Negative cooperativity in alkaline phosphatase from E. coli: New kinetic evidence from a steady-state study

NEGATIVE COOPERATIVITY IN ALKALINE PHOSPHATASE FROM E. COLZ: NEW KINETIC EVIDENCE FROM A STEADY-STATE STUDY A. DEL ARCO. F. J. BURGUILLO. M. G. ROIG. J. L. USERO, C. and M. A. HERRAEZ Departamento

de Quimica

Fisica.

Facultad Salamanca.

(Rrceired

de Quimica. Spain

6 July

Universidad

IZQUIERDO

de Salamanca.

1981)

Abstract-l. A study has been carried out on the steady-state kinetics followed by the alkaline phosphatase from Escherichia co/i at different pH, temperatures, ionic strengths, phosphate concentrations and in the presence of the etTectors such as Tris, NH;---NH3 and CH,OH; p-nitrophenyl phosphate was used as substrate. 2. Contrary to what has generally been accepted. in most cases the enzyme follows non-Michaelian kinetics for a wide substrate concentration range, giving concave-down Lineweaver-Burk plots. Only at high phosphate concentrations (5’ lo-’ M) and at high ionic strengths (2.0 M) is a linear LineweaverBurk plot obtained (Michaelian kinetics). 3. In order to analyse the kind of kinetics obtained. a non-linear regression fitting method was used to obtain rate vs substrate concentration equations as polynomial quotients of minimum degree with positive coefficients. 4. Most of the data obtained follows 2:2 degree type equations. 5. These results tend to suggest an idea of cooperativity rather than one of independence between the sites of the dimeric enzyme. A model is discussed for cooperativity between the sites with a wide concentration range giving concave-down Lineweaver--Burk plots.

INTRODUCTION Alkaline from phosphatase Escherichia co/i (EC 3.1.3.1) is a zinc metalloenzyme composed of two apparently identical subunits (Rothman & Byrne, 1963; Knox & Wyckoff, 1973). In contrast, most of the investigations have indicated the existence of only one active site. but unfortunately many different values have been published and the situation is not clear. Essentially four types of methods have been used to investigate negative cooperativity: A. Phosphate labelling of the active-site seryl residue at acidic pH values resulted in the incorporation of from 0.6 to 1.3 mol of phosphate per mol of protein (EngstrGm, 1962; Pigretti & Milstein, 1965; Reid et al.. 1969; Applebury et al., 1970). but it has also been reported that Zn” -alkaline phosphatase can incorporate covalently bound 2 mol of Pi per mol of enzyme in an anticooperative manner (Lazdunski et al.. 1971) when the labelling of protein was studied at low pH with 32P-substrates. B. Studies performed with equilibrium dialysis have indicated the binding of phosphate in an anticooperative manner, 1 mol P, per mol of enzyme appears to be bound with dissociation constant of approx. 10. 6 M, the second mol of phosphate is much more weakly bound (Simpson & Vallee, 1970; Applebury et al.. 1970; Coleman & Chlebowski. 1979). ’ C. Rapid-flow kinetics at pH values below 6, in the pre-steady-state at low substrate concentration, have in general shown a burst of only 1 mol of alcohol/ enzyme dimer (Ko & Kezdy, 1967; Fernley & Walker. 1969: Halford. 1971; Bale et al., 1980a), while at high substrate concentration the magnitude of the 127

