Morphologically structured model for growth and citric acid accumulation by Aspergillus niger

Enzyme and Microbial Technology 32 (2003) 268–281

Morphologically structured model for growth and citric acid accumulation by Aspergillus niger Marcin Bizukojc∗ , Stanislaw Ledakowicz Department of Bioprocess Engineering, Technical University of Lodz, ul. Wolczanska 213/215 93-005 Lodz, Poland Accepted 20 October 2002

Abstract A morphologically structured model for the batch process of biomass growth and citric acid accumulation by Aspergillus niger is presented in this paper. The model consists of ten ordinary differential equations, which balance biomass and four physiological zones of hyphae, and includes the most important medium components, such as carbon sources, nitrogen source and citric acid. Digital analysis of microscopic images was employed to determine the hyphal fractions within each physiological zone. All model parameters were determined on the basis of data obtained in four experiments carried out in two types of bioreactors and under various process conditions, specifically normal and increased pressure. Some parameters were directly calculated from the experimental data by means of linear and non-linear regression. This allowed minimisation of the number of parameters to be found by means of an optimisation procedure, down to 11 and thus, significantly reduced computation time. The simulated curves are largely consistent with the experimental data and some parameters appeared to be practically independent of process conditions. These findings contribute to the universality of the model proposed. © 2002 Elsevier Science Inc. All rights reserved. Keywords: Structured model; Digital image analysis; Aspergillus niger; Citric acid fermentation

1. Introduction The structured modelling of microbial processes is an approach to mathematically describing microbial growth and metabolite production, in which cells are not treated as a “black box”, in which neither intracellular reactions nor microorganisms’ morphology are taken into account. Generally, there are two types of structured models that can be applied to describe the process of microbial growth. These are intracellularly structured models, where one formulates the kinetic expressions for the intracellular reactions of basic metabolic pathways, and morphologically structured models. In morphologically structured models, biomass is divided into subsections or compartments of various function and biochemical properties and/or the dimensions of cells are also taken into account. The latter are often used to describe the growth of filamentous microorganisms. If a morphologically structured model is to describe non-filamentous bacteria or yeast, then so-called population models are usually applied, in which statistical relations describing the sets of objects (microorganisms) are introduced. Finally, both concepts of structured model can ∗

Corresponding author. Tel.: +48-42-631-3700; fax: +48-42-636-5663. E-mail address: [email protected] (M. Bizukojc).

be united together into an intracellularly- and morphologically structured model. However, such a model is extremely complicated and demands powerful calculation algorithms. It is also very difficult to determine proper parameters for such a model and to verify it experimentally [1]. There are many structured models for various microorganisms presented in the literature, showing various levels of complexity and robustness. An example of a very advanced work on microbial physiology is the set of experiments performed by Theobald et al. [2], leading to the formulation of the complex intracellularly structured model for Saccharomyces cerevisiae by Rizzi et al. [3]. Intracellularly structured models for Aspergillus niger have rarely been formulated. Only Torres [4,5] and Alvares-Vasquez et al. [6] made serious attempts to model biomass growth and citric acid production by A. niger. However, these models are very complicated and involve many parameters adapted from various sources, which is their major disadvantage. Also, experimental verification seems to be extremely difficult. The filamentous fungi are usually the objects of morphologically structured modelling and a number of models for Penicillium sp. have lately been published [7–10]. They all describe fungal growth and antibiotic formation in fed-batch culture.

0141-0229/02/$ – see front matter © 2002 Elsevier Science Inc. All rights reserved. PII: S 0 1 4 1 - 0 2 2 9 ( 0 2 ) 0 0 2 8 4 - 3

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Nomenclature A AMON B CIT FRU GLU k1 k2 k3 k4 ka kaAMON KAMON kCIT/F kCIT/G KFRUCIT KGLUCIT KI kXX0 rCIT/F rCIT/G rFRU rGLU rH rXA rXS rXX S SUC t tB u1 u2

