Enzyme and Microbial Technology 32 (2003) 92–98
The double substrate growth kinetics of Pseudomonas aeruginosa
Haluk Beyenal a, Suet Nee Chen a, Zbigniew Lewandowski a,b,∗
a Center for Biofilm Engineering, Montana State University, P.O. Box 173980, Room 366 EPS, Bozeman, MT 59717, USA
b Department of Civil Engineering, Montana State University, Bozeman, MT 59717, USA
Received 14 June 2001; received in revised form 19 September 2002; accepted 23 September 2002
Abstract
Growth parameters of Pseudomonas aeruginosa were quantified based on steady-state concentrations, utilization rates of glucose
and dissolved oxygen, and microorganism concentration in a chemostat that was operated at 25 ◦C, pH 7.2, and an agitation rate
350 rpm. The results showed that the microbial growth was limited by the concentration of glucose and the concentration of oxygen.
A dual-substrate, Tessier growth kinetics for oxygen and glucose, was in good agreement with the experimental data using the fol-
lowing biokinetic parameters: µmax = 0.29 h−1, Kg = 26.9 mg/l, Ko = 1.18 mg/l, Yx/g = 0.628 g microorganism/g glucose and, Yx/o =
0.635 g microorganism/g oxygen. Maintenance factors for glucose and oxygen were:mg = 0.0078 g glucose consumed/g microorganism h,
and mo = 0.014 g oxygen consumed/g microorganism h.
© 2002 Elsevier Science Inc. All rights reserved.
Keywords: Pseudomonas aeruginosa; Growth kinetics; Multiple-substrate; Biokinetics
1. Introduction
To our best knowledge, there are not any available
multiple-substrate growth kinetic model developed for
Pseudomonas aeruginosa. The goal of this study is to de-
velop such a model and to calculate biokinetic parameters
associated with the model. P. aeruginosa is often used in
biofilm studies and modeling biofilm accumulation, proba-
bly because microbial geneticists have been studying this
organism intensively and its physiology and genetics are
well known [1–3]. Biokinetic parameters for microbial
growth of P. aeruginosa have been determined in biofilms
by Bakke et al. [4], and in planktonic cultures by Robinson
et al. [5]. However, in both papers the growth parameters
of P. aeruginosa have been determined at relatively low
glucose concentrations, less than 7.5 mg/l in the chemostat
[4], and less than 1.4 mg/l in the biofilm reactor [5]. We can
only guess that the reason for using such low glucose con-
centrations was to assure that glucose—not oxygen—was
the limiting substrate. In biofilms, however, there is little
control over the substrates that may act as growth-limiting
factors [6,7]. Concentrations of electron donors and electron
acceptors in biofilms decrease toward the bottom because
of mass transfer limitations and microbial consumption,
and it may be difficult to assess which of them is exhausted
∗ Corresponding author. Tel.: +1-406-994-5915; fax: +1-406-994-6098.
E-mail address: zl@erc.montana.edu (Z. Lewandowski).
first in the deeper biofilm layers. In the excess of glucose
in solution, it is reasonable to assume that oxygen rather
than glucose will be the growth-limiting factor. However, to
quantify biofilm accumulation rate, models accounting for
multiple-substrate utilization by the microorganisms should
be used to judge whether the electron donor or the electron
acceptor is the growth-limiting factor [8].
The inherent difficulty associated with developing rele-
vant multiple-substrate growth models stems from the ne-
cessity of providing relevant experimental data and solving
non-linear equations. Appropriate techniques to build such
models are available [5,9]. We have generated experimen-
tal data and constructed a multiple-substrate growth model
for P. aeruginosa. To acquire experimental data we used a
chemostat, measured concentrations, consumption rates of
glucose and dissolved oxygen, and concentration of the mi-
croorganism. All measurements were made at steady states.
2. Materials and methods
2.1. Microorganism and growth conditions
A pure culture of P. aeruginosa (ATCC 700829) was
used throughout the study. To grow the microorganism
we used an artificial growth medium containing Na2HPO4
(1.83 g/l); K2HPO4 (0.35 g/l); MgSO4·7H2O (0.01 g/l);
yeast extract (0.001 g/l); (NH4)2SO4 (0.1 g/l) and glucose
0141-0229/02/$ – see front matter © 2002 Elsevier Science Inc. All rights reserved.
