Mathematical modeling of continuous enzyme extraction by aqueous twophase system
*D. Maretić, +S. Bogdan, *Đ. Vasić-Rački, *B. Zelić
*D. Maretić, Đ. Vasić-Rački, B. Zelić
University of Zagreb, Faculty of Chemical Engineering and Technology, Marulićev trg 19,
HR-10000 Zagreb, Croatia, Phone: +385 1 4597 146, Fax: +385 1 4597 133, E-mail address:
bzelic@fkit.hr,
+
S. Bogdan
Pliva d.d., Research and Development, Prilaz baruna Filipovića 25, HR-10000 Zagreb,
Craotia
Abstract
The aqueous two-phase system consisting of PEG-6000 and ammonium sulfate was
used for extraction of BS Albumine (BSA) model solution. Influence of the mass fraction of
PEG-6000, the mass fraction of ammonium sulfate, pH and concentration of BSA was
investigated in the batch experiments by use of genetic algorithm to optimize the partition
coefficient of BSA. The mass fraction of PEG-6000 of 0.1138, the mass fraction of
ammonium sulfate of 0.0970, pH of 5.5 and BSA concentration of 1.5 g L-1 are estimated to
be the best working conditions. After performing twenty experiments the partition coefficient
of K = 0.0874 was determined.
The continuous separation of BSA was carried out in the mixer-settler at previously
optimized process conditions for serious of different flow rates of feeding medium.
Mathematical model of the continuous separation process in the mixer-settler was developed,
and the model adequacy was verified by comparing experimental and computed concentration
of BSA in the extract phase and in the rafinate phase of the aqueous two-phase system.
Keywords: aqueous two-phase system, continuous extraction, mathematical model, BS
Albumine
1 Introduction
Aqueous two-phase systems (ATPS) are formed by mixing two or more polymers or a
structuring salt and a polymer with water. Usually polyethylene glycol (PEG) and ammonium
sulfate (AMS) (or system PEG-dextran) are required. ATPS are commonly used for the
separation of enzymes from cells or cell debris and also for the separation of enzyme from
each other 1.
Despite the fact that ATPS have a great potential for the extraction of different
bioproducts 2 - 14, it is especially suited for the large scale isolation of proteins when large
volumes have to be processes. The aqueous environment constitutes mild conditions for
biological material due to the high water contents and the low surface tension between the
phases, so that denaturation which often occurs in organic solvents hardly takes place 15.
Furthermore, proteins can be isolated on large-scale using commercially available equipment,
with relatively low-cost chemicals, and time consumption is lower compared to the
conventional separation methods such as batch centrifugation and ion exchange
chromatography 16.
The general properties of ATPS have been studied by several researchers 17, 18.
However, the mechanism governing the partition of biological materials is still not well
understood. The observed partition coefficient is a result of van der Waals, hydrophobic,
hydrogen bond, and ionic interactions of the bio-molecules with the surrounding phase. ATPS
separate biopolymers according to their size, charge, and surface characteristics. Therefore,
the partition coefficient can be influenced by the number of phase system parameters such as
the concentrations and molecular weights of the phase-forming compounds, type and
concentration of salting-in ions, temperature and pH of the system, etc 19. The effect of
these parameters must be studied in order to develop empirically suitable extraction
conditions.
In this work the aqueous two phase system, consisting of PEG-6000 and ammonium
sulfate, was used to investigate the behavior of batch and continuous system for extraction of
BS Albumin model solution. The batch experiments were used to examine the effects of pH,
concentration of PEG-6000, concentration of ammonium sulfate and the concentration of
protein model solution on partitioning in aqueous two phase system. The partition coefficient
was optimized using the genetic algorithm.
Genetic algorithm (GA) is a stochastic optimization method based on the principals of
evolution. It is quite commonly used for experimental optimization, but is also used for
1
parameter estimation of the nonlinear systems 20. It can also be used for optimization of
initial conditions when mathematical model of the process is available. In comparison to other
methods, GA considerably decreases the number of experiments 21. GA was proved to be a
reliable method for the optimization of process conditions for protein extraction in the PEGsalt system 2, 22. Since GA is not based on any assumption it can easily cope with
irregularities of the aqueous two-phase system. It is neither harmed by very small values nor
is it limited at the maximum. In comparison to other optimization methods (e.g. steepest
ascent, simplex), GA does not need to be further adopted or limited just for beginning of the
optimization process.
The continuous separation of BSA model solution in aqueous two-phase system was
carried out in the mixer-settler at process conditions previously optimized in batch
experiments. Serious of different flow rates of feeding and outgoing streams were applied in
order to investigate process behavior in the continuous system. Considering the kinetic of
phase separation and the design of the mixer-settler the mathematical model of continuous
separation process was developed and applied to describe the continuous separation of BSA
model solution in the mixer-settler. The model was verified comparing the computed and
experimental data. Success of the extraction process of BSA was characterized through the
efficiency of used mixer-settler.
2 Mathematical Model of the Continuous Aqueous Two-phase Extraction
In order to describe continuous extraction process, a mathematical model based on the
flow of process streams, mass transfer, phase chemical concentrations and protein
concentrations was formulated. It describes the time dependency of concentration of PEG6000 (PEG), ammonium sulfate (AMS) and BSA model solution in the mixer (mix)
(Equations 1-4) and in the settler section (Equations 5-12) respectively. Furthermore, model is
extended for each phase in the settler section, namely for the rafinate (R) phase (Equations 6,
8, 10 and 12) and the extract (E) phase (Equations 5, 7, 9 and 11). The following constraints
were formulated and used:
-
mixture is ideally mixed in the mixer section;
-
each phase, namely, the rafinate and the extract phase of the settler section are
individually and ideally mixed.
The following system of balance equations may be derived for the process:
2
a) Settler section:
d mmix
 q0  q1
dt
mix
d  mmix  wPEG

