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Lumping kinetic study on the process of tryptic hydrolysis of bovine serum albumin
Process Biochemistry 40 (2005) 1943–1949 www.elsevier.com/locate/procbio
Lumping kinetic study on the process of tryptic hydrolysis of bovine serum albumin Deqing Shi*, Zhimin He, Wei Qi Chemical Engineering Research Center, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, PR China Received 21 August 2003; accepted 20 July 2004
Abstract Bovine serum albumin was hydrolyzed with trypsin in a batch stirred tank reactor. The influence of operating parameters on the degree of hydrolysis was investigated by pH-stat method. Molecular weight distribution of hydrolysates was analyzed by high performance sizeexclusive chromatography. The kinetic model of hydrolysis reaction was studied by a lumping technique. The hydrolysates were combined into several lumps according to their molecular weights. Reaction of the lumps was described with intrinsic kinetic equations, and the lumping kinetic model for bovine serum albumin tryptic hydrolysis reaction was established. The rate constant of each reaction was estimated by Marquardt method in two steps from lower level to upper level. The reliability of the model was tested by comparing the computed values with the experimental values. # 2004 Elsevier Ltd. All rights reserved. Keywords: Bovine serum albumin; Hydrolysis; Enzyme; Lumping model; Kinetics
1. Introduction Protein enzymatic modification has widely been used because it can adapt the functional properties of protein. Some bioactive peptides have been obtained by limited digestion of protein for food, pharmaceutical and cosmetic industries during the last two decades. The bioactive mechanism and structure of some peptides have been identified. For example, insulin-stimulating peptide [1], which can enhance the action of insulin in vitro on fatty acid synthesis, has been obtained from a tryptic digest of bovine serum albumin (BSA). For another example, bovine albutensin A [2] is an ileum-contracting peptide isolated from the tryptic hydrolysates of BSA, which exhibits ileal contraction in the longitudinal muscle strips of guinea pig ileum. The kinetic model of protein hydrolysis reaction is one of the important aspects of the studies, but to date, work has focused on product development, and the kinetic model has been restricted to the Michaelis–Menten equation, which * Corresponding author. Fax: +86 546 8391029. E-mail address: [email protected] (D. Shi). 0032-9592/$ – see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.procbio.2004.07.009
can only describe the one substrate enzymic reactions [3–5]. The kinetic behaviour of components cannot be described quantitatively. Protein enzymic hydrolysis is a complicated reaction system that contains multi-component and multireaction. For example, a component could act as the product of a hydrolysis reaction and the substrate for another reaction at the same time. Parallel reactions exist with consecutive reactions simultaneously. The reactions are coupled and restricted with each other. This work tried to introduce a lumping method into the study of the tryptic hydrolysis process of BSA. First, the factors that influence the degree of hydrolysis (DH) of BSA were studied and the molecular weight distribution of hydrolysates was characterized by high performance sizeexclusion chromatography (HPSEC). The kinetic model of the process was then studied by a lumping technique. The lumping method combines groups of components whose kinetic behaviour are similar into several lumps in order to reduce the number of variables and parameters and simplify the complicated system. It has been widely used in petrochemical industries [6–10], and has been applied to a biochemical reaction system [11]. The establishment of the lumping kinetic model will contribute to further under-
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D. Shi et al. / Process Biochemistry 40 (2005) 1943–1949
standing of the mechanism of protein enzymic hydrolysis, and help to optimize the operational conditions to yield the target product. Furthermore, the lumping method can also be applied to the investigation of reaction kinetics of similar complicated reaction systems involving polysaccharides, lipids and nucleic acids.
where h is the number of peptide bonds broken, is called the hydrolysis equivalence and is expressed as the equivalents per kg protein; htot the total number of peptide bonds in the bovine serum albumin protein substrate; B the base consumption in ml; Nb the normality of the base; a average degree of dissociation of the a-NH groups; and MP is the mass of protein in grams. The degree of dissociation was found in the following way:
2. Materials and methods 2.1. Materials Bovine serum albumin (BSA) at high purification level was obtained from Tianjin Blood Research Center. Trypsin and molecular standard samples were purchased from Sigma Co. All other chemicals were of analytical grade.
a¼
10pHpK 1 þ 10pHpK
The pK value varies significantly with temperature, but is relatively independent of the substrate. The pK value at different temperatures (T) can be calculated according to Steinhardt and Beychok [13]. pK ¼ 7:8 þ
2.2. Hydrolysis of BSA BSA, which was dissolved in water, was hydrolyzed with trypsin at different substrate to enzyme ratios in a batch stirred tank reactor. The hydrolysis reaction was carried out at different temperatures. The pH was kept at a stable value by adding 0.1 M NaOH solution with a pH-stat method. Samples were taken at different times, and the hydrolysis reaction terminated by heating in boiling water for 10 min. The molecular weight distribution of the samples was then analyzed by HPSEC. 2.3. Analysis of the hydrolysates of BSA Molecular weights distribution of hydrolysates was analyzed by HPSEC on a Protein Pak 125 column (Waters Co.). The WDL-95 Chromatograph was equipped with a UV-200II ultraviolet detector and a P200II high-pressure constant-flow pump (Elite Scientific Instrument Co.). Injection volume was 20 ml. The elution was 0.1 M phosphate buffer, pH 7.0 at a flow rate of 0.5 ml/min. Elution was monitored at 215 nm to detect small peptides. The molecular weights were determined with a calibration curve made with bovine serum albumin (67 kDa), bovine hemoglobin (64 kDa), ovalbumin (43 kDa), cytochrome c (12 kDa) and vitamin B12 (1355) as standards. The relation of molecular weight (Mw) and retention time (Rt) was determined by five standard samples as:
298 T 240 298T
3. Results and discussion 3.1. Influence factors for the degree of hydrolysis In enzymatic hydrolysis reaction, the reaction rate can be expressed by the hydrolysis degree in unit time. The primary factors that affect DH are the temperature, pH, concentration of substrate and the ratio of enzyme to substrate, etc. This work investigates the influence of these factors on the degree of protein hydrolysis. 3.1.1. Influence of temperature It is well known that the ratio of reaction rate to initial rate is 1–2 when the reaction temperature rises by 10 8C. High temperature promotes the activity of enzyme and helps to the spread of the folding structure of substrate, which will result in high reaction rate. But the rising of temperature accelerates the inactivation of enzyme simultaneously, which will decrease the reaction rate. Fig. 1 shows the relationship between DH and reaction time at different temperatures. It can be found that DH rises accompanied with the rising of temperature at the same reaction time.
