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Modeling and Optimization of Microbial Hyaluronic Acid Production by
Streptococcus zooepidemicus Using Radial Basis Function Neural Network
Coupling Quantum-Behaved Particle Swarm Optimization Algorithm
Long Liu
School of Biotechnology, Jiangnan University, Wuxi 214122, China
Key Laboratory of Industrial Biotechnology, Ministry of Education, Jiangnan University, Wuxi 214122, China
Jun Sun and Wenbo Xu
Institute of Information Technology, Jiangnan University, Wuxi 214122, China
Guocheng Du
School of Biotechnology, Jiangnan University, Wuxi 214122, China
Key Laboratory of Industrial Biotechnology, Ministry of Education, Jiangnan University, Wuxi 214122, China
Jian Chen
Key Laboratory of Industrial Biotechnology, Ministry of Education, Jiangnan University, Wuxi 214122, China
State Key Laboratory of Food Science and Technology, Jiangnan University, Wuxi 214122, China
DOI 10.1002/btpr.278
Published online August 18, 2009 in Wiley InterScience (www.interscience.wiley.com).
Hyaluronic acid (HA) is a natural biopolymer with unique physiochemical and biological
properties and ?nds a wide range of applications in biomedical and cosmetic ?elds. It is important to increase HA production to meet the increasing HA market demand. This work is
aimed to model and optimize the amino acids addition to enhance HA production of Streptococcus zooepidemicus with radial basis function (RBF) neural network coupling quantumbehaved particle swarm optimization (QPSO) algorithm. In the RBF-QPSO approach, RBF
neural network is used as a bioprocess modeling tool and QPSO algorithm is applied to
conduct the optimization with the established RBF neural network black model as the objective function. The predicted maximum HA yield was 6.92 g/L under the following conditions:
arginine 0.062 g/L, cysteine 0.036 g/L, and lysine 0.043 g/L. The optimal amino acids addition allowed HA yield increased from 5.0 g/L of the control to 6.7 g/L in the validation
experiments. Moreover, the modeling and optimization capacity of the RBF-QPSO approach
was compared with that of response surface methodology (RSM). It was indicated that the
RBF-QPSO approach gave a slightly better modeling and optimization result compared with
RSM. The developed RBF-QPSO approach in this work may be helpful for the modeling and
C 2009
optimization of the other multivariable, nonlinear, time-variant bioprocesses. V
American Institute of Chemical Engineers Biotechnol. Prog., 25: 1819?1825, 2009
Keywords: hyaluronic acid, Streptococcus zooepidemicus, modeling, optimization
Introduction
Hyaluronic acid (HA) is a naturally occurring polymer
comprising unbranched, polyanionic disaccharide units of
D-glucuronic acid and N-acetyl glucosamine linked by
b-(1!3) and b-(1!4) glycosidic bonds.1 With its unique
physicochemical and biological properties such as viscoelastivity, high water-holding capacity, and biocompatibility,2
HA ?nds wide applications in food, biomedical, cosmetic,
and healthcare ?elds.3 Conventionally, HA was extracted
from animal tissues like rooster combs and now is increas-
Correspondence concerning this article should be addressed to G. Du
at [email protected] or J. Chen at [email protected]
C 2009 American Institute of Chemical Engineers
V
ingly produced via microbial cultivation with high puri?cation ef?ciency and low production cost.3 HA from microbial
cultivation will become the predominant source in the biomedical and cosmetic markets, and thus it is important to
improve HA yield or productivity. Currently, most studies
focus on the selection of high yield HA-producing strain and
culture conditions optimization. Kim et al.4 obtained a high
molecular mass HA-producing strain by nitrosoguanidine
treatment and further investigated the in?uence of culture
conditions (pH, temperature, agitation speed, aeration rate,
and impeller type) on the microbial HA production. Zhang
et al.5 enhanced microbial HA production by expressing polyhydroxybutyrate synthesis genes in Streptococcus zooepidemicus, and Krahulec and Krahulcova?6 improved HA yield
via the selection of a b-glucuronidase de?cient strain.