dt
mix
d  mmix  wAMS

dt
mix
d  mmix  wBSA

dt
(1)
mix
 wPEG,0  q0  wPEG
 q1
(2)
mix
 wAMS,0  q0  wAMS
 q1
(3)
mix
 wBSA,0  q0  wBSA
 q1
(4)
b) Mixer section
*
d mE
 q2  k1   mE  mE  t  


dt
(5)
*
d mR
 q1  q3  k1   mE  mE  t  


dt
(6)
E
d  mE  wPEG

dt
R
d  mR  wPEG

dt
E
d  mE  wAMS

dt
R
d  mR  wAMS

dt
E
d  mE  wBSA

dt
R
d  mR  wBSA

dt
E
E
E
  wPEG
 q2  k1   mE  wPEG
 mE  t   wPEG
 t 

(7)
mix
R
E
E
 wPEG
 q1  wPEG
 q3  k1  m E  wPEG
 mE  t   wPEG
 t 

(8)
E
R
R
  wAMS
 q2  k2   mR  wAMS
 mR  t   wAMS
 t 

(9)
mix
R
R
R
 wAMS
 q1  wAMS
 q3  k2   mR  wAMS
 mR  t   wAMS
 t 

(10)
E
R
R
  wBSA
 q2  k3   mR  wBSA
 mR  t   wBSA
 t 

(11)
mix
R
R
R
 wBSA
 q1  wBSA
 q3  k3  mR  wBSA
 mR  t   wBSA
t 

(12)
*
*
*
*
*
*
*
*
*
*
*
*
where m is mass, w is mass fraction, q0 is mass flow rate of the stream feeding the mixer
section, q1 is mass flow rate of the stream feeding the settler section, q2 is mass flow rate of
the stream draining the extract phase, q3 is mass flow rate of the stream draining the rafinate
phase, k1, k2 and k3 are the phase equilibrium constant rates for PEG, AMS, and BSA
respectively, and t is time. m* and w* indicate equilibrium mass and equilibrium mass
fraction, respectively.
3
3 Materials and Methods
3.1 Materials
PEG-6000 with an average molecular weight of 6000, ammonium sulfate, and Bovine
Serum Albumine (BSA) were obtained from ''Merck''. Two-phase systems were prepared
from the stock solutions of PEG-6000, ammonium sulfate, BSA, mono- and dibasicpotassium phosphate and deionized water. Concentration of stock solutions of PEG-6000 and
ammonium sulfate were 40 % (w/w). The concentration of NaCl of 0.9 % (w/w) was used to
prepare stock solution of BSA with an accurately known concentration of 10 g/dm3. Different
stock solutions of K2HPO4 and KH2PO4 were used to prepare the aqueous two-phase system
at different pHs 23.
3.2 Aqueous Two-phase Extraction - Batch System
Aqueous two phase partitioning experiments were performed at 20 °C by mixing the
determined volume of the phase forming polymer solution with solutions of salt and BSA in
the graduate cylinder. The buffer solution was then added to obtain the final volume of 5 cm3.
The system was mixed by vortexing and then left overnight for separation of phases. After 24
hours samples were carefully withdrawn from the top (extract) phase and from the bottom
(rafinate) phase and analyzed for BSA concentration. Each experiment was done in triplicate.
Partition coefficient, K, was calculated as a ratio between equilibrium concentrations of BSA
in the extract and in the rafinate phase.
3.3 Aqueous Two-phase Extraction - Continuous System
The continuous separation of BSA was performed in the mixer-settler shown in Figure
1 at process conditions previously optimized in the batch system. Mixer-settler consisted of
two sections, cylinder form mixer section with capacity of 103 cm3 (1), and cone shaped
edges settler section with capacity of 261 cm3 (2). A settler section was divided in two
compartments: bottom phase compartment (2a) (rafinate) and top phase compartment (2b)
(extract). The mixer and the settler sections were placed inside the thermostated cylinder
vessel (3).
Stock solutions of PEG-6000, ammonium sulfate, BSA and buffer pH 5.5 were fed
into the mixer section of the mixer-settler and mixed. When the mixture approached the edge
of the mixer section, it overflowed into the settler section where the phases separate. When
mixture approached flooding limit two pumps for draining the rafinate and the extract phase
where turned on and set at a desired constant value. During the separation process the samples
4
from the rafinate and the extract phase were taken in predetermined time schedule and
analyzed for concentration of BSA and in the steady-state for concentrations of PEG-6000
and ammonium sulfate. Additionally, flow rate of each process stream was controlled. The
