Appl Microbiol Biotechnol (1998) 49: 682±690
Ó Springer-Verlag 1998
ORIGINAL PAPER
C. AÊkerberg á K. Hofvendahl á G. Zacchi
B. Hahn-HaÈgerdal
Modelling the in¯uence of pH, temperature, glucose and lactic acid
concentrations on the kinetics of lactic acid production by Lactococcus
lactis ssp. lactis ATCC 19435 in whole-wheat ¯our
Received: 28 October 1997 / Received revision: 3 February 1998 / Accepted: 6 February 1998
Abstract A kinetic model of the fermentative production of lactic acid from glucose by Lactococcus lactis ssp.
lactis ATCC 19435 in whole-wheat ¯our has been developed. The model consists of terms for substrate and
product inhibition as well as for the in¯uence of pH and
temperature. Experimental data from fermentation experiments under di€erent physical conditions were used
to ®t and verify the model. Temperatures above 30 °C
and pH levels below 6 enhanced the formation of byproducts and D-lactic acid. By-products were formed in
the presence of maltose only, whereas D-lactic acid was
formed independently of the presence of maltose although the amount formed was greater when maltose
was present. The lactic acid productivity was highest
between 33 °C and 35 °C and at pH 6. In the concentration interval studied (up to 180 g l)1 glucose and 89 g
l)1 lactic acid) simulations showed that both substances
were inhibiting. Glucose inhibition was small compared
with the inhibition due to lactic acid.
Introduction
Lactic acid is produced by fermentation of whey, for
example, or synthetically from substrates such as lactonitrile (Vickroy 1985; Atkinson and Mavituna 1991). Its
technical applications include use as a preservative in
food, pharmaceuticals and cosmetics, and the production of polylactic acid, a biodegradable polyester used in
C. AÊkerberg á G. Zacchi (&)
Department of Chemical Engineering 1,
Lund Institute of Technology/Lund University,
P.O. Box 124, SE-221 00 Lund, Sweden
Tel.: +46 46 2228297
Fax: +46 46 2224526
e-mail: Guido.Zacchi@kat.lth.se
K. Hofvendahl á B. Hahn-HaÈgerdal
Department of Applied Microbiology,
Lund Institute of Technology/Lund University,
P.O. Box 124, SE-221 00 Lund, Sweden
medical sutures and clips for wound closure and selfdegradable prosthetic devices (Kharas et al. 1994).
Lactic acid occurs naturally in two optical isomers and,
since elevated levels of the D-()) form are harmful to
humans (Expert Committee on Food Additives 1967),
L-(+)-lactic acid is the preferred isomer. Polylactic acid
with di€erent properties can be produced, depending on
the optical composition of the lactic acid used for polymerisation (Lipinsky and Sinclair 1986; Kharas et al.
1994). The synthetic production of lactic acid results in a
racemic mixture of the two isomers, while fermentative
production can yield either form alone or a racemate,
depending on the organism, substrate and growth conditions used. The control of the optical composition and
the reduction of by-product formation is essential for
cost-e€ective fermentative production of L-lactic acid,
since puri®cation constitutes a considerable fraction of
the total production cost (Evangelista et al. 1994).
Cheap raw materials, such as whey, molasses, starch
waste and beet- and cane-sugar have been used for the
fermentative production of lactic acid (Vickroy 1985;
Atkinson and Mavituna 1991). Enzymatically hydrolysed whole-wheat ¯our, containing both gluten and
bran, has been found to contain all the necessary nutrients for L. lactis 19435 (Hofvendahl and HahnHaÈgerdal 1997a). Hydrolysis is performed in two enzymatic steps, liquefaction and sacchari®cation, where
fermentation could be integrated with sacchari®cation
(simultaneous sacchari®cation and fermentation) and a
kinetic model of the entire process is required to optimise the production of L-lactic acid. The model parameters for sacchari®cation and fermentation must be
determined individually to evaluate whether the two
steps should be performed simultaneously or separately.
A number of kinetic models for the fermentation of
glucose to lactic acid have been proposed (Luedeking
and Piret 1959; Mercier et al. 1992; Parente et al. 1994).
Models including terms for both substrate and product
inhibition have been suggested (GoncËalves et al. 1991;
Venkatesh et al. 1993), as well as a model considering
only product inhibition (Yeh et al. 1991; Cachon and
683
DivieÁs 1994; Gadgil and Venkatesh 1997). The hydrolysis and fermentation steps have di€erent pH and
temperature optima, and models considering the pH and
temperature dependence of the lactic acid production
rate have been developed for Lactobacillus casei fermenting whey (Rincon et al. 1993). A number of models
considering only the e€ect of pH on the production rate
have been proposed for Lactococcus lactis ssp. lactis
biovar diacetylactis (Cachon and DivieÁs 1994), Lactobacillus bulgaricus (Venkatesh et al. 1993; Gadgil and
Venkatesh 1997) and Lactobacillus delbrueckii (Yeh
et al. 1991) using lactose or glucose. In the present
study, the kinetics were determined for fermentations at
various pH and temperature values and initial glucose
and lactic acid concentrations. Based on these data, an
empirical model consisting of rate expressions for cell
growth, product formation, starch degradation and
substrate consumption was developed. For optimisation
purposes, terms for pH and temperature in¯uence were
also included in the model.
