Quantification of two-step proteolysis model with consecutive demasking and hydrolysis of peptide bonds using casein hydrolysis by chymotrypsin

Biochemical Engineering Journal 74 (2013) 60–68

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Regular article

Quantification of two-step proteolysis model with consecutive demasking and hydrolysis of peptide bonds using casein hydrolysis by chymotrypsin Mikhail M. Vorob’ev ∗ A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, 28 ul. Vavilova, 119991 Moscow, Russia

a r t i c l e

i n f o

Article history: Received 17 May 2012 Received in revised form 21 February 2013 Accepted 27 February 2013 Available online 7 March 2013 Keywords: Proteolysis model Chymotryptic digestion Enzymatic kinetics Peptide bond demasking Casein hydrolyzates

a b s t r a c t Enzymatic hydrolysis of peptide bonds becomes possible after removing steric obstacles shielding polypeptide sites against enzymatic attack, i.e. after demasking of these sites. In a simple two-step model, proteolysis was regarded as a two-step process with consecutive demasking and hydrolysis stages. A new analytical procedure was suggested to determine three experimental kinetic parameters: demasking rate constant kd , degree of initially masked peptide bonds m and maximum hydrolysis rate constant kh . The approach was shown on the example of the hydrolysis of summary casein by chymotrypsin (25 ◦ C, pH 7.5). Kinetic analysis includes the determination of an apparent Michaelis constant that we regard as a function of the degree of peptide bond hydrolysis. Two sets of hydrolysis rate constants were used to calculate the parameters of a two-step model. It was found that kd is lower than the hydrolysis rate constants for specific sites consisting of aromatic amino acid residues, and at least a half of peptide bonds is initially masked in casein. Using parameters of a two-step model, we calculated second-order rate constant and degrees of hydrolysis for specific peptide bonds as functions of the hydrolysis degree. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Proteolysis, the enzymatic hydrolysis of a protein, plays an important role in various fields of bioscience and biotechnology. Technologically, there are broad applications in food processing, including processing of casein and whey milk proteins [1]. Practically important examples of the proteolysis with these proteins are the preparation of hypoallergenic hydrolysates with low size peptides [2], the modification of proteins by limited proteolysis to improve functional properties [3], the preparation of biologically active peptide mixtures from protein precursors [4,5], etc. For all these patterns, it is important to know how the fragmentation of the polypeptide chain proceeds in time, i.e. the kinetics of proteolysis. The substrate specificity of proteolytic enzymes was studied extensively for small synthetic substrates with one bond to be hydrolyzed [6]. On the contrary, a polymeric polypeptide chain may be split during proteolysis at various sites resulting in many different peptide fragments. A hydrolysis of single peptide bonds with appearance of a few peptide fragments may occur only in the case of very specific proteases like rennin [7]. The hydrolysis by endoprotease like chymotrypsin or trypsin gives a large number of

∗ Tel.: +7 499 1356502; fax: +7 499 1355085. E-mail address: [email protected] 1369-703X/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.bej.2013.02.020

peptide fragments, a fact that makes kinetic studies difficult [5]. A detailed kinetic description of proteolysis should include the time dependent concentrations of all proteolytic components including the concentrations of initial proteins, intermediate peptides, and resulting short peptides. A more simple way is to characterise the proteolysis kinetic by total concentration of all components, e.g. by the concentration of all free ␣-amino groups, the amino nitrogen. In the proteolysis studies, an important task is the characterisation of the conformational changes in polypeptide segments, which are initially buried inside protein structures or micelles [8]. An increase in accessibility of these segments for the enzyme, the process known as the demasking of peptide bonds [1], causes an acceleration in the peptide bond hydrolysis [9,10]. A progress in the real-time monitoring of conformation changes during proteolysis was made recently with FTIR, circular dichroism and fluorescence spectroscopy [11,12]. One needs to take into consideration the kinetic of demasking to be able to describe the proteolysis kinetics as a whole [10,12]. The numerical evaluation of the hydrolysis rate constants is based on the kinetic studies implemented for small synthetic or peptide substrates, where chemical bonds are accessible for enzymatic attack, i.e. demasked. It is well-known that rate constants of the hydrolysis are dependent on the composition and sequence of amino acid residues of the cleavage site [13,14]. For the hydrolysis of synthetic substrates, the primary specificity is determined by the interaction of one amino acid residue at the P1 position of the

M.M. Vorob’ev / Biochemical Engineering Journal 74 (2013) 60–68

Nomenclature t  i X Y Xi X0i Yi Y0i Ni N N0 S0 s0 E0 E kd k kh ki d V

v kII (d) KM (d) KP (l, j) KS (l, j) j

Sl /S x m i i0 V  (d) V  (d) aj , bj nj

original proteolysis time (min) reduced proteolysis time (min) type of peptide bonds concentration of all masked peptide bonds (M) concentration of all demasked peptide bonds (M) concentration of masked peptide bonds of ith type (M) initial concentration of masked peptide bonds of ith type (M) concentration of demasked peptide bonds of ith type (M) initial concentration of demasked peptide bonds of ith type (M) concentration of the proteolysis products with Cterminal residues of ith type (M) concentration of all ␣-amino groups (amino nitrogen) (M) initial concentration of amino nitrogen (M) concentration of all ␣-amino groups and peptide bonds (M) substrate concentration (g L−1 ) enzyme concentration (M) concentration of free enzyme (M) first-order rate constant of demasking (min−1 ) second-order rate constant of demasking (M−1 min−1 ) first-order maximum rate constant of hydrolysis of the demasked bonds (min−1 ) second-order hydrolysis rate constant for bonds Yi (M−1 min−1 ) degree of hydrolysis total rate of the peptide bond hydrolysis (M min−1 ) relative hydrolysis rate (min−1 ) second-order rate constant, the function of d (M−1 min−1 ) apparent Michaelis constant, the function of d (g−1 L) dissociation productive constant dissociation non-productive (inhibition) constant (g−1 L) probability that a random bond in a random peptide is the jth bond in the lth peptide degree of masking of peptide bonds initial degree of masking relative hydrolysis rate constant for ith bonds fraction of initially masked bonds of ith type rate of hydrolysis at the hydrolysis degree d and the substrate concentration s0 (M min−1 ) rate of hydrolysis at the hydrolysis degree d and the substrate concentration s0 (M min−1 ) coefficients, the parameters of two-step model hydrolysis degree of the bonds of jth type