continuous separation was carried out at 20 C for serious of different flow rates of feeding
and outlet streams ranging from 10 cm3/min to 50 cm3/min.
q3
q0
Rafinate
q2
2b
Extract
2
2a
1
3
Buffer
BSA
pH = 5.5 c = 1.5 g dm-3
Figure 1
PEG-6000
40% w/w
(NH4)2SO4
40 % w/w
Schematic diagram of the experimental set-up used for continuous aqueous
two-phase extraction of BSA model solution. 1 – mixer section; 2 – settler
section; 2a – rafinate compartment; 2b – extract compartment; 3 – thermostated
cylinder vessel; q0 - stream feeding the mixer section; q2 - stream draining the
extract phase; q3 – stream draining the rafinate phase
3.4 Analysis
In addition to the BSA concentration determination, the absorbance of each sample
was measured using the spectrophotometer (Lamda EZ 210, Perkin Elmer) at 280 nm.
The contents of phase forming components (PEG and AMS) were quantified
simultaneously using a HPLC system with a Maxi Star K-1001 pump, a K1501 LPG Solvent
organizer (Knauer, Germany), a HPLC Control Box (Knauer, Germany), a Midas autosampler
(Spark, Netherlands) and ELSD 2000 detector (Alltech, USA). Data were acquired and
processed by Eurochrom software (Knauer). The chromatographic separation was carried out
5
at 40 C on a Symmetry Shield RP18 column (5 m particle size, 250 x 4.6 mm I.D.)
protected by a guard column (20 x 4.6 mm I.D. Symmetry C18, Waters, USA). Sample
injection volume was 50 l and mobile phase flow-rate was set to 1 ml/min. Mobile phase A
was constituted by Methanol (Merck, Germany) and mobile phase B by ultra pure water
(Millipore, USA). The gradient program employed is shown in Table 1.
Table 1
Gradient used for the elution of AMS and PEG
Percentage solvent
Time [min]
A
B
0
45
55
30
70
30
40
45
55
Calibration curves for AMS and PEG were plotted using concentration data of
solutions of pure compound, ranging from 75 – 200 g/mL for AMS and 2 – 8 mg/mL for
PEG prepared in ultra pure water. Experimental data were fitted by linear regression analysis
(R2 = 0.9997 for AMS and R2 = 0.9986 for PEG).
3.5 Data Handling
The model equations were solved numerically by the fourth order Runge-Kutta
algorithm, which is offered in the "Scientist" [24] software. The software GALOP (Genetic
Algorithm for the Optimization of Processes) Version 1.24 developed at the Institute of
Biotechnology, Research Centre Jülich, Germany, was used for experimental optimization of
aqueous two-phase system. Originally it was written for the optimization of fermentation
procedures [21]. The principle of experimental optimization using genetic algorithm was as
follows: GA offers the first random population of 4 individuals with given characteristics.
Experiments were performed under process conditions given by GA. After the equilibrium
has been reached, equilibrium concentrations of BSA in the rafinate and in the extract phase
were measured and partition coefficient calculated. These experimentally obtained values of
6
partition coefficients were written in GA as return information, which GA used for further
adjustments of next generation.
4 Results and Discussions
4.1 Experimental Optimization of Aqueous-two Phase Extraction in the Batch System
Phase diagram and thermodynamic parameters of aqueous two-phase system
consisting of PEG-6000 and ammonium sulfate were determined previously and published
elsewhere 4, 5. It was assumed that the presence of different concentrations of BSA and pH
used in the experimental optimization do not have any influence on thermodynamic
equilibrium of system.
To reduce the number of parameters mass fraction of PEG-6000 and ammonium
sulfate were replaced with the tie-line length (TLL) 3, 22, 25. The tie-line relates to the mass
ration between the phases. If two-points of bi-nodal curve, the top and the bottom phase
composition, for a particular mixture composition are known distance between them is the tieline length and may be calculated using equation 13.
TLL 
w
E*
AMS
R
 wAMS
*
  w
2
E*
PEG
R
 wPEG
*