Materials and methods
Inoculum preparation and microorganism used
For the propagation of the inoculum, a ¯our-free, reference medium (Hofvendahl and Hahn-HaÈgerdal 1997b) was used. For
plates, 20 g l)1 agar (Merck) was added. Lactococcus lactis ssp.
lactis ATCC 19435 (L. lactis 19435) (American Type Culture
Collection, Rockville, Md., USA) stored at )80 °C was plated on
an agar plate and incubated at 30 °C for 48±72 h. A single colony
was transferred to another plate and incubated for another 24 h. A
single colony was then transferred to 5 ml liquid medium and incubated in a Gallenkamp INR-200 orbital incubator (Leicester,
UK) for 12±24 h at 140 rpm. The cells were harvested by centrifugation (8000 g, 2 min, 4 °C), resuspended in 100 ml fresh medium
and incubated in the same way for another 6±12 h. The bacteria
were harvested by centrifugation (9000 g, 10 min, 4 °C; Beckman
J2-21, Beckman Instruments Inc., Fullerton, Calif., USA) and resuspended in 100 ml NaCl 9 g l)1 (Across Organics, N.J., USA),
corresponding to 5% of the total working volume of the fermentor.
This suspension was used to inoculate the fermentor.
Media composition
Two di€erent fermentation media were used, both containing
whole-wheat ¯our suspended in water. The hydrolysed ¯our medium contained ¯our at a concentration of 120 g l)1 or 240 g l)1,
which was completely hydrolysed to glucose by the sequential action of the enzymes Termamyl 120 L (Novo Nordisk, Bagsvaerd,
Denmark) at 95 °C for 30 min and SAN Super 240 L (Novo
Nordisk) at 55 °C for 16±20 h (Hofvendahl and Hahn-HaÈgerdal
1997a). This resulted in glucose concentrations of 89 g l)1 and
about 170 g l)1 respectively. The supplemented ¯our medium contained glucose added to a 240 g l)1 ¯our suspension to act as a
substrate at concentrations around 45 g l)1 (Hofvendahl and
Hahn-HaÈgerdal 1997b). In some fermentation experiments the
¯our-free medium used for inoculum preparation was used.
Fermentation
Cultivation was carried out in a 3-l Chemoferm FLC-B-3 fermentor
(HaÈgersten, Sweden), coupled to a Chemoferm LMS 500 control
unit, controlling the temperature and rate of stirring. The working
volume was 2 l. The pH was measured with a pH electrode (Schott
GeraÈte H63, Germany) and was kept constant at 4.0, 5.0 or 6.0 by a
pH meter and titrator (pHM61 and TTT80, Radiometer, Copenhagen, Denmark) with the addition of 200 g l)1 NaOH (Akzo Nobel, Eka Nobel, Bohus, Sweden). The stirring rate was 350 rpm, and
the temperature 30 °C, 33.5 °C, 37 °C, or 40 °C. To ensure anaerobic conditions, N2 was bubbled through the fermentor at a rate of
150 ml min)1 or 500 ml min)1, controlled by a rotameter (Sho-Rate,
Brooks, Instrument N. V. Veenendaal, The Netherlands). A sterile
anti-foaming agent (Silicone antifoam, Kebo Lab, SpaÊnga, Sweden)
was added with a sterile syringe, via a septum, as required. In two
fermentation experiments lactic acid (sodium salt solution, ICN
Biomedicals Inc., Aurora, Ohio, USA) was added, either 80 g l)1 at
the time of inoculation or 35 g l)1 12 h after inoculation.
Analysis
Double measurements of the cell mass of the inoculum as dry
weight were performed. The samples were ®ltered through 0.2-lm
membrane ®lters (Supor-200, Gelman Science, Ann Arbor, Mich.,
USA) and dried in a microwave oven at low power (420 W) for
15 min. Owing to the high particle content of the ¯our, dry-weight
analyses of the cell mass during fermentation could not be carried
out. The amount of carbon dioxide in the outgoing gas was measured by photoacoustic spectroscopy (BruÈel & Kjñr type 1308;
BruÈel & Kjñr, Nñrum, Denmark).