burst corresponds to the release of 2 mol of phenol/ dimer (Chappelet-Tordo er al., 1974). D. A direct observation of the covalent and noncovalent enzyme phosphate complexes by NMR, has shown contradictory results: Norne et a/. (1974) and Chlebowski et al. (1977) found 1 mol P,/dimer, while Hull & Sykes (1976) found 2 mol P,jdimer and finally Hull et a/. (1976) have found 1.5-2.0 molidimer. In spite of these discrepancies, the idea of anticooperativity seemed to be generally accepted (Halford. 1971) and in fact a new mechanism of extreme cooperativity (flip-flop) was proposed (Lazdunski et d., 1971); however in recent years evidence has appeared which contradicts the above. Bloch & Schlesinger (1973). thus reported that the enzyme contains up to two molecules of tightly bound inorganic phosphate per dimer, and they suggested that the endogenous phosphate may be responsible for the apparent anticooperativity in the binding phosphate. The same authors in 1974 worked with a molecular hybrid containing one subunit from an inactive alkaline phosphatase showing one half the normal burst amplitude in transient kinetics from the wild type enzyme; this suggests that the two active sites on the molecule may be independent and equivalent. In both reports they found the site stoichiometry to be 1.5 and 0.8 approx.; these results are explained by the hypothesis that 25:: of the total of two sites per molecule have been inactivated irreversibly by some unknown cause. Bloch & Bickar (1978) working with purged enzyme and an equilibrium dialysis technique found a site stoichiometry of ZP,/dimer and a better fitting for the experimental data with a non-cooperative model.

A. DTL AKC’O et (I/.

12x

Finally, Bale et ul. (1980a). using a quenched flow method. have reported the lack of effect of substrate on the rate of dephosphorylation of the phosphoryl enzyme and on the rate of phosphate dissociation. These findings indicate that the flip-flop mechanism in which the product released is supposedly facilitated by the binding of a second molecule of substrate, is not valid for alkaline phosphatase. The results obtained by Otvos c’t trl. (1979) with 13’P]NMR have shown that there was a direct relationship between the metal ion content and phosphate binding. this offers a new explanation for the different NMR reports published. Recently Cocivera et 01. (1980) using a new technique (McManaman & Wilson, 1978) found that more than half the sites are phosphorylated at pH 7.5 and 7.0 and this phosphorylation is independent of substrate concentration leading them to assume the absence of absolute anticooperativity. It has been observed however, that the results from steady-state kinetics are scarce. Simpson & Vallee (1970) completed kinetic studies. finding that the Lineweaver-Burk plot is biphasic and that the K, values agreed with the ones found with equilibrium dialysis; in the same way Lazdunski et rrl. (1971) supported his incubation tests with kinetic ones. Only Waight et N/. (1977) studied steady-state kinetics in a more systematic manner, concluding as well that a 3:3 fitting is the lowest degree rate equation required to explain their results. that is. the non-validity of the Michaelis Menten kinetic model. They proposed a two-sited cooperatively linked Ping-Pong Uni-Bi-mechanism. Very recently Bale ef nl. (1980b) have proposed a method to investigate the nature of strong negative cooperativity in oligomeric enzyme. Their steady-state studies on E. co/i alkaline phosphatase using alternative substrates together with the product inhibition studies, reveal that the flip-flop mechanism. despite its attractiveness. does not seem to operate in this particular enzyme svstem. The aim of this communication is to provide new data about steady-state kinetics. It follows the reaction in different conditions (temperature, pH. I. (Pi), and other effecters) and in almost all cases deviation from Michaelis-Menten kinetics was found. the best fitting in most cases being 2:2. These results seem to support the idea of anticooperativity rather than of Independence between the sites.

MATERIALS

AND

METHODS

Chromatographically purified (Type III) E. coli alkaline phosphatase (EC 3.1.3.1). and p-nitrophenyl phosphate (Sigma 104) were purchased from Sigma Chemical Co. and used without further purification: all other chemicals were of analytical grade (Merck).

was present in suspension (18 mg.ml- ’ in and stock solutions were made up using Fife‘s method (Fife. 1967): the protein solution was centrifuged at 1600 LJ for 30 min at 0 C and the portion deposited was diluted in 10.0 ml of IO-’ M Tris. pH 8.0 and 0.1 M NaCI. The enzyme