PII: S 0141 -0229 (02 )00246 -6
H. Beyenal et al. / Enzyme and Microbial Technology 32 (2003) 92–98 93
Nomenclature
Bg constant in Contois model for glucose
Bi constant in Contois model for substrate i
Bo constant in Contois model for oxygen
D dilution rate (h−1)
Kg Monod saturation constant for glucose (g/l)
Ko Monod saturation constant for oxygen (g/l)
Ksi half-saturation constant for substrate i (g/l)
mg maintenance factor for glucose (h−1)
mi maintenance factor for limiting substrate i (h−1)
mo maintenance factor for oxygen (h−1)
mo microorganism
N number of experimental data
OUR oxygen uptake rate (mg oxygen/h)
Q flow rate (l/h)
Sei substrate concentration in effluent stream (g/l)
Sfg concentration of glucose in fresh feed (g/l)
Sfi substrate concentration in influent stream (g/l)
Sfn concentration of ammonium sulfate in fresh feed (g/l)
Sg concentration of glucose in chemostat (g/l)
Si concentration of substrate i (g/l)
So concentration of dissolved oxygen (g/l)
SOUR specific oxygen uptake rate (g oxygen/g microorganism/h)
SSD sum of squares of the differences (see Eq. (10))
T temperature (◦C)
V reactor volume (l)
X microorganism concentration in chemostat (g/l)
Yx/g yield coefficient for glucose (g microorganism/g glucose)
Yx/o yield coefficient for oxygen (g microorganism/g oxygen)
Yx/si yield coefficient for limiting substrate i (g microorganism/g limiting substrate)
Greek letters
µ specific growth rate (h−1)
µexperimental experimental specific growth rate (h−1)
µi specific growth rate for limiting substrate i (h−1)
µmax maximum specific growth rate (h−1)
µpredicted theoretical specific growth rate (h−1)
λg Moser’s constant for glucose (g/l)
λi Moser’s constant for substrate i (g/l)
λo Moser’s constant for oxygen (g/l)
(1 g/l). One milliliter of trace elements was added to the
growth medium for every liter of growth medium. The
solution of trace elements had the following composi-
tion; MnCl2·4H2O (527 mg/l); CuCl2·2H2O (228 mg/l);
CoCl2·2H2O (317 mg/l); (NH4)Mo7O4·H2O (231 mg/l);
Na2B4O7·10H2O (127 mg/l); ZnCl2 (363 mg/l); FeCl3
(2160 mg/l); and CaCl2 (3700 mg/l). The growth medium
was prepared using distilled water sterilized in an autoclave
at 121 ◦C and 1 atm absolute pressure for 3 h. Glucose,
yeast extract, and (NH4)2SO4 were autoclaved separately.
Trace elements were added to the sterile growth medium
using a disposable sterile syringe filter (0.2
m, Corning).
2.2. Experimental setup
We used a New Brunswick (BioFlo 2000) chemostat with
a working volume of 2 l, equipped with pH, agitation, tem-
perature, and dissolved oxygen controllers. The sensitivities
of the control units for dissolved oxygen, pH, and agitation
rate were 0.05%, 0.1 unit, and ±1 rpm, respectively. Prior to
use, the chemostat was autoclaved for 30 min at 121 ◦C. The
pH was controlled using solutions of 0.1N NaOH and 0.1N
H2SO4. The agitation rate was 350 rpm (optimized) to main-
tain a homogeneous culture. Dissolved oxygen concentra-
tion was controlled in the range of 0.5–7.3 mg/l by sparging
94 H. Beyenal et al. / Enzyme and Microbial Technology 32 (2003) 92–98
filtered air or mixtures: air + oxygen or air + nitrogen, de-
pending on the needs. The air flow rate was fixed between 1
and 5 l/h. The reactor was inoculated with microorganisms
using 10% (v/v) solution at exponential growth phase.