1819
1820
Biotechnol. Prog., 2009, Vol. 25, No. 6
Currently, the commonly used strain for microbial HA production is Streptococcus zooepidemicus, which cannot synthesize some necessary nutrients such as amino acids,7 and
thus it is necessary to supply balanced amino acids to
improve HA yield and productivity.
To achieve a best performance of bioprocesses, various
optimization strategies were developed. The most frequently
used approach is ??one at a time?? strategy.8,9 This approach
is not only time consuming but also ignores the combined
effect of all the factors involved especially in the complicated bioprocesses.10 Some mathematical and statistical
methods such as orthogonal array design and response surface methodology (RSM) have been developed for bioprocess modeling and optimization.11 However, the level of
orthogonal array design is limited and the model of RSM is
only a second-order polynomial, which has a limited simulating ability to the nonlinear bioprocesses.12,13
Radial basis function (RBF) neural network has emerged
as an attractive tool for developing nonlinear empirical
models, especially in situations wherein the development of
conventional empirical models becomes impractical.14 The
ability to approximate functions to any desired degree of
accuracy makes RBF neural network preferable for use as
empirical models to other empirical models.15,16
Inspired by the quantum mechanics, we developed a novel
variant form of particle swarm optimization (PSO) algorithm: quantum-behaved particle swarm optimization
(QPSO) algorithm.17?19 QPSO algorithm is a powerful stochastic search and global optimization technique and has
received a considerable attention. Compared with PSO algorithm, QPSO algorithm is globally convergent and can ?nd
the global optima more ef?ciently and quickly especially for
complex problems.20 In the previous work, we combined
RBF neural network with QPSO algorithm (RBF-QPSO) as
a novel approach for mixing performance modeling and optimization.21 In RBF-QPSO approach, RBF neural network
was used as a bioprocess modeling tool and QPSO algorithm
was applied to conduct the optimization with the established
RBF black model as the objective function.
In this work, the metabolic kinetics of amino acids during
microbial HA production of Streptococcus zooepidemicus
was characterized and the key amino acids for cell growth
and HA synthesis were determined. Then, the RBF-QPSO
approach was applied to model and optimize the key amino
acids addition to improve HA productivity. The results
obtained here may be helpful to improve microbial HA production on an industrial scale.
RSM
RSM combines statistical experimental designs and empirical regression models with a purpose of process optimization. An empirical model (usually a second-order quadratic
polynomial) is used to correlate the response of the process
with some independent variables. The general form of the
second-order quadratic polynomial is
X
b i xi ώ
X
bi x2i ώ
RBF neural network
RBF neural network is structured by embedding RBF with
a two-layer feed-forward neural network. The architecture of
RBF neural network is shown in Figure 1.
Mathematically, RBF neural network can be formulated as
m
X
gπxή Ό
kk uk πjjx ck jjή
(2)
kΌ1
where m is the neuron number of hidden layer, which is
equal to cluster number of training set. kxckk represents
the distance between the data point x and the RBF center ck.
kk is the weight related with RBF center ck. Therefore, the
output of RBF neural networks is a weighted sum of the hidden layer?s activation functions. Here, we adopt the most
commonly used Gaussian RB functions as basis functions
shown in Eq. 3:
Rk πxή
uk πxή Ό P
m
Ri πxή
iΌ1
jjx ck jj2
Rk πxή Ό exp 2r2k
(3)
!
(4)
In Equ. (4), rk indicates the width of the kth Guassian RB
functions. One of the rk selection methods is shown as follows:
r2k Ό
1 X
jjx ck jj2
Mk x2h
(5)
k
where hk is the kth cluster of training set, and Mk is the number of sample data in the kth cluster.
The simulating accuracy of RBF neural network was evaluated by the root-mean square error (d) in Eq. 6:
Model Theory
y Ό b0 ώ
Figure 1. Structure of RBF neural network for process
modeling.
X
bij xi xj ώ e
(1)
where y is the predicted response, xi and xj stand for the independent variables, b0 is the intercept, bi and bj are regression coef?cients, and e is a random error component.
dΌ
v??????????????????????????????
uP
un
u πYi;e Yi;p ή2
tiΌ1
n
(6)
where Yi,e is the experimental data and Yi,p is the corresponding predicted data by the RBF model, and n is the number
of the experimental data.