Rt ¼ 8:135 log ðMw Þ þ 53:927 2.4. Determination of the degree of hydrolysis The degree of hydrolysis is defined as the percentage of peptide bond cleaved during the enzymatic reaction. It is expressed by the following equation [12]: DHð%Þ ¼
h 100 BNb 100 ¼ htot ahtot MP
Fig. 1. Hydrolysis curve for different temperatures (s0 = 4 g/l; e0 = 0.04 g/l; pH 8.0).
D. Shi et al. / Process Biochemistry 40 (2005) 1943–1949
Fig. 2. Hydrolysis curve for different pH (s0 = 4 g/l; e0 = 0.04 g/l; T = 40 8C).
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Fig. 4. Hydrolysis curve for different enzyme concentrations (s0 = 2.5 g/l; pH = 8.0; T = 40 8C).
However, it is evident that the reaction rate declines fast at high temperature due to the denaturing of enzyme protein. For example, the initial rate of hydrolysis reaction at 50 8C is the fastest and the decreasing rate of DH is the fastest, too.
substrate inhibition exists in the BSA tryptic hydrolysis system. It is possible to generate inactive middle complexes from enzyme and excessive substrate, and the inactive complex cannot decompose to yield hydrolysates.
3.1.2. Influence of pH The activity of enzyme is strongly affected by pH because the active enzyme exists as a kind of ionized form. The changing of pH can influence the dissociation of active groups of the enzyme, which affects the banding of enzyme and substrate. As a result, there is an appropriate interval of pH for each enzyme, which can be determined by experiments. Fig. 2 is the experimental results of BSA hydrolysis at different pH conditions. It is shown that the reaction rate is slowest at pH 7.0, and is fastest at pH 9.0. The reaction rate at pH 10.0 declines fast with time than that at other pH conditions although the initial rate is fast. It is possible that the denaturation rate of enzyme protein is fast at too high pH condition. Therefore, maintaining pH at a stable and appropriate value is important for protein enzymic hydrolysis.
3.1.4. Influence of the ratio of enzyme to substrate Generally speaking, reaction rate is in proportion to the amount of enzyme when the quantity of substrate is adequate, which also can be found in Fig. 4. The reaction rate deals with the rate of yielding the middle complex, which is dependent on the amount of enzyme. But the amount of enzyme used in the hydrolysis reaction is restricted by a lot of factors, such as the price of enzyme and self-hydrolysis of some kinds of enzyme. The problem of self-hydrolysis is serious for trypsin at high concentration. As a result, a high concentration of trypsin is not suitable for hydrolysis reaction. 3.2. Molecular weight distribution of tryptic hydrolysates of BSA
3.1.3. Influence of concentration of substrate The concentration of substrate is an important factor for protein enzymic hydrolysis, since substrate inhibition often exists in enzymic reactions. The degrees of hydrolysis at different initial concentrations of substrate are shown in Fig. 3. The reaction at low substrate concentration exhibits a high reaction rate, which is slow, at high substrate concentration. It can be concluded from Fig. 3 that serious
The molecular weight distribution of hydrolysates is regular because of the influence of the specification of enzyme and the space structure of substrate. HPSEC was used to analyze the molecular weight distribution of tryptic hydrolysates of BSA. Fig. 5 is the chromatogram of BSA hydrolysates at 2.5 min, 20 min and 60 min. There are nine absorption peaks in the chromatogram, which can be vested in four evident districts corresponding to molecular weight ranges: 127,000–24,000; 24,000–6300; 6300–3000 and
Fig. 3. Hydrolysis curve for different initial substrate concentrations (e0 = 0.03 g/l; pH = 8.0; T = 40 8C).
Fig. 5. HPLC of bovine serum albumin tryptic hydrolysates after 2.5 min (curve a), 20 min (curve b) and 60 min (curve c).
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3000–300. The area of the first district decreased with time while that of other districts increased. This shows that the polypeptides whose molecular weights are large carry out a decomposition reaction primarily, while the generating rate of small peptides is faster than the decomposition rate.
B.
3.3. Lumping kinetic model for tryptic hydrolysis of BSA 3.3.1. Establishment of kinetic model The mechanism of protein enzymic hydrolysis can be described by the following steps. First, free enzyme combines with substrate to form an active middle complex. Then, the peptide chain cracks, and the complex decompose to two products. At the same time, the enzyme is set free. This is the rate deterministic step as shown in Eq. (1). Product inhibition and substrate inhibition exist in the hydrolysis reaction. Km
kcat
E þ S , ES ! E þ P
D. E.
(1)
The inactivation of enzyme fits well with first-order model [14], i.e. dCE ¼ kd CE (2) dt Taking into account product inhibition, substrate inhibition and enzyme inactivation, the performance of each lump in the system can be described by following Eq. (3). dCS ¼ kcat CES dt ¼
C.
kcat CS CE0 exp ðkd tÞ ð1 þ ðCp =Kmp ÞÞKm þ CS ð1 þ ðCS =KsÞþðCp =KpÞÞ (3)
Before the establishment of the model, some hypotheses have been put forward as follows: A. Hydrolysis reaction is affected by the space structure of substrate, the specificity of enzyme and other factors.
F.