sucrose hydrolysis rate parameter at quadratic term (l (g SUC h)−1 ) concentration of ammonium ions (g l−1 ) sucrose hydrolysis rate parameter at linear term (h−1 ) concentration of citric acid (g l−1 ) concentration of fructose (g l−1 ) concentration of glucose (g l−1 ) metamorphosis reaction zone A into B rate constant (h−1 ) metamorphosis reaction zone A into C rate constant (h−1 ) metamorphosis reaction zone B into C rate constant (h−1 ) metamorphosis reaction zone C into D rate constant (h−1 ) carbohydrates uptake reaction rate constant (h−1 ) ammonium ions uptake reaction rate constant (h−1 ) ammonium ions saturation constant (g AMON l−1 ) fructose uptake reaction rate constant (h−1 ) glucose uptake reaction rate constant (h−1 ) fructose saturation constant (g FRU l−1 ) glucose saturation constant (g GLU l−1 ) inhibition constant (g CIT l−1 ) storage compounds utilisation reaction rate constant (h−1 ) citric acid production rate from fructose (g CIT l−1 h−1 ) citric acid production rate from glucose (g CIT l−1 h−1 ) fructose utilisation rate (g FRU l−1 h−1 ) glucose utilisation rate (g GLU l−1 h−1 ) rate of sucrose hydrolysis (g SUC l−1 h−1 ) biomass growth rate due to substrate (N-source) utilisation (h−1 ) biomass growth rate due to substrates (C-source) utilisation (h−1 ) biomass growth rate due to internal storage compounds utilisation (h−1 ) concentration of substrates (glucose and fructose) (g l−1 ) concentration of sucrose (g l−1 ) time (h) boundary time (h) metamorphosis reaction zone A into B rate (g A g X−1 h-1 ) metamorphosis reaction zone A into C rate (g A g X−1 h−1 )

u3 u4 X YAMON/X YFRU/CIT YGLU/CIT YS/CIT YS/X ZA ZB ZC ZD

269

metamorphosis reaction zone B into C rate (g B g X−1 h−1 ) metamorphosis reaction zone C into D rate (g C g X−1 h−1 ) concentration of biomass (g l−1 ) ammonium ions to biomass yield coefficient (g AMON g X−1 ) fructose to citric acid yield coefficient (g FRU g CIT−1 ) glucose to citric acid yield coefficient (g GLU g CIT−1 ) substrates to citric acid yield coefficient (g S g CIT−1 ) substrates to biomass yield coefficient (g S g X−1 ) zone A fraction (g A g X−1 ) zone B fraction (g B g X−1 ) zone C fraction (g C g X−1 ) zone D fraction (g D g X−1 )

Greek letters µ specific biomass growth rate (h−1 ) µa specific growth rate for zone A (h−1 ) stoichiometric coefficient for hydrolysis of νS sucrose (g GLU g SUC−1 ) or (g FRU g SUC−1 )

Some data concerning the influence of morphology on citric acid production by A. niger have also been published. Papagianni et al. [11,12] and Paul et al. [13] investigated aspects of the influence of morphology on citric acid production by A. niger, especially in terms of the formation of hyphal clumps, fragmentation due to shearing forces and the type of bioreactor. Papagianni et al. [14] also considered hyphal vacuolation and McIntyre and McNeil [15] tried to correlate the morphology of A. niger in batch fermentation with the carbon dioxide concentration. Nevertheless, morphologically structured modelling has not yet been applied to A. niger. In this paper, a morphologically structured model for A. niger is proposed. The mathematical framework for modelling formulated by Nielsen and Villadsen [1] was applied. Six extracellular components, detected in the fermentation medium, were taken into account. Hyphae were divided into four zones of different physiology and functionality on the basis of colour microscopic images, which were subjected to digital image analysis.

2. Materials and methods The citric acid accumulating strain A. niger BIO4F was used in the experiments. The cultivation medium was as

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follows: sucrose 10%, (NH4 )2 SO4 —0.2%, KH2 PO4 — 0.015%, MgSO4 ·7H2 O—0.015%. The initial pH of the medium was 2.5. Four batch experiments were performed in fully controlled Biostat ED bioreactors (B-Braun): stirred tank and air-lift of 16.5 l working volume at 30 ◦ C, equipped with off-gas analysers (Servomex). The following process parameters were recorded on-line: medium pH and oxygen saturation (pO2 ), air volumetric flow-rate, rotational speed of stirrer and concentrations of CO2 and O2 in the off-gas. The medium was inoculated with 6 h inoculum, which contained germinating spores in the phase of tube emerging and elongation. The approximate biomass concentration in the inoculum did not exceed 0.4 g l−1 . Inoculation medium contained the same components as fermentation medium. Only sucrose concentration was 5%. Inoculum was cultivated in shake flask culture. The first run was conducted under normal pressure in the stirred tank bioreactor. The second run was conducted at an overpressure of 0.25 MPa, also in the stirred tank bioreactor. The third and fourth runs were carried out in the air-lift bioreactor under normal pressure and overpressure, respectively. In all runs the air flow-rate and rotational speed of the stirrer (only in the stirred tank bioreactor) were controlled in the range 1–20 l min−1 and 150–300 min−1 , respectively, in order to achieve oxygen saturation not lower than 15% (with regard to pressure conditions in the bioreactor). The application of overpressure let increase the oxygen concentration in the fermentation broth approximately three times. At least 13 samples were taken from the bioreactor in a single run. The concentrations of sucrose, glucose, fructose and citric acid were determined by means of HPLC (Waters) on a Shodex-1011 column at 40 ◦ C (0.01N H2 SO4 as a mobile phase, refractive index detector). The concentration of the nitrogen source was determined alkacymetrically (Büchi) as ammonium ions concentration. Biomass was assayed as dry weight. The microscopic observations were performed using an OLYMPUS BX40 light microscope under a magnification of 200 with phase contrast.

