Biochemical Engineering Journal

ELSEVIER Biochemical Engineering Journal 2 ( 1998) 1 l-21

A structured model for penicillin production on mixed substrates

G.C. Paul, M.T. Syddall, C.A. Kent, C.R. Thomas * Centre for Bioprocess Engineering, School of Chemical Engineering, The University of Birmingham, Edgbaston, Birmingham, B15 2lT, UK

Received 23 January 1998; accepted 7 May 1998

Abstract

A structured kinetic model previously developed to describe the growth, differentiation, and penicillin production of Penicillium chryyso- genum has been enhanced and extended in order to apply it to a mixed carbon source fermentation. The filamentous hyphae are divided into four distinct regions on the basis of their activities and the physiological structure (i.e., vacuolation) of the hyphal compartments: viz., actively growing (mainly apical) regions, non-growing or penicillin producing regions, vacuoles, and degenerated or metabolically inactive regions. A simple approach is taken to give quantitative descriptions of hyphal extension, branch formation, vacuolation and differentiation. The fermentation medium contained glucose and lactose monohydrate as the main carbon sources. The source of the lactose was whey powder used in excess in the inoculum medium, whilst glucose was fed continuously throughout the fermentation. Lactose, adisaccharide, is hydrolysed to two monosaccharides, glucose and gaiactose, when the residual glucose concentration in the medium drops to a very low level. The utilisation of glucose and that of galactose following the hydrolysis of lactose were observed to occur simultaneously. This allowed the assumption of simple lactose utilisation kinetics in which lactose hydrolysis could be considered as producing an equivalent amount of glucose. The model has been used for successful predictions of fed-batch penicillin fermentations using an industrial P. chyogenum strain under different glucose feed rates. Quantitative information on proportions of the hyphal regions was obtained from image analysis measure- ments and the parameters of the model were identified. When the glucose feed rate to the production culture was switched between a high and a low value, the model successfully predicted the dynamic changes of differentiation and the resulting penicillin production caused by the variations in the nutrient conditions. The use of image analysis to characterise differentiation as a basis for structured modelling of the penicillin fermentation appears to he very powerful, and such models have great potential for use in process simulation and control of antibiotic fermentations. 0 1998 Elsevier Science S.A. All rights reserved.

Keywords: Structured model: Differentiation; Vacuolation; Penicillin production: Penicillium chrysogenum; Image analysis

1. Introduction

The commercial production of penicillin is from Penicil- lium chrysogenum, a filamentous microorganism consisting of a multicompartment structure of morphologically hetero- geneous hyphae. The physiology and differentiation of the compartments change along the length of the hyphae and during fermentation. Biochemical and morphological aspects of P. chrysogenum growth, morphology, differentiation and penicillin production have been discussed in several papers [ l-71. Increasing understanding and the availability of experimental data allow successful process models to be built which incorporate previously unmeasurable biological vari- ables [8].

There are many structured models of the penicillin fer- mentation based on some understanding of P. chrysogenum

* Correspondingauthor.Tel.: +44 1214145355;Fax: +44 1214145324: E-mail: c.r.thomas@bham.ac.uk

physiology 19-121. Although these models involve many parameters and kinetic constants, they are indispensable if the extremely complex nature of the microorganisms is to be taken into account, and they ought to have considerable prac- tical value. Recently, Paul and Thomas [ 121 developed such a model using data acquired by image analysis. The model considered differentiation of the hyphae into apical (actively growing) regions, non-growing or penicillin producing regions, vacuoles, and degenerated or metabolically inactive regions. The model was verified on a range of simple fed- batch penicillin fermentations using an industrial P. chtyo- geaum strain I 12). However, to apply this model to real industrial fermentations, it will be necessary to incorporate further states. In particular, one ought to allow for the com- plex substrate mixtures commonly used in fed-batch fermentations.

The work reported here is of a development of the struc- tured model of Paul and Thomas [ 121. The part of the model describing hyphal vacuolation and degeneration kinetics has

1369-703X/98/$ - see front matter 0 1998 Elsevier Science S.A. All rights reserved PUS1369-703X(98)00012-6

12 G.C. Paul et al. /Biochemical Engineering Journal 2 (1998) 11-21

been simplified in order to improve the computational speed of simulations and to make the mathematical analysis more tractable. This simplified model has been expanded to incor- porate mixed carbon sources containing glucose and lactose. This latter medium ingredient is significant for the study of the penicillin process when an industrial-type complex medium is used. The other essential nutrients (phenylacetic acid, nitrogen and oxygen) were assumed to be in excess during the whole fermentation. The different physiological states of the biomass were obtained by image analysis meas- urements [5,6] and the model has been tested using data from several fed-batch penicillin fermentations.

