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Solid–liquid extraction of phycocyanin from Spirulina platensis: Kinetic

modeling of influential factors

Chia-Hung Su a,⇑, Chang-Sung Liu a, Pei-Cheng Yang a, Kun-Siang Syu a, Chuang-Chun Chiuh b

a Graduate School of Biochemical Engineering, Ming-Chi University of Technology, Taipei 24301, Taiwanb Far East Bio-Tec. Co., Ltd., Taipei 11503, Taiwan

a r t i c l e i n f o

Article history:

Received 3 July 2013

Received in revised form 10 December 2013

Accepted 21 December 2013

Available online 3 January 2014

Keywords:

Phycocyanin

Spirulina platensis

Solid–liquid extraction

Kinetics

Modeling

a b s t r a c t

To effectively extract value-added phycocyanin from Spirulina platensis, the effects of processing param-

eters (pH and temperature) on extraction performance and global kinetics were systematically studied.

The extraction kinetics was investigated by varying pH levels (5–8) and temperatures (30–60 C). An

empirical kinetic model incorporating the aforementioned factors was developed. A good agreement

between the experimental and fitted data was obtained, which indicated that the extraction process fol-

lowed second-order kinetics. Furthermore, the model parameters (equilibrium concentration, extraction

rate constants, and initial rates of extraction) were calculated and formulated as a function of the oper-

ating factors. The activation energy of the extraction was 67.1 kJ mol1, indicating that the process was

endothermic. The predictions obtained from the developed model were compared with the experimental

data under the same operating conditions. The predicted and experimental data were consistent, indicat-

ing the reliability of the model.

2014 Elsevier B.V. All rights reserved.

1. Introduction

Cultivation of S pirulina microalga is an effective process for

obtaining several valuable biochemicals, such as polysaccharides

[1],c-linolenicacid [2], b-carotene [3], chlorophyll a [4], and phyco-biliproteins [5]. Phycobiliproteins, which are brightly colored pig-

ments, function as a receiver of light for driving photosynthesis in

the S pirulina microalga [6]. Microalgal phycobiliproteins are classi-

fied into three major groups: phycoerythrin, allophycocyanin, and

phycocyanin [6]. The predominant pigment in the phycobiliprotein

family is phycocyanin [7]. Phycocyanin is commonly used as a nat-

ural colorant in food and cosmetic industries because it is inher-

ently blue [6]. Moreover, it can be incorporated into health foods

because of its physiological properties, such as antioxidant, anti-

inflammatory, and hepatoprotective activities [8,9]. Because of these benefits, numerous researchers have focused on developing

efficient processes for mass production of phycocyanin-producing

strains [10,11] and extraction of phycocyanin from microalgae

[5,12].

Isolating phycocyanin from microalgae typically begins with

solid–liquid extraction using aqueous solvents [5]. In general,

solvent type, extraction temperature, and solid–liquid ratio are

influential factors in the extraction process [5,7]. The response

surface methodology has beenused to optimize these operating fac-

tors for phycocyanin extraction [5]; however, this empiricalapproach does not account for the mechanism governing the

process [13]. Developing a kinetic model couplingthe operating fac-

torson phycocyaninextractionis a solutionthat is crucialfor design-

ing an efficientphycocyaninextraction process. However, a relevant

kinetic model of phycocyanin extraction has not been developed.

In this study, Spirulina platensis was used as a source for phyco-

cyanin. The effects of the operating factors (solvent pH and extrac-

tion temperature) on the aqueous solid–liquid extraction of

phycocyanin from S. platensis were examined. Because a second-

order kinetic model effectively depicts solid–liquid extraction

processes [13–16], the kinetic model was used to determine corre-

sponding kinetic parameters and predict the extraction process.

Finally, the predicted phycocyanin concentrations were verified

using actual experiments under the same conditions. This study isrequired before developing and performing a systematic process

for phycocyanin extraction from S. platensis.