substrate with the amino acid residues at the bottom of the S1 site of an enzyme [14,15]. Casein as a substrate represents conformationally flexible polypeptide chains with loosely packed spatial structures [16]. Caseins, especially ␤-casein, as the most hydrophobic protein among ␬-, ␣s1 -, and ␣s2 -caseins, may form micelles and submicelles [16,17]. Compared with globular proteins, casein is known to be easily hydrolysed by proteases because of its elevated conformational flexibility and the abundance of the

61

enzyme-accessible peptide bonds [15,18–20]. It was reported that clusters of hydrophobic amino acid residues in the polypeptide chain of casein substrate cause hydrophobic interactions to be responsible for the steric obstacles which protect peptide bonds against enzymatic attack [15]. For the proteolysis of ␤-casein by trypsin, the process was regarded as a two-step model involving consecutive demasking and hydrolysis stages [15,21]. The parameters of a two-step model are specific for a given enzyme–substrate pair, while hydrolysis rate constants for various demasked bonds are assumed to be constant in all substrates. The sequential hydrolysis by an endoprotease and a carboxypeptidase can be used for the generation of hydrolysates with low Phe content, being suitable for the phenylketonuria patients [22,23]. Hydrolysis by endoprotease like chymotrypsin yields peptides with C-terminal residues of Phe, which subsequently may be liberated by the action of carboxypeptidase A [22,23]. The role of peptide bond demasking to facilitate the liberation of the proteolysis products with Phe in carboxyl position is an important question. Besides this case, an optimisation of proteolysis considering the demasking stage would be of interest for the debittering of hydrolysates, production of bioactive peptides, etc. Here, we report a method to describe the kinetics of a total proteolysis by using a two-step proteolysis model. To perform calculations, one needs only the time dependent amino nitrogen concentrations for proteolysis experiments implemented at different substrate concentrations. On the example of chymotrypsin action on casein, we demonstrate an easy procedure to determine three parameters of the two-step model: the demasking rate constant, the degree of initially masked peptide bonds, and the maximum hydrolysis rate constant. 2. Materials and methods 2.1. Materials Chymotrypsin was a product of Sigma–Aldrich (EC 3.4.21.1). Submicellar casein was obtained from defatted bovine milk. Casein proteins were precipitated three times by HCl (pH 4.6, temperature 6–8 ◦ C), filtered, washed and solved by adding NaOH (pH 7.0). After the addition of acetic acid (pH 4.0), the precipitate was carefully washed, solved by adding NaOH, purified by charcoal, centrifuged and dried in vacuum [10]. 2,4,6-Trinitrobenzenesulfonic acid (TNBS) was obtained from Biokhimreactive, Russia. All other reagents were of analytical grade obtained from commercial sources. 2.2. Proteolysis as registered by TNBS method Proteolysis of casein by chymotrypsin was carried out in 0.01 M phosphate buffer (pH 7.5) at 25 ◦ C with stirring by a magnetic stirrer. The enzyme concentration was constant (2.5 mg L−1 ). To monitor the proteolysis reaction by the TNBS method [10,24], 1 mL samples from proteolysis reactor were placed in the test-tubes with 1 mL 1% (w/v) SDS solution at 80 ◦ C and held at this temperature for 10 min. Then 2 mL of trinitrobenzenesulfonic acid solution (TNBS, 0.2 g L−1 ) in 0.1 M borate buffer (pH 8.2) was added to each of the tubes. Trinitrophenylation of the amino groups of the proteolysis products was performed at 40 ◦ C for 2 h [10,24]. This reaction was stopped by the adding 1 ml 1 N HCl to each tube. Then the absorption was measured at 340 nm against a buffer sample. The latter was prepared in the same way except for the absence of the enzyme and substrate. In the result, the values of amino nitrogen N(ti ) were determined at time points ti . They were taken as follows: 0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 20, 23, 27, 30, 35, 40, 50, 60, 70, 80, 90, 100,

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M.M. Vorob’ev / Biochemical Engineering Journal 74 (2013) 60–68

110, 120 min at s0 = 0.1 g L−1 , for example. Values of the current rate of hydrolysis V were calculated as V(t) = (N(ti+1 ) − N(ti ))/(ti+1 − ti ) at the time points t = (ti+1 + ti )/2.

Therefore, proteolysis can be presented in time scale  as a new process, which goes at constant free enzyme concentration E0 with the relative rate  = V/S0 :

2.3. Kinetic analysis

=

On the first stage of a two-step proteolysis process, the initially enzyme-inaccessible peptide bonds X are converted to the demasked bonds Y, which become accessible for the action of the enzyme. On the second stage, these bonds are hydrolysed as [10,12,21]:

On the other hand, the relative rate  can be determined from the experimental rate V by equation

kd

kh

X −→Y −→N,

ki E

kE

X i −→Y i −→N i

(1)

where kd is the first-order rate constant of demasking, kh is the first-order maximum rate constant of hydrolysis of the demasked bonds, and N is the amino nitrogen, the chemical outcome of the reaction. Xi and Yi are the concentrations of masked and demasked peptide bonds of ith type, the type of the peptide bond i is determined by the type of amino acid residue, forming the C O group of the hydrolysed bond (primary specificity) [13], k is the secondorder rate constant of demasking, ki is the second-order hydrolysis rate constant for the bonds Yi , which gives products Ni , E is the concentration of free enzyme. The important characteristic is the hydrolysis degree d (or DH = 100% d), the portion of the hydrolysed peptide bonds d = N/S0 = N/(N + X + Y ). The total rate of the peptide bond hydrolysis can be presented as kII (d)E0 S0 dN S0 d(d(t)) = =E = V= dt 1 + s0 /KM (d) dt



i

kY

i

(2)