Sterile samples were collected regularly, and analysed with
HPLC as described previously (Hofvendahl and Hahn-HaÈgerdal
1997b). D- and L-lactic acid concentrations were measured enzymatically as described (Hofvendahl and Hahn-HaÈgerdal 1997a).
Modelling
The rates of cell growth, product formation and substrate consumption were expressed by an unstructured model for batch fermentation. The parameters in the model were ®tted to experimental
data, obtained from the fermentation experiments, by non-linear
least-squares ®tting.
Cell growth
For fermentation with L. delbrueckii, it has been observed that
both substrate and product inhibition is of importance (GoncËalves
et al. 1991). In the present study, the cell growth rate, rx (g l)1 h)1),
was described by Monod kinetics, including terms for both types of
inhibition.
rx ˆ
lmax Sg X
Sg ‡ Ks ‡
Sg †2
Ki
1 ÿ Kp P †n
1†
where X, Sg and P represent the cell, substrate and product concentrations (g l)1) respectively, lmax is the maximum speci®c
growth rate (h)1), Ks the saturation parameter (g l)1), Ki the substrate inhibition parameter (g l)1), Kp the parameter representing
the pH dependence of product inhibition (l g)1) and n the parameter used to describe product inhibition.
The cells are inhibited by the glucose and lactic acid concentrations prevailing in the fermentor, and thus concentrations not
adjusted for dilution due to NaOH addition (marked*) were used
when calculating the glucose and lactic acid inhibition.
Product formation
The lactic acid formation rate, rp, (g l)1 h)1) was modelled using the
Luedeking-Piret expression (Luedeking and Piret 1959):
rp ˆ a rx ‡ b X
2†
where a is a growth-associated constant for product production
and b is the non-growth-associated constant for product produc-
684
tion (h )1). The lactic acid concentration in the model represents the
total lactic acid concentration, and thus no distinction was made
between the D and L isomers. At temperatures higher than 30 °C
the formation of the by-products acetic acid, formic acid and ethanol increased. Acetic acid was the major by-product, and its formation rate, rpa (g l)1 h)1), was modelled as a measure of the total
by-product formation.
rpa ˆ aa rx ‡ ba X
3†
where aa is the growth-associated constant for by-product production and ba the non-growth associated constant for by-product
production (h)1)
In the hydrolysed ¯our medium, no by-products were found,
and rpa was set to zero.
A limited amount of glucose was produced by unintentional hydrolysis of the supplemented ¯our medium. This degradation, rst
(g l)1 h)1) was expressed as:
rst ˆ ÿkst Sst
4†
)1
where Sst is the concentration of starch (g l ), de®ned as the sum of
non-soluble polysaccharides and soluble oligosaccharides larger
than glucose, and kst is an empirical parameter for starch degradation (h)1). The hydrolysed ¯our medium contained no residual
starch.
Substrate consumption
The substrate consumption rate, rsg (g l)1 h)1), was described using
the expression
1
1
1
rp ÿ
rpa ÿ rx ÿ rst ÿ m X
Yp
Ypa
Yx
5†
describing the glucose consumption during fermentation, resulting
in cell mass, lactic acid and by-product formation, and the glucose
formation from the unintentional starch degradation. A certain
amount of glucose is also used for maintenance energy, described
with the m áX term. Yp and Yx are the stoichiometric parameters
(g/g substrate) describing the theoretical yield of lactic acid and cell
mass respectively, i.e. Yp ˆ 1 g lactic acid/g glucose and
Yx ˆ 0.79 g cell mass/g glucose, using an experimentally determined cell mass composition of CH1.52O0.45N0.22; Ypa is the byproduct yield coecient. Ypa is the by-product yield coecient
(g by-product/g substrate) and m is the maintenance energy parameter (g substrate/g cell mass á h).
pH dependence
The parameters for maximum speci®c growth rate, lmax, and
product inhibition, Kp in Eq. 1 are dependent on pH. The pH
dependence of lmax and Kp was expressed according to Sinclair
(1989):
lm
lmax ˆ
6†
1 ‡ kl1 =‰H ‡ Š† ‡ kl2 ‰H ‡ Š
Kp ˆ
Kpm
1 ‡ kp1 =‰H ‡ Š† ‡ kp2 ‰H ‡ Š
ÿE1
7†
where [H+] ˆ 10)pH, and lm, kl, Kpm and kp are kinetic parameters describing the e€ect of pH on lmax and Kp.