2.5 M (NH&SO,)

The protein concentration was determmed apectrophotometrically at 280 nm using a molar absorptivity calculated by Schlesinger & Barrett (1965) of 0.77 (UA mg protein ’ ml). Comparing its activity with the maximum activity of the pure crystalline enzyme obtained by Malamy & Horecker (1964). we conclude that approx. 45”,, of the protem was active enzyme. This value and the mol wt of 86.000 (Schlesinger & Barrett, 1965) were used to calculate the concentration of active enzyme. The enzyme stock solutions were later stored in a refrigerator. in this way. it is stable for months (Roig, 1981). Workmg samples of enzyme were prepared immediately before use by dilution with appropriate buffer. and were discarded 3-5 hr after their preparation. thereby avoiding loss of enzymic activity. Metal analysis for Zn(l1) and Mg(l1) of the enzyme were performed by atomic absorption spectroscopy with the use of a Jarrel-Ash X2-270 spectrometer according to the method of Bosron et u/. (1975). The Zn content of the enzyme was 2.5 f 0.2 g-atomi86.000 mol. wt and the Mg content was 1.3 + 0.1 g-atom.‘86,000 mol. wt. Endopenous phosphate of the enzyme was essayed by the method of Chappelet-Tordo ef trl. (1974): we found an average content of 1.98 + 0.13 mol P,/mol enzyme. Substrate solutions were prepared by weight and dilution immediately before each kinetic run and were discarded 3-5 hr later to avoid spontaneous hydrolysis of the substrate. The phosphate and phenol impurities in the suhstrate were approx. 0.5”,,.

Tri(hydroxymethyl)-aminomethane (Tris) and 5.5-diethylbarbituric acid sodium salt (sodium Barbital) were used as buffers. The buffer’s pH was achieved by adding HCI and was determined at room temperature with a standardized radiometer pH-meter model 51, using glass combined electrode type GK 2311 C. The pH was compensated for temperature changes and measured before and after each reaction. the variation always being less than 0.05 pH units. Ionic strengths (I) were adjusted with NaCI.

A direct and continuous spectrophotometric method for initial rate measurements of p-nitrophenyl phosphate hydrolysis was carried out at 4lOnm with a Schimadzu model QV-50 spectrophotometer to which an automatic recording Servoscribe 1-S. equipped with control to expand the scale. was adapted. The spectrophotometer was equipped with a thermostated cell holder, the temperature was maintained at 25.0 +_ 0.1 C. except when the study with other temperatures was carried out. The reaction rate at steady-state was determined at 10 different substrate concentrations within the range the last five points two times: 10-“~10~2 M. repeating moreover we performed a statistical study for four substrate concentrations: 10m2, 6, 10m5. ?.lO-‘. IO-’ M: its rates and its standard deviations were. respectively: 19.7 + 0.3: 40.5 + 0.6; 33.6 f 0.9: 25.4 5 2.7 mol.min~’ mg!.? I, A graphical recorder was used. and the initial rates were obtained from the absorbance vs time data. For this reason. it is very tedious to make the runs ir triplicate or more. and only those at the most dilute concentration in substrate (subject to the greatest error) were made in duplicate. The hydrolysis rate of p-nitrophenyl phosphate was determined by the rate of formation of p-nitrophenol. measured at 410nm. The total concentration. C, of the ionic and undissociated forms IS given by the modified Beer’s law equation:

Negative

cooperativity

where A,. is the total absorbance at 410nm apparent molar absorptivity, is given by lA ‘z

+

and c,,,~. the

CWJ'h'KJ~m

(2)

x2-

.‘PP

in alkaline

1 + (H+)I’K,

here. c4 and lHA are the molar absorptivities (at 410 nm) of the anion and the neutral p-nitrophenol. and K, the acid dissociation constant. Values ofe, (l.70.104cm-‘~M-‘). E,,& (29.1 cm- ’ M ‘) were determined by direct measurements with p-nitrophenol at acidic pH (3.9) and alkaline pH (11.7). and (H +) and K. at different ionic strengths were c.llculated considering the effects due to activity coefficients b! means of Davies’s modification of the DebyeeHiickel relationship (King. 1969): (H’)

‘_!:“: pi, =

=

7.15

?+

_

2

0.511, _ 1+,1

I + 0.31.