2. Materials and methods

An industrial strain of P. chr)lsogenum (SmithKline Bee- cham Pharmaceuticals, Worthing, UK) was used. The inoc- ulum culture was grown in a 2 1 shake flask ( inoculum volume 0.5 1) using a complex medium [ 131 containing whey pow- der and corn-steep liquor (Sigma, Poole, UK). A 32-h-old vegetative culture was inoculated in a 6 1 (working volume 5 1) fermenter (Life Science Laboratories, Luton, UK) using a complex medium [ 41. The initial volume after inoculation was 4.0 1. The agitation speed was started at 800 ‘pm and increased to 1000 rpm after 20 h of the fermentation. The temperature was controlled at 25”C, pH at 6.5 and aeration at 1 vvm.

Various protocols for the addition of glucose (50% w/v) solution were implemented via a computer controlled peri- staltic pump (Watson Marlow, Cornwall, UK). Glucose feeding protocols used in fermentations Rl-R4 are presented in Fig. 1. 5%( w/v) phenylacetic acid (PAA) neutralised with sodium hydroxide at pH 7.1 and supplemented with 5%(w/v) ammonium sulphate was added continuously to keep the residual PAA concentrations below 0.2 g/l from inoculation to 20 h, and between 0.45 and 0.60 g/l from 20 h to the end of the fermentation. This was done to avoid the toxic effect of PAA on biomass growth [ 141. All the oper- ating variables were monitored and controlled via the SET- CIM data management and control system (AspenTech, MA, USA).

Cell dry weight was measured according to the method of Paul et al. [ 61. Analysis of glucose, lactose, PAA and peni- cillin G concentrations was performed by two on-line HPLC systems (Model 1050, Hewlett Packard, Waldbronn, Ger- many). Cell-free samples from the fermenter were pumped out continuously through a sterilisable membrane sampling system (ABC, Puchheim, Germany) and passed through a 300 ~1 flow cell built in-house. The flow cell was mounted on a Gilson 232XL on-line column switching device (Gilson, Villiers-le-Bel, France) fitted with two injection ports and connected to the Hewlett-Packard pump modules. The first system, fitted with a Spherisorb S5C8 200 X 4.6 mm column (Hichrom, Reading, UK) and a UV detector was used to monitor PAA, penicillin G and other minor compounds ( such

12

8- RI

0 20 40 60 80 100 120 140 160

Time (h) Fig. I. Protocols for the addition of 50% w/v glucose solution for femen- tations R144.

as penicillin G degradation compounds and PAA oxidisation compounds). The second system, fitted with a Bio-Rad fer- mentation monitoring column ( 100 X 7.8 mm column, Cat. No. 1250155, Bio-Rad Laboratories, Hertfordshire, UK) and a RI detector gave concentration measurements of glu- cose, lactose, galactose, lactic acid and some other minor organic acid compounds. The injection sequences were pro- grammed to give simultaneous sample analysis. Analysis of results, including integration, quantification and report gen- eration was customised using Hewlett-Packard ChemStation application software. The final report was transferred to the SETCIM process computer ( Micro-Vax 3 100 model 40, Dig- ital Equipment, MA, USA) via a RS 232 link. The concen- tration of PAA in the medium was controlled using a peristaltic pump.

A Quantimet 570 (Leica Cambridge, Cambridge, UK) was used for automatic characterisation of hyphal differen- tiation of P. chlysogenum fermentation samples. The detailed image analysis method and the estimation of the volumes and weights of the differentiated regions have been published previously [ 61.

3. Model description

The details of the earlier model have been described in Paul and Thomas [ 121. This section will summarise theover- all structure and provide the kinetic expressions associated with each reaction scheme. The part of the model incorpo- rating the lactose metabolism will be described in full, with

G.C. Paul et al. /Biochemical Engineering Journal 2 (1998) 11-21 13

supporting experimental data from the penicillin fermentations.

In submerged fermentations the hyphae can be divided into four distinct regions on the basis of the activity and structure of the cells [ 121:

Actively growing (mainly apical) regions

Non-growing cytoplasm

Vacuoles (small vacuoles in the non-growing regions) Degenerated or metabolically inactive regions

In this paper, the biomass states are represented by Ai (where i = 0 represents the growing regions; i = 1, the non-growing regions; i = 2, the vacuoles in the non-growing regions; and i = 3, the degenerated regions), the dry weight concentrations corresponding to these regions by a, and the volumetric con- centrations by ui. The dry weight contributions of vacuoles were assumed to be negligible. Total biomass (represented by A,, and its concentration by a,) is obtained by a summation of the growing, non-growing and degenerated regions (A,,, A,, and A,). Other states: autolysed biomass, glucose, lactose monohydrate and penicillin G are represented by Ad, S,, Sz and P, respectively and their concentrations (all in g/l) by a4, s,, s2 and p. respectively.