Temperature dependence
There are a number of temperature-dependent parameters in the
kinetic model: a, b, aa, ba and kst, and it was assumed that the
ÿE2
parameter ˆ A1 e RT ÿ A2 e RT
8†
)1
where E1 and E2 have the dimensions J mol and R is the universal
gas constant (J mole)1 K)1). The model was evaluated in the
temperature interval 30±37 °C. The temperature was raised above
the standard conditions of 30 °C since the optimal temperature for
the enzymatic hydrolysis of wheat starch is 55 °C. The upper limit
was chosen to be 37 °C because, at 40 °C, the unstructured model
could not account for all by-products formed. The high by-product
formation also renders this temperature cost-ine€ective. Since the
temperature interval is relatively small, the temperature parameter
T, in Eq. 8, was expressed as:
T ˆ T1 ÿ Tref
Starch consumption
rsg ˆ ÿ
temperature dependence of the parameters can be described with
the following expression:
K†
where T1 is the temperature (K) under investigation. The reference
temperature, Tref, was chosen as 300 K to increase the e€ect of
temperature in Eq. 8.
Results
The kinetic parameters in Eqs. 1, 2, 4 and 5 were determined by minimising the objective function
X
X
Q1 ˆ
Xcalc ÿ Xexp †2 ‡
Pcalc ÿ Pexp †2
X
9†
‡
Sg;calc ÿ Sg;exp †2
using experimental data from fermentation experiments
in the ¯our-free medium with initial glucose concentrations between 40 g l)1 and 130 g l)1 (Table 1) exp and
calc represent experimental and simulated data, respectively. The ¯our-free medium was used to determine the
cell mass, which could not be determined in the wholewheat ¯our medium because of the particle content.
Experimental and simulated data from one fermentation
are presented in Fig. 1. A relationship between lactic
acid concentration and dry weight of cells has previously
been observed in a medium free from particles (Hofvendahl and Hahn-HaÈgerdal 1997b). Assuming that the
bacteria produced the same amount of lactic acid per cell
mass in whole-wheat ¯our medium as in ¯our-free medium, the parameters a and b in Eq. 2, describing the
Table 1 Parameter values in the fermentation model under standard conditions (pH 6.0 and 30 °C) for fermentation in a particlefree medium. lmax maximum speci®c growth rate, Ks saturation
parameter in Monod expression, Ki substrate inhibition parameter,
Kp parameter representing pH dependence of the product inhibition, n parameter describing product inhibition, a growth-associated constant for product production, b non-growth-associated
constant for product production, m maintenance energy parameter
(g substrate/(g cell mass á h)).
Parameter
)1
lmax (h )
Ks (g l)1)
Ki (g l)1)
Kp (l g)1)
n
a
b (h)1)
m (g g)1 h)1)
Value
0.403
0.790
164
1.60 ´ 10)2
2.06
13.2
6.45 ´ 10)2
3.70 ´ 10)3
685
conditions and the corresponding results are summarised in Table 2. In all fermentation experiments the
molar amount of carbon dioxide produced was two to
three orders of magnitude lower than the amounts of the
other by-products measured (data not shown). The data
used for modelling were adjusted for dilution caused by
NaOH addition required to maintain a stable pH.
However, all concentrations given in text and tables are
the concentrations prevailing in the fermentor.
Fig. 1 Experimental and simulated data for a fermentation in ¯ourfree medium at pH 6, 30 °C. Experimental data for lactic acid (m),
glucose (j) and cell mass (d), and simulated results for lactic acid,
glucose and cell mass (б). The experimental data have been adjusted
for dilution due to NaOH addition
In¯uence of glucose inhibition, lactic acid inhibition and
pH on the kinetics
relationship between the growth rate and the product
formation rate, were set to the same values for fermentation experiments in a whole-wheat ¯our medium as
those in the ¯our-free medium. In all subsequent fermentation experiments one of the whole-wheat ¯our
media, hydrolysed ¯our or supplemented ¯our, was used.
Fermentation experiments were carried out under
di€erent physical conditions in supplemented ¯our medium. To control the sugar concentration, di€erent
amounts of glucose were added, and the whole-wheat
¯our contributed nutrients. However, a sudden change
in glucose consumption and lactic acid production rates
was observed in all fermentation experiments. Therefore,
some of the fermentation experiments were repeated in
hydrolysed ¯our, since previous observations have indicated that nutrients were released during the enzymatic hydrolysis of whole-wheat ¯our (Hofvendahl and
Hahn-HaÈgerdal 1997a, b). The experimental data were
used to determine the parameters in the kinetic model.
Unless otherwise stated, the pH was 6.0 and the temperature 30 °C (standard conditions). The physical
The e€ect of glucose and lactic acid inhibition was investigated by varying the initial glucose concentration
between 44 g l)1 and 182 g l)1 resulting in lactic acid
concentrations up to 86 g l)1 (Fig. 2). In one fermentation in supplemented ¯our medium, 35 g l)1 lactic acid
was added 12 h after inoculation (Fig. 2A). The in¯uence of pH was investigated in fermentation experiments
at pH 6.0, 5.0 and 4.0 in hydrolysed ¯our medium
(Fig. 2B±D) and in supplemented ¯our medium (data
not shown).