(4)

Computc~r,fitrrny datu Values for the slopes and intercepts of all the linear plots (absorbance vs time and absorbance vs product concentration) were calculated using a least-squares fitting method with statistical weights. The experimental dependence of the reaction velocity on the substrate concentration was approximated by a reiterative computer program (Feraudi er al., 1977). The algebraic form of the equation for reaction rates at steady-state would always be expressed by a polynomial quotient as:

z

P,(S)

,=I

n,m < 5

=

(5)

where n. m. p and q. were estimated as follows: each equation was approximated by a numerator polynome of degree n (n = 1.2.3.. ) and a denominator polynome equal to 1: we increased for each n in the numerator the degree of the denominator by 1. All these series were linearized and approximated iteratively. For each series we obt,Gned a Pad6 table of minimized sums of squares. As a statlstical criterion of the reliability of the fitting. we took the standard deviation defined as: L7 =

z

Ir, -

C,,)‘,lr - 1)

I=1 where I‘, and ‘,j are the measured values at the ith experimental points. the number of points.

(6)

and calculated rate respectively. and r is

129

Of the polynomial quotients obtained according to this method what is of interest is the algebraic form of the equation rather than the actual coefficients obtained. The main advantage of Feraudi’s method is that no preliminary hypotheses concerning the mechanism of enzyme action are required. Taking into account the standard deviations obtained, tt is possible to establish which degrees of the numerator and denominator are the most suitable and thus the values of pi and 4,. That degree of n and m which gives the smallesl standard deviation is chosen as the function which is closest to the experimental data. As long as an increase in the degree of the numerator and denominator polynomes does not cause the standard deviation to decrease appreciably, the polynomial quotient of least degree is chosen as the best fitting. RESULTS

for the interest shown in the alkaline phosphatase from E. coli was that, in spite of having two active sites. it apparently followed Michaelis-Menten kinetics, though it had been reported that, under certain conditions, the Lineweaver_Burk plot gave a curve (Lazdunski et al., 1969; Simpson & Vallee, 1970; Chlebowski & Coleman, 1974). Recently, Waight et al. (1977) reported that the enzyme clearly follows non-Michaelian kinetics under different conditions, giving non-linear double-reciprocal plots. Similar behaviour of non-Michaelian kinetics has been found with many other enzymes as has been reported in a recent review (Hill rr ul.. 1977). In order to further elucidate the kinetic behaviour of this enzyme, we programmed a study under different conditions to estimate cooperativity. One

these plots were linear for 3-5”” of hydrolysis. Accordingly, reagent concentrations were calculated in such a way that this percentage was achieved in 5 min, making it possible. to determine accurate initial overall rates. In all our studies. the rates determined in this way referred to mg of active enzyme. Beer’s law for inorganic phosphate followed a molar absorptivity value of 2.73 104cm-‘~Mat 820nm in analysis mixtures (Chappelet-Tordo et NI.. 1974).

(’

from E. c,o/i

(3)

were between 1.55 lo3 The values of c,,,,,, calculated cm-’ Mm I (at pH 6.3 and I = 2.0 M) and 1.68 IO“ cm I M ’ (at pH 9.0 and I = 0.02 M). The initial rates were always measured because a strong inhibition took place due to the products. Rates of p-mtrophenyl phosphate hydrolysis were obtained from the initial slopes of absorbances vs time plots: dc 1 dA m L’ = dt = EAvp z = EAPP