Microorganisms used to inoculate the chemostat were
prepared as follows: 1 ml frozen stock sample (stored
at −70 ◦C) of P. aeruginosa (ATCC 700829) was intro-
duced into separate flasks containing growth medium com-
posed of glucose (5 g/l), yeast extract (0.2 g/l), (NH4)2SO4
(1 g/l), and the remaining components of the growth me-
dia (as described before). The volume of the solution was
100 ml, and the microorganisms were grown for 20–30 h.
The flasks were placed on a shaker, set at 150 rpm, at
room temperature, approximately 25 ◦C. The typical cell
concentration, when plated on R2A agar and grown for
24 h in the incubator at 30 ◦C, was 9.4 × 106 CFU/ml of
solution.
After inoculation, the chemostat was initially run in a
batch mode. Continuous pumping of fresh feed started after
the culture had entered the exponential growth phase (ca.
after 20–30 h). To establish a steady state, the reactor was run
for six to seven retention times, and steady state was assumed
if the absolute differences in consecutive measurements of
effluent substrate concentration differed by less than 3%.
Several dilution rates up to the washout point were used,
and the corresponding steady-state data were recorded. To
find a new steady state, the dilution rate was increased by
a gradual increase in the feed-flow rate. The chemostat was
operated using different combinations of influent substrate
concentration, pH, agitation rate, and temperature.
2.3. Analytical methods
The microorganism concentration was determined using a
standard dry-weight method [10]. The glucose concentration
was measured using Sigma® procedure 510 (Sigma® Diag-
nostics, St. Louis, MO). The ammonium sulfate concentra-
tion was measured using a Hatch® ion-selective electrode
(Loveland, CO). Dissolved oxygen and pH were monitored
by Ingold® dissolved oxygen and pH electrodes integrated
with the chemostat. The ammonium electrode was calibrated
using a standard ammonia solution from Hatch® (catalog
#24065–49). The dissolved oxygen electrode was calibrated
in the autoclaved growth medium purging the solution with
pure nitrogen and air. The electrode that measured pH was
calibrated using pH buffers at pH 4, 7 and 10 from Fisher
(catalog numbers SB98-1, SB108-1, and SB116-1, respec-
tively).
The oxygen uptake rate was estimated using a method
suggested by Bandyopdhyay et al. [11]. In this method, the
gas space of the chemostat is flushed with nitrogen gas to
remove the oxygen, and the decrease of dissolved oxygen
concentration in the reactor is recorded against time, the
value of (−dSo/dt) at the linear region yields the oxygen
uptake rate per unit volume. The term (−dSo/dt)/(X) is the
specific oxygen uptake rate (SOUR) [12].
2.4. Estimation of biokinetic constants
Three types of multiple-substrate growth models can be
considered when growth is limited by more than one sub-
strate [6]:
Interactive or multiplicative form:
µ
µmax
= [µ(S1)][µ(S2)] · · · [µ(Si)] (1)
Additive form:
µ
µmax
= µ(S1)+ µ(S2)+ · · · + µ(Si)
i
(2)
Non-interactive form:
µ
µmax
= µ(S1) orµ(S2) or . . . orµ(Si) (3)
Many mathematical models are available to correlate the
single substrate concentration with microbial growth rate, µ
versus Si (presented in the literature [6,13–16]). To develop
multiple-substrate growth kinetics, these individual models
can be combined in a manner described by Eqs. (1)–(3),
to obtain equations consistent with the experimental data
[16]. In our tests, we used the following growth kinetics
[13,17–19] for a single substrate, Si :
Monod µ = µmax Si
Ksi + Si (4)
Tessier µ = µmax(1− e−Si/Ksi ) (5)
Moser µ = µmax(1+KsiS−λi )−1 (6)
Contois µ = µmax Si
BiX + Si (7)
The mass balance for the microorganism in an ideal chemo-
stat yields Eq. (8):
µ = D = Q
V
(8)
To develop growth models for multiple-substrates, the spe-
cific growth rate, µ, is calculated from Eq. (8) for each
steady state. Different growth models based on single sub-
strate (Eqs. (4)–(7)) are then inserted into Eq. (1) or (2),
or (3) to find the best multiple-substrate model. From the
same data, the maintenance factor, mi , and yield factor, Yx/si