The cleavage position of peptide is not random, and the molecular weight contribution is regular. In the same reaction system, dynamic performances of substrates are similar if their molecular weights are alike. In the enzymatic reaction, primarily two processes determine the kinetic behaviour of substrates. (a) The combination of enzyme and substrate and the dissociation of the complex. (b) The release of free enzyme and product. The two processes are affected by molecular weight of the substrate. Product inhibition, substrate inhibition and enzyme deactivation exist in the hydrolysis process and the kinetic behaviour of each lump can be described by the modified Michaelis–Menten equation, i.e., Eq. (3). There is no interaction of the products, which means that enzymic synthesis does not take place. The lumps whose molecular weights are large can yield the smaller lumps. The lump which molecular weight is the smallest does not hydrolyze. The reaction is carried out in homogeneous phase, and the influence of diffuse resistance does not exist.
Then, the components in the hydrolysis reaction can be combined to several lumps based on the data obtained from HPSEC. The number of lumps should accord with the practical demand. Not only the number of absorption peaks is considered, but also the difficulty of experiments and the estimation of parameters. According to the hypothesis and the molecular weight distribution of hydrolysates, the products of BSA tryptic hydrolysis were combined into four lumps. After all components were grouped into lumps, the network for BSA hydrolysis can be built up, and is shown in Fig. 6. The kinetic model contains four lumps and six kinetic parameters. Lump ‘A’ represents the components which molecular weights are the biggest, and the lump ‘D’ represents the smallest. Then, the differential equation set, which describes the lumping network of BSA hydrolysis, is shown as follows.
dCA ðk1 þ k2 þ k3 ÞCE0 CA exp ðkd tÞ ¼ CB CC CD CA CB CC CD dt þ þ þ þ þ 1þ KmA þ CA 1 þ KmB KmC KmD KsA KpB KpC KpD = (k1 + k2 + k3) A1 dCB ¼ k 1 A1 dt
ðk þ k5 ÞCE0 CB exp ðkd tÞ 4 = k1 A1 (k4 + k5) A2 CC CD CA CB CC CD þ þ þ þ 1þ KmB þ CB 1 þ KmC KmD KsA KsB KpC KpD
dCC k6 CE0 CC expðkd tÞ ¼ k 2 A1 þ k 4 A2 ð1 þ ðCD =KmD ÞÞKmC þ CC ð1 þ ðCA =KsA Þ þ ðCB =KsB Þ þ ðCC =KsC Þ þ ðCD =KpD ÞÞ dt = k2 A1 + k4 A2 k6 A3 dCD ¼ k 3 A1 þ k 5 A2 þ k 6 A3 dt
D. Shi et al. / Process Biochemistry 40 (2005) 1943–1949
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Table 1 Results of parameters estimation Reaction
Reaction constant
30 8C
40 8C
50 8C
A!B A!C A!D B!C B!D C!D
k1 k2 k3 k4 k5 k6
2.6465 0.2898 0.06293 0.5613 0.2484 0.6030
4.6174 0.4578 0.1107 0.8213 0.4268 0.9085
10.2481 0.8737 0.1830 1.3482 0.8052 1.3517
The unit of k is min1. Fig. 6. Four lumps network for BSA tryptic hydrolysis.
3.3.2. Parameter estimation The problem of multi-value dependency often exists in parameter estimation in the lumping kinetic model, since the number of parameters is larger than the number of differential equations. In order to avoid the problem, the kinetic constants of the model were estimated by Marquardt’s method in two steps from lower level to upper level. First of all, the parameters of the sub-reaction system, which contains lumps B, C and D, were calculated. Then the residual three parameters of the four lumps network at different temperatures were estimated. Table 1 shows the results of parameter estimation. It is shown in Table 1 that there are several products for the large lump and the rate of generating different small lumps from the large lump is different. The rate of yielding a large lump is faster than that of small lump. For example, the rate constant of the reaction that yields lump B from lump A is larger than that of the reaction yielding lump C. The reason is that hydrolysis reaction rate is affected by the decomposition of the enzyme–substrate complex. The
combination position of substrate and enzyme is not random, and inclined to form the complex that can decompose easily. It is easy to be set free from the complex for the product whose volume is large because of the space repulsion. As a result, the apparent rate is fast for this kind of reaction. Fig. 7 is the comparison of the observed values of each lump with the computed values for parameter estimation at 30 8C, 40 8C and 50 8C, respectively. The initial reaction rates rise along with the temperature increase. Accompanied by the proceeding of the hydrolysis reaction, however, the reaction rates decrease faster at high temperature than at low temperature, due to the faster inactivation rate of trypsin at high temperature. The concentration of lump B and C increases with time, since the decomposition rates are lower than the generating rates. Compared with lumps C and D, the generating rate of lump B is fast, which also certifies that the hydrolysates with large volume can be produced easily. When the conditions of the concentration of substrate, ratio of enzyme to substrate and pH are settled, the rate constant is the function of temperature and follows the Arrhenius equation. The relationship between rate constants
Fig. 7. Comparison between observed values and computed values at different temperatures. Line: computed values; Sign: observed values: (&) lump A; (*) lump B; () lump C; and (~) lump D.