2. Materials and methods

2.1. Extraction procedure

The lyophilized S. platensis was provided by Far East Bio-Tec Co.,

Ltd. (Taipei, Taiwan). The dried microalgae were ground to reduce

the average particle size to less than 25 lm before examining theextraction process. The extraction was conducted by mixing 2.5 g

of the ground biomass with 50 mL of sodium phosphate buffer

1383-5866/$ - see front matter 2014 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.seppur.2013.12.026

⇑ Corresponding author. Tel.: +886 2 29089899x4665; fax: +886 2 29083072.

E-mail address: [email protected] (C.-H. Su).

Separation and Purification Technology 123 (2014) 64–68

Contents lists available at ScienceDirect

Separation and Purification Technology

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solution (10 mM, pH 7.0) in a 125-mL stoppered conical flask

equipped with a magnetic stirrer. The pH level of the buffer solu-

tion was adjusted by mixing 10 mM KH2PO4 (pH 4.67) and

10 mM K2HPO4 (pH 8.99) stock solutions. The various pH levels

(5–8) and extraction temperatures (30–60 C) were examined in

this experiment. The phycocyanin in the liquid extract was ana-

lyzed using the method described in Section 2.3.

2.2. Kinetic model

The second-order rate law provides a satisfactory representa-

tion of the solid–liquid extraction process [13–17]. Therefore, this

mathematic model was used to depict the kinetics of phycocyanin

extraction from S. platensis. The general second-order kinetic mod-

el can be expressed as

dC t dt ¼ kðC e C t Þ

2; ð1Þ

where dC t dt

represents the extraction rate (g L 1 min1), k is the

extraction rate constant (L g1 min1), C e is the equilibrium concen-

tration of phycocyanin (g L 1) in the extract, and C t is the concentra-

tion of phycocyanin (g L 1) in the suspension at a specific extraction

time t . The initial extraction rate defined as h when t and C t approach 0 can be expressed as

h ¼ kC 2e ; ð2Þ

To obtain the kinetic parameters (k and C e), Eq. (1) was integrated

under the initial and boundary conditions, t = 0 to t and C t = 0 to

C t , as the following equation:

C t ¼ C

2ekt

1þ C ekt ; ð3Þ

The linear form derived from Eq. (3) is shown as Eq. (4).

t

C t ¼ 1

kC 2

e

þ t

C e; ð4Þ

Thus, k and C e can be determined experimentally from the slope and

intercept of a linear line by plotting t /C t against t . After rearranging

Eqs. (2) and (3), C t can be expressed as

C t ¼ t

ð1=hÞ þ ðt =C eÞ; ð5Þ

The Arrhenius equation was used to evaluate the effect of extraction

temperature on the kinetic model, which is written as

k ¼ k0eE aRT ; ð6Þ

where k0 is the pre-exponential factor for extraction rate constant

(L g1 min1), E a represents the activation energy of extraction

(J mol1), R is the ideal gas constant (J mol1 K1), and T is the

extraction temperature (K). The pre-exponential factor, k0, and the

activation energy, E a, can be determined using the natural logarithm

of Eq. (6).

2.3. Analysis

The phycocyanin concentration during the extraction process

was determined according to the procedure used by Chen et al.

[4]. The sample withdrawn from the extraction broth was centri-

fuged and the optical density of the supernatant was determined

spectrophotometrically at 615 and 652 nm using an Ultrospec

3100 pro spectrophotometer (GE Healthcare Bio-Sciences Corp.,

USA). The phycocyanin concentration was estimated using Eq. (7)

[18].

PC ¼OD

615 0:474 OD

6525:34 ; ð7Þ

where PC is the phycocyanin concentration (g L 1), and OD615 and

OD652 are the optical density of the sample at 615 and 652 nm,

respectively.

2.4. Validity of model prediction

The consistency between the predicted and experimental data

was evaluated using the coefficient of determination (r 2), which

is defined as

r 2 ¼ 1

Pni¼1ð yi ^ yiÞ

2

Pni¼1ð yi yÞ

2 ; ð8Þ

where n is the number of samples, yi is the actual experimental data

of the ith sample, ^ yi is the model-fitting data of the ith sample, and y

is the mean value of all experimental data. The coefficient r 2 is nor-

malized between 0 and 1, with a high r 2 value indicating superior

consistency between the experimental data and model fitting.