are calculated from the mass balance for the substrate as
given by Eq. (9):
D(Sfi − Sei ) = µiX
Yx/si
+miX (9)
2.5. Non-linear regression
To estimate the biokinetic parameters from the experi-
mental data, we used Microsoft Excel 2000® Solver®, which
solves non-linear regression problems using Newton’s
method [20]. The equations were solved to find values of
H. Beyenal et al. / Enzyme and Microbial Technology 32 (2003) 92–98 95
Table 1
The search range for biokinetic constants of P. aeruginosa in the non-linear
regression analysis
Constants Allowable range
µmax (h−1) 0–1
Kg (mg/l) 0–1000
Ko (mg/l) 0–7.8
the biokinetic parameters that minimize the objective func-
tion, the sum of squares of the differences (SSD) between
experimental and theoretical data for specific growth rates,
as given by Eq. (10):
SSD =
N∑
i=1
(µexperimental − µpredicted)2 (10)
To calculate the maintenance and yield factors (Eq. (9)), we
have described the objective function as the SSD between
the substrate consumption rates, which were experimentally
measured and theoretically estimated, separately for oxygen
and glucose. Because the solution was sensitive to initial
guesses, the search was constrained to a predetermined
range, determined as the range of biokinetic constants for
bacteria reported in literature and shown in Table 1 [12,15].
2.6. Best kinetic model
Using non-linear regression and the selected multiple-
substrate growth kinetics, we calculated the biokinetic pa-
rameters as described before. The best multiple-substrate
growth model was selected from among different combina-
tions of Eqs. (4)–(7) to give the minimum sum of squares of
differences (SSD) between the experimental data and model
solutions.
3. Results and discussion
3.1. Optimum operating conditions
In aerobic systems, dissolved oxygen acts as the elec-
tron acceptor during substrate oxidation [21]. Research
on suspended cell cultures has revealed that the SOUR
(g oxygen/g dry biomass/h) is proportional to microbial ac-
tivity, which makes it suitable as an indicator of microbial
activity [13,22–25]. Therefore, we selected SOUR to deter-
mine the optimum operating conditions in the chemostat.
Fig. 1 shows SOUR for different agitation rates in the
chemostat. It was expected that at low agitation rates the
growth of microorganisms was limited by external mass
transport. Therefore, when the agitation rates increased, the
mass transfer rate to the microorganisms increased, along
with the SOUR, which reached a maximum value. Increasing
the agitation rate beyond this maximum actually decreased
the SOUR, probably because the agitation was injuring the
Fig. 1. The SOUR for different agitation rates in the chemostat
(D = 0.124 h−1, pH 7.2, T = 25 ◦C, Sfg = 5 g/l, and Sfn = 0.1 g/l, air
flow rate = 3 l/h).
microorganisms. Based on the results in Fig. 1, we selected
350 rpm as the working agitation rate. Microscopic exam-
inations showed that the microorganisms were distributed
uniformly in the chemostat, and neither flocculation nor ag-
glomeration were observed.
We have measured the effect of pH on SOUR (Fig. 2).
The SOUR increases, reaches a maximum value, and then
decreases. The optimum pH 7.2 was used in all runs.
The data (Table 2) collected at steady states were used for
the modeling of growth kinetics.
3.2. Modeling microbial growth kinetics
In addition to the data in Table 2, we also tested the
growth-limiting substrates and their interactions. According
to these results, the growth rate of P. aeruginosa in the ab-
sence of oxygen or glucose was negligible. Furthermore,
changing NH4+ concentration in the feed did not affect the
effluent concentrations of glucose, oxygen, and microorgan-
isms (results not shown). These observations, combined with
the results in Table 2, demonstrate that glucose and oxygen
influenced the growth kinetics of P. aeruginosa. Hence, the
growth of P. aeruginosa should be represented by a kinetic
Fig. 2. The effect of pH on SOUR in the chemostat (D = 0.124 h−1,
agitation rate = 350 rpm, T = 25 ◦C, Sfg = 5 g/l, and Sfn = 0.1 g/l, air
flow rate = 3 l/h).
