Bioelectrochemistry: Ions, Surfaces, Membranes - ACS Publications

8 Enzymatic Clotting Processes. IV. The Chymosin-Triggered Clotting of p-κ-Casein

1

Downloaded by IOWA STATE UNIV on March 2, 2017 | http://pubs.acs.org Publication Date: June 1, 1980 | doi: 10.1021/ba-1980-0188.ch008

T. A .

PAYENS

2

and P A U L A B O T H

Netherlands Institute for Dairy Research, Ede, The Netherlands

The clotting of p-κ-casein brought about by chymosin has been studied under different conditions of enzyme concen tration, ionic strength, and temperature. Flocculation rate constants of p-κ-casein have been estimated from the length of the clotting time. The following results have been obtained: (a) the rule of Segelcke and Storch, which states that the product of clotting time and enzyme concentration is constant, is approximately obeyed; (b) the activation energy of the clotting process proper becomes negative beyond 33°C; (c) the flocculation rate of p-κ-casein is re tarded severely, which is attributed to an orientational constraint in the clotting; and (d) the clotting time shows a pronounced minimum at an ionic strength of about 0.05, which is explained to arise from the opposing effects of an overall electrostatic repulsion and local electrostatic bond formation in the ES complex.

T h e kinetics of the protease-triggered clotting of blood and milk has been formulated i n a number of recent publications from this labora tory (1,2,3). I n milk clotting, the coagulation is initiated through the limited proteolysis of κ-casein, the milk protein component which nor mally protects the casein micelles from flocculation by calcium ions (4). Kappa-casein is a single polypeptide chain of 169 residues, the sequence Dedicated to Prof. E. Havinga on the occasion of his retirement from the chair of organic chemistry at the University of Leiden. 1

Current address: Physico-Chemical Department, Netherlands Institute for Dairy Research, P.O. Box 20, 6710 BA E D E , The Netherlands. 2

0-8412-0473-X/80/33-188-129$05.00/l © 1980 American Chemical Society

Blank; Bioelectrochemistry: Ions, Surfaces, Membranes Advances in Chemistry; American Chemical Society: Washington, DC, 1980.

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BIOELECTROCHEMISTRY: IONS, SURFACES, M E M B R A N E S

of which imparts the protein with an amphipatic character ( 5 ) . Its specific splitting between residues Phe (105) and Met (106) by chymosin ( E C 3.4.23.4) yields insoluble p-*-casein and starts the coagulation of the casein micelles i n milk (4,6). The specificity of this proteolysis has been studied using peptide analogs, which were synthesized i n Havinga's laboratory (7,8,9).


This chapter deals with the clotting of *-casein which follows its proteolysis. T h e rate of change of the weight-average molecular weight, M ^ , of the solute can be calculated by allowing for the enzymatic production of the clotting species i n V o n Smoluchowski's rate theory for the coagulation of unstable colloids (10). The result is (1,2): M /M w

0

-

1 - M o ( l - /) V M l {f(t/r)

-

(1 - /) ( * / T ) 7 3 } / C

0

(1) where M is the weight-average molecular weight; M that of the substrate; / the ratio of the molecular weight of the peptide split off by the enzyme to M ; v the rate of proteolysis; k the flocculation rate constant of the product; and C the solute concentration in g m L " . The parameter T i n Equation 1 is defined as w

0

0

B

1

0

T -

(fc.v/2)"%

(2)

and governs the kinetics of the clotting process. Thus it is clear from Equation 1 that the clotting time, t , of enzymatic clotting reactions to a fair extent is given by c

*C«T

(3)

For a proper discussion of some of the results to be described below, it is instructive to investigate the rate of the clotting as predicted by Equation 1 somewhat closer. Therefore i n Figure 1 we have plotted the progress curve of the reduced weight-average molecular weight for different values of the parameters v and k . The molecular weight passes through a shallow minimum, which is caused by the dominancy of the proteolysis of the substrate during the lag phase. Indeed, one easily verifies from Equation 1 that the depth of the minimum is given b y B

(M /M ) w

0

m l B

-

1 - {MJ**/

(1 - /) %} V 3 2 v / 9 f c

8

(4)

which becomes more pronounced as the ratio v/k increases. Consequently, the same increase i n t brought about by either a decrease of k or v works out quite differently. In the first case, the minimum becomes more pronounced, i n the latter it tends to disappear. B

c

9


8.