The maximal volumetric lactic acid productivity increased with decreasing initial glucose concentration and
was considerably inhibited at lower pH values (Table 2).
However, the productivities of lactic acid and by-products decreased throughout the whole fermentation process. When 35 g l)1 lactic acid was added 12 h after
inoculation (Fig. 2A), the lactic acid productivity decreased from 2.1 g l)1 h)1 to 0.40 g l)1 h)1. No glucose
consumption or lactic acid production was observed
when 80 g l)1 lactic acid was present from the start of the
fermentation (data not shown). The lactic acid concentration at the end of the exponential phase decreased with
decreasing pH, but increasing the initial glucose concentration from about 80 g l)1 to about 170 g l)1 did not
result in signi®cantly higher lactic acid concentrations at
the end of the exponential phase (Table 2).
Table 2 Results of fermentation experiments in whole-wheat ¯our
media. Std standard conditions, Glc glucose, Temp temperature,
LA lactic acid, LA add 35 g/l LA added after 12 h, Hydr hydrolysed
¯our medium, Suppl supplemented ¯our medium, LA prod LA
produced, end expon at the end of the exponential phase, Q maximal volumetric LA productivity
Variable
Medium
pH
Temp
(°C)
Glucose
initial
(g l)1)
Cell mass
initial
(mg l)1)
LA prod
(end expon)
(g l)1)
L-LA
(end expon)
(% of total LA)
Q
(g l)1 h)1)
Std
Glc
Glc, pH
Hydr
Hydr
Hydr
Hydr
Hydr
Suppl
Suppl
Suppl
Suppl
Suppl
Suppl
6.0
6.0
5.0
5.0
4.0
6.0
6.0
6.0
6.0
6.0
6.0
30
30
30
30
30
30
30
33.5
37
40
30
182
79
174
85
170
47
72
44
40
43
44
11
6
12
3
3
20
10
15
17
20
13
86
70
20
21
7
39
49
50
31
32
42
99
99
99
96
97
99
98
90
96
82
99a
2.9
4.0
0.42
0.83
0.23
2.2
2.1
2.8
2.3
1.5
2.1
pH
Std
Glc
Temp
LA add
a
Before lactic acid addition
686
Table 3 Parameter values in the fermentation model under standard conditions (pH 6.0 and 30 °C) for fermentation experiments
in hydrolysed ¯our and supplemented ¯our media parameters as in
Table 1
Parameter
Value
)1
Ks (g l )
Ki (g l)1)
n
a
b (h)1)
m (g g)1 h)1)
0.790
164
2.36
13.2
6.45 ´ 10)2
6.78 ´ 10)3
Experimental data from Fig. 2B±D were used to determine the parameters for growth, glucose and lactic
acid inhibition, and to determine how these parameters
were in¯uenced by pH. Thus, Ks, Ki, n, m, lm, kl1, kl2,
Kpm, kp1 and kp2 were determined by minimising the
objective function
X
X
Q2 ˆ
Pcalc ÿ Pexp †2 ‡
Sg;calc ÿ Sg;exp †2
10†
using the values of a and b in Table 1 exp and calc
represent experimental and simulated data, respectively.
The parameter values are summarised in Tables 3 and 4.
In¯uence of temperature on the kinetics
Fig. 2A±D Experimental and simulated data for fermentation experiments at 30 °C, performed in supplemented ¯our medium (A) and
hydrolysed ¯our medium (B±D); pH 6 with and without 40 g l)1 lactic
acid added after 12 h (A), pH 6 in high and low concentrations of ¯our
(B), pH 5 in high and low concentrations of ¯our (C) and pH 4 (D).
The experimental data are for lactic acid (m, n) and glucose (j, h).
Simulated results are represented by lines. j±j, m±m No lactic acid
added (A) and high concentrations of ¯our (B±D); h- - -h, n- - -n
lactic acid added (A) and low concentrations of ¯our (B±C). The
experimental data are adjusted for dilution due to NaOH addition
The initial glucose concentration did not in¯uence
which isomer of lactic acid that was produced at pH 6
(Table 2). However, at pH 5 a lower initial glucose
concentration resulted in increased D-lactic acid formation. At initial glucose concentrations of around 40, 80
or 180 g l)1, a lower pH increased D-lactic acid formation. In supplemented ¯our medium, where maltose was
present, the D-lactic acid content, 42% and 10% of total
amount of lactic acid, at pH 4 and 5, was higher than in
hydrolysed ¯our medium (Table 2).