The schematic representation of the four hyphal regions is shown in Fig. 2 and the overall reaction scheme is given in Fig. 3. In the model, glucose and lactose are the main carbon sources limiting the growth, differentiation and penicillin production. The influences of nitrogen, oxygen and PAA were not considered because they were kept in excess during the fermentations to avoid limitations by these compounds. Although, the supply of sufficient amounts of oxygen might become a critical problem at high biomass concentrations, particularly at large scales, the mode1 reported here was tested (at the 5-1 scale) with dissolved oxygen levels held above 50% saturation. Squires [ 151 and Konig et al. [ 161 reported critical dissolved oxygen concentrations for penicillin pro- duction of around 5-lo%, whilst Vardar and Lilly [ 171 observed this critical value to be at the higher level of 30%. A very recent study by Henriksen et al. [ 181 with a steady- state P. chrysogenum culture reported that the specific pro- ductivity of penicillin remained unchanged at dissolved oxygen concentrations above 23% whilst a drastic drop was observed just below this level. No significant influence on the growth and respiration was observed with dissolved oxy- gen concentrations between 7-134%. This suggests that a minimum dissolved oxygen level of 50% in all the experi- ments presented here was high enough to prevent limitation of growth, differentiation and penicillin production.

The kinetics of branching, extension, differentiation, vac- uolation, degeneration and penicillin production are briefly described below. The full details can be found in Paul and Thomas [ 121. The mechanisms for branch formation and hyphal extension closely follow the concepts of Megee et al. 1191.

Growing tips, A0

Vacuote. A*

Non-growmg repion, A,

Autolysed region. Aq

Highly v/acuolated compartment

Fig. 2. Schematic representation of differentiation of a P. chryogenum

mycelium in submerged fermentation.

Hydrolysis b

Vacuolation

Autolysis b

Fig. 3. The reaction scheme for the overall process. Glucose and lactose are the limiting substrates for growth, differentiation and penicillin production.

Oxygen, nitrogen and phenylacetic acid are kept in excess throughout the fermentation.

3. I. Kinetic expressions

3. I. I. Branch formation A new tip, A,, is produced by the appearance of a branch

from the non-growing regions, A,. The branch formation occurs in response to the substrate concentration, and the rate expression for branch formation is given by the following kinetic expression:

wOalsl r -- bra- K('fs, (1)

where h is the rate constant (h - ’ ) , a, is the concentration of A, (g DW/l), si is the concentration of glucose (g S, /l), and K, is the saturation constant (g S, /l) .

3.i.2. Extension When an apical cell, Ao, is produced the hypha extends in

length by utilising substrate. Simultaneously non-growing

14 G. C. Paul et al. /Biochemical Engineering Journal 2 (1998) 1 l-21

regions, A,, are formed. Thus, the first differentiation occurs as a result of extension. The growth of this process is described by the following expression:

where CL, is the rate constant (h- ’ ), a, is the concentration of A0 (g DWA), and K= is the saturation constant (g S1 /I).

3.1.3. Differentiation from A0 to A, This differentiation of A0 to A, responds to the substrate

concentration in the medium. The kinetic expression for this is given below. The detailed explanation for the chosen form can be found in Paul and Thomas [ 121 and Megee et al. [ 191:

ylao r -- d”- K,+s,

(3)

where y, is the maximum rate of substrate utilisation (g S, / h) for this differentiation process. This equation implies that differentiation is inhibited by the presence of high concentra- tion of substrate, but at very low substrate concentrations (e.g., during the production phase) the differentiation might be adequately described by first order kinetics in a,.

3.1.4. Vacuolation Differentiation of non-growing regions, A,, by the forma-

tion of vacuoles (AZ) and further growth of vacuoles by this continuing process are assumed to occur because of limita- tions of the substrates. The reaction mechanism for vacuole formation and growth is described by Eq. (4) :

rd.2=p1”Ic+p2u2 (4)

where ,u, is the first order rate constant for vacuole formation (h- ’ ), ulc the volumetric concentration of the non-growing cytoplasm ( cm3/1, total regions-vacuoles+ell walls), b the first order rate constant for vacuole growth (h- ’ ) and v2 is the volumetric concentration of vacuoles ( cm3/1). This is a simplified expression of the vacuolation kinetics compared to that in the previous model [ 121, which was based on a population balance of vacuoles. This simplification is sug- gested to improve the computational speed of the model sim- ulation, and in recognition of the poor physiological knowledge underpinning the previous kinetic expression.