1 = KM

l

l,j

KS (l, j)

S

where summation in Eq. (3) is taken over all possible peptides l and all possible amino acid units j in them [25], KP (l, j) and KS (l, j) are the dissociation productive and non-productive (inhibition) j constants and Sl /S has the meaning of probability that a random bond in a random peptide is the jth bond in the peptide Sl [25]. j The ratios Sl /S are supposed to be independent on S0 and E0 , being functions of d only. This is proved by the establishing of similarity of peptide compositions obtained at the same hydrolysis degree in various experiments with different S0 and E0 [26]. Eq. (2) looks like Michaelis–Menten equation but it includes the functions kII (d) and KM (d) instead of constant parameters. One can describe the proteolysis reaction in a shorter time-scale by introducing a new time coordinate . From Eq. (2) we obtain dt d(d) = d = kII (d)E0 1 + s0 /KM (d(t))

(4)

where



= 0

t

1 dt  1 + s0 /KM (d(t  ))

(5)

(7)

i

For E = E0 = const, demasking and hydrolysis kinetics for the individual masked and demasked bonds, respectively, were described by the following equations: dX j = −kX j E0 d

(8)

dY j = −kj Y j E0 + kX j E0 d

(9)

where kj is the hydrolysis rate constant for the bonds of jth type, k is the rate constant of demasking, which is proposed to be the same for any type of peptide bonds j. For k = / kj , the solutions of Eqs. (8) and (9) are X j = X0 e−kE0  j

(10)

and j

Y =

i

(3)

(6)

 s0 ki Y i = E0 KM (d)

=



j

where kII (d) is the second-order rate constant, whose variation during proteolysis is connected with continuous changing of the composition of peptide bonds, KM (d) is the apparent Michaelis constant responsible for the inhibition and productive binding, E0 and S0 (s0 ) are constant parameters, the enzyme and substrate concentrations, respectively. Both kII (d) and KM (d) are assumed to depend only on the hydrolysis degree as being ensemble-averaged values determined by averaging over the multiplicity of all peptide bonds in all peptides of the reaction mixture [25]. For example, 1/KM (d) was introduced as [25]:

 KP (l, j) + 1 Sj

d(d()) = kII (d)E0 d

kX0 kj − k

e

−kE0 

+

j Y0



j

−

kX0

j

e−k E0 

kj − k

(11)

From Eq. (10), it follows for the degree of peptide bond masking x = X i /X0i



x=

X1 X01

=

X2 X02

=

X3 X03

Xj

j

= ··· =

(12)

S0 − N0 − Y0

The mass balance equations were presented in the following form: X1 + X1

X02 X01

+ X1

X03 X01



+ ··· =

X j = S0 − N −

j



Yj

(13)

j

and S0 = N0 + X0 + Y0

(14)

of the total concentration of all pepwhere S0 = const ⎛ is the sum ⎞ tide bonds

⎝



Xj +

j



Y j ⎠ and amino nitrogen N, N0 is the

j

initial concentration of amino  nitrogen, Y0 is the sum of all inij

tially demasked peptide bonds

masked peptide bonds



Y0 , X0 is the sum of all initially

j j

X0 .

j

Eq. (12) shows that it is possible to describe demasking kinetics by using only one type of peptide bonds (first type, for example) because k is independent on the type of peptide bonds. The mass balance equations (13) and (14) come from the constancy of the sum of amino acid residues in all molecules participating in the reaction. According to Eq. (13), the concentrations of the masked and demasked bonds are not independent, while S0 and N0 are constants for the given protein substrate, being independent on the state of masking.

M.M. Vorob’ev / Biochemical Engineering Journal 74 (2013) 60–68

From Eqs. (7) and (11), it is easy to obtain an equation for the relative hydrolysis rate as a function of ␶ (N0 = 0):



1  =  (0) (1 − m) i i0 i



+m



i i0

i

mkd e−kd 

kh i − kd

kd 1−m − m kh i − kd

The procedure of data processing includes the following steps:

i

e−kh  

(15)

where m is the initial degree of masking, i.e. m = X0 /S0 , kh = k1 E0 is the maximum first-order hydrolysis rate constant (k1 = kTrp ), i = ki /k1 is the relative hydrolysis rate constant for ith bonds, kd = kE0 is the first-order demasking rate constant, (0) is the value of  at  j

 = 0, and i0 = X0i /

X0 .

j

According to Eq. (2), the current hydrolysis rate at the hydrolysis degree d can be presented as kII (d)E0 S0

V  (d) =

(16)

1 + s0 /KM (d)

for the proteolysis experiment implemented at the substrate concentration s0 , and V  (d) =

kII (d)E0 S0

V  (d)s0 − V  (d)s0 1 = (V  (d) − V  (d))s0 s0 KM (d)

(18)

where V  (d) and V  (d) are the current hydrolysis rates measured at the same hydrolysis degree d in two different proteolysis experiments with substrate concentrations s0 and s0 , respectively. The solutions (10) and (11) can be presented regarding to x and d in the following form [12]:

⎛

aj

j

⎞

0 ⎠ = 1 − d − mx j

(19)

where the coefficients aj and bj are defined as aj =

kj −1 k

(20)

bj =

−1

(21)

An appearent second-order hydrolysis rate constant can be calculated as [10] kII (d) = mx

 kj (1 + xaj bj ) j

aj

j

0

(22)

To calculate kII (d) from Eq. (10) one needs first to determine x as a function of d from the transcendent Eq. (19). Using Eqs. (10), (11) and (19), the concentration of proteolysis j products with jth type of amino acid residues at C-end N j = X0 + j

Y0 − X j − Y j can be calculated as a function of d: nj =



Nj j

The values of m, kh , and kd were calculated by the method of nonlinear least squares fitting (Origin® 5.0, Levenberg–Marquardt algorithm). Initial parameter values for kd = 0.03 and kh = 1 were taken from the fluorescence studies of tryptic proteolysis of ␤casein [12]. The parameters of a Lorentz function (Eq. (24)) were determined by the same method.