Chymosin-Triggered Clotting

P AYENS A N D BOTH

131

/ M


Mw o

0

720

480

240

0

clotting time (s)

Figure 1. Progress curve of the weight-average molecular weight of clotting p-K-casein. Model parameters (cf. Equation 1): M = 19,000; f = 0.33; C = 0.02 g mL' . Note that (1) v = 10~ mol mL' sec- , k = 10 mL mol' sec' ; (2) v = 10 mol mL sec' ; k = IO mL mol' sec' ; (3) v = 10' mol mL' sec' ; k, = IO mL mol sec' . 0

1

0

s

1

8

1

8

9

1

1

1

1

1

1

4

8

5

1

8

1

1

1

Alais and Lagrange ( I I ) and Hamdy and Edelstein (12) have studied the effect of the ionic strength on the clotting time of milk. Their results are quite remarkable i n so far as a pronounced minimum is observed at a total ionic strength of about 0.125. W e have confirmed this observation i n clotting experiments with pure #c-casein and with micellar casein. As explained above, changes i n t can be due to either a change i n v or k . W e shall show, however, that in the present case salt mainly affects the rate of proteolysis v. A qualitative explanation of the salt effect w i l l be given in terms of Bronsted's theory of the influence of the ionic strength on the rate of ionic reactions ( 1 3 ) . Besides we have measured the flocculation rate constant of p-x-casein at different temperatures and estimated the activation energies involved. c

B

Experimental Details and Results Kappa-casein was prepared according to McKenzie and Wake (14). The protein was dissolved in 0.001M imidazole buffer, p H 6.7, the ionic strength of which was adjusted by adding N a C l . To study the clotting of micellar casein skim milk prepared from low-heat skim milk powder was diluted 16 times with 0.01M C a C l , to which N a C l was added to adjust the ionic strength. 2



132


Clotting was brought about with appropriately diluted rennets ( C S K F Leeuwarden, The Netherlands) of an original clotting strength of 10,000 Soxhlet Units (SU) (15). The clotting was monitored i n the Cary 14 spectrophotometer at 500 nm as described previously (2,3). Clotting times were estimated by linear extrapolation of the absorbancetime curves to zero absorbance increase. Some characteristic clotting curves of micellar casein at 35 °C and different ionic strength are shown in Figure 2. It is seen that an increase of the ionic strength brings about an extension of the lag phase with a simultaneous disappearance of the minimum. This indicates, as explained in the introduction, that salt chiefly decreases the rate of proteolysis. Typical clotting curves for *-casein at 31.5 °C and different enzyme concentrations are presented i n Figure 3. Note that the minimum i n the absorbance is perceptible only at the highest enzyme concentrations, suggesting that with *-casein the ratio v/k is smaller than with micellar casein. The influence of the ionic strength on the clotting time of #c-casein at 35 °C is shown i n Figure 4. The pronounced minimum is strongly reminiscent of the minimum found with milk (11,12), though it occurs at a considerably lower ionic strength. In Figure 5 we have given a typical example of the double logarithmic regression of the clotting time on the enzyme concentration. From the slope of such plots we find the exponent y i n the relation s

t ( E ) = constant c

y

(5)

to vary between 0.90 and 1.00 (cf. Table I ) .

Figure 2. Clotting of micellar casein by rennet at different ionic strengths. Absorbance measurements in the Cary 14 spectrophotometer at 500 nm in 0.5-cf cuvettes; 35°C skim milk diluted 16 times; clotting strength in reaction mixture: 1.43 SU. Time flows to the left. (A) I = 0.04; (B) I = 0.06; (C) I = 0.12. Blank; Bioelectrochemistry: Ions, Surfaces, Membranes Advances in Chemistry; American Chemical Society: Washington, DC, 1980.


8.