3.1.5. Degeneration When vacuoles increase in size under the condition of

nutrient limitation in the medium, they produce regions with little or no cytoplasm left in the compartments. Compartments with large vacuoles are degenerated and do not contribute to penicillin biosynthesis. The generation of these regions causes a loss of non-growing cytoplasm (A, ) as indicated in Fig. 3. In the model, first order kinetics in A2 are assumed to describe this degeneration process:

r,,3=P3(2u2)p3 (5)

where m is the first order rate contant (h- ’ ), vZ the volumetric

concentration of vacuoles (cm3/1) and p3 the density of the degenerated regions (g DW/cm3). It was previously shown that in the heavily vacuolated regions, the volume proportion of the large vacuoles was approximately 50% of the com- partments [ 61; this lead to the factor 2 appearing in Eq. (5).

3.1.6. Autolysis The regions in the hyphae containing large vacuoles can

either be autolysed or fragmented by ‘shear’ forces [7,20] and the rate of loss of materials by this process is assumed to be first order, proportional to the concentration of the degen- erated regions:

rd,4=&a 1 (6)

where pa is the first order rate constant (h- ’ ) and a3 is the concentration of the degenerated regions (g DWA). This accounts for the total biomass lost by autolysis and fragmen- tation. No recycling of autolysed materials is considered.

3. I. 7. Penicillin production Penicillin production is assumed to occur at regions con-

taining non-growing cytoplasm in the presence of substrate. Excess substrate can inhibit penicillin production. Introduc- ing substrate inhibition kinetics of the type used by Bajpai and Reuss [ 21,221, the following expression can be obtained for the rate of penicillin production:

lIpL’lcPcS1 %= K,+s,(l+s,/K,) (7)

where pp is the specific penicillin production rate (hh’), vlc is the volumetric concentration of thenon-growing cytoplasm ( cm3/1) in the non-growing regions, enclosed by and exclud- ing the cell walls, Kp is the saturation constant for substrate limitation for product formation (g S, A), and K, is the sat- uration constant for substrate inhibition for product formation (g S,/l).

3.1.8. Penicillin hydrolysis Penicillin hydrolysis is considered to follow first order

kinetics in penicillin concentration in the broth:

rh=phP (8)

where ~~ is the first order penicillin hydrolysis constant (h- ’ ) and p is the penicillin concentration (g P/l).

3.1.9. Lactose conversion The metabolism of mixed substrates is poorly understood

in fungi. It is assumed here that the processes are analogous to those occurring in bacteria, particularly Escherichia coli [ 23 1. With growth of E. coli on a medium containing glucose and lactose, there are two distinct phases of substrate utilis- ation. Glucose is metabolised first, and when the glucose concentration becomes very low, B-galactosidase is synthes- ised and growth continues on lactose. Considering Fig. 4, a similar kind of substrate utilisation is observable in P, chrysogenum.

G. C. Paul et al. /Biochemical Engineering Journal 2 (1998) I l-21 15

0 20 40 60 80 100

Time (h) Fig. 4. Typical profiles for glucose and lactose monohydrate concentrations in a fed-batch penicillin fermentation (Rl). The utilisation of lactose started when the residual glucose concentration dropped to a low level. Due to the

carbon limited growth, neither glucose nor galactose (one of the hydrolysed components of lactose) were detected in the medium after 32 h of the fermentation.

The source of lactose monohydrate in the fermentation medium was whey powder used in excess as a carbon source in the inoculum medium. The concentration of lactose mono- hydrate after inoculation in the fermenter varied, typically in the range of 5 to 6 g/l. Lactose, a disaccharide, is hydro- lysed to two monosaccharides, glucose and galactose, by p- galactosidase. The total weight of glucose and galactose equals the weight of lactose monohydrate utilised. The util- isation of these two monosaccharides following the hydrol- ysis of lactose monohydrate appeared to occur simulta- neously (i.e., without any preferential utilisation of these two substrates) in the fermentations. This allows simple lactose utilisation kinetics to be assumed, in which lactose hydrolysis can be considered as a process producing an equivalent amount of glucose, when the residual glucose concentration drops to a very low level. The activity of the enzyme respon- sible for lactose hydrolysis is assumed proportional to the amount of active biomass, i.e., the combined amount of grow- ing (A,) and non-growing regions (A,) in the broth. The following competitive substrate inhibition kinetic expression is appropriate to describe the rate of conversion of lactose to an equivalent amount of glucose, given the assumptions above:

k%(ao+a,) %= (K,,+s,)(l+s,lK,,)

(9)

where pL is the rate constant for lactose conversion (h- ’ ), s, the concentration of glucose (g S, /l), s2 the concentration of lactose monohydrate (g S,/l), KsL the saturation concen- tration of lactose monohydrate limiting the conversion (g Sz/ 1), and K,, the saturation constant for glucose inhibition lactose of conversion (g S, /I).