Determination of the parameters of a two-step model is demonstrated on the example of the proteolysis of summary casein by chymotrypsin. Experimental values of the hydrolysis degree d = N(t)/S0 at various times of proteolysis t are presented in Fig. 1 for proteolysis experiments implemented at substrate concentrations s0 0.4, 0.2, and 0.1 g L−1 (S0 = 1.76, 0.88, and 0.44 mM) at a constant enzyme concentration. Additionally, experimental values of the hydrolysis rate V(t) derived from amino nitrogen data are plotted as a function of t in Fig. 1. The errors of the hydrolysis rate determination by TNBS method were obtained for the hydrolysis of ␤-casein [10] and the average relative error for V over the whole range of proteolysis was estimated to be 16%. To determine the dependence of 1/KM (d), we used Eq. (18), for which the values of hydrolysis rates V  (d) and V  (d) were obtained in two different proteolysis experiments with the substrate concentrations s0 and s0 , respectively. The pair of hydrolysis rates V  (d) and V  (d) corresponds to the same hydrolysis degree d, the argument of the 1/KM (d) function. The experimental values of 1/KM were fitted using a Lorentz function with the following parameters (Fig. 2): 1 1.209 ± 0.321 = (0.21 ± 0.52) +  KM (d)

and j Y aj 0 j X0

Determination of N(ti ) by TNBS-method. Calculation of V(t) = (N(ti+1 ) − N(ti ))/(ti+1 − ti ). Calculation of d(t) = (N(ti ) − N(0))/S0 . Calculation of 1/KM (d). Calculation of (t). Calculation of (t) by Eq. (7). Exclusion of time t and the presentation of data as a massive  vs. . 8. Fitting of these data by Eq. (15) and determination of m, kh , and kd .

3. Results and discussion

for the proteolysis experiment at the substrate concentration s0 . For the determination of KM (d) dependence, the following expression was obtained by dividing Eq. (16) by Eq. (17):

mx ⎝

1. 2. 3. 4. 5. 6. 7.

(17)

1 + s0 /KM (d)

 1 + xaj bj

where nj is the degree of hydrolysis of jth bond. 2.4. Data processing

 i i 0 i

63

j

X0 + Y0

= 1 − mx

j

1 + xa bj aj



+1

(23)

×

0.0399 ± 0.0077 2

4(d − (0.0520 ± 0.0012)) + (0.0399 ± 0.0077)2

(24)

Standard deviations of the parameters are presented in Eq. (24) as obtained by non-linear fitting with program Origin (r2 = 0.910). Using Eq. (24), a new time coordinate  was introduced with Eq. (5) (Fig. 3). Fig. 3 shows that the lower is S0 the close is dependence to the line  = t. By plotting /(0) versus  for the proteolysis experiments implemented at different S0 it becomes obvious that /(0) is independent on S0 (Fig. 4). This feature is in accordance with Eq. (15). Previously, two approaches to quantify the hydrolysis rate constants for chymotrypsin proteolysis were proposed: either by using statistical data on the bond splitting in protein substrates (first approach), or on the basis of kinetic data obtained for small synthetic substrates (second approach) [25]. In the first case, the relative hydrolysis rate constants i were estimated from the

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M.M. Vorob’ev / Biochemical Engineering Journal 74 (2013) 60–68

Fig. 1. Kinetic data for casein proteolysis by chymotrypsin (2.5 mg L−1 ) at different substrate concentrations at temperature 25 ◦ C, and pH 7.5: hydrolysis degree d (䊉) and current hydrolysis rate V (). (a) Casein concentration 0.4 g L−1 ; (b) casein concentration 0.2 g L−1 ; (c) casein concentration 0.1 g L−1 .

radical Ri2 (Table 1). The values of i were calculated from experimental values of kcat /KM for these substrates and the parameters of correlation equations allowing the prediction of kcat /KM on the basis of molar refractions of NHCOR1 , Ri2 and OR3 . In this case, only primary specificity as an impact on catalysis of the amino acid residue at the position P1 was taken into account. Nonlinear regression analysis of the kinetic data was performed in accordance with Eq. (15) when the relative hydrolysis rate constants were kept unchanged. We used one measurement of

analysis of the splitting of various sites in protein substrates (Table 1). The logarithm of the probability that ith bonds remain unhydrolysed in the proteolysis products was accepted to be a reciprocal value of i . In this case, the kinetic parameters are ruled not only by primary specificity but also by secondary specificity, which is determined by amino acid residues out of the position P1. The second set of the hydrolysis rate constants was derived from kinetic data for the hydrolysis of the N-acyl esters of the amino acids R1 CONH CH(Ri2 ) CO OR3 , which have only one side chain Table 1 Values of unchangeable parameters for Eq. (15). Type of peptide bonds i

1 2 3 4 5 6 7 a b c

Amino acid residue at the P1 position

Trp Tyr Phe Met Leu Low-specificc Non-specificc

i0 a

0.0051 0.0385 0.0398 0.0253 0.0897 0.1199 0.6817

Relative hydrolysis rate constant i = ki /k1 b I (statistical method)

II (hydrolysis of synthetic substrates)

1 0.36 0.27 0.085 0.13 0.03 0

1 0.58 0.14 0.005 0.003 0.001 0

The occurrence of the peptide bonds was calculated taking into consideration the relations between individual caseins (␣s1 -, ␤- and ␬-casein) as 4:3:1. Relative hydrolysis rate constants ki /k1 (Trp = 1) were taken from [25]. Low-specific residues (Asn and Gln) and non-specific residues (Gly, Ala, Val, Ile, Ser, Thr, Cys, Pro, His, Lys, Arg, Asp, and Gln).