phosphatase

of the reasons

Stud!, at dijjerent

pH

Figure 1 shows the double-reciprocal plot at four different pHs, 6.30. 6.81. 7.51, and 9.00 in 0.01 M Barbital buffer and 0.02 M ionic strength. The profile of these plots are all biphasic and concave-down. However, it may be seen that, at alkaline pH. the profiles change phase at higher substrate concentrations. The corresponding data for velocity vs substrate concentration were fitted according to the method described in the previous section; the results are shown in Table 1. in which we observe that the 2:2 fitting gives the smallest standard deviation, though for pH 6.81 it gave negative terms. Working under similar conditions, Waight et al. (1977) found that the minimum degree necessary to fit their curves was that of a 3:3 type polynomial equation. As may be seen from Table 1. for our working conditions, and using our fitting method the 3:3 equation always gives negative terms, from which no interpretation may be deduced. Thus, in spite of the anomaly that the fitting shows at pH 6.81 and bearing in mind that the double-reciprocal plot of the experimental data is also concavedown. we may conclude that within the pH range studied. the enzyme follows non-Michaelis-Menten kinetics. Study at diflerent

temperatures

A study was then carried

out at three different temperatures: 10.3, 25.0 and 39.8.C. using 0.01 M sodium Barbital. pH 9.0 and I = 0.02 M as shown in Fig. 2.

A. DEL ARC-O et ul

130

1

0

100

50

0

l/ [s]

100

50

(mM_‘)

Fig. I. LineweaverrBurk plots for the hydrolysis of p-nitrophenyl phosphate at four different pH: (A) pH 6.30; (B) pH 6.81: (C) pH 7.51 : (D) pH 9.00. The buffer was: (A) and (B) in 0.01 M Barbital/O.01 M sodium acetate: (Cl and (D) in 0.01 M Barbital. Other conditions were: 0.47 ~g~rnl-’ (A): 0.24~g’ml-’ (B); 0.038 ~~g~rnl I (C) and 0.024 ~cg.rnl~ I (D) enzyme concentrations. Ionic strength was 0.02 M: T= 25 C. and the range of p-nitrophenyl phosphate concentration was 7’ 10W4~1.5. 1O‘5 M to (C) and ID): and lO~‘~lO-s M to (A) and (B).

Table

I. Rate equations

fitted according to the Iterative program hydrolysis of p-nitrophenyl phosphate

Range of r (Itmol.min~‘.mgE~‘I

PH

Data

6.30

7

5.92 3.44

6.81

x

6.35 4.27

7.51

X

4.94 2.57

9.0

8

13X6-6.85

of Feraudi (Feraudi et trl.. 1977) for kinetic in Barbital at different pH

I:1

1.53 IO’*(S) + 3.08. IO’“(S) ” = l-+ 5.12. IO”(S) + 4.86. 10”(S) 4.91 r = i-+x.zs

I’ =

0.2

10’(S) ___~ 104(S)

5.09’ 105(S) + 1.93 lo”(s)2

0.14

1.45. 10”(S) + 2.58. 10”(S)* r = ~ -~~-~-~ 1 + 1.39. IO’(S) + 1.36’ 10*(S)

* Neither n:rn fittings with negative terms nor those n:m fitttngs with positive greater than 3 are included. All 3:3 fitttngs leave some negative terms.

I

0.40

I + 1.30’ 10Z(S) + 3.47’ lo*(s)*

or negative

0.44

terms

of

OPher fittings*

0

Best fitting equation

essays

which

2:l 2:3

0.54 0.38 0.36

2:I 3:l 3:2

0.32 0.32 0.32

1:l 2:1 3:2 3:3

0.21 0.14 0.13 0.13

1:1 2:I

0.76 I .JO

have

11 or rn

Negative

cooperattvity

in alkaline

phosphatase

linear,

from E.

though

m/i

at high

131

temperatures

they

are

also

curved.

