal chemical species, our study is building upon the concepts of elementary structured steps that have been
0
100
200
300
time (h)
Figure 8. Simulation of the effect of initial exogenous L-valine concentration on time courses of (a) internal L-valine concentration and (b) CyA production. employed previously in models of secondary metabolism. For example, in the case of clavine alkaloid production by
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62
C. purpurea, internal phosphate was logistically correlated with external phosphate, cell growth, and alkaloid production (Pazoutovl et al., 1981). Also, the induction of cephalosporin C production by methionine in C. acremonium was explained by the transient accumulation of endogenous methionine (Matsumura et al., 1981). In our own model, the intermediate complex was introduced in an attempt to include explicitly one of the multiple catalytic functions (i.e., N-methylation) that are involved in the thiotemplate mechanism of peptide secondary metabolite production. The regulatory mechanisms of peptidic secondary metabolites have special features compared to other microbial metabolites (Katz and Demain, 1977). Amino acids that are members of the peptide molecule can direct the biosynthesis toward the desired product among the spectrum of homologues (congeners) that are normally produced concurrent!y in the fermentation. Occasionally, an amino acid can enhance tremendously the production yield of the peptide by acting not only as a limiting precursor but also as an inducer (Haavik and Frrayshov, 1982)or in vivo stabilizer (Agathos and Demain, 1986) of the biosynthetic machinery. In modeling the key effects of L-valine on CyA production in our system, we have been guided by the current understanding of peptide biosynthetic mechanisms (Lipmann, 1973; Kleinkauf and von Dohren, 1985,1990). In the biosynthesis of such peptides through a nonribosomal route, multifunctional enzymes (synthetases) play the role of template, on which the intermediates are linked through thioester bonds, (hence the term thiotemplate mechanism), and the nascent peptide is formed in a series of processing and postprocessing steps. Recent progress in CyA synthesis in vitro showing that CyA synthetase accepts only the unmethylated precursor amino acids and that the methylation during the postprocessing step is an integral part of this enzyme (Lawen and Zocher, 1990; Billich and Zocher, 1990) could be reflected in improved versions of our modeling framework. Nonetheless, the putative role of L-valine as a limiting precursor and biosynthetic inducer of CyA formation is supported by (a) the strong stimulation of CyA titer by exogenous addition of the amino acid early in the fermentation, (b) the sizable transitory increase of the intracellular L-valine pool, and (c) the concomitant prolongation of the production phase beyond the period of active fungal growth (Lee and Agathos, 1991). Compatible with this scheme is also the idea of an intermediate between amino acid precursors and CyA, which is transiently accumulated and subsequently consumed to synthesize CyA in its final form. The existence of an optimal level of exogenous L-valine for overproduction of CyA may signify that, beyond this level, the amino acid ceases to be a limiting precursor in the biosynthetic scheme and/or that this value of L-valine affords saturation of the putative induction of cyclosporin synthetase. Overall, the present model with the parameters estimated by regression of batch experimental kinetic data was shown to be capable of describing the trends of a variety of batch cultures and may be applied to predict or compare the performance of different types of fermentation systems, including fed-batch and continuous modes (Lee and Agathos, Manuscript in preparation).
estimated through nonlinear regressional analysis. The two cell yield coefficients, YX/Gand Yxp,were in good agreement with overall experimental values. Our model profile simulation results showed excellent fitting to experimental biokinetics in both L-valine-supplemented and unsupplemented cultures. Also, the effects of addition time and initial concentration of L-valine on CyA production and other fermentation variables were successfully predicted. The earlier the amino acid was added, the higher the CyA final titer. There was also a dosedependent response of CyA production on the level of L-valine added, up to about 6 g/L of this key amino acid. Finally, the transitory increase of internal L-valine concentration was successfully simulated through the proposed model. The optimal timing and level of external L-valine addition for highest CyA production were also reflected correctly in the trends obtained by the model simulation, underscoring the general advantages of early and moderate level supplementationsof the fermentation with L-valine. The predictions of CyA synthetase activity and unmethylated intermediate concentration are also valuable and remain to be verified. On the whole, this work fills a gap in our still limited current understanding of the CyA fermentation and offers rational bioprocess engineering alternatives for further improvement of the production process for this life-saving drug.
Conclusions A physiological kinetic model was formulated for cell growth, external and internal L-valine,and CyA production in T. inflatum culture. All of the parameters were
non-growth-associated utilization rate of L-valine (g/g of DCW/h) total cell mass (g/L) cell mass of hyphae (g/L)
Notation concentration of CyA (g/L) concentration of CyA synthetase (unita/gof DCW)saturation constant of KHzPO4 (g/L) saturation constant in amino acid transport (g/W rate constant in synthesis of L-valine (g/gof DCW) saturation constant in synthesis of intermediate complex (g/g of DCW) saturation constant in synthesis of CyA synthetase (h-9 glucose concentration (g/L) concentration of intermediate complex (g/g of DCW) KHzP04 concentration (g/L) concentration of exogenous L-valine (g/L) concentration of endogenousL-valine (g/gof DCW) concentration of endogenous L-valine in hyphae (g/g of DCW) transport rate of L-valine per unit cell mass per unit time (g/g of DCW/h) maximum rate of U, (g/g of DCW/h) specific rate of synthesis of intermediate complex (g/g of DCW/h) specific rate of synthesis of endogenous L-valine in hyphae (g/g of DCW/h) rate constant in L-valinesynthesis (g/g of DCW/h) rate constant in the synthesis of intermediate complex (g/g of DCW/h) rate of synthesis of CyA synthetase (unita/g of DCW/h) maximum rate of synthesis of CyA synthetase (units/g of DCW/h) specific rate of glucose consumption in stationary phase (g/g of DCW/h) growth-associatedutilization rate of (g/g of DCW/ h)
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cell mass of spores (g/W yield coefficient of cell mass on glucose (g of DCW/g of glucose). yieldcoefficient of cell mass on phosphate (g of DCW/g of KHzPOd. rate cons-tant in CyA production (g of CyA/g of intermediate/h). specific transformation rate of hyphae to spores (h-9 specific decay rate of CyA synthetase (h-l) rate constants for glucose consumption (h-l) degradation rate constant of intermediatecomplex (h-9 degradation constant of CyA (h-l) degradation constant of endogenous L-valine in hyphae (h-l) rate constant related to V2l.util rate constant related to V 2 ~ . ~ (L/g tg of DCW/h) rate constant related to V22.util (g/L) maintenance coefficient (g/g of DCW/h) stoichiometric constants in eqs 10 and 11,respectively specific growth rate (h-l) maximum specific growth rate (h-l)
Acknowledgment This work was supported by National Science Foundation Grant CBT 87-09083and by Public Health Service Biomedical Research Support Grant 07058-21 to S.N.A. We thank SandozCorporation (East Hanover, NJ) for the gift of cyclosporin standards. Supplementary Material Available: Figures detailing the statistical analysis of the model summarized in the text (4pages). Ordering information is given on any current masthead page.
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