The slides were prepared immediately after sampling. A 0.1 ml sample was diluted in phosphate buffer (pH = 7.0) and stained with 0.05 ml 1% methylene blue (Fluka) for 10 min. Then 0.044 ml Ziehl–Neelsen fuchsin solution (Fluka) was added [16]. Images of about 40–60 objects from each sample were acquired by image analysis system (MicroImage 4.0, Media Cybernetics for OLYMPUS). The acquired RGB images were stored for subsequent processing. Image processing and analysis were performed as follows. The colour RGB images were enhanced by median and high-pass Gauss filter, and segmented in order to obtain four zones of different colours (Table 1), corresponding to various physiological states of the hyphae [16–18]. The ratio of the zone area to total hyphal area was calculated to obtain the zone fraction. The final zone fraction values were calculated as the arithmetical mean taken from the set of objects. Vanhoutte et al. [16] suggest that the analysis of only 40 objects is sufficient to obtain the reliable values of zone fractions. Nevertheless, due to inhomogeneity of the fermentation broth and different sizes of analysed hyphal objects, especially in the later stages of the run (even from 1000 to 50,000 ␮m2 in the single sample), the estimation of minimum number of objects was performed. It occurred that about 60 objects should be analysed for A. niger in these conditions. This number of objects assured the confidence band ±0.05 for the single value of zone fraction obtained. Such an attempt seemed to be a good compromise between the accuracy of the method and demanded time for image processing and analysis [19]. The solution of the system of ordinary differential equations and parameters evaluation was performed using the software Easy-fit (©Klaus Schittkowski, University of Bayreuth, 2001). The implicit 5th order Runge–Kutta method for stiff ODEs was applied to find the solution of the system [20]. The parameters were found by means of the optimisation procedure joining the elements of Gauss–Newton and quasi-Newton procedures [21]. Other parameters were directly calculated from the experimental data by means of linear and non-linear regression.

Table 1 Classification of physiological zones Zone

Physiological description

Morphological description

A

Bright orange (apical and sub-apical cells) to dark orange (some hyphal cells); high respiratory activity and fast hyphal growth White, highly vacuolised cells, often very thick filaments; moderate respiratory activity; assumed to play an important role in citric acid excretion Greyish orange to grey cells, the transient form between zones A and D, and B and D; low respiratory activity, thin filaments—transitional hyphal state Dark grey to black cells, thick cell walls, very low level or lack of viability, thin filaments

Cell width varies from 3.5 ± 0.7 ␮m for the apical and subapical cells to 6.8 ± 1.3 ␮m for some hyphal cells

B

C

D

Cell width varies from 5.5 ± 0.2 to 9.8 ± 0.8 ␮m independent of the location (mainly distal) of the cells in the hypha Cell width varies from 2.5 ± 0.3 to 5.9 ± 0.6 ␮m, depending on its origin (zones A or B) Cell width varies from 2.4 ± 0.1 to 5.7 ± 1.3 ␮m, depending on its origin and location in the hypha (both apical and distal)

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Fig. 1. Changes of substrate concentrations (run 3: air-lift, normal pressure).

3. Results 3.1. Typical run of the process A typical experimental run for biomass growth and citric acid accumulation by A. niger lasted approximately 160–180 h. The cultivation medium contained relatively large amounts of carbohydrates and ammonium ions, approximately 100 and 0.545 g l−1 , respectively. In Figs. 1

and 2 typical time courses for medium components and biomass are shown. The process was characterised by two distinct phases: trophophase and idiophase. The trophophase lasted from 48 to 60 h, depending on the process conditions, and typically was longer in the overpressure runs. The trophophase was characterised by fast, practically exponential biomass growth, fast uptake of the nitrogen source (ammonium ions) to complete utilisation and very intensive excretion of carbon

Fig. 2. Changes of biomass and citric acid concentrations (run 3: air-lift, normal pressure).