QPSO algorithm
PSO was originally proposed by Eberhart and Kennedy.22
Compared with the other evolutionary algorithms like
Biotechnol. Prog., 2009, Vol. 25, No. 6
1821
ticles, run the algorithm for 50 iterations and decrease the
value of contraction-expansion coef?cient a of QPSO from
1.0 to 0.5 linearly on the course of the run.
Materials and Methods
Microorganism and media
Figure 2. Schematic representation of QPSO algorithm for
process optimization.
genetic algorithm, PSO algorithm has some attractive properties such as the easy implementation, high computational ef?ciency, and constructive cooperation between individuals.
However, the global convergence cannot be guaranteed
when executing the optimization task by PSO algorithm. In
the previous work,17?19 we developed a novel variant form
of PSO, QPSO algorithm. For QPSO algorithm, the particle
moves according to the following equation:
Xid Ό pid ajCd Xid jlnπ1=uή; u Ό Rand πή
(7)
where Rand () is the uniform random function within [0, 1],
u is another uniformly distributed random number within [0,
1], Pid is the best previous position, and a is a parameter
called contraction-expansion coef?cient, C is the mean of
personal best positions among the particles, that is
M
1X
Pi
M iΌ1
M
1X
Ό
Pi1 ;
M iΌ1
CΌ
M
1X
Pi2 ;
M iΌ1
:::;
M
1X
Pid
M iΌ1
!
(8)
and pid is determined by pid Ό u Pid ώ (1u)Pgd with u
as a random number distributed uniformly within [0, 1]. The
main advantage of QPSO over PSO is that QPSO algorithm
is a global convergent algorithm, while PSO is not as demonstrated by Bergh.23 Figure 2 shows the application procedure of QPSO algorithm, that is,
Step 1: Initialize the population by randomly generating
the position vector Xi (i Ό 1, 2, and 3) of each particle and
set Pi Ό Xi.
Step 2: Evaluate the objective function value of each particle. That is, employ the particle?s position vector as the
input of RBF estimator and obtain the output as the objective function value.
Step 3: Update the personal best (pbest) position of each
particle if the objective function value of the current position
Xi is better than that of the pbest position.
Step 4: Select the global best particle among the all
particles.
Step 5: Calculate the mean best position C according to
Eq. 8.
Step 6: For each dimension of each particle?s current position, execute the position update by Eq. 7.
Step 7: If the stop criterion is not met, return to Step 2; or
else, stop the optimization procedure and output the optimal
solution (the current global best position) and its corresponding objective function value. In this work, we use 30 par-
S. zooepidemicus WSH-24 used in this study was isolated
by our laboratory. Fresh slants were cultured at 37 C for 12
h and were used for inoculation. Slant culture medium consisted of brain heart infusion (Difco, Detroit, MI 482327058) 37 g/L, glucose 1 g/L, yeast extract (Angel Yeast Co.,
Ltd, Hubei, China) 10 g/L, and agar powder 20 g/L. Seed
culture medium consisted of sucrose 20 g/L, yeast extract 20
g/L, MgSO47H2O 2.0 g/L, MnSO44H2O 0.1 g/L, KH2PO4
2.0 g/L, CaCO3 20 g/L, and 1 mL trace elements solution.
The trace element solution consisted of CaCl2 2.0 g/L,
ZnCl2 0.046 g/L, and CuSO45H2O 0.019 g/L. Fermentation
medium contained yeast extract 25 g/L, sucrose 70 g/L,
K2SO4 1.3 g/L, MgSO47H2O 2.0 g/L, Na2HPO412H2O 6.2
g/L, FeSO47H2O 0.005 g/L, and 2.5 mL trace element solution (pH 7.2). Culture medium was sterilized at 121 C for
15 min.
Microbial HA production by batch culture of
S. zooepidemicus
Microbial HA production by batch culture of S. zooepidemicus was conducted with an initial sucrose concentration of
70 g/L. One loop of cells from a fresh slant was transferred
to 50-mL seed culture medium and cultured on a rotary
shaker at 200 rpm and 37 C for 12 h. The seed culture was
inoculated into a 7-L fermentor (Model KL-7L, K3T Ko Bio
Tech, Korea) with a working volume of 4.0 L. The pH was
automatically controlled at 7.0 by adding 5 mol/L NaOH solution. The agitation speed and aeration rate were 200 rpm
and 0.5 vvm, respectively.