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D. Shi et al. / Process Biochemistry 40 (2005) 1943–1949
Table 2 Comparison between observed and computed values at 35 8C Reaction time (min) Lump A (mg/ml)
Lump B (mg/ml)
Lump C (mg/ml)
Lump D (mg/ml)
Observed value Computed value Observed value Computed value Observed value Computed value Observed value Computed value 15 25 40 60 80 110
3.2373 2.8681 2.5906 2.2180 1.9878 1.7250
3.0994 2.8305 2.5045 2.1712 1.9178 1.6380
0.5025 0.7023 0.9126 1.1590 1.3302 1.4808
0.6397 0.8326 1.0578 1.2799 1.4437 1.6195
0.2306 0.2874 0.3323 0.4097 0.4518 0.5149
0.2394 0.2849 0.3431 0.4046 0.4524 0.5058
0.5296 0.6222 0.6709 0.7433 0.7902 0.8293
0.4714 0.5020 0.5447 0.5944 0.6363 0.6868
Table 3 Comparison between observed and computed values at 45 8C Reaction time (min) Lump A (mg/ml)
Lump B (mg/ml)
Lump C (mg/ml)
Lump D (mg/ml)
Observed value Computed value Observed value Computed value Observed value Computed value Observed value Computed value 10 18 30 45 65 90
2.9144 2.7207 2.2894 1.8440 1.3597 1.1659
2.6616 2.3653 1.9989 1.6981 1.4400 1.2491
0.9837 1.1419 1.3541 1.6159 1.9792 2.1624
1.1547 1.3713 1.6298 1.8341 2.0028 2.1229
of each lump and reaction temperatures is shown in Fig. 8. The straight line in Fig. 8 indicates that the relationship can fit the Arrhenius equation well. The reaction active energy for each lump can be calculated by the Arrhenius equation, and that of the lumps is between 32 kJ/mol to 55 kJ/mol. 3.3.3. Verification of the lumping mode In order to examine the ability of prediction and extrapolation of the lumping kinetic model and the liability of the obtained rate constants, the hydrolysis experiment was preceded under other conditions different from that of estimating the parameters. For example, the composition of initial substrate, reaction temperatures and sampling time are changed. The results of comparing observed values with computed values show that the lumping kinetic model can predict the mass concentration of each lump effectively. Tables 2 and 3 are the results of the comparison of experimental values and computed values at 35 8C and 45 8C, respectively.
Fig. 8. Relationship between ln k and temperatures.
0.3499 0.4062 0.4600 0.5263 0.6244 0.6787
0.3601 0.4077 0.4703 0.5246 0.5734 0.6110
0.6520 0.7412 0.7965 0.8538 0.9276 0.9830
0.6202 0.6523 0.6975 0.7397 0.7802 0.8132
There are some deviations between observed values and computed values from the lumping model. In the kinetic model, there are some other parameters such as the Michaelis–Menten constants, substrate inhibition constants and product inhibition constants of each lump to be determined in experiments. Too much parameter will result in some errors for the rate constant estimations. In addition, the quantitative analysis of mass concentration for the hydrolysates is not sufficiently precise owing to the multicomponent complexity of products. Furthermore, the rate constants at 35 8C and 45 8C calculated by Arrhenius equation are not very accurate.
4. Conclusion This work investigated the influence of operating parameters on the degree of hydrolysis of BSA by pHstat in a batch stirred tank reactor. The molecular weight distribution of tryptic hydrolysates of BSA was analyzed by HPSEC. Four lumps kinetic model for bovine serum albumin tryptic hydrolysis reaction were then established. Some hypothesis about the mechanism of the reaction and the lumping criteria were made before the establishment of the model. The reaction of the lumps was described with intrinsic kinetic equations, which contain the influence of product inhibition, substrate inhibition and enzyme inactivation. The rate constants were calculated by Marquardt’s method in two steps from lower level to upper level. The reliability of the lumping model was tested by comparing the computed values with the experimental values. The results showed that the lumping kinetic model could predict the distribution of the mass concentration of products.
D. Shi et al. / Process Biochemistry 40 (2005) 1943–1949
Acknowledgment The authors are very grateful for the financial support from the National Natural Science Foundation of China (Grant No. 20276052).
References [1] Akemichi U, Yeong-Man H, Naokatu A, Yoshiro T. Insulin-stimulating peptide from a tryptic digest of bovine serum albumin: purification and characterization. J Biochem 1985;98:269–78. [2] Masakazu T, Shigeo M, Toshiko M, Hiroyuki S, Akira S, Yasuyuki T, et al. Albutensin A, an ileum-contracting peptide derived from serum albumin, acts through both receptors for complements C3a and C5a. Lett Pep Sci 1998;5:29–35. [3] Gonzalez-Tello P, Camacho F, Jurado E, Pa´ ez M, Guadix E. Enzymatic hydrolysis of whey proteins: kinetic models. Biotech Bioeng 1994;44:523–8. [4] Marquez M. Enzymatic hydrolysis of vegetable proteins: mechanism and kinetics. Proc Biochem 1993;28:481–90. [5] Marquez M, Vazquez M. Modeling of enzymatic protein hydrolysis. Proc Biochem 1999;35:111–7.
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[6] Cao G, Viol A, Baratti R, Morbidelli M, Sanseverino L, Cruccu M. Lumped kinetic model for propene–butene mixtures oligomerization on a supported phosphoric acid catalyst. Appl Catal 1988; 41:301–12. [7] Carraway R, Mitra S, Cochrane D. Structure of a biologically active neurotensin-related peptide obtained from pepsin-treated albumin. J Biochem Chem 1987;262:5968–73. [8] Fang X, Tan H, Zhao Y. Study on hydrocracking lumped kinetic model. Acta Petrolei Sin Petroleum Processing Section 1996;12: 33–8. [9] Froment G. Kinetic modeling of acid-catalyzed oil refining processes. Catal Today 1999;52:153–63. [10] Weng H, Ouyang F, Ma J. Lumped model for heavy oil catalytic cracking reaction (I) establishment of the model. J Chem Ind Eng China 1995;46:663–7. [11] James C, Edwin N. Lumping analysis of biochemical reaction systems with time scale separation. Biotech Bioeng 1988;31:869–79. [12] Alder-Nissen J. Enzymatic Hydrolysis of Food Protein. London: Elsevier; 1986. [13] Steinhardt H, Beychok S. Interaction of protein with hydrogen ions and other small ions and molecules. In: Neurath H, editor. The Proteins. New York: Academic Press; 1964. p. 139–304. [14] Zhimin H, Ziding Z, Mingxia H. Kinetic study of thermal inactivation for native and methoxypolyethylene glocol modified trypsin. Proc Biochem 2000;10:1235–40.