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dioxide. Sucrose hydrolysed quickly and was not detected in the medium after the first 24 h of the run. However, it is known that sucrose is not directly utilised by the fungus [22]. Two simultaneous processes are involved in the hydrolysis: biochemical process (extracellular invertase activity) and physicochemical process (low pH and elevated temperature 30 ◦ C). Also in the trophophase only a small amount of carbohydrates was consumed. After the first 24 h of the process only 3–4% of the total C-source pool was utilised and no more than 15% of the carbohydrate pool available to the microorganism was metabolised for biomass growth during the trophophase. It was also observed, during the trophophase, that fructose was assimilated slightly faster than glucose. Furthermore, during the very early hours of the process (t < 10 h) neither carbohydrates nor ammonium ions were consumed, although biomass growth was observed. This suggested that the microorganism utilised storage compounds contained in the spores. Finally, in the trophophase almost no citric acid was detected in the medium. When the concentration of citric acid started to increase significantly, it was assumed that the microorganism had entered the idiophase. In this phase practically no significant biomass growth was observed. The concentration of ammonium ions remained at a very low level. The concentration of citric acid started to increase rapidly at about t = 50 h, achieving the maximum production rate at 90–100 h. At the same time fast utilisation of glucose and fructose was observed. However, in runs where the final concentration of citric acid was relatively high (over 30 g l−1 ), the fructose uptake rate became lower than glucose uptake rate, already in the early idiophase.

Therefore, it was hypothesised that high concentration of citric acid influenced the enzymatic carriers of monosaccharides. This phenomenon can, to a certain extent, be explained by the observations of Torres et al. [23], who claim the existence of separate glucose carriers, dependent on citric acid and glucose concentration in the medium. Unfortunately, no fructose carrier has yet been discovered or described [24]. In the runs of highest citric acid productivity the substrates were totally utilised by the end of the process. Off-gas composition during the idiophase (Fig. 3) varied only slightly constant but the amount of excreted carbon dioxide was not in agreement with the amount of oxygen consumed. This demand for additional oxygen is a typical phenomenon at this stage of fermentation and proves that citric acid accumulation can be expected in the medium [25]. Additionally, the carbon dioxide excretion curve was used to evaluate the time of the initial phase of growth without substrate uptake. On the basis of hyphal staining four physiological zones were distinguished. A summary of the relevant physiological and morphological characteristics is presented in Table 1. A representative single hypha derived from the processed colour microscopic image schematically is presented in Fig. 4. Methylene blue is a redox stain and is reduced by active mitochondria. Together with the applied counterstain (carbol solution of basic fuchsin), it renders the most active cells bright orange (zone A). The less active and more vacuolised a cell is, the more greyish/white it remains (zone B representing the whitest cells and zone C representing the darker cells). Under these staining conditions the least

Fig. 3. Changes of the off-gases composition and determination of the boundary time tB (run 3: air-lift, normal pressure); on-line data smoothed by adjacent averaging.

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Fig. 4. Schematic representation of a hyphal entity derived from a microscopic image.

active and dead compartments of hypha appear as dark grey to black (zone D). The profiles of the hyphal zone fractions during a typical run are shown in Fig. 5. At the beginning of the trophophase, only zone A could be observed. After 24–30 h, the zone B fraction increased. Up until the end of trophophase little of the biomass had deteriorated, i.e. low concentrations of zones C and D were observed (sum of zone fractions ZC + ZD was lower than 0.1). In the early idiophase the fraction of zone B began to increase rapidly, accompanied by citric acid production rate, which is evidence of direct correlation between the hyphal physiology and citric acid

production. A linear correlation was observed between the fraction of zone B and citric acid production rate, especially in the runs in which high yields of citric acid were obtained (Fig. 6). The fraction of zone A decreased quickly in the early idiophase and remained constant thereafter. At the same time the presence of zones C and D could be observed. The value of ZC practically remained constant throughout the idiophase, mainly due to the fact that zone C is a transition zone. The fraction of zone D increased gradually during the process. At the end of fermentation, zones C and D accounted for almost 50% of the biomass.

Fig. 5. Changes in the physiological zones fractions (run 3: air-lift, normal pressure).

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Fig. 6. Linear relation between the zone B fraction and citric acid excretion rate (run 4, overpressure; air-lift).