M.M. Vorob’ev / Biochemical Engineering Journal 74 (2013) 60–68

65

Table 2 Quantification of the parameters of two-step model. Approach

Substrate concentration (g L−1 )

kh (min−1 )

I I I I

0.4 0.2 0.1 0.4, 0.2, 0.1a

2.76 0.84 0.81 1.22

± ± ± ±

0.71 0.38 0.14 0.25

0.044 0.056 0.022 0.048

± ± ± ±

0.007 0.038 0.010 0.010

0.84 0.51 0.56 0.65

± ± ± ±

0.04 0.07 0.02 0.01

0.940 0.906 0.968 0.908

II II II II

0.4 0.2 0.1 0.4, 0.2, 0.1a

0.64 0.44 0.42 0.45

± ± ± ±

0.31 0.16 0.10 0.11

0.061 0.058 0.040 0.052

± ± ± ±

0.045 0.041 0.024 0.025

0.60 0.51 0.49 0.51

± ± ± ±

0.04 0.04 0.03 0.03

0.870 0.893 0.946 0.860

I II

0.05b 0.05b

0.76 ± 0.21 0.44 ± 0.11

0.48 ± 0.05 0.51 ± 0.04

0.907 0.898

a b

kd (min−1 )

0.042 ± 0.020 0.053 ± 0.025

r2

m

Merged set of data obtained at concentrations 0.4, 0.2 and 0.1 g L−1 were fitted by Eq. (15). Data obtained at concentration of 0.05 g L−1 were fitted by Eq. (15) with  = V and  = t, where V is the original reaction rate, and t is the original proteolysis time.

Fig. 2. Variation of 1/KM for different values of hydrolysis degree and fitted Lorentz function. Values of 1/KM were calculated by Eq. (18) when V  and V were measured at substrate concentrations of 0.4 and 0.2 g L−1 (䊉); 0.2 and 0.1 g L−1 ().

Fig. 3. Dependence of new time-coordinate  on original time-coordinate t at substrate concentrations of 0.4 g L−1 (䊉), 0.2 g L−1 (), and 0.1 g L−1 ().

the hydrolysis rate at one moment of time for each of concentrations. Thus, the experimental massive of data included 26 points for one concentration and 26 × 3 points for the merged set of experiments with different s0 in the interval 0.4–0.1 g L−1 . This allowed us to determine three parameters (the demasking rate constant kd , the initial degree of masking m, and the maximum hydrolysis rate constant kh ) for two sets of the relative hydrolysis rate constants summarised in Table 1. The results of non-linear fitting are summarised in Table 2 and plotted in Fig. 4. Errors for the determination of m, kh , kd and r2 are presented in Table 2. It is obvious that two parameters, i.e. kh and m depend on the used approach for the quantification of ki /k1 (Table 1). The value of kd seems to be independent on the set of relative hydrolysis constants, being around 0.05 min−1 . Mean ratio of kd /kh was found to be 0.039 for the first set of relative hydrolysis constants and 0.11 for the second one. For both approaches one can state that the value of kd is less than the hydrolysis rate constant for Phe X bonds (k3 = 3 kh = 0.27 × 1.22 min−1 = 0.33 min−1 for the first approach, and 0.14 × 0.45 min−1 = 0.063 min−1 for the second one). Thus, the demasking process goes slower than the hydrolysis of the specific peptide bonds constituted by aromatic amino acid residues of Trp, Tyr, and Phe.

Fig. 4. Dependence of relative hydrolysis rate /(0) on  at substrate concentrations of 0.4 g L−1 (䊉), 0.2 g L−1 (), and 0.1 g L−1 () with fitted functions for the first approach (—) and the second one (- - -).

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M.M. Vorob’ev / Biochemical Engineering Journal 74 (2013) 60–68

1,2

1

1

0,8

Relative kII(d)

V /V (0)

0,8

0,6

0,4

1 0,6

0,4 3

0,2

0,2

2

0 0

20

40

60

80

100

Proteolysis time, t (min) Fig. 5. Dependence of relative hydrolysis rate /(0) on t at substrate concentration 0.05 g L−1 (䊉) with fitted functions for the first approach (—) and the second one (- - -).

For all studied cases, the values of the parameter m were found to be less than 1. According to a two-step model, parameter m (initial degree of masking) can not be higher than 1. This is now supported experimentally since m was calculated to be near 0.65 for the first approach and 0.51 for the second one. Thus, at least 1/2 part of the peptide bonds in casein is initially inaccessible for chymotrypsin. As it could be expected, some increase in kh should be compensated by a decrease in 1 − m to keep the overall hydrolysis rate the same. In fact, for the first approach, kh is higher and 1 − m (initial degree of demasking) is lower than these parameters are for the second approach. The first approach takes into consideration the cleavage probabilities estimated for chymotryptic proteolysis of various proteins. In this case, the enzyme interacts with several amino acid residues of the substrate polypeptide chain [25]. From the viewpoint of the completeness of the analysis of enzyme–substrate interaction, this approach looks beneficial. However, the calculation of the hydrolysis rate constants was based on the significant simplifications that reduce the validity of the first approach [25]. In particular, for the first approach, the relative hydrolysis rate constants for Met X, Leu X, and low-specific bonds seem to be overestimated. As an alternative to the determination of kh , kd and m based on the merged set of experiments with different s0 in the interval 0.4–0.1 g L−1 , we analysed the kinetics of a single proteolysis reaction at substrate concentration 0.05 g L−1 . In this case, the approximation KM  s0 is supposed to be valid and the fraction of free enzyme is close to 1. The original reaction rate V and proteolysis time t were used in Eq. (15) instead of  and  (Fig. 5). At a substrate concentration of 0.05 g L−1 , the values of kh , kd and m were found to be close to the parameters obtained for the merged set of data in the interval 0.4–0.1 g L−1 (Table 2). Thus, this simple way of kinetic analysis without 1/KM determination may serve properly if the substrate concentration is low enough. By using fluorescent spectroscopy [12], the value of kd = 0.031 was obtained for tryptic hydrolysis of ␤-casein when the maximal hydrolysis rate constant for the most specific Arg X bond was kh = 1, and, consequently, kd /kh = 0.031. This value of kd allowed an estimation of the ratio kd /kLys X , which was discussed previously in relation to the demasking of hydrophobic C-terminus of ␤-casein [15,27]. The mean rate constant for the tryptic hydrolysis of Lys X bonds was 0.04, and kd /kLys X ratio was calculated to be