3.2. Generalised balance equations

The kinetic expressions described in Eqs. ( 1 )-( 9) are used to produce generalised balance Eqs. ( lo)-( 18) for the fed- batch penicillin fermentation. These incorporate substrate accumulation, broth dilution by feed (F,) and precursor (F,,) additions, and filtered sample removal for on-line HPLC analysis (H,).

Growing regions:

da,- (Ff+Fa,-H,)ao dt -rb,O-ld,!-

V

Non-growing regions:

!&- (F,+Fa,-H,b, dt -‘e.] -rb,0+r,.l-r,.3- V

Vacuoles:

dl;,- (Ff+Fap-Hr)UZ dt -r,,2-rda31P2- V

Degenerated regions:

da,- (F,+Fa,-H,)a3 dt -ld.3 -rd.4- V

Autolysed biomass:

da,- (F,+Fa,-Hrh dt -ld,4-

V

Penicillin:

dp -z rp - r, - (F,+F,,)p

dr V

Glucose:

(12)

(13)

(14)

(15)

ds,- mOaOS1 mlwvl

dt --Lyorb,o-~,r,,,- - -

K,+s, K,+s, (16)

-cxprp- (F,+F&, + FGP

V --y +r,2

Lactose:

ds, -=-r -

(F~+Fap)sz dt s2 V

(17)

Fermenter volume:

dV - =F,+F,,-H, dt (18)

where V is the fermenter volume (I), s, the concentration of glucose in the feed (g S, /l), cu, the stoichiometric coefficient for glucose conversion to A, (g S, /g A,), CX~ the stoichio- metric coefficient for conversion of glucose to A, (g S, /g A, ) , (Y,, the stoichiometric conversion of glucose to penicillin G (g S, /g P), m, the maintenance coefficient for A, (g S, /g A,lh) and m, the maintenance coefficient for A,, (g S,/g

16 G.C. Paul et al. /Biochemical Engineering Journal 2 (1998) 11-21

A ,,/h). It is to be noted here that the maintenancerequirement terms used in Eq. (16) are glucose concentration dependent [ 10,121.

4. Estimation of model parameters

The model as represented by Eqs. ( lo)-( 18) contains 23 parameters and 9 states (A,, Al, A,, A,, A,, S,, S,, P and V) . Total biomass (A,) is obtained by a summation of the phys- iological states A,, A, and A,. The dry weight contribution of vacuoles (A2) is assumed to be negligible as stated previ- ously. The parameter estimation was performed using Simu- solv (Dow Chemical, Midland, USA) simulation, optimisation and parameter estimation software installed on a DEC Alpha workstation (Model 250 41266, Digital Equip- ment, MA, USA). The parameter estimates and the uncer- tainty in the estimates were obtained by maximising the log of the likelihood function as the non-linear objective function. In the log likelihood method the Gaussian probability distri- bution function was used as the error model, i.e., the experi- mental errors were assumed to be normally distributed. The objective function was solved by the generalised-reduced- gradient (GRG) method. The GRG algorithm implemented in Simusolv (referred to as GRG2) uses an optimisation code following some improvements proposed by Lasdon and Waren [24]. The model equations were integrated numeri- cally using the method of Gear.

The estimates of model parameters were obtained from two sets of experimental data, 1~1 and R2. Fermentation Rl was carried out at constant glucose feed rate and R2 at a constant feed rate during the rapid growth phase and a pulsed square-wave feed rate during the production phase (see Fig. 1). In using the Simusolv parameter estimation method, a set of initial parameter estimates should be provided. Most of these were chosen from previous work [ 121 and the others were chosen based on experimental experience and subse- quently refined through successive parameter estimation. The estimation of the whole set of parameters was considered necessary primarily due to the use of a different fermentation method from that used previously, and the incorporation of lactose utilisation into the model. Table I gives the parameter values estimated for these two data sets.

In the estimation process it was also decided to obtain estimates of the initial conditions of the hyphal differentiation states (A,,, A,, A, and A3). These are listed in Table 2. Nor- mally A,-A, would be measured by image analysis [ 61. Table 2 suggests that a consistent inoculation protocol would allow the use of estimated initial values of these states, It could then be possible to use the model (with predetermined parame- ters) on fermentations without the need for image analysis. This is discussed further below.