2
(13)
The total mixture composition (wPEG, wAMS) was always prepared at the critical point (or plait
point, PP) of bi-nodal curve at which volumes of the extract (VE) and the rafinate phase (VR)
theoretically become equal (Figure 2).
List of parameters used in the optimization of partitioning using GA, namely, tie-line
length, pH and BSA concentration, investigated area of parameters and optimization steps are
shown in Table 2. Accumulation of BSA in the rafinate phase was observed in previous
experiments 22 which was reason to set weighting factor of target function K to “-1”. Target
function was written as linear combination of investigated parameters. Mutation occurrence in
a program was set to 0.01, the crossover occurrence was set to 0.95 and the number of
individuals in a generation was 4.
7
wPEG [-]
E (wAMS*, wPEG*)
PP (wAMS, wPEG)
R (wAMS*, wPEG*)
wAMS [-]
Figure 2
Phase diagram for aqueous two-phase system consisting of PEG-6000,
ammonium sulfate and water. Concentrations above the bi-nodal curve ()
result in phase separation, below the curve the mixtures are homogeneous. The
tie-line () relates to the mass ratio between the phases. Thus, the
expression can be rewritten as mE/mR = E-PP/R-PP, where E-PP and R-PP are
the distances between indicated points on the tie-line. In practice, the mass
ratio is considered equal to the volume ratio, VE/VR.
Table 2
Start values of investigated parameters, investigated area of parameters
(defined by lower and upper border) and step of the optimization for
experimental optimization of aqueous two-phase extraction in the batch system
parameter
unit
step
lower border
upper border
TLL
cm
1
1
51
pH
-
0.5
5.5
7.5
cBSA
g/dm3
0.5
1.0
2.5
8
The primary factor affecting the substrate utilization rate in the natural system is pH.
The internal environment of the living cells is believed to be approximately neutral and most
of the organism cannot tolerate pH bellow 4 or above 9. It was the reason to restrict
investigates pHs in area of 5.5 – 7.5 even in this model system. The same is for relatively low
upper border of BSA concentration (2.5 g/dm3) while low intracellular concentrations of
enzyme are known problem in they separation.
Experimental optimization of process parameters was carried out through 5
generations. Normalized values of investigated parameters in the first and in the fifth
generation are shown in the Figure 3. Average value of K of a certain generation is shown in
Figure 4.
a)
b)
1.0
TLL [-], pH [-], cBSA [-]
TLL [-], pH [-], cBSA [-]
1.0
0.8
0.6
0.4
0.2
0.0
0.8
0.6
0.4
0.2
0.0
1
2
3
4
1
Individual
Figure 3
2
3
4
Individual
a) Normalized values of the optimized parameters for the first generation; b)
Normalized values of the optimized parameters for the fifth generation.
normalized tie-line lenght,
normalized pH,
normalized concentration
of BSA.
It can be noticed that complete uniformity of all parameters did not occur.
Experiments 1, 2 and 3 in the fifth generation are the best performing of these four and show
striking homology in process conditions. Namely, in the fifth generation TLL differed in one
individual. From the first to the fourth generation a constant and a huge improvement of K is
found. Only minor improvements were found going further on to generations four and five.
Data of Figure 3 show that low pH (normalized value of pH under the best process
conditions is equal to 0 which matches an absolute value of pH of 5.5) has a strong positive
influence on the partition coefficient reached. Furthermore, small tie-line length has a strong
positive effect on K. Since a large improvement in the partitioning was not achieved between
9
fourth and fifth generation and process conditions given by GA in fifth generation were quite
homolog, the optimization was stopped after fifth generation.
0.30