PAYENS A N D BOTH


133

Figure 3. Clotting of K-casein (0.1 g/100 mL) by rennet at I = 0.2, pH = 6.7, and 31.5°C. Absorbance measurements in the Cary 14 spectrophotometer at 500 nm in 1-cm cuvettes. Time flows to the left. Clotting strength in reaction mixture from left to right: 1.98; 2.65; 3.97; 7.94; and 15.88 SU. The influence of the temperature on the clotting time of p-*-casein is presented i n Figure 6. T h e least-squares regression curve through the experimental points is In t = -496.75 + 4.79218 X 10 /T - 1.6063 X 1 0 / T + 1.7896 X 1 0 / T 5

c

8

2

10

3

l D ;

Discussion The Relationship Between Clotting Time and Enzyme Concentration. Table I shows that with /c-casein the rule of Segelcke and Storch (15) which states that t - (E) = constant c

(7)

is approximately obeyed. It has been explained before ( I ) that this simple result is fortuitous because on the basis of Equations 2 and 3 one would expect t • (E)^ = Q

constant


(8)

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BIOELECTROCHEMISTRY:

Table I. Double Logarithmic Regression of Clotting Time on Enzyme Concentration Found with the Clotting of /.-Casein by Rennet. Number of Experimental Points 5 Everywhere Temperature (°C)

Slope

r

15.7 21.0 26.4 31.5 35.5 42.5

0.896 0.982 0.946 1.019 1.055 1.002

0.9926 0.9920 0.9981 0.9930 0.9871 0.9997

2


PAYENS AND BOTH


135


8.

Figure 6. Arrhenius plot for the clotting of K-casein brought about by rennet. Experimental conditions: pH 6.7; I = 0.2; 31.5°C. Kappa-casein concentration: 0.1 g/100 mL; clotting strength in reaction mixture, 3.97 SU.


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BIOELECTROCHEMISTRY:

IONS, SURFACES, M E M B R A N E S

The discrepancy between Equations 7 and 8 has been ascribed to a flocculation rate constant depending on enzyme concentration ( J ) . Thus in the present case (cf. Equations 2 and 3 ) , one would have approximately fc cc


8

(E)

(9)

This conclusion is in agreement with the recent studies of Vreeman et al. (16) , which have shown that x-casein is a strongly associating protein, forming micelles of about 30 subunits. The particle that flocculates is thus polyfunctional and its flocculation rate constant w i l l increase with the number of p-x-casein residues per particle, that is with the concentration of the enzyme. The Flocculation Rate Constant. I n principle Equation 1 contains all of the information to determine both v and k from a single lightscattering experiment as has been demonstrated earlier with the clotting of fibrin( 3 ) . However, the present turbidity measurements suffer from multiple scattering (2), which makes an estimate of v from the previously proposed plot of ( M — M ) / M * vs. t unreliable. Therefore v was estimated with the catalytic constants recalculated from Garnier's data (17) , assuming that the molecular weight of chymosin was 34,000 (15) and the clotting strength of the purified enzyme was 10 S U ( 1 8 ) . The flocculation rate constants then could be computed from the clotting times by Equations 2 and 3. Some typical examples have been collected in Table II. One should realize that the rate constants thus obtained are only rough estimates on account of the approximate character of Equation 3, the possible exhaustion of the substrate, and the uncertainties that occur i n the computation of v. Notwithstanding this, there can be little doubt that the flocculation rate constant of p-x-casein, like that of micellar casein and fibrin ( 3 ) , is much smaller than the diffusion-controlled value (10). B

w

0

0

2

7

Table II. Clotting Time (* ), Flocculation Rate Constants (k ), and Activation Energies (e ) * Observed with the Clotting of ^-x-Casein at p H 6.7, I = 0.1, and Different Temperatures c

a

H

8

Temperature (°C)

10' • k , (mL mol sec' ) c (kJ mol' ) 5

k

(s- )

t (s)

21 ± 3 31 ± 3 39 ±2

282 206 192

cat

26.4 35.4 42.5

1

0

c

1

1.0 1.3 1.2

1

1

8

47 -13 -36

2

°/c = 2/Uc „). i

c = 2Rd In t /d(l/T) - « and e = 41.8 k J mol" (19). ° Recalculated from Ref. 17 accepting the molecular weight of chymosin to be 34,000 (16). b

e

P

P

1


8.