As may be seen from Table 2, for a temperature of 10.3 C the best fitting of the rate vs substrate concentration data is that of a 2:2 polynomial equation, this being in agreement with the experimental data (Fig. 2A). At temperatures of 25.0 and 39.8 C, fitting is also that of a 2:2 equation. It may be seen that for all the temperatures studied a 3:3 Iitting gives polynomial equations with negative terms. Thus, for the experimental results presented, and according to our fitting method, a 2:2 polynomial equation is sufficient, within the temperature range studied, and the enzyme thus follows non-Michaelian kinetics across this range.

w

IF .-i E 7

0 E

a. > \ N

'0 -

35r ., ,/' I

/'a

W* 25;

_~ 0

50

25 I/ [S]

J 75

(mM_‘I

Ftg. 7. Lineweaver Burk plots for the hydrolyses of p-nitrophrnyl phosphate at three different temperatures: (A) T= 10.3 C; (B) T= 25 C and (C) T= 39.8 C. Other condittons were: 0.01 M Barbital; 0.01 M ionic strength; enzyme concentration. The pH 9.00 and 0.024 pg.ml-’ range of p-nitrophenyl phosphate concentration used was: (A) and (C) 1O--‘-1O-5 M and (B) 7, 10-JP1.5. IO-’ M.

The results show that across the whole temperature range studied. the profiles are also biphasic and concave-down in a Lineweaver-Burk plot. They are in direct contradiction with those obtained by Waight et r/l. (1977). whose Lineweaver-Burk plot at 11-C is

Table

2. Rate equattons

T

( C)

Data

10.3

8

A study with 0.01 M sodium Barbital (pH 8.8) was programmed at different ionic strengths in order to observe the kind of kinetics followed by the enzyme at a wide I range. principally high ones; little attention was paid to the lower ionic strengths since this has already been discussed by other workers (Heppel et uI., 1962; Simpson & Vallee. 1970) and we have also observed that non-Michaelian kinetics are followed (Fig. 1D). The experiment was carried out within an ionic strength range of 0.2.~2.0 M. and the results are shown in Fig. 3 in double-reciprocal plot. Table 3 shows the fittings of the experimental rate vs substrate concentration data. It may be seen that in the interval between I = 0.2 and I = 1.0 M. the best fitting corresponds to a 2:2 polynomial equation, since it has the least standard deviation, and this is in agreement with the concave-down plot found (Fig. 3B). For I = 2.0 M. both those corresponding to the 2:2 and the I : 1 littings are acceptable, since both are within the range of experimental error. Thus, according to our criterion, we accept the lower fitting as valid: this is also in agreement with the linear double-reciprocal plot obtained (Fig. 3A), then. the enzyme would only follow Michaelian kinetics at high ionic strength. t@c,r of phosphate

concenrrurion

A rate vs substrate concentration study was also carried out in 0.01 M sodium Barbital. pH 8.5 and

fitted according to the iterative program of Feraudi (Feraudi rr trl., 1977) for kmettc hydrolysis of p-nitrophenyl phosphate in Barbital at different temperatures

Range of I (~mol~min~‘~mgE-‘)

7.588 4.23

25.0

8

13.86

39.8

8

37.233 13.90

* Neither n:rn fittings with negative greater than 3 are included.

L‘ =

6.85

terms

nor those

8.65. 109(.S) + 2.34.

IOLJ(S)’ 1--;y5~10’(S)+,jjT~(j13($

0.2

of

OtIrer fittings*

fl

Best fitting equation

essays

I

I:I 2:3

0.61 0.52 0.14

2:l

’

1.45. + 2.58 IO”(S)2 lob(S) 1 + 1.39. 10’(S) + 1.36. 108(S)2

0.44

I:1 2:l

0.8 1 0.45

L

3.77 + 5.99 lOh(S) lo’(S)2 1 + 1.19.105(S) + 1.40.108(S)’

0.26

2:l l:I

0.26 0.29

II :m fittings

wtth positive

or negative

terms

whtch

have II or rn

132

A. DFL ARCH ef (I/.

11 [s]