2.5. Statistical analysis

The data were analyzed by conducting a one-way analysis of

variance (ANOVA) or Fisher’s F -test using Microcal Origin 6.0(Microcal Software, Inc., MA, USA) software. Statistical differences

were established according to a probability threshold (P ) of 0.05.

3. Results and discussion

3.1. Effect of pH

The effect of pH on solid–liquid extraction is crucial because the

solubility of bio-compounds and apparent kinetic constants are

directly dependent on the pH variation [13,19]. The extraction

was performed with pH ranging from 5 to 8 at a temperature of

50 C. The pH range of 5–8 was selected because phycocyanin is

unstable below pH 5 and above pH 8 [7]. The results (Fig. 1) show

that a higher pH increased the extraction rate and equilibrium con-centration. However, a substantial decrease in the equilibrium con-

centration occurred at pH 8. Protein denaturation may contribute

to this result [7]. Because the maximal equilibrium concentration

was obtained at pH 7, further experiments were performed at this

level to examine other operating conditions.

3.2. Effect of extraction temperature

The extraction temperature varied from 30 to 60 C to evaluate

its effect on the extraction efficiency of phycocyanin at a pH of 7.

0 50 100 150 200 2500.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

C t

( g L - 1 )

Time (min)

pH 5

pH 5.5

pH 6

pH 6.5

pH 7

pH 8

Fig. 1. Effect of solvent pH on phycocyanin extraction. The data points and solidlines represent the experimental results and model predictions, respectively.

C.-H. Su et al. / Separation and Purification Technology 123 (2014) 64–68 65

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The evolution of the phycocyanin concentration for various tem-

peratures is shown in Fig. 2. A faster rate was obtained with higher

temperatures. This may be attributed to the increased diffusion

coefficient of solutes at a higher temperature [17]. The figure also

shows that the equilibrium concentration of phycocyanin de-

creased slightly with increasing extraction temperature from 30

to50 C. In general, charged proteins have aqueous solubilities that

increase substantially with temperature [20,21]. However, the

slight decrease in the equilibrium concentration indicates that

the phycocyanin was degraded by heat during the extraction pro-

cess [22,23]. With further elevation of temperature to 60 C, the

equilibrium concentration of phycocyanin reached only 0.4 g L 1

in 4 h. This result is similar to those of previous studies on the

thermal degradation kinetics of phycocyanin [22].

3.3. Establishment of the kinetic model

To establish the kinetic model, the model parameters (k, C e, and

h) can be estimated using a linear equation, defined as Eq. (4). Fig. 3

shows the correlation between t /C t and t under all experimental

conditions. A straight line is a clear indication that the proposed

model is valid. Hence, the equilibrium concentration of phycocya-

nin C e and the extraction rate constant k can be calculated from the

slope and intercept of each straight line, respectively. Table 1

shows the calculated model parameters for various extraction

conditions.

The relationship between the model parameters and pH varia-

tion at 50 C is shown in Fig. 4. The ANOVA results indicated that

the pH variation significantly (P < 0.05) affected the model param-

eters. The values of these parameters increased slightly with an in-

crease in pH from 5 to 6. However, an obvious increase in those

quantities was observed with further elevation of the pH to 7. This

may be attributed to the fact that phycocyanin is negatively

charged at a pH above its isoelectric point; consequently, the

negatively charged protein is attracted by the aqueous solvent

[7]. Because k, C e, and h were dependent on pH, the estimated

values were used to fit the quadratic empirical equations (Eqs.(9)–(11)):

kð pH Þ ¼ 1:37 103 X 2 pH 1:32 10

2 X pH þ 4:51 102; r 2 ¼ 0:99;

ð9Þ

C eð pH Þ ¼ 1:46 101 X 2 pH 1:49 X pH þ 5:66; r

2 ¼ 0:99; ð10Þ

hð pH Þ ¼ 1:98 102 X 2 pH 2:05 10

1 X pH þ 5:78 101; r 2 ¼ 0:99;

ð11Þ

where X pH represents the variation of the pH level. The goodness-of-

fit of the equations was evaluated using the coefficient of determi-

nation (r 2). The high values of r 2 indicated that the correlations

between the model parameters and pH variation are reliable.