The final citric acid productivity varied from run to run, with citric acid concentrations at t = 164 h of 28.57, 33.79, 68.47, and 83.75 g l−1 for runs 1, 2, 3 and 4, respectively. 3.2. Verbal model On the basis of the experiments conducted and drawing on basic microbial physiology, a verbal model of the process of biomass growth and citric acid accumulation by A. niger can be formulated as follows. • As sucrose hydrolysis has not been considered, the proposed equation for the hydrolysis rate reflects only the mathematical relation for the change in sucrose concentration with time. • The fungus directly assimilates only glucose and fructose. • Due to high carbohydrates concentrations, biomass growth in the later trophophase is unlimited with regard to the concentration of both glucose and fructose. In the description of biomass growth, for the sake of simplicity, the pools of glucose and fructose are lumped together, because, as mentioned earlier, practically no substrate preferences were observed during the trophophase. • On one hand, the concentration of ammonium ions is a limiting factor in biomass synthesis. On the other hand, however, the concentration of ammonium ions in the medium hardly influences the citric acid production. Accordingly, it is assumed that there is no correlation between ammonium ions and citric acid concentration. • At the very beginning of the process (t ≈ 10 h or earlier, depending on process conditions), biomass growth without any uptake of substrates, either carbohydrates

• • • •

•

or ammonium ions, is observed. Furthermore, no hyphal metamorphosis was observed. Therefore, the boundary time, tB , and the biomass growth rate, kXX0 , due to internal storage compounds were estimated. The boundary time is estimated from the CO2 excretion curve as shown in Fig. 3. The physiological zone A is responsible for the uptake of all substrates. The physiological zone A is the only growing part of the hypha. The physiological zone B is responsible for citric acid excretion, although it is certain that both zones A and B participate in citric acid synthesis [14,22]. The metamorphosis reactions are assumed to have the simplest mathematical expression (first-order rate equations). Zone A is assumed to be the original zone from which other zones are created in a couple of reactions. Part of the most active apical and subapical cells is metamorphosed into vacuolised cells of zone B. Cells of both zones A and B co-operate in the metabolism: biomass growth and citric acid accumulation, although only zone A can grow actively. The cells of zone B are responsible for metabolite supply. Cells of both zones A and B may deteriorate: the cell walls thicken and intracellular structure disappears; they become inactive (zone D). Zone C was assumed to be a transition zone. The scheme of metamorphosis reactions is shown in Fig. 7. On the basis of experimental data, it is deduced that citric acid has an inhibiting influence on fructose uptake, so a term of uncompetitive inhibition was incorporated into the reaction rate equation for fructose uptake.

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275

where rCIT/F = kCIT/F

Fig. 7. Model of the metamorphosis reactions between physiological zones A–D.

3.3. Reaction rates The rate of sucrose hydrolysis was expressed solely on the basis of changes in sucrose concentration with time by means of non-linear regression and has neither microbiological nor biochemical significance: rH = A · SUC2 + B · SUC.

(1)

The rates of biomass formation due to carbon sources, nitrogen source and internal storage substances vary during the process and are described, respectively, as follows. If t < tB then rXS = 0

(2)

rXA = 0

(3)

rXX = kXX0

(4)

otherwise

rXA

(5)

AMON = kaAMON AMON + KAMON

rXX = 0.

rAMON = YAMON/X rXA ZA .

rCIT = (rCIT/G + rCIT/F )ZB .

(16)

(6)

u1 = k1 ZA ,

(7)

The reaction rate for the metamorphosis of zone A into zone C is, likewise, dependent on the phase of the process:

and

(8)

(9)

Substrates are utilised for both biomass growth and citric acid accumulation. So, for glucose uptake rate one obtains rGLU = 0.5YS/X rXS ZA + YGLU/CIT rCIT/G (ZA + ZB ) (10) where rCIT/G is the rate of citric acid production from glucose, defined as:

if t > tB .

if t < tB

u2 = k2 ZA ,

and the total specific biomass growth rate is defined as:

if t > tB .

(17)

(18)

(19)

The reaction rate for the metamorphosis of zone B into zone C is expressed by u3 = k3 ZB .

(20)

The reaction rate for the metamorphosis of zone C into zone D always equals u4 = k4 ZC .

(21)

3.4. Mass balance

(11) Four substrates (SUC, GLU, FRU and AMON), one product (CIT), biomass (X) and four physiological zones (ZA , ZB , ZC , ZD ) were balanced:

For fructose the equation has the following form: rFRU = 0.5YS/X rXS ZA + (YS/CIT − YGLU/CIT )rCIT/F (ZA + ZB )

if t < tB

and

µa = rXS + rXA + rXX

rCIT/G

(15)

As stated earlier, the metamorphosis reactions (Fig. 5) are expressed by first order kinetic equations. The reaction rate for the metamorphosis of zone A into zone B, dependent on the time of the process, is expressed as:

u2 = 0,

GLU = kCIT/G . GLU + KGLUCIT

(14)

Finally, the rate of citric acid production is expressed as:

Further, the specific growth rate of zone A is considered as the sum of the rates of biomass formation:

µ = µa ZA .