0 0

0,02

0,04

0,06

0,08

0,1

0,12

Hydrolysis degree, d Fig. 6. Simulation of kII (d) in the framework of a two-step model. Hydrolysis of initially demasked substrate by trypsin (1) with kd = 0.08, and m = 0.05. Hydrolysis of masked substrate by trypsin (2) with kd = 0.08, and m = 0.6. Hydrolysis of masked substrate by chymotrypsin (3) with kd = 1.1, and m = 0.6. The arrows show the interval where the demasked peptide bonds are massively hydrolysed.

0.78 [12]. An analysis of the lag-type kinetics of the accumulation of hydrophobic C-terminal peptide of ␤-casein gave the estimation for kd /kLys X to be around 1 [10]. Thus, for the tryptic proteolysis of ␤-casein, the value of kh exceeds kd at least by one order of magnitude. Present studies revealed that the similar estimation for kd /kh ratio is also valid for chymotrypsin proteolysis of casein (0.039 or 0.11). It is convenient to plot the hydrolysis rate as a function of the hydrolysis degree V(d) [10]. V(d) dependence allowed to express more compactly the curve tail, which corresponds to the slow hydrolysis of non-specific bonds. At low concentrations of the protein substrate (s0  KM ), the fraction of free enzyme, 1/(1 + s0 /KM (d)), is close to 1. Consequently, changes in KM during proteolysis may not influence significantly the fraction of free enzyme and, thereby, the rate of hydrolysis. For low substrate concentration, the proportionality of V(d) to kII (d) is valid (Eq. (2)), and a considerable simplification in the proteolysis description can be achieved. The substrate concentrations in the range of 0.4–0.1 g L−1 are not low enough, therefore, the determination of 1/KM (d) and the transformation of the time coordinate with Eq. (5) was undertaken. It is quite problematic to formulate general model of proteolysis which would be valid at any substrate concentration. Probably, the following ranges of substrate concentration can be selected: s0 < 10 g L−1 , 10 g L−1 < s0 < 100 g L−1 , and s0 > 100 g L−1 . Our model is valid at s0 < 10 g L−1 , because it doesn’t take into consideration secondary masking that should be in the range 10 g L−1 < s0 < 100 g L−1 , transpeptidation (s0 > 100 g L−1 ) and other complications. At s0 < 10 g L−1 , one can reach the maximal simplicity of the kinetic equations (s0 /KM  1 or s0  KM ) by taking the lowest concentration at which accurate monitoring of hydrolysis kinetics is still possible. We analysed the kinetics of a single proteolysis reaction at substrate concentration 0.05 g L−1 that is 13 and 2 times lower than KM (d) at d = 0 and d = 0.05, correspondingly (Fig. 2). The ratio E0 /S0 was in the range from 0.5 × 10−4 (s0 = 0.4 g L−1 ) to 4 × 10−4 (s0 = 0.05 g L−1 ), though this parameter seems to be not so critical. Using Eqs. (19)–(22), we simulated the kII (d) function at various kd and m parameters with hydrolysis parameters presented here for chymotrypsin and published previously for trypsin

M.M. Vorob’ev / Biochemical Engineering Journal 74 (2013) 60–68

(a)

1

0,8

Trp Tyr

0,6

n

i

Phe Met 0,4

Leu Asn+Gln

0,2

0 0

0,05

0,1

0,15

0,2

Hydrolysis degree, d

(b)

1

0,8

Trp 0,6

Tyr

n

i

Phe Met Leu

0,4

Asn+Gln 0,2

0 0

0,05

0,1

0,15

0,2

Hydrolysis degree, d Fig. 7. Simulation of nj in the framework of a two-step model for chymotrypsin with kh = 1, kd = 0.05, and first approach for the determination of relative hydrolysis rate constants. (a) Hydrolysis of initially demasked substrate by chymotrypsin with m = 0.01. (b) Hydrolysis of masked substrate by chymotrypsin with m = 0.6.

[12]. It is convenient to present this function in the relative 

ki i0 (Fig. 6). For the case of demasked substrate

form kII (d)/

i

(m = 0.05), the monotonously decreasing dependence takes place, while for the substrate with the considerable amount of initially masked peptide bonds (m = 0.6), the dependence decreases nonmonotonously. Thus, a non-monotonous drop of kII (d) function is an indication of the demasking of peptide bonds during proteolysis. In the case of masked substrate (m = 0.6), the dependence has a part, where it drops relatively slow (an interval indicated by arrows in Fig. 6). This part of proteolysis process corresponds to the massive hydrolysis of those bonds, which were initially masked and became demasked during proteolysis. In the framework of a twostep model, a transition of peptide bonds from masked to demasked state supplies the population of Y bonds. At some values of the parameters in some time-interval of hydrolysis, a supplement of demasked bonds may exceed a consumption of these bonds. In this case, one should expect even a local maximum of the relative kII (d) function (curve 3 in Fig. 6). The existence of the proteolysis patterns with the maximum of hydrolysis rate was demonstrated for the proteolysis of ␤-casein by chymotrypsin [10]. Generally, the presentation of the hydrolysis rate vs. hydrolysis degree and an analysis of the form of this dependence can help to elucidate the demasking step of proteolysis. Simulation of the evolution of the individual hydrolysis degrees nj in the course of proteolysis were performed by Eq. (23). For the chymotryptic proteolysis, the types of peptide bonds are Trp X,