(mM_‘)

F’g. 3. Double-rec’procal plot for the hydrolyses of p-nitrophenyl phosphate at dtfferent iomc strengths: (A) I = 2.0 M (m-0 m). I = 1.0 M (mm--);(B) (0) I = 0.2 M. (0) I = 0.4 M. (A) I = 0.7 M. (0) I = 1.0 M Other conditions were: 0.01 M Barbital: pH 8.7; 0.024~g.ml~’ of enzyme concentratton except I = 2.0 M where enzyme was 0.027 ~g~rnl~ ’ : T= 25 C. The range of p-nitrophenyl phosphate concentration used was 10-3-10~s M.

Table

3. Rate equations titted according to the tterattve program of Feraudi (Feraud’ et III.. 1977) for kinettc hydrolysis of p-nitrophenyl phosphate in Barbital at d’fTerent ionic strengths (I)

Data

Range of L (/lmol.min~‘.rngE-‘)

2.0

IO

50.41. 16.85

I .o

10

50.592227

1

(M)

0.7

9

48.61

0.4

8

40.01~ 18.1 I

0.2

9

33.1 I-17.65

* Neither ~t:nt fittings with negative greater than 3 are included.

(i

Best fitting equatton 1:I

5.64. 10’(S) + 3.51. lOLo( r = 1 + 1.56.10’(S)

essays

OtLer fittings*

0.69

2: I ,.? -.-

0.54 0.55

0.50

2:

I

I .o

0.81

I.1 ‘:I

+ 6.44~108(S)’

of

21.5X

terms

1.16. IO’(S) + 2.41. 101’(S)z r = r +6.09.

nor those PI:VI fittmgs

10’(S) + 6.84. lO”(S?

wtth pos’tive

or negattve

terms

which

1.96 I 55

have )I or at

Negative

cooperativity

in alkaline

phosphatase

from E.
of interest when analysing and will be discussed later.

-d E i >

i ,

“0 500

-

/’

/’ 250: /

./II-.’

lA !

0

7,

CL__

~ 25

I / [S] ( m M

’1

Fig. 4. Hydrolysis of p-nitrophenyl phosphate at different phosphate concentrations in Lineweaver-Burk plots: (A) IO “M phosphate; (B) 10e3 M phosphate: and (C) 5. IO-” M phosphate. For all the cases the buffer was 0.01 M Barbital. pH 8.5, I = 2.0 M and T= 25 C. The enzyme concentrations used were 0.062~g~ml-’ (A); 0.25 pg.ml-’ (B); 2.08 pg.rnl-’ (C). The range of substrate

concentration

1 = 2.0 M. The phosphate

was 1O-3-lO-5

M.

concentrations used were: and 5,10m3 M. Figure 4 shows the double-reciprocal plot of the experimental data. It may be seen that at a phosphate concentration of 5’ 10e3 M the Lineweaver-Burk plot is linear while at lower concentrations it is concave-down. The fittings of the rate vs substrate concentration data are shown in Table 4: these are in fact in agreement with the plots obtained (Fig. 4). We can observe that the 3: 3 fitting is unviable at these phosphate concentrations since it gives polynomial equations with negative terms. while the 2:2 fittings for phosphate concentrations of 10e4 and 10m3 M, and 1: 1 for 5.10--’ M concentration are perfectly acceptable. The above is contrary to Waight’s data (Waight et ul.. 1977); they carried out experiments with phosphate under similar conditions, concluding that a 3:3 polynomial equation was necessary to fit their experimental data. It seems too, that the double-reciprocal plots are concave-up. These differences, together with the reduction from 2:2 to 1: 1 on increasing phosphate concentration observed in our study, could be 10

4, lo-’