(13)

In the equations above, the constraint YS/CIT = YGLU/CIT + YFRU/CIT is fulfilled. Of course, when t < tB none of the substrates is assimilated for citric acid accumulation, therefore kCIT/G and kCIT/F are equal to 0. The coefficient 0.5 in both rGLU and rFRU expressions is derived from the assumption made upon experimental data that practically no substrate preference occurs while carbohydrates uptake for biomass growth. Therefore, equal amounts of glucose and fructose are supposed to be assimilated. The additional term in Eq. (13) describes inhibition of fructose uptake rate due to high citric acid concentrations.The consumption of ammonium ions due to biomass growth is expressed as:

u1 = 0,

rXS = ka

FRU KI . FRU + KFRUCIT KI + CIT

(12)

dSUC = −rH dt

(22)

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Table 2 Initial model conditions Initial condition

Run

(g l−1 )

SUC GLU (g l−1 ) FRU (g l−1 ) AMON (g l−1 ) CIT (g l−1 ) ZA (g A g X−1 ) ZB (g B g X−1 ) ZC (g C g X−1 ) ZD (g D g X−1 ) X (g l−1 )a a

Source

1

2

3

4

94.189 0 0 0.534 0 1 0 0 0 0.024

90.929 0 0 0.525 0 1 0 0 0 0.024

94.999 0 0 0.534 0 1 0 0 0 0.024

90.474 0 0 0.524 0 1 0 0 0 0.024

HPLC analysis HPLC analysis HPLC analysis Alkacymetric analysis HPLC analysis Image analysis Image analysis Image analysis Image analysis

The initial concentration of biomass was evaluated on the basis of a separate experiment concerning the spores germination kinetics [26].

dGLU = νS rH − rGLU X dt

(23)

dZC = u2 + u 3 − u 4 − Z C µ dt

(29)

dFRU = νS rH − rFRU X dt

(24)

(30)

dAMON = −rAMON X dt

dZD = u4 − Z D µ dt

(25)

(31)

dCIT = rCIT X dt

dX = µX. dt

(26)

dZA = −u1 − u2 + ZA (µA − µ) dt

(27)

dZB = u1 − u3 − ZB µ dt

(28)

3.5. Model parameters and solution Estimation of the parameters and model solution were processed using the initial conditions detailed in Table 2. In order to minimise the number of parameters to be found via the optimisation algorithm, some were determined

Table 3 Model parameters Parameter (unit)

ν S (g GLU g SUC−1 , g FRU g SUC−1 ) A × 103 (l (g SUC h)−1 ) B (h−1 ) tB (h) kXX0 (h−1 ) YS/X (g S g X−1 ) YS/CIT (g S g CIT−1 ) YAMON/X (g AMON g X−1 ) ka (h−1 ) kaAMON (h−1 ) KAMON (g AMON l−1 ) kCIT/G (h−1 ) KGLUCIT (g GLU l−1 ) YGLU/CIT (g GLU g CIT−1 ) kCIT/F (h−1 ) KFRUCIT (g FRU l−1 ) KI (g CIT l−1 ) k1 (h−1 ) k2 (h−1 ) k3 (h−1 ) k4 (h−1 )

Run

Parameter estimation

1

2

3

4

0.526

0.526

0.526

0.526

ST

−7.03150 ± 0.00001 0.66230 ± 0.00002 12.0 ± 0.5 0.19 ± 0.02 4.18 ± 1.60 1.24 ± 0.04 0.21 ± 0.02 4.78 × 10−6 ± 1.12 × 10−6 0.119 ± 0.095 0.210 ± 0.075 0.155 ± 0.033 <10−4 0.60 ± 0.08 0.438 ± 0.16 <10−4 8.49 ± 2.50 0.0213 ± 0.0050 0.00250 ± 0.00089 0.0210 ± 0.0098 0.0378 ± 0.0034

−5.7514 ± 0.0002 0.54640 ± 0.00002 12.0 ± 0.5 0.22 ± 0.03 2.65 ± 0.32 1.50 ± 0.05 0.21 ± 0.02 1.58 × 10−3 ± 2.3 × 10−4 0.110 ± 0.051 0.250 ± 0.010 0.0676 ± 0.0158 <10−4 1.28 ± 0.40 0.873 ± 0.15 <10−4 13.28 ± 6.58 0.00890 ± 0.00210 0.00195 ± 0.00065 0.0195 ± 0.0082 0.0505 ± 0.0124