5. Results and discussion

Figs. 5 and 6 show the model fits for the reference fermen- tation Rl, comparing simulation results obtained using the

Table I List of model parameters and their values obtained from two fed-batch

penicillin fermentations

Parameters Rl R2

PC 0.033 f 0.001 0.027 + 0.001

Pe 0.409 f 0.007 0.398 * 0.004

Pa 0.044 * 0.009 0.050 i 0.003

@P 0.0287 f 0.0003 0.0380 + 0.0005

CLh 0.0028 f 0.000 I 0.0031 f 0.0002

PI. 0.24 I f 0.005 0.245 k 0.023

CL1 0.019+0.001 0.025 + 0.001

P2 0.0020 f 2.0e - 5 0.0025* l.Oe-4

IL3 0.054 f 0.002 0.052 + 0.002

f% 0.0256 f 0.001 I 0.0252 If 0.0003

ml 0.0242 f 0.0009 0.0275 f 0.0008

YI 0.0122 *0.0004 0.0107 *o.o001

% 1.85 f 0.04 1 X6+0.05

a, 1.83 + 0.06 2.00 f 0.05

% 0.85 k 0.02 0.83 kO.04

&I. 0.086 f 0.00 1 0.102 f 0.003

KS1 0.0011 * 0.0003 0.0012~0.0002

4 0.366 +O.OS 1 0.415 f 0.005

KP 0.041+_0.006 0.048 f 0.002

Ku 0.0352 f 0.0005 0.0348 f 0.0002

K 0.079 + 0.002 0.117+0.003

K, 0.09 1 f 0.003 0.106*0.003

K2 0.302 f 0.008 0.287 lir 0.003

The parameter values are listed with their standard deviations.

Table 2 Estimates of initial differentiation states from fermentations Rl and R2

Differentiation states RI R2

A0 0.15+0.003 0.18rtO.002

A, 0.7 1 IO.02 0.8OiO.05

4 0.12rtO.003 0.15 * 0.01

4 0.02 f 0.05 0.00 f 0.0 I

Rl parameter values from Table 1 with experimental data. The glucose feed rate was kept constant throughout this run. Fig. 5 shows the time profiles of glucose, lactose monohy- drate and, penicillin G concentrations and Fig. 6 the corre- sponding four hyphal differentiation states and the total biomass concentration. The model fits the experimental data extremely well. The competitive substrate inhibition kinetic form chosen in the model is clearly successful in describing lactose utilisation in the penicillin fermentation.

Model fitting was examined further on fermentation R2 in which the feed rate of glucose was pulsed in a square wave during the production phase (Figs. 7 and 8). The R2 param- eter values estimated using this fermentation are given in Table 1. This provided a good test of how the model would represent fermentations with rapid transients of the substrate feeding. From Figs. 7 and 8, it can be seen that the agreement between the experimental data and model simulation remains very good. Changes in the penicillin titre caused by the repeated switching of the glucose feed rate were matched well by the model, and there was reasonable agreement for

G.C. Paul et al. /Biochemical Engineering Journal 2 (1998) II-21 17

0 20 10 60 80 IW 120 140

Time(h)

Fig. 5. Model fits of glucose, lactose monohydrate, and penicillin G concen-

trations and glucose feed rate for fermentation Rl

the other model states. The discrepancies between the meas- ured vacuolation (AZ) and degenerated regions (A,), and the model predictions (Fig. 8) was expected owing to the great simplification of this part of the model compared to the pre- vious version [ 121. It is worth mentioning that lack of detailed knowledge about vacuole formation and vacuole growth makes it difficult to choose an exact form of these kinetics. The incorporation of a more complex mathematical expression, as suggested previously [ 121, may give a better fit but may not necessarily reflect the underlying physiology. Until further studies reveal the mechanism of this process, it has been decided to use a simple form (i.e., first order kinet- ics) in the model. Nevertheless, this simple approach still provides a reasonable representation of these two states (A2 and A,) by the model and an excellent representation of the remaining six concentration states.

In both cases (fermentations Rl and R2), the model describes the lactose and glucose utilisation remarkably well. The approach of using simple competitive substrateinhibition kinetics in the model was validated by experimental obser- vations using on-line HPLC to quantify the substrates. On- line HPLC is clearly a powerful tool for this sort of study. In principle, its use would allow incorporation of the utilisation kinetics of minor substrates such as lactic acid (typically around 1 to 2 g/l in the complex medium used in this work). However, this was deemed undesirable in practice, to avoid further model complexity and the addition of extra parame- ters. Nevertheless, the present success opens up the possibil-

00 8

0 20 40 60 SO loo 120 140

Time(h)

Fig. 6. Model fits of the biomass states of fermentation Rl. Symbols are for

experimental data and lines for model fits.

ity of further modelling to accommodate other mixed substrates found in industrial complex media.