The evolution of concentration C t as a function of pH can be ob-

tained by substituting Eqs. (10) and (11) into (5). The relationship

is described as

C t ð pH Þ¼ t

ð1=ð1:98102 X 2 pH 2:05101 X pH þ5:7810

1ÞÞþðt =ð1:46101 X 2 pH 1:49 X pH þ5:66ÞÞ;

ð12Þ

The model can be used to predict the phycocyanin extraction under

various pH levels at a specified time with an extraction temperature

of 50 C.

The effect of temperature on the model parameters at a pH of 7

is shown in Fig. 5. The ANOVA results indicated that the model

parameters were significantly (P < 0.05) affected by varying the

temperatures from 30 C to 50 C. The temperature had an acceler-

ative influence on the extraction rate constant k and initial extrac-

tion rate h. However, a reverse trend was observed when the

equilibrium concentration C e decreased with increasing tempera-

ture. The following empirical equations (Eqs. (13) and (14)) were

developed to correlate temperature with the equilibrium concen-

tration of phycocyanin and the initial extraction rate. The reliabil-

ity of these equations has been proved using r 2.

C eðT Þ ¼ 2:6 103T 2 0:25T þ 8:29; r 2 ¼ 0:98; ð13Þ

hðT Þ ¼ 1:14 104T 2 5:55 103T þ 1:03 101; r 2 ¼ 0:99;

ð14Þ

0 50 100 150 200 2500.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

C t

( g L - 1 )

Time (min)

30 °C

35 °C

40 °C

45 °C

50 °C

60 °C

Fig. 2. Effect of temperature on phycocyanin extraction. The data points and solidlines represent the experimental results and model predictions, respectively.

0 50 100 150 200 2500

20

40

60

80

100

120

140

160

pH 5

pH 5.5

pH 6

pH 6.5

pH 7

t / C t

( m i n L g

- 1 )

Time (min)

0 50 100 150 200 250

Time (min)

(A)

0

20

40

60

80

100

120

30oC

35oC

40oC

45oC

50oC

t / C t

( m i n L

g - 1 )

(B)

Fig. 3. Kinetic model to estimate the extraction rate constant and equilibrium

concentration for various (A) pH levels, and (B) extraction temperatures. In these

figures, the values of the abscissa and ordinate were obtained from the relation-

ships t and t /C t .

66 C.-H. Su et al. / Separation and Purification Technology 123 (2014) 64–68


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The dependence of the rate constant k on the extraction tempera-

ture can be described using the Arrhenius equation (Eq. (6)). An

Arrhenius-Van’t Hoff plot was used to determine the pre-exponen-

tial factor and the activation energy of extraction. As shown in

Fig. 6, the higher linear correlation coefficient (r 2 = 0.98) indicated

that the Arrhenius model parameters, k0 and E a, can be determined

from the slope and intercept of the straight line, respectively. There-

fore, the relationship of k and T is written as

kðT Þ ¼ 1:47 109 exp

67100

8:314ðT þ 273:15Þ

; r 2 ¼ 0:98; ð15Þ

For the phycocyanin extraction process, the activation energy was

67.1 kJ mol1

, indicating that the extraction is an endothermicprocess [15].

Using a similar derivation as that in Eq. (12), substituting Eqs.(13) and (14) into (5) yields an equation describing the evolution

of C t versus time and temperature:

C t ðT Þ¼ t

ð1=ð1:14104T 25:55103T þ1:03101ÞÞþðt =2:6103T 20:25T þ8:29Þ

ð16Þ

This model can be used to predict the phycocyanin extraction under

various temperatures at a specified time with a pH level of 7.