Lumping kinetic study on the process of tryptic hydrolysis of bovine serum albumin Deqing Shi*, Zhimin He, Wei Qi Chemical Engineering Research Center, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, PR China Received 21 August 2003; accepted 20 July 2004
Abstract Bovine serum albumin was hydrolyzed with trypsin in a batch stirred tank reactor. The influence of operating parameters on the degree of hydrolysis was investigated by pH-stat method. Molecular weight distribution of hydrolysates was analyzed by high performance sizeexclusive chromatography. The kinetic model of hydrolysis reaction was studied by a lumping technique. The hydrolysates were combined into several lumps according to their molecular weights. Reaction of the lumps was described with intrinsic kinetic equations, and the lumping kinetic model for bovine serum albumin tryptic hydrolysis reaction was established. The rate constant of each reaction was estimated by Marquardt method in two steps from lower level to upper level. The reliability of the model was tested by comparing the computed values with the experimental values. # 2004 Elsevier Ltd. All rights reserved. Keywords: Bovine serum albumin; Hydrolysis; Enzyme; Lumping model; Kinetics
1. Introduction Protein enzymatic modification has widely been used because it can adapt the functional properties of protein. Some bioactive peptides have been obtained by limited digestion of protein for food, pharmaceutical and cosmetic industries during the last two decades. The bioactive mechanism and structure of some peptides have been identified. For example, insulin-stimulating peptide [1], which can enhance the action of insulin in vitro on fatty acid synthesis, has been obtained from a tryptic digest of bovine serum albumin (BSA). For another example, bovine albutensin A [2] is an ileum-contracting peptide isolated from the tryptic hydrolysates of BSA, which exhibits ileal contraction in the longitudinal muscle strips of guinea pig ileum. The kinetic model of protein hydrolysis reaction is one of the important aspects of the studies, but to date, work has focused on product development, and the kinetic model has been restricted to the Michaelis–Menten equation, which * Corresponding author. Fax: +86 546 8391029. E-mail address: [email protected] (D. Shi). 0032-9592/$ – see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.procbio.2004.07.009
can only describe the one substrate enzymic reactions [3–5]. The kinetic behaviour of components cannot be described quantitatively. Protein enzymic hydrolysis is a complicated reaction system that contains multi-component and multireaction. For example, a component could act as the product of a hydrolysis reaction and the substrate for another reaction at the same time. Parallel reactions exist with consecutive reactions simultaneously. The reactions are coupled and restricted with each other. This work tried to introduce a lumping method into the study of the tryptic hydrolysis process of BSA. First, the factors that influence the degree of hydrolysis (DH) of BSA were studied and the molecular weight distribution of hydrolysates was characterized by high performance sizeexclusion chromatography (HPSEC). The kinetic model of the process was then studied by a lumping technique. The lumping method combines groups of components whose kinetic behaviour are similar into several lumps in order to reduce the number of variables and parameters and simplify the complicated system. It has been widely used in petrochemical industries [6–10], and has been applied to a biochemical reaction system [11]. The establishment of the lumping kinetic model will contribute to further under-
1944
D. Shi et al. / Process Biochemistry 40 (2005) 1943–1949
standing of the mechanism of protein enzymic hydrolysis, and help to optimize the operational conditions to yield the target product. Furthermore, the lumping method can also be applied to the investigation of reaction kinetics of similar complicated reaction systems involving polysaccharides, lipids and nucleic acids.
where h is the number of peptide bonds broken, is called the hydrolysis equivalence and is expressed as the equivalents per kg protein; htot the total number of peptide bonds in the bovine serum albumin protein substrate; B the base consumption in ml; Nb the normality of the base; a average degree of dissociation of the a-NH groups; and MP is the mass of protein in grams. The degree of dissociation was found in the following way:
2. Materials and methods 2.1. Materials Bovine serum albumin (BSA) at high purification level was obtained from Tianjin Blood Research Center. Trypsin and molecular standard samples were purchased from Sigma Co. All other chemicals were of analytical grade.
a¼
10pHpK 1 þ 10pHpK
The pK value varies significantly with temperature, but is relatively independent of the substrate. The pK value at different temperatures (T) can be calculated according to Steinhardt and Beychok [13]. pK ¼ 7:8 þ
2.2. Hydrolysis of BSA BSA, which was dissolved in water, was hydrolyzed with trypsin at different substrate to enzyme ratios in a batch stirred tank reactor. The hydrolysis reaction was carried out at different temperatures. The pH was kept at a stable value by adding 0.1 M NaOH solution with a pH-stat method. Samples were taken at different times, and the hydrolysis reaction terminated by heating in boiling water for 10 min. The molecular weight distribution of the samples was then analyzed by HPSEC. 2.3. Analysis of the hydrolysates of BSA Molecular weights distribution of hydrolysates was analyzed by HPSEC on a Protein Pak 125 column (Waters Co.). The WDL-95 Chromatograph was equipped with a UV-200II ultraviolet detector and a P200II high-pressure constant-flow pump (Elite Scientific Instrument Co.). Injection volume was 20 ml. The elution was 0.1 M phosphate buffer, pH 7.0 at a flow rate of 0.5 ml/min. Elution was monitored at 215 nm to detect small peptides. The molecular weights were determined with a calibration curve made with bovine serum albumin (67 kDa), bovine hemoglobin (64 kDa), ovalbumin (43 kDa), cytochrome c (12 kDa) and vitamin B12 (1355) as standards. The relation of molecular weight (Mw) and retention time (Rt) was determined by five standard samples as:
298 T 240 298T
3. Results and discussion 3.1. Influence factors for the degree of hydrolysis In enzymatic hydrolysis reaction, the reaction rate can be expressed by the hydrolysis degree in unit time. The primary factors that affect DH are the temperature, pH, concentration of substrate and the ratio of enzyme to substrate, etc. This work investigates the influence of these factors on the degree of protein hydrolysis. 3.1.1. Influence of temperature It is well known that the ratio of reaction rate to initial rate is 1–2 when the reaction temperature rises by 10 8C. High temperature promotes the activity of enzyme and helps to the spread of the folding structure of substrate, which will result in high reaction rate. But the rising of temperature accelerates the inactivation of enzyme simultaneously, which will decrease the reaction rate. Fig. 1 shows the relationship between DH and reaction time at different temperatures. It can be found that DH rises accompanied with the rising of temperature at the same reaction time.