P A Y E N S A N D BOTH

137


In order to get some insight into the factors reducing the clotting rate, the influence of the temperature on the clotting time was analyzed. By combining Equations 2 and 3 we have d i n t /d(l/T) e

-

(10)

(c + c )/272 8

p

where R is the gas constant, c the activation energy of the clotting process proper, and c the activation energy of proteolysis. The latter has been determined by Nitschmann and Bohren (19) as 41.8 k J mol" . W i t h this value one finds from Equations 6 and 10 the activation energies, c , given i n the last column of Table II. They become negative at about 33°C, suggesting that the retardation of the clotting can be explained only partially by the presence of an energy barrier and must be caused largely by a steric factor. Therefore one concludes that only a small fraction of the surface of the x-casein micelle consists of sticking residues of p-x-casein and that this constitutes a severe orientational constraint i n the clotting. The recent computations of Schurr and Schmitz (20) demonstrate also that Brownian movement cannot speed up the clotting rate to the diffusion-controlled limit: rotary diffusion produces only a modest enhancement of the rate by a factor of about 2. 8

p

1


B

The negative activation energies of Table II point to a dominant attraction between the flocculating particles (10). The origin of this attraction is not clear. It probably can be explained by the Coulomb attraction between the positively charged residues of p-x-casein (5) and the residual, negatively charged x-casein on the micelle surface. A n alternative though less likely explanation is that long-range van der Waals ( V D W ) forces become more important at the higher temperatures. The Influence of the Ionic Strength on the Clotting Time. W e have seen that between I = 0.03 and 0.5 an increase of the ionic strength chiefly brings about a decrease of the rate of proteolysis. W e shall now present a simple argument to explain the effect of salt and to show the importance of the cluster of cationic residues around the labile P h e - M e t bond i n x-casein (5) i n stabilizing the ES-complex. If the latter is identified with Bronsteds activated complex (13), one has for the rate of proteolysis v=

- d ( E S ) / d * = fceat

K{r*r*/r™) (E)

(S)

(ID

where K is the equilibrium constant for the complex formation; y ^ , y ^ , and are the electrostatic activity coefficients of the enzyme, the substrate, and the ES-complex; and fc at is the catalytic constant. C


138


By definition we further have T V ^ S / V E S = exp ( - A F W f c ? ) ,

(12)

7

where A P is the electrical work connected with the formation of the complex. Let the simple model shown i n Figure 7 stand for the ES-complex. The complex, consisting of two globules of the same size and charge, is supposed to be stabilized by a number of electrostatic bonds. It is probable that H i s 98, 100, and 102 are among the residues i n *-casein that participate i n such bonds. Their importance for the proteolysis is indicated by the photooxidation experiments of H i l l and L a i n g (21) and Zittle (22). O n the enzyme, among others, Asp (290) near the active center could be involved, because it is known that Chymosin A , i n which this residue is replaced by G l y , is catalytically less active than Chymosin B (23). F o r the above model, according to S. N . Timasheff (24), A F s is approximately equal to the sum of a Verwey-Overbeek potential to account for the net repulsion plus a sum of screened Coulomb potentials to take care of the electrostatic bonds, viz.


E S

e

AF*

E S

—*

0

2

D r / 2 + (e /D) £

exp ( - i c r , , ) / ^

8

E

(13)

where # is the surface potential of the partners, D the dielectric constant, r the particle radius, the distance between the charges z e and Zje, and K the reciprocal D e b y e - H i i c k e l length defined as 0

{

* = 3.33 • 10 V 7 7

'

i i

Figure 7.

(14)

i

i i

A simple model to account for electrostatic interactions in the ES-complex of chymosin and K-casein



8.

PAYENS AND BOTH


139

-8

Figure 8. Model calculation of the influence of the ionic strength on the rate of proteolysis of K-casein by chymosin. Model parameters (cf. Equations 13 and 14): Z = —8; r = 2.5 nm; a = 2.75 nm; 3 pairs of electrostatic bonds formed at = 0.25 nm. (A) Overall electrostatic repulsion (first term on rhs of Equation 13); (B) Local side-chain attractions (second term on rhs of Equation 13); (C) y y aly Es (Equation 11). e

E

e

e

In the D e b y e - H i i c k e l approximation ¥ is calculated from 0

* = 0

( Z e / D ) {1/r

+*

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