Analytical methods
Cell concentration was measured from the optical density
of culture broth at 660 nm with a 722S spectrophotometer.
HA concentration was measured by the carbazole method
based on uronic acid determination.24 The free amino acids
in the culture broth were analyzed according to the procedure as described previously.25
Results and Discussion
Metabolic kinetics of amino acids in batch culture of
S. zooepidemicus
Figure 3 shows the time pro?les of microbial HA production by batch culture of S. zooepidemicus. Cells entered the
exponential phase at 2 h and reached a maximum concentration of 13.2 g/L at 14 h. Sucrose concentration decreased
from 70 g/L at 0 h to 2.6 g/L at 20 h. HA concentration
increased from 0.30 g/L at 0 h to 5.0 g/L at 16 h. Lactic
acid was the main product of batch culture of S. zooepidemicus and increased from 2.0 g/L at 0 h to 55 g/L at 20 h. HA
was produced by S. zooepidemicus at a growth-associated
manner at exponential phase and at a nongrowth-associated
manner at stationary phase. The elongation of the exponential phase would be favorable for enhanced HA production.
The maintenance time of exponential phase may be related
to the metabolism of some key nutrition factors like amino
1822
Biotechnol. Prog., 2009, Vol. 25, No. 6
Figure 3. Time pro?les of cell growth (a), sucrose consumption (b), HA synthesis (c), and lactic acid production (d) during batch culture of S. zooepidemicus.
Table 1. Metabolic Kinetics of Amino Acids During Batch Culture of S. zooepidemicus
Culture Time (h)
Amino acid
Glutamic acid
Histidine
Arginine
Tyrosine
Cystine
Valine
Methionine
Phenylalanine
Leucine
Lysine
Aspartic acid
Serine
Glycine
Threonine
Alanine
Iioleucine
Proline
Tryptotine
0
2
4
6
8
10
12
14
16
18
0.93
0.16
0.02
0.20
0.12
0.37
0.21
0.46
0.78
0.06
0.37
0.38
0.30
0.38
0.82
0.43
0.21
0.12
0.81
0.10
0.017
0.16
0.10
0.29
0.17
0.41
0.71
0.04
0.32
0.32
0.25
0.33
0.78
0.39
0.17
0.09
1.03
0.12
0.01
0.21
0.05
0.35
0.22
0.47
0.76
0.02
0.35
0.37
0.28
0.38
0.83
0.45
0.22
0.13
0.86
0.10
0.003
0.17
0.02
0.28
0.13
0.39
0.70
0.01
0.31
0.31
0.23
0.32
0.77
0.39
0.16
0.08
1.05
0.14
0.001
0.20
0.007
0.36
0.20
0.45
0.75
0.001
0.36
0.39
0.29
0.39
0.85
0.43
0.23
0.15
0.92
0.12
0
0.18
0.001
0.27
0.15
0.36
0.69
0
0.33
0.32
0.25
0.33
0.79
0.37
0.17
0.09
1.07
0.15
0
0.22
0
0.35
0.21
0.45
0.73
0
0.37
0.38
0.31
0.38
0.86
0.42
0.25
0.16
0.85
0.13
0
0.19
0
0.26
0.16
0.38
0.70
0
0.32
0.32
0.26
0.34
0.80
0.38
0.18
0.09
0.98
0.16
0
0.21
0
0.39
0.22
0.43
0.73
0
0.36
0.37
0.30
0.39
0.85
0.43
0.23
0.15
0.82
0.12
0
0.18
0
0.25
0.17
0.39
0.71
0
0.30
0.31
0.24
0.32
0.81
0.37
0.16
0.13
Note: the unit of the amino acid concentration is g/L.
acids, which cannot be synthesized by S. zooepidemicus.
Although the amino acid requirements of S. zooepidemicus
have been characterized with at least 12 (arginine, cystine,
glutamine, histidine, isoleucine, leucine, lysine, methionine,
phenylalanine, tryptophane, tyrosine, and valine) identi?ed
as essential,7 the metabolic kinetics of these amino acids
was not clear.