The parameters obtained by tuning the model with exper- imental data for fermentations Rl and R2 are presented in Table 1. In most cases, corresponding parameters estimated from each run have similar values and agree within the con- fidence limits. This implies that the model structure appro- priately describes the penicillin G fermentation and is able to cope with disparate feeding profiles. The values of the yield and maintenance parameters obtained from each experiment are within the ranges suggested in the literature [ 1,2,2 1,221. These are common parameters used to characterise a fermen- tation process and without appropriate values the model may not provide an adequate description of substrate utilisation, biomass growth and product formation. The penicillin hydrolysis rate constant is within the range reported by other workers [9,21,22]. The values for the saturation constants (K,,, K,, K,, and K2) are similar to those proposed by Nielsen [ 111. The parameters associated with the penicillin produc- tion kinetics (b, Kp and K,) are expected to be dependent on strain as well as on the medium. The values of the other parameters are difficult to compare directly with previous studies due to differences in model structure.

18 G.C. Paul et al. /Biochemical Engineering Journal 2 (1998) I l-21

2-1 0 M 40 60 S” IW iZ0 140 160

Time(h)

Fig. 7. Model fits of glucose, lactose monohydrate, and penicillin G concen- trations and glucose feed rate for fermentation R2.

Model simulations are compared with data for fermenta- tions R3 and R4 in Figs. 9 and 10, respectively. Fermentation R3 was performed at a constant glucose feed rate throughout the run and R4 at a constant feed rate during the rapid growth phase and a pulsed square wave feed rate during the produc- tion phase. In each case both sets of parameter values esti- mated from experimental data of Rl and R2 (see Table 1) were used to make predictions. Additionally, the simulations used the initial estimates for differentiation states A,-A, from fermentations Rl and R2 (see Table 2).

Fig. 9 shows good agreement between the experimental data for total biomass, glucose, lactose and penicillin G, and the corresponding predictions using either set of parameter values. The simulations for fermentation R4 presented in Fig. 10 demonstrate the excellent predictive power of the model. In this case, the glucose feed rate during the production phase was pulsed in a square wave, giving a very variable behaviour throughout the fermentation. Reasonably good predictions to the experimental data are evident, even for the very stringent test of this fermentation, and even without access to measured initial values of the states A,-A,. On the basis of the graphs shown in Figs. 9 and 10, it is not possible to say which of the two sets of parameter estimates (shown in Table 1) gives the better predictions; the two sets of parameter values are quite similar. This suggests that it may be possible to estimate the model parameters and initial A,-A, values using image anal- ysis measurements on just a few test fermentations. Provided

0 20 40 60 so 100 120 140 160

Time (h)

Fig. 8. Model fits of the biomass states of fermentation R2. Symbols are for

experimental data and lines for model fits.

the inoculation protocols lead to consistent operation, it could then be possible to forgo further use of image analysis.

Although the incorporation of mixed carbon sources (i.e., glucose and lactose) in the model was remarkably successful, the effects of other fermentation conditions such as dissolved oxygen concentration and agitation speed were not included. These might well affect the parameter values and possibly the structure of the model, and remain to be investigated.

The mechanisms for vacuolation, degeneration and frag- mentation (or autolysis) rely on simple first-order kinetics. The simple form is justified due to the lack of adequate knowl- edge of vacuolation and of how the vacuolation affects hyphal degeneration and fragmentation and/or autolysis. Recent work did indicate a relationship between vacuolation and fragmentation [20]. Detailed experimental data under a range of operating conditions (particularly agitation speed) may be necessary to determine the mechanistic basis of this process. Alternatively, it may be possible to incorporate into the model the energy dissipation/circulation time function recently proposed by J&ten et al. [7,25,26] for correlating mycelial fragmentation with agitation conditions.

G.C. Paul et al. /Biochemical Engineering Journal 2 (1998) 11-21

12 I

Fig. 9. Model predictions of fed-batch fermentation R3 using parameters estimated fromfermentationsR1 andR2. Thefeedrate wasconstant through- out the fermentation. Symbols are for experimental data, solid lines represent simulation using R 1 parameters, and broken lines represent simulation using R2 parameters.