Rt ¼ 8:135 log ðMw Þ þ 53:927 2.4. Determination of the degree of hydrolysis The degree of hydrolysis is defined as the percentage of peptide bond cleaved during the enzymatic reaction. It is expressed by the following equation [12]: DHð%Þ ¼
h 100 BNb 100 ¼ htot ahtot MP
Fig. 1. Hydrolysis curve for different temperatures (s0 = 4 g/l; e0 = 0.04 g/l; pH 8.0).
D. Shi et al. / Process Biochemistry 40 (2005) 1943–1949
Fig. 2. Hydrolysis curve for different pH (s0 = 4 g/l; e0 = 0.04 g/l; T = 40 8C).
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Fig. 4. Hydrolysis curve for different enzyme concentrations (s0 = 2.5 g/l; pH = 8.0; T = 40 8C).
However, it is evident that the reaction rate declines fast at high temperature due to the denaturing of enzyme protein. For example, the initial rate of hydrolysis reaction at 50 8C is the fastest and the decreasing rate of DH is the fastest, too.
substrate inhibition exists in the BSA tryptic hydrolysis system. It is possible to generate inactive middle complexes from enzyme and excessive substrate, and the inactive complex cannot decompose to yield hydrolysates.
3.1.2. Influence of pH The activity of enzyme is strongly affected by pH because the active enzyme exists as a kind of ionized form. The changing of pH can influence the dissociation of active groups of the enzyme, which affects the banding of enzyme and substrate. As a result, there is an appropriate interval of pH for each enzyme, which can be determined by experiments. Fig. 2 is the experimental results of BSA hydrolysis at different pH conditions. It is shown that the reaction rate is slowest at pH 7.0, and is fastest at pH 9.0. The reaction rate at pH 10.0 declines fast with time than that at other pH conditions although the initial rate is fast. It is possible that the denaturation rate of enzyme protein is fast at too high pH condition. Therefore, maintaining pH at a stable and appropriate value is important for protein enzymic hydrolysis.
3.1.4. Influence of the ratio of enzyme to substrate Generally speaking, reaction rate is in proportion to the amount of enzyme when the quantity of substrate is adequate, which also can be found in Fig. 4. The reaction rate deals with the rate of yielding the middle complex, which is dependent on the amount of enzyme. But the amount of enzyme used in the hydrolysis reaction is restricted by a lot of factors, such as the price of enzyme and self-hydrolysis of some kinds of enzyme. The problem of self-hydrolysis is serious for trypsin at high concentration. As a result, a high concentration of trypsin is not suitable for hydrolysis reaction. 3.2. Molecular weight distribution of tryptic hydrolysates of BSA
3.1.3. Influence of concentration of substrate The concentration of substrate is an important factor for protein enzymic hydrolysis, since substrate inhibition often exists in enzymic reactions. The degrees of hydrolysis at different initial concentrations of substrate are shown in Fig. 3. The reaction at low substrate concentration exhibits a high reaction rate, which is slow, at high substrate concentration. It can be concluded from Fig. 3 that serious
The molecular weight distribution of hydrolysates is regular because of the influence of the specification of enzyme and the space structure of substrate. HPSEC was used to analyze the molecular weight distribution of tryptic hydrolysates of BSA. Fig. 5 is the chromatogram of BSA hydrolysates at 2.5 min, 20 min and 60 min. There are nine absorption peaks in the chromatogram, which can be vested in four evident districts corresponding to molecular weight ranges: 127,000–24,000; 24,000–6300; 6300–3000 and
Fig. 3. Hydrolysis curve for different initial substrate concentrations (e0 = 0.03 g/l; pH = 8.0; T = 40 8C).
Fig. 5. HPLC of bovine serum albumin tryptic hydrolysates after 2.5 min (curve a), 20 min (curve b) and 60 min (curve c).
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3000–300. The area of the first district decreased with time while that of other districts increased. This shows that the polypeptides whose molecular weights are large carry out a decomposition reaction primarily, while the generating rate of small peptides is faster than the decomposition rate.
B.
3.3. Lumping kinetic model for tryptic hydrolysis of BSA 3.3.1. Establishment of kinetic model The mechanism of protein enzymic hydrolysis can be described by the following steps. First, free enzyme combines with substrate to form an active middle complex. Then, the peptide chain cracks, and the complex decompose to two products. At the same time, the enzyme is set free. This is the rate deterministic step as shown in Eq. (1). Product inhibition and substrate inhibition exist in the hydrolysis reaction. Km
kcat
E þ S , ES ! E þ P
D. E.
(1)
The inactivation of enzyme fits well with first-order model [14], i.e. dCE ¼ kd CE (2) dt Taking into account product inhibition, substrate inhibition and enzyme inactivation, the performance of each lump in the system can be described by following Eq. (3). dCS ¼ kcat CES dt ¼
C.
kcat CS CE0 exp ðkd tÞ ð1 þ ðCp =Kmp ÞÞKm þ CS ð1 þ ðCS =KsÞþðCp =KpÞÞ (3)
Before the establishment of the model, some hypotheses have been put forward as follows: A. Hydrolysis reaction is affected by the space structure of substrate, the specificity of enzyme and other factors.
F.