96 H. Beyenal et al. / Enzyme and Microbial Technology 32 (2003) 92–98
Table 2
The results of steady-state experiments (T = 25 ◦C, pH 7.2, agitation
rate = 350 rpm, Sfg = 5 g/l, Sfn = 0.1 g/l)
D (h−1) So (mg/l) Sg (mg/l) X (mg/l) OUR (mg oxygen/h)
0.03 1 5 1725 323
0.04 7.2 3.8 3000 424
0.0556 0.5 19.4 2381 581
0.069 7.2 7.1 2820 719
0.118 0.8 45.7 3150 1212
0.124 7.2 15.1 3070 1273
0.162 7.2 22.7 3225 1658
0.187 1.5 69.4 3285 1912
0.24 6.6 255 2760 2565
0.24 2.5 87.4 3105 2440
0.275 3.3 112.65 3090 2799
0.299 5.4 217 2850 2599
0.325 5.6 154.9 3045 3306
expression taking into account the dual-substrate limitations
of oxygen and glucose combined.
Table 3 shows possible growth models using combi-
nations of Eqs. (4)–(7), calculated biokinetic parameters,
SSD, and regression coefficients (R2). The minimum SSD
were found for models #12 and #17, with R2 between
0.96 and 0.97. Model 17 combined the Moser and Tessier
kinetics. However, according to the Moser kinetic (model
#17), P. aeruginosa should grow in the absence of the oxy-
gen, which contradicts experimental results. Consequently,
as the best growth model we have selected the double
Table 3
Growth models, biokinetic parameters, SSD, and regression coefficients (R2)
Model
number
Equation number
for oxygen
Equation number
for glucose
λo λg Bo Bg Ko Kg µmax SSD R2
1 – 4 – – – – – 31.97 0.30 0.0272074 0.78
2 – 5 – – – – – 39.76 0.26 0.0256887 0.80
3 – 6 – 1.06 – – – 37.42 0.29 0.027141 0.79
4 – 7 – – – 1.13E−02 – – 0.30 0.0308807 0.76
5 4 – – – – – 0.65 – 0.21 0.1055993 0.17
6 4 4 – – – – 0.50 20.32 0.32 0.0192399 0.85
7 4 5 – – – – 0.51 20.00 0.21 0.1012759 na
8 4 6 – 1.49 – – 0.62 66.67 0.30 0.0174575 0.86
9 4 7 – – – 6.81E−03 0.55 – 0.32 0.021275 0.83
10 5 – – – – – 0.98 – 0.19 0.0980918 0.22
11 5 4 – – – – 0.85 19.13 0.29 0.016236 0.87
12 5 5 – – – – 1.18 26.89 0.29 0.0041595 0.97
13 5 6 – 1.49 – – 0.96 60.30 0.27 0.0146219 0.88
14 5 7 – – – 1.13E−02 9.9E−06 – 0.30 0.0308807 0.76
15 6 – 3.32 – – – 0.76 – 0.20 0.0956579 0.24
16 6 4 2.5 – – – 0.40 18.78 0.29 0.0163252 0.87
17 6 5 – 1.51 – – 0.78 27.30 0.30 0.0045242 0.96
18 6 6 2.29 1.47 – – 0.59 105.56 0.27 0.0154927 0.88
19 6 7 2.56 – – 6.36E−03 0.44 – 0.29 0.0176969 0.86
20 7 – – – 1.97E−04 – – – 0.20 0.1126745 0.11
21 7 4 – – 1.53E−04 – – 21.14 0.32 0.0202808 0.84
22 7 5 – – 2.05E−04 – – 25.96 0.29 0.0164883 0.87
23 7 6 – 1.53 2.00E−04 – – 76.13 0.30 0.0181868 0.86
24 7 7 – – 1.64E−04 7.27E−03 – – 0.32 0.0232337 0.82
The second and third columns show numbers of the equations we combined to assemble the double substrate kinetics. na, not available.