3.4. Validity of the developed model

Because all kinetic parameters were determined, the developed

models (Eqs. (12) and (16)) were used for predicting phycocyanin

extraction from S. platensis under diverse operating conditions,including various pH levels (5–7) and temperatures (30–50 C).

Table 1

Model parameters (k and C e) obtained for all tested conditions.

Model parameters Solvent pH Temperature (C)

5 5.5 6 6.5 7 30 35 40 45 50

ka 1.33102 1.41102 1.49102 1.74102 1.98102 3.82103 6.2103 1.06102 1.41102 1.98 102

C eb 1.84 1.89 1.93 2.14 2.36 3.14 2.81 2.44 2.39 2.36

r 2 0.99 0.99 0.99 0.99 0.99 0.98 0.99 0.99 0.99 0.99

a Unit of extraction rate constant is L g1 min1.b Unit of saturation extraction capacity is g L 1.

5.0 5.5 6.0 6.5 7.01.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

h x 1 0 2

( g L - 1 m

i n - 1 )

C e ( g L - 1 )

k x 1 0 2

( L g

- 1 m

i n - 1 )

pH

1.6

1.8

2.0

2.2

2.4

0

2

4

6

8

10

12

h

Ce

k

Fig. 4. The effect of solvent pH on the extraction rate constant k, equilibrium

concentration C e, and initial extraction rate h at 50 C. The solid lines represent

prediction results of the empirical equations (Eqs. (9)–(11)).

30 35 40 45 50

0.4

0.8

1.2

1.6

2.0

k x 1 0 2

( L g - 1

m i n - 1 )

Temperature (°C)

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

h x 1 0 2

( g L - 1 m

i n - 1 )

0

2

4

6

8

10

12

h

Ce

k

C e ( g L - 1 )

Fig. 5. The effect of extraction temperature on the extraction rate constant k,

equilibrium concentration C e, and initial extraction rate h at a pH of 7. The solid

lines represent prediction results of the empirical equations (Eqs. (13)–(15)).

3.10 3.15 3.20 3.25 3.30-6.0

-5.5

-5.0

-4.5

-4.0

-3.5

l n k

Temperature reciprocal x103 (K-1)

Fig. 6. Arrhenius-Van’t Hoff plot for phycocyanin extraction in the temperature

within a range of 30–50 C.

0.0 0.5 1.0 1.5 2.0 2.50.0

0.5

1.0

1.5

2.0

2.5

The predictions from Eq.12, r 2= 0.99

The predictions from Eq.16, r 2= 0.98

A c t u a l c o n c e n t r a t i o n

( g L - 1 )

Predicted concentration (g L-1

)

Fig. 7. Correlation between the actual and predicted concentration of phycocyanin.

C.-H. Su et al. / Separation and Purification Technology 123 (2014) 64–68 67

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The phycocyanin concentration obtained using Eqs. (12) and (16)

was compared with the experimental results under the same oper-

ating conditions. As shown in Fig. 7, the predicted and experimen-

tal data were consistent with coefficients of determination (r 2) of

0.98 and 0.99 for the extraction under diverse pH levels and tem-

peratures, respectively. The results showed that the developed

models are valid for the extraction system. Thus, the kinetic

models can provide useful information on operation strategies

and economic descriptions of the extraction process.

4. Conclusions

This study examined the effects of solvent pH and extraction

temperature on the aqueous extraction of phycocyanin from

S. platensis. The results showed that a higher pH increased the

extraction rate and equilibrium concentration because the nega-

tively charged phycocyanin is attracted by the aqueous solvent.

For the temperature tests, the extraction rate increased with

increased temperature, whereas the equilibrium concentration of

phycocyanin decreased with increased temperature. This indicated

that phycocyanin was degraded by heat during the extraction pro-

cess. A second-order kinetic model for depicting the extraction

processes under diverse conditions was successfully developed.

The activation energy of phycocyanin extraction was 67.1 kJ mol1,

indicating that the extraction was an endothermic process. Finally,

the developed models (Eqs. (12) and (16)) were used for the pre-

diction of phycocyanin concentration under various extraction

conditions. The predicted values were consistent with the actual

results, indicating their reliability.

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