6. Conclusions

The model presented here gives a quantitative description of penicillin fermentations utilising mixed substrates, ascom- monly used in industry. The competitive substrate inhibition kinetic describing the utilisation of glucose and lactose appeared to be remarkably successful. The model describes the physiological structure of fungal biomass and has been validated against states measured using image analysis. The capability of the model in predicting the dynamic behaviour of fed-batch penicillin fermentations is likely to be the con- sequence of its structure, and the accurate and reliable meth- ods used to quantify the model parameters. The model has potential use in process simulation and optimisation of pen- icillin production, at least in cases where oxygen limitation is not severe. However, parameter estimation would be needed for each industrial medium and strain, and the model might need further development to allow for yet more com- plex industrial fermentations.

Fig. 10. Model predictions of fed-batch fermentation R4 using parameters estimated from fermentations Rl and R2. The feed rate was constant through-

out the fermentation. Symbols are for experimental data, solid lines represent simulation using R 1 parameters, and broken lines represent simulation using R2 parameters.

7. Nomenclature

Ai Differentiated regions of hyphae i = 0: growing regions i = 1: non-growing regions i = 2: vacuoles i = 3: degenerated regions i = 4: autolysed biomass i = t: total biomass

A,, Non-growing cytoplasm a, Concentrations of the differentiated regions (i = 0, 1,

2,3,4, t; see Ai for meaning of i values) (g DW/l) a,, Concentration of non-growing cytoplasm (g DW/l) Far, Precursor (PAA) addition rate (l/h) Ff Feed rate (l/h) H, Sample removal rate for on-line HPLC (l/h) K0 Saturation constant for branch formation (g S,/l) K, Saturation constant for hyphal extension (g S1 /l)

G.C. Paul etal. /Biochemical Engineering Journal 2 (1998) II-21 20

Kl

K2

Kl

KP

KS,

K SL

m.

ml

P

P rb.O

rd,l

rd,2

ld.3

ld.4

re,,

rh

‘P

rs2

Sl

Xl

s2

s2

Sf

I

V L’i

"IC

Saturation constant for A, to A r differentiation (g S, / 1) Saturation constant for A, maintenance (g S, 11) Glucose inhibition constant for penicillin production (g S/l) Saturation constant penicillin production (g S, /l) Glucose inhibition constant for lactose monohydrate conversion (g S,/l) Saturation constant for lactose monohydrate conversion (g S,/l) Maintenance coefficient for A0 (g S, /g A,lh) Maintenance coefficient for A, (g S, /g A, /h) Penicillin G Penicillin G concentration (g P/l) Rate of branch formation (g A,lh) Rate of formation of A, by differentiation of A, (g A, / hf Rate of vacuolation ( cm3 A,/h) Rate of formation of A3 by degeneration of A 1 ( g A, / h) Rate of loss of A, by autolysis (g A,lh) Rate of formation of Al by hyphal extension (g A, /h) Rate of loss of penicillin G by hydrolysis (g P/h) Rate of penicillin G production (g P/h) Rate of formation of glucose by conversion of lactose monohydrate (g S, /h) Glucose Glucose concentration (g S, /I) Lactose monohydrate Lactose monohydrate concentration (g S,/l) Concentration of glucose in the feed (g S, /l) Fermentation time (h) Fermenter volume (L) Volume concentrations of the differentiated regions ( cm3/1) (i = 0, 1,2, 3,4, t; see Ai for meaning of i values) Volume concentration of non-growing cytoplasm ( cm3/1)

Greek symbols

Stoichiometric coefficient for A, (g S, /g A,) Stoichiometric coefficient for A, (g S, /g A, ) Stoichiometric coefficient for penicillin G (g S, /g P) Rate of substrate utilisation for differentiation of A, to A, (g&/h) Rate constant for branch formation (h- ’ ) Rate constant for vacuole formation (h-l) Rate constant for vacuole growth (h-l) Rate constant for hyphal degeneration (h- ’ ) Autolysis rate constant (he- ’ ) Rate constant for hyphal extension (hh ’ ) Penicillin hydrolysis constant (h- ’ ) Rate constant for lactose monohydrate conversion (h-l) Penicillin production rate constant (h- ’ )

PI Density of the differentiated regions (g A,lcm3) (i = 0, 1,2, 3, t; see Aj for meaning of i values)

pc Density of the cytoplasmic regions ( g/cm3)

Acknowledgements

This work was supported by the Biotechnology and Bio- logical Sciences Research Council (BBSRC), UK. The authors thank SmithKline Beecham Pharmaceuticals (Worthing, UK) for providing a Penicillium chrysogenum strain for this research. Ms. S. Wijesinghe, University of Birmingham, UK, is thanked for assisting with the fermentations.

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