Fig. 3. The specific growth rates predicted from Eq. (12), Double Tessier
kinetics vs. measured specific growth rates.
Tessier kinetics:
µ = µmax(1− e−So/Ko) (1− e−Sg/Kg) (11)
For the selected model, the biokinetic parameters are
µmax = 0.29 h−1, Kg = 26.9 mg/l, Ko = 1.18 mg/l, Yx/g =
0.628 g biomass/g glucose, and Yx/o = 0.635 g biomass/
g oxygen. Maintenance factors are mg = 0.0078 g glucose
consumed/g microorganism h, and mo = 0.014 g oxygen
consumed/g microorganism h. Fig. 3 shows the growth
rates both measured and predicted from Eq. (11). The high
H. Beyenal et al. / Enzyme and Microbial Technology 32 (2003) 92–98 97
Table 4
Comparison of biokinetic parameters calculated in this study for dual-substrate growth models with literature studies
Study µmax
(h−1)
Kg
(mg/l)
Ko
(mg/l)
Yx/g
(g mo/g glucose)
Yx/o
(g mo/g oxygen)
mg
(g glucose/g mo h)
mo
(g oxygen/g mo h)
Our work 0.29 26.9 1.18 0.628 0.635 0.0078 0.014
Bakke et al. [4] chemostat 0.4 2 na 0.34 na na na
Robinson et al. [5] biofilms 0.45 2 na 0.3 na na na
na: not available.
correlation coefficient (0.97) demonstrates that the growth
model accurately represents the growth of P. aeruginosa.
Though the literature shows double Monod kinetics (#6)
as more commonly used for this procedure, the double
Tessier (model #12) proved to better fit our needs with a
correlation of R2 = 0.97. To select the kinetic expressions,
we accepted the R2 higher than 0.85 as a cutoff value. Mod-
els indicating R2 > 0.85 were considered options. Double
Monod kinetics showed R2 = 0.85, which according to our
definition was a borderline for the kinetic expressions we
decided to consider.
The comparison of the biokinetic parameters evaluated
in this study (Table 4) with those reported by Bakke et al.
[4] and Robinson et al. [5] shows that our µmax was slightly
lower but on the same order of magnitude as those reported.
However, our Kg value was nearly an order of magnitude
higher than those reported. This difference was most likely
caused by our chemostat being operated at much higher
glucose concentration than the systems used by Bakke et al.
[4] and Robinson et al. [5]. As mentioned earlier, Bakke
et al. [4] and Robinson et al. [5] used relatively low glucose
concentration to assure that glucose—not oxygen—was
the limiting substrate. This is to say they did not consider
oxygen as a limiting substrate. Also, Bakke et al. [4] and
Robinson et al. [5] considered only Monod kinetics to de-
scribe microbial growth, a model that was not found below
the acceptance level (R2 = 0.85) in our study.
Our half-saturation constant for oxygen, Ko = 1.18 mg/l,
was fairly high compared to those reported in the literature:
0.022 mg/l by Beyenal and Tanyolac [12], 0.048 mg/l by
Seker et al. [26], 0.075 mg/l by Tado and Sato [27]. We do
not offer any explanation for these differences.
4. Conclusions
We have found that a dual-substrate microbial growth
kinetics, dual Tessier kinetics for oxygen and glucose,
was in agreement with the chemostat data, yielding the
following biokinetic parameters describing growth of P.
aeruginosa: µmax = 0.29 h−1, Kg = 26.9 mg/l, Ko =
1.18 mg/l, Yx/g = 0.628 mg microorganism/mg glucose and,
Yx/o = 0.635 mg microorganism/mg oxygen. Maintenance
factors for glucose and oxygen were mg = 0.0078 g glucose
consumed/g microorganism h, and mo = 0.014 g oxygen
consumed/g microorganism h.
Acknowledgments
The research was supported by the cooperative agreement
EED-8907039 between the National Science Foundation and
Montana State University.
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