Table 1 shows the metabolic kinetics of 18 kinds of amino
acids. It was indicated that most amino acids (except arginine, cystine, and lysine) maintained a dynamic balance during the batch culture of S. zooepidemicus. Most lactic acid
bacteria have developed proteolytic systems allowing them
to ef?ciently transport and utilize the peptides contained in
complex nitrogen sources such as yeast extract used in this
study.26 The amino acids including arginine, cystine, and lysine were metabolized quickly and their concentrations
decreased to zero at 10 h, at which the cells entered the stationary phase. It seemed that the end of the exponential
phase followed closely the depletion of the key amino acids
such as arginine, cystine, and lysine. If the exponential phase
could be extended via the addition of three key amino acids,
then the improvement in HA yield could be achieved as HA
was produced by S. zooepidemicus as a growth-associated
manner at exponential phase.
Figure 4 shows the in?uences of three key amino acids
(arginine, cystine, and lysine) addition on HA yield. There
existed an optimal concentration for three key amino acids
in terms of HA yield, and the addition of arginine (0.05 g/
L), cystine (0.03 g/L), and lysine (0.04 g/L) increased HA
yield by 25%, 18%, and 21%, respectively. As expected, the
addition of three key amino acids extended the exponential
phase and achieved the enhancement of HA yield. However,
Biotechnol. Prog., 2009, Vol. 25, No. 6
1823
Figure 4. In?uence of arginine (a), cystine (b), and lysine (c) addition on HA synthesis.
Table 2. Independent Variables and Experimental Design Levels for Response Surface
Levels
Independent Variables
Coded Symbols
1.682
1
0
1
1.682
X1
X2
X3
0.03
0.02
0.01
0.04
0.03
0.02
0.05
0.04
0.03
0.06
0.05
0.04
0.07
0.06
0.05
Arg concentration (g/L)
Cys concentration (g/L)
Lys concentration (g/L)
Table 3. Experimental and Predicted HA Yield for Constructing RSM and RBF Model
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Arg
(g/L)
Cys
(g/L)
Lys
(g/L)
1
0
1
1
0
1
1.682
0
0
0
1
1
1.682
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1.682
1.682
1
0
1
1
1.682
1
0
0
0
0
1
1
0
1
1
0
0
1.682
0
0
Experimental HA
Yield (g/L)
Predicted Yield
by RSM (g/L)
Predicted Yield
by RBF (g/L)
5.89
6.32
5.73
5.53
5.79
5.71
5.82
6.32
6.32
6.32
5.60
5.72
5.98
6.15
5.83
6.32
6.32
6.12
5.78
5.96
5.92
6.53
5.99
5.68
6.13
5.58
6.02
6.52
6.55
6.51
5.63
5.95
6.32
6.06
5.99
5.53
5.53
5.91
5.97
6.08
5.93
6.52
5.99
5.67
6.13
5.57
6.01
6.53
6.55
6.51
5.64
5.95
6.33
6.07
5.98
6.53
6.52
5.90
5.97
6.08
0.02
0.02
0.03
0.01
0.01
0.02
0.02
0.03
0.02
0.03
0.01
0.02
0.01
0.01
0.01
0.01
0.01
0.03
0.01
0.02
Table 4. The Optimization Results of QPSO Algorithm in Accordance with the Different Spread Parameters of RBF Neural Network
Spread
X1
X2
X3
Y
0.5
0.6
0.7
0.8
0.9
1.0
1.01
0.056
0.032
0.035
6.72
0.058
0.035
0.037
6.75
0.059
0.038
0.036
6.78
0.060
0.039
0.045
6.80
0.061
0.037
0.040
6.83
0.062
0.038
0.042
6.89
0.062
0.036
0.043
6.92
the interactive effects of three amino acids addition were not
considered and it was necessary to further optimize the key
amino acids addition to improve HA yield
Modeling and optimization of amino acids addition
by RBF-QPSO approach
In this work, the Box-Behnken design (Tables 2 and 3)
was used to obtain data for the construction of RBF model.