−8.525155 ± 0.000002 0.775186 ± 0.000001 9.0 ± 0.5 0.25 ± 0.02 4.46 ± 0.82 0.98 ± 0.02 0.16 ± 0.02 8.32 × 10−3 ± 1.15 × 10−3 0.175 ± 0.070 0.151 ± 0.096 0.187 ± 0.140 <10−4 0.52 ± 0.02 0.562 ± 0.21 <10−4 6.65 ± 4.4 0.0290 ± 0.0127 0.00590 ± 0.00150 0.0180 ± 0.0070 0.0391 ± 0.0163

−4.052 ± 0.003 0.367 ± 0.001 17.0 ± 0.5 0.19 ± 0.02 3.80 ± 0.85 0.96 ± 0.07 0.16 ± 0.01 4.84 × 10-4 ± 1.5 × 10−5 0.0994 ± 0.0502 0.253 ± 0.150 0.205 ± 0.069 7.06 × 10−4 ± 10−5 0.74 ± 0.09 0.670 ± 0.085 1.36 × 10−4 ± 10−5 204 ± 80 0.0165 ± 0.0089 0.000767 ± 0.000125 0.0249 ± 0.0011 0.0259 ± 0.0062

NLR NLR OFF NLR LR LR LR OPT/LR OPT OPT OPT OPT OPT OPT OPT OPT OPT OPT OPT OPT

ST, stoichiometry; LR, linear regression; NLR, non-linear regression; OPT, optimisation; OFF, off-gas time courses.

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Fig. 8. Simulated and experimental carbohydrate profiles (run 4: air-lift, overpressure).

Fig. 9. Simulated and experimental ammonium ions, citric acid and biomass profiles (run 4: air-lift, overpressure).

directly from stoichiometry, linear or non-linear regression. All parameters are presented in Table 3. Figs. 8–13 present the simulated curves with selected experimental data.

4. Discussion The obtained citric acid yields occurred to be strongly different in four experimental runs. Generally, in the air-lift

bioreactor much higher citric acid concentration (over 65 g l−1 ) was achieved than in the stirred-tank bioreactor (below 35 g l−1 ). Different hydrodynamic conditions in the bioreactors seem to be the reason of such results obtained. In stirred tank bioreactors hyphae are subjected to higher shearing stress. It may deteriorate the viability of the hyphae and thus, disturb citric acid accumulation. Nevertheless, one should note that final citric acid concentration was not of primary importance because the aim of this work was to formulate a mathematical model and achieve good agree-

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Fig. 10. Simulated and experimental zones A–D profiles (run 4: air-lift, overpressure).

ment between experimental points and simulated curves for runs in different bioreactors and process conditions. The application of overpressure proved to be stimulating for citric acid accumulation. It let obtain higher citric acid concentration (28.57 g l−1 in run 1 versus 33.79 g l−1 in run 2 and 68.47 g l−1 in run 3 versus 83.75 g l−1 in run 4). The better aeration of the broth in the overpressure conditions strongly contributed to this [25].

Although both operating conditions and final citric acid concentrations varied from run to run, the simulated curves generally describe all experimental data well. Only in the overpressure runs (Figs. 9 and 12) were ammonium ions still observed in the idiophase, which caused a slight discrepancy between experimental and simulated curves (Fig. 12). The best fit was obtained for the medium components (Figs. 8, 9, 11 and 12). The zone simulated curves deviate slightly

Fig. 11. Simulated and experimental carbohydrates profiles (run 2: stirred tank, overpressure).

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Fig. 12. Simulated and experimental ammonium ions, citric acid and biomass profiles (run 2: stirred tank, overpressure).

further from the experimental data due to the fact that their determination is subject of higher measurement error. This error derives mainly from the difficulty in obtaining a truly representative group of hyphal objects from an inherently inhomogeneous suspension. However, some attempts were made to minimise the influence of sample inhomogeneity, as described above in Section 2. Comparing the values of the determined parameters some important relations can be observed. First of all the values

of rate constants k1 –k4 (Table 3) seem to be very similar from run to run and almost independent of the process conditions investigated. However, they are strongly influenced by the metamorphosis and the physiology of the fungus. Furthermore, the whole process is strictly dependent on these values because they have an effect on both substrate uptake and product excretion. This dependence also contributes to the fact that taking a sample of hyphae from the bioreactor and subjecting it to image analysis, one is able directly to

Fig. 13. Simulated and experimental zones A–D profiles (run 2: stirred tank, overpressure).