By-product formation was not observed in the hydrolysed ¯our medium (Fig. 2B±D), whereas in the
supplemented ¯our medium (Fig. 2A) a slight increase
in acetic acid and ethanol, and in some cases formic acid,
was observed. The by-product formation increased with
decreasing pH (data not shown).
The in¯uence of temperature on product formation was
investigated between 30 °C and 40 °C in fermentation
experiments in supplemented ¯our medium (Fig. 3, 4).
The maximal volumetric lactic acid productivity was
highest at 33.5 °C: 2.8 g l)1 h)1. At 33.5 °C and above,
lactic acid formation decreased and the formation of
equimolar amounts of acetic acid and ethanol increased
(Fig. 4). In addition, a number of unidenti®ed compounds were detected in the chromatograms. Formic
acid production, on the other hand, decreased with increasing temperature, and diminished as the fermentation continued. At higher temperatures, more of the
lactic acid produced was in the D form (Table 2).
When 20 g l)1 glucose was consumed, the rates of
glucose consumption and lactic acid production decreased suddenly, e.g. Fig. 3A at 10 h. At this point, the
maltose liberated by starch degradation diminished, and
the maltose concentration remained constant at around
10 g l)1. Maltose was consumed when the glucose concentration became suciently low: 5 g l)1; see, for example, Fig. 3A at 27 h. Maltose was not modelled
Table 4 Parameter values in the expression for the pH dependence
of lmax and Kp in hydrolysed ¯our medium (Eqs. 6, 7)
lmax
lm (h)1)
kl1 (M)
kl2 (M)1)
Kp
1.10
9.42 ´ 10)7
1.27 ´ 105
Kpm (l g)1)
kp1 (M)
kp2 (M)1)
0.154
1.02 ´ 10)5
3.82 ´ 104
687
Fig. 3A±D Experimental data and simulations of fermentation
experiments at pH 6, performed at 30 °C (A), 33.5 °C (B), 37 °C
(C), and 40 °C (D). Symbols as in Fig. 1; experimental data for
maltose (r) and simulated results using two (±±) and one ( ) value
of lmax. The experimental data have been adjusted for dilution due to
NaOH addition
because, in an industrial process, the whole-wheat ¯our
is either totally hydrolysed to glucose prior to fermentation (hydrolysed ¯our medium), or sacchari®cation
and fermentation are performed simultaneously, resulting in the continuous production of glucose by starch
hydrolysis. Thus, only experimental data obtained at
glucose concentrations higher than 5 g l)1 were used to
®t the model for fermentaiton in supplemented ¯our
medium.
The objective function Q2 was minimised using the
experimental data shown in Fig. 3A±C and 4A±C, and
assuming that Ks, Ki, Kpm, kp1, kp2, n and m had the
same values as when modelled for fermentation under
standard conditions (Tables 3, 4). The parameter Ypa, as
well as the temperature dependence of a, b, aa, ba and
kst, was determined and A1, A2, E1 and E2 are presented
in Table 5. No stoichiometric value was used for Ypa
since it accounts for all by-products formed, and not
only the acetic acid. To account for the sudden change in
productivity after 20 g l)1 glucose had been consumed,
di€erent values of lmax were determined before and after
the drop (Table 5).
Fig. 4A±D Production of acetic acid, ethanol and formic acid. A±D
as in Fig. 3. Experimental data for acetic acid (´), ethanol (s) formic
acid (+) and simulated results for acetic acid (Ð). The experimental
data have been adjusted for dilution due to NaOH addition
Table 5 Parameter values in the expression for the temperature
dependence of the parameters a, b, aa, ba and kst and values of the
parameters Ypa, lmax, before and lmax, after in supplemented ¯our
medium. aa growth-associated constant for by-product formation,
ba non-growth-associated constant for by-product formation, kst
empirical starch degradation parameter, Ypa by-product yield
coecient (g by-product/g substrate), before/after before or after
drop in product formation rate. Parameters as in Table 1
Parameter
A1
A2
E1
E2
a
b (h)1)
aa
ba (h)1)
kst (h)1)
Ypa (g g)1)
lmax, before (h)1)
lmax, after (h)1)
287
1.77
2.88
2.97 ´ 10±2
7.52 ´ 10±2
0.169
0.525
0.216
8.88 ´ 103
76.9
82.4
53.9
543
151
376
0.590
343
Comparison of simulation and experimental data
Parameter values for Ks, Ki, n and m (Table 3) and all
parameter values summarised in Tables 4 and 5 were
used for simulations. The resulting curves are shown in
Fig. 2±4, together with the experimental data. To illustrate the di€erence between using one or two values of
688
lmax in supplemented ¯our medium, simulations were
also performed using only lmax, before (Table 5), shown
in Fig. 3A±C. The model was veri®ed by simulating data
from fermentation experiments not used for model parameter determination, e.g. those in Fig. 2A. The model
showed that both substrate and product inhibition are
present, the latter being dominant. The simulated maximum speci®c growth rate, lmax, was highest at pH 6.0:
0.53 h)1, in agreement with the observed lactic acid
productivity in the hydrolysed ¯our medium (Table 2).