If Box-Behnken design was not used, one can conduct 15 to
30 runs of experiments under different conditions and thus
obtain 15 to 30 groups of data for RBF training. The constructed black-box model of RBF was not expressed by an
explicit mathematical model, and Table 3 shows the estima-
tion of the established RBF black-box model to the experiment data. The root-mean square error d of RBF model was
0.023, and the determination coef?cient R2 was 0.998, indicating that 99.8% of the variability in the response could be
explained by the established RBF model.
With the RBF black-box model as the objective function,
QPSO algorithm was applied to execute the optimization
task. Table 4 shows the optimization results of QPSO algorithm in accordance with the different spread parameters of
RBF neural network. With a spread parameter of 1.01, HA
yield reached a maximum predicted value of 6.92 g/L when
arginine, cystine, and lysine concentration were 0.062 g/L,
0.036 g/L and 0.043 g/L, respectively. Three repeated validation experiments under the optimal conditions were
1824
Biotechnol. Prog., 2009, Vol. 25, No. 6
performed, and a maximum HA yield of 6.70 g/L was
obtained, verifying the effectiveness of the proposed RBFQPSO approach for bioprocess optimization.
Comparison of modeling and optimization capacities
of RBF-QPSO approach with RSM model
The modeling and optimization capacities of RBF-QPSO
approach were compared with those of RSM. By applying
multiple regression analysis on the experimental data, the
second-order quadratic polynomial model was constructed as
shown in Equ. (9):
Y Ό 5:8329 ώ 0:0526X1 ώ 0:0926X2 ώ 0:0127X3
0:1667X12 0:2179X22 0:2213X32 ώ 0:0375X1 X2
ώ 0:0425X1 X3 0:025X2 X3
π9ή
where Y was HA yield, X1 was arginine concentration, X2
was cystine concentration, and X3 was lyscine concentration.
Table 3 shows the modeling results of RSM model in terms
of the predicted HA yield. The root-mean square error d of
RSM model was 0.125, and the determination coef?cient R2
was 0.978, indicating that 97.8 % of the variability in the
response could be explained by the established RSM model.
From the equations derived from the differentiation of Eq. 9,
the optimal values of X1, X2, and X3 in the coded units were
0.3, 0.1, and 1.477, respectively. Accordingly, the optimal
concentration of three amino acids was arginine 0.053 g/L,
cystine 0.039 g/L, and lysine 0.047 g/L. The predicted maximum HA yield was 6.53 g/L under the optimal conditions
obtained by RSM model. Three repeated validation experiments under optimal conditions (arginine 0.053 g/L, cystine
0.039 g/L, and lysine 0.047 g/L) were conducted, and a maximum HA yield of 6.42 g/L was obtained.
The performance of RBF black-box model was compared
with RSM model. The root-mean square error d between the
measured and predicted output by any of RSM and RBF
model was employed as a means of comparison. The d by
RBF in terms of HA yield was 0.023, whereas the d by
RSM in terms of HA yield was 0.125. It was indicated that
both models provided similar quality predictions for the
above three independent variables in terms of HA yield, but
RBF model gave a slightly better ?t to the measured data
compared with RSM model, possibly due to the fact that the
RSM model is only a second-order polynomial, which has
the limited simulating ability to the nonlinear bioprocesses.16
Conclusion
This work applied RBF-QPSO approach to model and
optimize the amino acids addition for enhanced HA productivity. The predicted maximum HA yield by RBF-QPSO
approach was 6.92 g/L, and a maximum HA yield of 6.70 g/
L was achieved in the validation experiments, enhanced by
34% compared with the control without amino acids addition. It was indicated that RBF-QPSO approach gave a
slightly better modeling and optimization result compared
with RSM model. The results obtained here may be helpful
for the enhancement of microbial HA production on an
industrial scale.
Acknowledgments
This project was ?nancially supported by Program for
Changjiang Scholars and Innovative Research Team in University (No.IRT0532), the National Science Fund for Distinguished Young Scholars of China (No.20625619), Program for
Cultivation and Innovation of Graduate Students in Jiangsu
Province (CX08B_128Z), and 973 Project (2007CB714306).
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