0.25
K [-]
0.20
0.15
0.10
0.05
0.00
Generation 1 Generation 2 Generation 3 Generation 4 Generation 5
Figure 4
Changes in the average value of partition coefficient through generations.
Under optimal process conditions, namely, tie-line length of 18 cm (representing the
mass fraction of PEG-6000 of 0.1138 and the mass fraction of ammonium sulfate of 0.0970),
pH of 5.5 and BSA concentration of 1.5 g/dm3, the optimal partition coefficient of K = 0.0874
was achieved.
4.2 Mathematical Model of Aqueous-two Phase Extraction in the Continuous System
The continuous separation of BSA enzyme was carried out in the mixer-settler (Figure
1) at previously optimized process conditions for serious of different flow rates of feeding
medium. Developed mathematical model based on the flow of process streams, mass transfer,
phase chemical concentrations and protein concentrations was simulated and results of the
simulation were compared with the experiments. The calculated values obtained by
simulation compared to the experimental data points, for protein concentration in the settler
section for retention time of 10 minutes, are shown in the Figure 5. As it can be seen, model is
able to mirror the dynamic behavior of the process.
Furthermore, partition coefficient calculated from the simulated data points in the
steady-state of continuous experiment (K = 0.0914) was practically equal to partition
coefficient measured in the batch experiment (K = 0.0874) for the same process conditions
(tie-line length, pH and protein concentration). It can be stated that easy-to-use and robust
model has successfully been developed which can be used for typical process engineering
applications such as process optimization and design. Of course, developed model should be
extended with thermodynamics terms to give them the real mechanistic background.
10
2.5
-3
cBSA [g dm ]
2.0
1.5
1.0
0.5
0.0
0
10
20
30
40
50
60
70
t [min]
Figure 5
Comparison of the calculated values obtained by the simulation (rafinate phase
- ; extract phase - ------) and the experimental data points (rafinate phase ■; extract phase - ○), for protein concentration in the settler section for
retention time of 10 minutes (cBSA = 1.5 g/dm3, pH = 5.5, TLL = 18 cm)
5 Conclusion
GA is a simple program that makes optimization of highly complex systems possible,
i.e. systems with high parameter number. Furthermore, GA allows relatively fast, extensive
and effective optimization of process conditions. For experimental optimization of aqueous
two-phase system containing PEG-6000 and ammonium sulfate, the maximal partition
coefficient of K = 0.0874 was achieved at the tie-line length of 18 cm (representing the mass
fraction of PEG-6000 of 0.1138 and the mass fraction of ammonium sulfate of 0.0970), pH of
5.5 and BSA concentration of 1.5 g/dm3. Comparing the full experimental plan, which would
take 1530 experiments, process optimum using GA was achieved only in twenty experiments.
The developed model for the continuous extraction of the BSA model solution in the
mixer-settler should be qualified as a promising tool for modeling studies as well as for
further, more detailed thermodynamic modeling approaches.
Acknowledgments
This work was partially funded by the Croatian Ministry of Science and Technology,
contract grant number 0125 021.
11
Symbols used
k
- phase equilibrium constant rate, min-1
K
- partition coefficient, -
m
- mass, kg
m*
- equilibrium mass, kg
q
- mass flow rate, kg min-1
t
- time, min
TLL
- tie-line length, cm
V
- volume, m3
w
- mass fraction, -
w*
- equilibrium mass fraction, -
Abbreviations
AMS - ammonium sulfate
ATPS - aqueous two-phase system
BSA
- Bovine Serum Albumine
E
- extract
mix
- mixer section
PEG
- polyethylene glycol
PP
- plain point
R
- rafinate
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