The cleavage position of peptide is not random, and the molecular weight contribution is regular. In the same reaction system, dynamic performances of substrates are similar if their molecular weights are alike. In the enzymatic reaction, primarily two processes determine the kinetic behaviour of substrates. (a) The combination of enzyme and substrate and the dissociation of the complex. (b) The release of free enzyme and product. The two processes are affected by molecular weight of the substrate. Product inhibition, substrate inhibition and enzyme deactivation exist in the hydrolysis process and the kinetic behaviour of each lump can be described by the modified Michaelis–Menten equation, i.e., Eq. (3). There is no interaction of the products, which means that enzymic synthesis does not take place. The lumps whose molecular weights are large can yield the smaller lumps. The lump which molecular weight is the smallest does not hydrolyze. The reaction is carried out in homogeneous phase, and the influence of diffuse resistance does not exist.
Then, the components in the hydrolysis reaction can be combined to several lumps based on the data obtained from HPSEC. The number of lumps should accord with the practical demand. Not only the number of absorption peaks is considered, but also the difficulty of experiments and the estimation of parameters. According to the hypothesis and the molecular weight distribution of hydrolysates, the products of BSA tryptic hydrolysis were combined into four lumps. After all components were grouped into lumps, the network for BSA hydrolysis can be built up, and is shown in Fig. 6. The kinetic model contains four lumps and six kinetic parameters. Lump ‘A’ represents the components which molecular weights are the biggest, and the lump ‘D’ represents the smallest. Then, the differential equation set, which describes the lumping network of BSA hydrolysis, is shown as follows.
dCA ðk1 þ k2 þ k3 ÞCE0 CA exp ðkd tÞ ¼ CB CC CD CA CB CC CD dt þ þ þ þ þ 1þ KmA þ CA 1 þ KmB KmC KmD KsA KpB KpC KpD = (k1 + k2 + k3) A1 dCB ¼ k 1 A1 dt
ðk þ k5 ÞCE0 CB exp ðkd tÞ 4 = k1 A1 (k4 + k5) A2 CC CD CA CB CC CD þ þ þ þ 1þ KmB þ CB 1 þ KmC KmD KsA KsB KpC KpD
dCC k6 CE0 CC expðkd tÞ ¼ k 2 A1 þ k 4 A2 ð1 þ ðCD =KmD ÞÞKmC þ CC ð1 þ ðCA =KsA Þ þ ðCB =KsB Þ þ ðCC =KsC Þ þ ðCD =KpD ÞÞ dt = k2 A1 + k4 A2 k6 A3 dCD ¼ k 3 A1 þ k 5 A2 þ k 6 A3 dt
D. Shi et al. / Process Biochemistry 40 (2005) 1943–1949
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Table 1 Results of parameters estimation Reaction
Reaction constant
30 8C
40 8C
50 8C
A!B A!C A!D B!C B!D C!D
k1 k2 k3 k4 k5 k6
2.6465 0.2898 0.06293 0.5613 0.2484 0.6030
4.6174 0.4578 0.1107 0.8213 0.4268 0.9085
10.2481 0.8737 0.1830 1.3482 0.8052 1.3517
The unit of k is min1. Fig. 6. Four lumps network for BSA tryptic hydrolysis.
3.3.2. Parameter estimation The problem of multi-value dependency often exists in parameter estimation in the lumping kinetic model, since the number of parameters is larger than the number of differential equations. In order to avoid the problem, the kinetic constants of the model were estimated by Marquardt’s method in two steps from lower level to upper level. First of all, the parameters of the sub-reaction system, which contains lumps B, C and D, were calculated. Then the residual three parameters of the four lumps network at different temperatures were estimated. Table 1 shows the results of parameter estimation. It is shown in Table 1 that there are several products for the large lump and the rate of generating different small lumps from the large lump is different. The rate of yielding a large lump is faster than that of small lump. For example, the rate constant of the reaction that yields lump B from lump A is larger than that of the reaction yielding lump C. The reason is that hydrolysis reaction rate is affected by the decomposition of the enzyme–substrate complex. The
combination position of substrate and enzyme is not random, and inclined to form the complex that can decompose easily. It is easy to be set free from the complex for the product whose volume is large because of the space repulsion. As a result, the apparent rate is fast for this kind of reaction. Fig. 7 is the comparison of the observed values of each lump with the computed values for parameter estimation at 30 8C, 40 8C and 50 8C, respectively. The initial reaction rates rise along with the temperature increase. Accompanied by the proceeding of the hydrolysis reaction, however, the reaction rates decrease faster at high temperature than at low temperature, due to the faster inactivation rate of trypsin at high temperature. The concentration of lump B and C increases with time, since the decomposition rates are lower than the generating rates. Compared with lumps C and D, the generating rate of lump B is fast, which also certifies that the hydrolysates with large volume can be produced easily. When the conditions of the concentration of substrate, ratio of enzyme to substrate and pH are settled, the rate constant is the function of temperature and follows the Arrhenius equation. The relationship between rate constants
Fig. 7. Comparison between observed values and computed values at different temperatures. Line: computed values; Sign: observed values: (&) lump A; (*) lump B; () lump C; and (~) lump D.