67

Tyr X, Phe X, Met X, Leu X, and low-specific bonds (Gln X and Asn X). nj (d) functions are presented in Fig. 7 for the case of demasked substrate (m = 0.01) and for the substrate with masking (m = 0.6). As one can see, kinetic curves are spread broader if there is no limitation connected with masking (Fig. 7a). Under masking, the hydrolysis of most specific bonds (Trp X, Tyr X and Phe X) is retarded, therefore, the distribution of kinetic curves looks narrower (Fig. 7b). Thus, our method allowed the prediction of the appearance of peptides with various C-terminal residues for substrates with different levels of peptide bond masking. This could be of practical interest for the optimisation of proteolysis conditions and quantitative evaluation of masking for various substrates. It was shown previously, that the difference in the state of masking significantly effects the initial stages of the proteolysis of milk proteins by chymotrypsin [28]. Present analysis reveals that variation in kd and m parameters leads to the changes the hydrolysis kinetics over the whole extent of proteolysis. Variations in initial kinetics and different patterns of kinetic curves were demonstrated for chymotrypsin and trypsin proteolysis of camel and bovine milk proteins [29]. Several methods, including pH-stat, OPA and TNBS methods, are engaged for proteolysis monitoring, but there is no consensus as to the best method for this purpose [1,30]. In our opinion, the most appropriate are TNBS and OPA methods [31,32], since they allow us the monitoring of amino nitrogen growth at low substrate concentrations directly by the chemical reaction with liberated amino groups [14]. The estimation of m, kh and kd was made in the framework of the model simplifications among which the reduction to zero of the peptide bond masking at the end of proteolysis is not so obvious. An association and folding of large peptide fragments may occur during proteolysis. These processes can be considered as a secondary masking effect that arises after the liberation of the specific peptide fragments. In the two-step model, the secondary masking and residual masking at the end of proteolysis was not taken into consideration. Verification of this point for various protein substrates and proteolysis conditions may require an additional study. A general problem of the proteolysis kinetic description consists in a large number of kinetic parameters corresponding to the elementary transformations of the components of the reaction. Even if one managed to determine individual kinetic curves for the main peptides, it would require mathematical modeling to determine parameters [33]. An alternative of the complete proteolysis description is the usage of simple empirical models, containing only a few parameters [34,35], or Michaelis–Menten model with constant coefficients [36]. These parameters can be accurately measured, though some of them might not have strong chemical background. The parameters of a two-step model have definite chemical sense and they can be measured with sufficient precision. Taking into consideration the different hydrolysis abilities of various peptide bonds is an important characteristic of our method. The hydrolysis rate constants needed for the two-step model were taken from other kinetic experiments [25]. However, we are going to develop a method that will be able to determine all parameters of a two-step model in one set of experiments.

4. Conclusions In the framework of a two-step model, proteolysis of casein by chymotrypsin was regarded as a two-stage process with consecutive demasking and hydrolysis stages. By analysis of the dependences of the hydrolysis rate on the proteolysis time it is possible to determine three parameters of the two-step model: demasking rate constant, degree of initially masked peptide bonds and maximum hydrolysis rate constant. Quantification of these

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parameters opens a way for the simulation of the practically important kinetic characteristics of proteolysis. As an example, we calculated second-order rate constant and degrees of hydrolysis for specific peptide bonds as functions of the hydrolysis degree. This approach is applicable for the analysis of proteolysis by an endoprotease with known primary specificity. Our method is useful for the elucidation of proteolysis mechanisms and evaluation of the demasking step of proteolysis. Acknowledgement This research was supported in part by RFBR, Grant no. 11-0401245. References [1] J. Adler-Nissen, Enzymatic Hydrolysis of Food Proteins, Elsevier, London/New York, 1986. [2] A. Clemente, Enzymatic protein hydrolysates in human nutrition, Trends Food Sci. Technol. 11 (2000) 254–262. [3] J.-M. Chobert, Milk protein modification to improve functional and biological properties, in: S.L. Taylor (Ed.), Advances in Food and Nutrition, vol. 47, Academic Press, New York, 2003, pp. 1–71. [4] D.A. Clare, H.E. Swaisgood, Bioactive milk peptides: a prospectus, J. Dairy Sci. 83 (2000) 1187–1195. [5] S.V. Silva, F.X. Malcata, Caseins as source of bioactive peptides, Int. Dairy J. 15 (2005) 1–15. [6] C.S. Craik, S. Roczniak, C. Largman, W.J. Rutter, The catalytic role of the active site aspartic acid in serine proteases, Science 237 (1987) 909–913. [7] L.K. Creamer, A study of the action of rennin on ␤-casein, N. Z. J. Dairy Sci. Technol. 11 (1976) 30–39. [8] A. Fontana, P.P. de Laureto, B. Spolaore, E. Frare, P. Picotti, M. Zambonin, Probing protein structure by limited proteolysis, Acta Biochim. Pol. 51 (2004) 299–321. [9] S.J. Hubbard, The structural aspects of limited proteolysis of native proteins, Biochim. Biophys. Acta 1382 (1998) 191–206. [10] M.M. Vorob’ev, Kinetics of peptide bond demasking in enzymatic hydrolysis of casein substrates, J. Mol. Catal. 58B (2009) 146–152. [11] G. Guler, E. Dzafic, M.M. Vorob’ev, V. Vogel, W. Mantele, Real time observation of proteolysis with Fourier transform infrared (FT-IR) and UV-circular dichroism spectroscopy: watching a protease eat a protein, Spectrochimica Acta 79A (2011) 104–111. [12] M.M. Vorob’ev, V. Vogel, G. Guler, W. Mantele, Monitoring of demasking of peptide bonds during proteolysis by analysis of the apparent spectral shift of intrinsic protein fluorescence, Food Biophys. 6 (2011) 519–526. [13] C. Niemann, Alpha-chymotripsin and the nature of enzyme catalysis, Science 143 (1964) 1287–1296. [14] V. Schellenberger, K. Braune, H.-J. Hofmann, H.-D. Jakubke, The specificity of chymotrypsin. A statistical analysis of hydrolysis data, Eur. J. Biochem. 199 (1991) 623–636. [15] M.M. Vorob’ev, M. Dalgalarrondo, J.-M. Chobert, T. Haertle, Kinetics of ␤casein hydrolysis by wild-type and engineered trypsin, Biopolymers 54 (2000) 355–364. [16] H.M. Farrell, E.D. Wickham, J.J. Unruh, P.X. Qi, P.D. Hoagland, Secondary structural studies of bovine caseins: temperature dependence of ␤-casein structure as analyzed by circular dicroism and FTIR spectroscopy and correlation with micellization, Food Hydrocolloids 15 (2001) 341–354.