Simulating the temperature dependence of a, b, aa and
ba con®rmed that maximum lactic acid productivity
occurred 33.5 °C (Table 2) and the increase in acetic
acid formation at higher temperatures (Fig. 4). In addition, the simulations showed that glucose formation
due to starch degradation was highest at 35 °C.
Discussion
The model developed in the present study describes
statisfactorily the kinetics of lactic acid fermentation in
whole-wheat ¯our medium with L. lactis 19435. The
model was veri®ed by simulating data from fermentation
experiments not used for model parameter determination
(e.g. Fig. 2A). It could be observed that simulated data ®t
experimental data satisfactorily except after lactic acid
addition. This could be due to the fact that lactic acid
added to the fermentation and lactic acid produced from
the bacteria do not inhibit the cell growth to the same
extent. The values of the model parameters are speci®c
for this bacterial strain. This model considers the e€ect of
both product and substrate inhibition on the kinetics,
while models presented previously often consider the
e€ect of product inhibition only (Yeh et al. 1991; Cachon
and DivieÁs 1994; Gadgil and Venkatesh 1997). A number
of models have been presented that include the in¯uence
of pH (Yeh et al. 1991; Venkatesh et al. 1993; Cachon
and DivieÁs 1994; Gadgil and Venkatesh 1997). Few
models consider the e€ect of temperature on the kinetics
(Rincon et al. 1993), whereas the model developed in this
study includes both pH and temperature. In addition, the
acetate formation rate was included as a measure of the
total formation of by-products. Similar expressions for
by-product formation have not been presented before.
The value of the parameter a in Eq. 2 was found to be
much higher than b (13.2 compared with 0.064 h)1) indicating that the production of lactic acid was growthassociated. The parameter m, in Eq. 5, representing the
maintenance energy, was higher for the ¯our media than
for the ¯our-free medium containing, among other
things, yeast extract and tryptone. Thus, in the ¯our
media more glucose was used for products besides cell
mass, lactic and acetic acid, than was used in the ¯ourfree medium. The model is not valid when all substrate
has been consumed. Because of the non-growth-associated term in Eq. 2 (báX) the simulation results in an
increase of the product concentration, although the
substrate concentration, and thus the cell growth rate, is
zero.
The sudden change in product formation rate observed in supplemented ¯our medium did not occur in
the fermentation of hydrolysed ¯our medium. The drop
in product formation rate in the supplemented ¯our
medium may be due to nutrient limitation, and indicates
that nutrients are released from the ¯our during enzymatic hydrolysis, in accordance with previous studies
(Hofvendahl and Hahn-HaÈgerdal 1997a, b), as well as
with work in progress. The value of lmax for fermentation in hydrolysed ¯our medium was the same (0.53 h)1)
as for the supplemented ¯our medium before the drop in
product formation rate. It could be observed that simulations in supplemented ¯our medium using only this
value of lmax did not ®t experimental data well, and
therefore two values of lmax were used (Fig. 3A±C).
For L. delbrueckii, susbtrate inhibition is of major
importance (GoncËalves et al. 1991), and both experimental data and simulations of L. lactis 19435 showed
that substrate inhibition is of importance in the glucose
concentration interval investigated: 40±82 g l)1. For
example, at an initial glucose concentration of 100 g l)1
the cell growth rate decreased by 37% compared with
fermentation without substrate inhibition. Lactic acid
concentrations above 70 g l)1 and 110 g l)1 inhibited the
growth of Streptococcus cremoris (Bibal et al. 1988) and
Lactobacillus plantarum (Giraud et al. 1991). Simulations showed that the growth of L. lactis 19435 was
totally inhibited by 74, 16 and 32 g l)1 lactic acid in
hydrolysed ¯our medium at pH 6, 5 and 4 respectively.
When modelling, it was observed that this inhibition
could not be related to the concentration of the undissociated acid alone. Neither could the inhibition be accounted for by the total concentration of lactic acid.
Thus, it was concluded that both the undissociated and
the dissociated forms of lactic acid contributed to the
inhibition. This has also been reported for L. bulgaricus
and L. rhamnosus growing on lactose and glucose, respectively (Venkatesh et al. 1993; GoncËalves et al. 1997).