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Table 2 Comparison between observed and computed values at 35 8C Reaction time (min) Lump A (mg/ml)
Lump B (mg/ml)
Lump C (mg/ml)
Lump D (mg/ml)
Observed value Computed value Observed value Computed value Observed value Computed value Observed value Computed value 15 25 40 60 80 110
3.2373 2.8681 2.5906 2.2180 1.9878 1.7250
3.0994 2.8305 2.5045 2.1712 1.9178 1.6380
0.5025 0.7023 0.9126 1.1590 1.3302 1.4808
0.6397 0.8326 1.0578 1.2799 1.4437 1.6195
0.2306 0.2874 0.3323 0.4097 0.4518 0.5149
0.2394 0.2849 0.3431 0.4046 0.4524 0.5058
0.5296 0.6222 0.6709 0.7433 0.7902 0.8293
0.4714 0.5020 0.5447 0.5944 0.6363 0.6868
Table 3 Comparison between observed and computed values at 45 8C Reaction time (min) Lump A (mg/ml)
Lump B (mg/ml)
Lump C (mg/ml)
Lump D (mg/ml)
Observed value Computed value Observed value Computed value Observed value Computed value Observed value Computed value 10 18 30 45 65 90
2.9144 2.7207 2.2894 1.8440 1.3597 1.1659
2.6616 2.3653 1.9989 1.6981 1.4400 1.2491
0.9837 1.1419 1.3541 1.6159 1.9792 2.1624
1.1547 1.3713 1.6298 1.8341 2.0028 2.1229
of each lump and reaction temperatures is shown in Fig. 8. The straight line in Fig. 8 indicates that the relationship can fit the Arrhenius equation well. The reaction active energy for each lump can be calculated by the Arrhenius equation, and that of the lumps is between 32 kJ/mol to 55 kJ/mol. 3.3.3. Verification of the lumping mode In order to examine the ability of prediction and extrapolation of the lumping kinetic model and the liability of the obtained rate constants, the hydrolysis experiment was preceded under other conditions different from that of estimating the parameters. For example, the composition of initial substrate, reaction temperatures and sampling time are changed. The results of comparing observed values with computed values show that the lumping kinetic model can predict the mass concentration of each lump effectively. Tables 2 and 3 are the results of the comparison of experimental values and computed values at 35 8C and 45 8C, respectively.
Fig. 8. Relationship between ln k and temperatures.
0.3499 0.4062 0.4600 0.5263 0.6244 0.6787
0.3601 0.4077 0.4703 0.5246 0.5734 0.6110
0.6520 0.7412 0.7965 0.8538 0.9276 0.9830
0.6202 0.6523 0.6975 0.7397 0.7802 0.8132
There are some deviations between observed values and computed values from the lumping model. In the kinetic model, there are some other parameters such as the Michaelis–Menten constants, substrate inhibition constants and product inhibition constants of each lump to be determined in experiments. Too much parameter will result in some errors for the rate constant estimations. In addition, the quantitative analysis of mass concentration for the hydrolysates is not sufficiently precise owing to the multicomponent complexity of products. Furthermore, the rate constants at 35 8C and 45 8C calculated by Arrhenius equation are not very accurate.
4. Conclusion This work investigated the influence of operating parameters on the degree of hydrolysis of BSA by pHstat in a batch stirred tank reactor. The molecular weight distribution of tryptic hydrolysates of BSA was analyzed by HPSEC. Four lumps kinetic model for bovine serum albumin tryptic hydrolysis reaction were then established. Some hypothesis about the mechanism of the reaction and the lumping criteria were made before the establishment of the model. The reaction of the lumps was described with intrinsic kinetic equations, which contain the influence of product inhibition, substrate inhibition and enzyme inactivation. The rate constants were calculated by Marquardt’s method in two steps from lower level to upper level. The reliability of the lumping model was tested by comparing the computed values with the experimental values. The results showed that the lumping kinetic model could predict the distribution of the mass concentration of products.
D. Shi et al. / Process Biochemistry 40 (2005) 1943–1949
Acknowledgment The authors are very grateful for the financial support from the National Natural Science Foundation of China (Grant No. 20276052).
References [1] Akemichi U, Yeong-Man H, Naokatu A, Yoshiro T. Insulin-stimulating peptide from a tryptic digest of bovine serum albumin: purification and characterization. J Biochem 1985;98:269–78. [2] Masakazu T, Shigeo M, Toshiko M, Hiroyuki S, Akira S, Yasuyuki T, et al. Albutensin A, an ileum-contracting peptide derived from serum albumin, acts through both receptors for complements C3a and C5a. Lett Pep Sci 1998;5:29–35. [3] Gonzalez-Tello P, Camacho F, Jurado E, Pa´ ez M, Guadix E. Enzymatic hydrolysis of whey proteins: kinetic models. Biotech Bioeng 1994;44:523–8. [4] Marquez M. Enzymatic hydrolysis of vegetable proteins: mechanism and kinetics. Proc Biochem 1993;28:481–90. [5] Marquez M, Vazquez M. Modeling of enzymatic protein hydrolysis. Proc Biochem 1999;35:111–7.
1949
[6] Cao G, Viol A, Baratti R, Morbidelli M, Sanseverino L, Cruccu M. Lumped kinetic model for propene–butene mixtures oligomerization on a supported phosphoric acid catalyst. Appl Catal 1988; 41:301–12. [7] Carraway R, Mitra S, Cochrane D. Structure of a biologically active neurotensin-related peptide obtained from pepsin-treated albumin. J Biochem Chem 1987;262:5968–73. [8] Fang X, Tan H, Zhao Y. Study on hydrocracking lumped kinetic model. Acta Petrolei Sin Petroleum Processing Section 1996;12: 33–8. [9] Froment G. Kinetic modeling of acid-catalyzed oil refining processes. Catal Today 1999;52:153–63. [10] Weng H, Ouyang F, Ma J. Lumped model for heavy oil catalytic cracking reaction (I) establishment of the model. J Chem Ind Eng China 1995;46:663–7. [11] James C, Edwin N. Lumping analysis of biochemical reaction systems with time scale separation. Biotech Bioeng 1988;31:869–79. [12] Alder-Nissen J. Enzymatic Hydrolysis of Food Protein. London: Elsevier; 1986. [13] Steinhardt H, Beychok S. Interaction of protein with hydrogen ions and other small ions and molecules. In: Neurath H, editor. The Proteins. New York: Academic Press; 1964. p. 139–304. [14] Zhimin H, Ziding Z, Mingxia H. Kinetic study of thermal inactivation for native and methoxypolyethylene glocol modified trypsin. Proc Biochem 2000;10:1235–40.