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evaluate the physiological state of the biomass. Such information can provide, together with other process parameters, the proper background to foresee the further run or even the expected yield. The boundary time tB was introduced to discriminate between two important periods of trophophase. For t < tB the uptake of carbohydrates and ammonium ions for biomass growth is extremely small, almost zero. In that time spore storage compounds are utilised. This phenomenon was observed in shake flask culture, while running the separate 18 h experiment concerning spores germination kinetics in the conditions of inoculum cultivation [26]. Having compared this run and bioreactor runs, it was arbitrarily assumed that the medium components start to be assimilated, when carbon dioxide concentration in the off-gas doubles (in relation to normal CO2 content in air). Hardly any connection between the duration of the first period of trophophase and process conditions or citric acid yield was found. An interesting phenomenon was observed when estimating saturation coefficients for citric acid production from carbohydrates (KGLUCIT , KFRUCIT ). In almost all cases their values about 10−4 g l−1 and lower. Such values are almost of no significance in the system because the observed concentration of glucose and fructose were at least 1000 higher, even in the end of the process. Only in one case, when early total glucose consumption was observed (run no. 4), these constants had slightly higher values. Nevertheless, these two saturation constants could be omitted and the model could describe the process fairly well with 19 parameters of which only 11 were obtained by means of optimisation. The extremely low values of saturation constants were expected. The initial concentration of sucrose 100 g l−1 exceeds the typical demands of any microorganism on carbohydrates, which is often even ten times lower. It is a typical feature of the process and a large carbohydrates demand is very characteristic of A. niger [25]. When considering the ratios of the yield coefficient YGLU/CIT to YS/CIT one may notice that in normal pressure processes approximately half of the citric acid pool (0.48 for run no. 1 and 0.53 for run no. 3) was generated from glucose. In overpressure processes, more citric acid was produced from glucose (0.85 for run no. 2 and 0.77 for run no. 4) than from fructose. This was probably due to inhibition of fructose uptake caused by the higher concentrations of citric acid in the medium, in comparison with normal pressure runs. As has already been stated in the description of the typical run of the process, at this level of investigation the influence of citric acid on the carbohydrates uptake cannot be described from the biochemical point of view. The properties of the specific carriers of monosaccharides may have contributed to this behaviour [23,24]. The substrates to citric acid yield coefficient YS/CIT reflects the obtained final productivity of the run the most accurately. In the high-yielded runs 3 and 4 they are very close to 1 (0.96 and 0.98 g S g CIT−1 ), whereas in low-yielded runs 1 and 2 they exceed one significantly (1.24 and 1.5 g

S g CIT−1 ). These values confirm that substrates were assimilated more effectively in runs 3 and 4. The amount of ammonium ions utilised for biomass growth, YAMON/X is similar in all processes and, therefore, independent of process conditions for the relevant ranges investigated. Also, the rate constant for ammonium ion utilisation, kaAMON , and saturation constants, KAMON , are almost the same from run to run. Additionally, the biomass growth rate associated with internal storage compounds, kXX0 , is very similar in all runs too. For the limited range of process conditions investigated, it may be possible to apply mean values for each of these parameters for the purpose of modelling. In case of utilisation of carbon source for biomass growth, such a phenomenon was not observed. The yield coefficients YS/X values were strongly dependent on process conditions. For normal pressure processes, YS/X was higher (4.18 and 4.46) in comparison with the overpressure processes (2.65 and 3.82, respectively). This is explained by the fact that the slower growth of A. niger was observed under overpressure (Figs. 9 and 12). In opposition to this, biomass growth rate constant, ka , showed no correlation with process conditions; values varied by three orders of magnitude for different processes. The rate constants kCIT/G were always lower than rate constants kCIT/F . This is explained by the fact that, in the early idiophase when the citric acid concentration is lower, fructose is utilised much faster. The inhibition constant KI is practically in the same range, apart from the value for run no. 4, in which early total utilisation of glucose and very fast increase of citric acid concentration correlated with it, might have contributed to such an unusually high value of KI .

5. Conclusions • Although not very complicated, the presented model describes the process of citric acid accumulation by A. niger well. • A direct linear correlation between the physiological zone B and citric acid excretion rate was found, confirming that this vacuolised zone is responsible for citric acid excretion. • A good agreement between all experimental data with simulated curves is obtained. The mathematical description of the process proved to be precise for various process conditions and in two different types of bioreactors: stirred tank and air-lift. • The advantage of the model is that all parameters were determined directly from experimental data and no parameters were based on literature values. • This model could be employed, in the future, for the purpose of optimising batch processes and establishing an appropriate feeding strategy in fed-batch fermentations of A. niger.

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• The investigations showed that the hyphal metamorphosis plays a very important role in growth and formation of metabolites by filamentous fungi, specifically A. niger. The applied image analysis method enables prediction of the behaviour of the fungus and product excretion in the early stages of the process.

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