Growth of lactic acid bacteria is notably slower below a
certain pH: pH 5 for Lactococci (Nannen and Hutkins
1991; Cachon and DivieÁs 1994) and pH 3.4 for
L. plantarum (Giraud et al. 1991). The present study
showed that the maximum speci®c growth rate, lmax, of
L. lactis 19435 in hydrolysed ¯our medium was only
slightly higher at pH 6 than at pH 5: 0.53 and 0.47 h)1
respectively. However, since the e€ect of product inhibition was much greater at pH 5 than at pH 6: Kp ˆ
0.064 l g)1 and 0.014 l g)1 respectively, the product
formation rate was substantially lower at pH 5. At pH 4,
lmax was much lower, 0.080 h)1, than at the higher pH
values, causing the lowest product formation rate.
Simulations showed that 32 g l)1 lactic acid inhibited cell
growth completely at pH 4. However, since this concentration was never reached and total inhibition of cell
growth was not observed in fermentation at pH 4 in this
study, this value is dicult to verify.
689
L. lactis switches from homolactic to mixed-acid
fermentation when grown under glucose-limited conditions (Fordyce et al. 1984; SjoÈberg et al. 1995) or when
grown on galactose or lactose (Thomas et al. 1980;
Garrigues et al. 1997), or maltose (Lohmeier-Vogel et al.
1986; Qian et al. 1994; Hofvendahl and Hahn-HaÈgerdal
1997b). In mixed-acid fermentation, pyruvate is metabolised into lactic acid, ethanol, acetic acid and either
formic acid or carbon dioxide (Fordyce et al. 1984). In
the present study, maltose was only present in the supplemented ¯our medium and consumption only started
when the glucose concentration had decreased to 5 g l)1,
in accordance with previous observations (Qian et al.
1997; Hofvendahl and Hahn-HaÈgerdal 1997b). This resulted in mixed-acid fermentation, with lactic acid being
the major product, and formic acid, acetic acid and
ethanol being by-products. The present study showed
that temperatures above 30 °C and pH levels below 6
also enhanced by-product formation in supplemented
¯our medium. When the temperature was increased,
only acetic acid and ethanol formation increased in
equimolar amounts, whereas the amount of formic acid
decreased with increasing fermentation time. Carbon
dioxide formation was two to three orders of magnitude
lower than acetic acid and ethanol formation, con®rming that carbon dioxide is only produced under aerobic
conditions (Cocaign-Bousquet et al. 1996). Pyruvate
may still be metabolised to formic acid, acetic acid and
ethanol, but the detection of formic acid may be masked
by compounds produced in higher concentrations at
higher temperatures.
A change from the formation of almost exclusively Llactic acid to a higher proportion of D-lactic acid was
seen at pH 4 and 5, as well as at 33.5±40 °C, resulting in
3%±42% of the lactic acid being in the D-form. Similar
observations were made when L. lactis 19345 was grown
without pH control (Hofvendahl and Hahn-HaÈgerdal
1997a) and for L. casei (HjoÈrleifsdottir et al. 1990) and L.
plantatrum (Bobillo and Marshall 1992), when grown
under starvation conditions or at acidic pH. It has been
suggested that this is because the enzymes D- and L-lactate dehydrogenase have di€erent pH optima (Mou et al.
1972; Gordon and Doelle 1975; Bobillo and Marshall
1992), or that L-lactate dehydrogenase exclusively is activated by fructose 1,6-bisphosphate (Mou et al. 1972).
However, the latter would imply that the mixed-acid
formation observed under carbon limitation should also
result in enhanced D-lactic acid formation, and this has
so far not been observed. In Escherichia coli, for example,
D-lactic acid can be formed from dihydroxyacetone
phosphate via methylglyoxal (Cooper 1984), and this
pathway might be present in L. lactis as well.
The in¯uence of temperature on lactic acid production has not been widely investigated. Earlier studies on
L. lactis have mainly been concerned with the in¯uence
of temperature on proteolytic activity and diacetyl formation (de Giori et al. 1985, 1986). The experimental
data obtained and the model developed in the present
study showed that lactic acid productivity was optimal
between 33 °C and 35 °C. However, D-lactic acid and
by-product formation increased at temperatures above
30 °C, which would increase the cost of puri®cation.
To simulate the simultaneous sacchari®cation of
starch to glucose and further fermentation to lactic acid,
the model developed in this study will be combined with
a kinetic model for the enzymatic sacchari®cation of
wheat starch. The model will be used to determine optimal operating conditions and to determine whether
sacchari®cation and fermentation should be performed
simultaneously or separately.
Acknowledgements We wish to thank Prof. A. H. Stouthamer for
his advice, and Elahe Behtoye and Daniel Kronhall for technical
assistance. This work was supported by the Swedish National
Board for Industrial and Technical Development.
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Note added in proof: Further investigations showed that the Dlactic acid formation observed was not produced by L. Lactis 19435