[17] S. Dauphas, N. Mouhous-Riou, B. Metro, A.R. Mackie, P.J. Wilde, M. Anton, A. Riaublanc, The supramolecular organisation of ␤-casein: effect on interfacial properties, Food Hydrocolloids 19 (2005) 387–393. [18] V. Gagnaire, J. Leonil, Preferential sites of tryptic cleavage on the major bovine caseins within the micelle, Lait 78 (1998) 471–489. [19] J. Leaver, D.G. Dalgleish, The topography of bovine ␤-casein at an oil/water interface as determined from the kinetics of trypsin-catalysed hydrolysis, Biochim. Biophys. Acta 1041 (1990) 217–222. [20] O. Diaz, A.M. Gouldsworthy, L. Leaver, Identification of peptides released from casein micelles by limited trypsinolysis, J. Agric. Food Chem. 44 (1996) 2517–2522. [21] M.M. Vorob’ev, E.A. Paskonova, S.V. Vitt, V.M. Belikov, Kinetic description of proteolysis. Part 2. Substrate regulation of peptide bond demasking and hydrolysis. Liquid chromatography of hydrolyzates, Nahrung 30 (1986) 995–1001. [22] G.A. Pinto, P.W. Tardioli, R.Y.C. Padilla, C.M.A. Galvao, R.C. Giordano, R.L.C. Giordano, Amino acids yields during proteolysis catalyzed by carboxypeptidase A are strongly dependent on substrate pre-hydrolysis, Biochem. Eng. J. 39 (2008) 328–337. [23] C.M.A. Galvao, G.A. Pinto, C.D.F. Jesus, R.C. Giordano, R.L.C. Giordano, Producing a phenylalanine-free pool of peptides after tailored enzymatic hydrolysis of cheese whey, J. Food Eng. 91 (2009) 109–117. [24] S.V. Vitt, M.M. Vorob’ev, E.A. Paskonova, M.B. Saporovskaya, HPLC separation and determination of N-trinitrophenil derivatives of amino acids and peptides, J. High Resolution Chromatogr. Chrom. Com. 6 (1983) 158–159. [25] M.M. Vorob’ev, S.V. Vitt, V.M. Belikov, Kinetic description of proteolysis. Part 3. Total kinetics of peptide bonds hydrolysis in peptide mixtures, Nahrung 31 (1987) 331–340. [26] G. Chabanon, I. Chevalot, X. Framboisier, S. Chenu, I. Marc, Hydrolysis of rapeseed protein isolates: kinetics, characterization and functional properties of hydrolysates, Process Biochem. 42 (2007) 1419–1428. [27] J.-M. Chobert, L. Briand, V. Tran, T. Haertle, How the substitution of K188 of trypsin binding site by aromatic amino acids can influence the processing of ␤-casein, Biochem. Biophys. Res. Commun. 246 (1998) 847–858. [28] M.M. Vorob’ev, I.Y. Levicheva, V.M. Belikov, Kinetics of the initial stages of the hydrolysis of milk proteins by chymotrypsin, Appl. Biochem. Microbiol. 32 (1996) 219–222. [29] M. Salami, R. Yousefi, M.R. Ehsani, M. Dalgalarrondo, J.-M. Chobert, T. Haertle, S.H. Razavi, A.A. Saboury, A. Niasari-Naslaji, A.A. Moosavi-Movahendi, Kinetic characterization of hydrolysis of camel and bovine milk proteins by pancreatic enzyme, Int. Dairy J. 18 (2008) 1097–1102. [30] S.M. Rutherfurd, Methodology for determining degree of hydrolysis of proteins in hydrolysates: a review, J. AOAC Int. 93 (2010) 1511–1522. [31] R. Panasiuk, R. Amarowicz, H. Kostyra, L. Sijtsma, Determination of ␣-amino nitrogen in pea protein hydrolysates: a comparison of three analytical methods, Food Chem. 62 (1998) 363–367. [32] F.C. Church, H.E. Swaisgood, D.H. Porter, G.L. Catignani, Spectrophotometric assay using o-phthaldehyde for determination of proteolysis in milk and isolated milk proteins, J. Dairy Sci. 66 (1983) 1219–1227. [33] R. Munoz-Tamayo, J. de Groot, P.A. Wierenga, H. Gruppen, M.H. Zwietering, L. Sijtsma, Modeling peptide formation during the hydrolysis of ␤-casein by Lactococcus lastis, Process Biochem. 47 (2012) 83–93. [34] A. Margot, E. Flaschel, A. Renken, Empirical kinetic models for tryptic wheyprotein hydrolysis, Process Biochem. 32 (1997) 217–223. [35] M.C. Marquez, M.A. Vazquez, Modeling of enzymatic protein hydrolysis, Process Biochem. 35 (1999) 111–117. [36] P.W. Tardioli, R.S. Sousa, R.C. Giordano, R.L.C. Giordano, Kinetic model of the hydrolysis of polypeptides catalyzed by Alcalase® immobilized on 10% glyoxylagarose, Enzyme Microbial Technol. 36 (2005) 555–564.