133

the reactton

mechanism

Detailed reports have been made which show that Tris has transphosphorylation acceptor properties, while Barbital behaves as a completely inert buffer (Neumann, 1969; Hinberg & Laidler, 1973; Burguillo, 1978). A study was therefore carried out in 0.1 M Tris. pH 8.7 and I = 2.0 M: using Barbital as the buffer, it had already been seen that the Lineweaver~-Burk plot was linear at I = 2.0 M, (Fig. 3A; Fig. 5). while 0.1 M Tris. and at the same ionic strength a curved plot appears (Fig. 5). Therefore, the behaviour of the enzyme is non-Michaelian in the presence of Tris. A similar phenomenon has already been observed by us with o-carboxyphenyl phosphate (Herraez et trl.. 1980; Roig, 1981). This behaviour, however, is contrary to that reported by Neumann (1969) and Hinberg & Laidler (1972). the latter working with chicken intestinal alkaline phosphatase, neither of whom observed such a phenomenon at high Ionic strength probably due to the fact that thctr studies on Tris did not cover a wide enough substrate concentration range. Table 5 shows that in Tris, the best fitting is a 2:2 polynomial equation, while in Barbital the 1: 1 titting is acceptable.

In order to provide a explanation of the nonMichaelian kinetics which had been observed in the presence of Tris and not in Barbital. the possibility was considered that the NHf-NH, group or the hydroxymethyl group constitutive of Tris. might be responsible for such an erect. Accordingly. experiments were programmed in the presence of different concentrations of NH;-NHj buffer and others in methanol medium. Thus with two concentrations of NH,CI : 0. I and 0.05 M ; Barbital as added buffer. pH 9.00 and ionic strength 2.0 M. the results shown in Fig. 6 were obtained. As may be seen, the double-reciprocal plot is concave-down. clearly indicating that the kinetics are non-Michaelian. Since the double-reciprocal plot is linear at this ionic strength. in the absence of the NH&NH, species (that is in Barbital at I = 2.0 M, see Fig. 3A). we were led to consider that this group might act as an effector of non MichaelissMenten kinetics. Table 6 shows the fitting of the experimental data. Similar results were found in the presence of methanoi. and concave-down double-reciprocal plots were also obtained (results not included). though in this case, they were not as good as those obtained with the NH:-NH, system. perhaps due to side effects of the solvent. We therefore conclude that It is possible that the effector properties of Tris could be due, among other causes, to the NH;-NH2 group of its molecule.

Since the alkaline phosphatase dimer. it has been proposed in the of the “non-Michaelian” kinetics kind of cooperativity between the

from E. Ai is a past that the cause found was of the two active sites of

134

A.

Table 4. Rate

ARCO

YI d.

equations litted according to the iterative program of Feraudi (Feraudi <“I trl.. 1977) for klnetlc hydrolysis of p-nitrophenyl phosphate in Barbital at different phosphate concentrations

Phosphate

(M)

DLL

Data

(itmol

Range of L min ’ mgE ’ 1

IO -l

IO

50.1 1~~7.36

10. 1

IO

27.45-l 03

5.10 z

I0

I I.18 ~0.18

Best titting equation 7.7 -._

[’ =

I :I

0

25

l/[S]

0.21 0.044

* Neither ,I:W fittings with negative terms nor those n:m fittings with positive greater than 3 are included. All 3:3 fittings leave some negative terms.

the enzyme molecule, either of the binding and of catalysis of the substrate. or only of the binding. For an enzyme with two active sites. such as alkaline phosphatase. the simplest scheme which considers these effects of cooperativity appears in Fig. 7 where the open circles represent free sites. the solid ones are occupied by substrate and where the constants represent the different individual binding (lkL, ‘kZ) and catalysis (‘k,,,. ‘kc.,0 constants. Under the conditions of measuring initial rates (excluding reversible enzyme reactions) and assuming an equilib-

O:her fittings*

(T I.82

9.22 IO”(S)+ 4.03 10S(SjZ I-+ 9.28 103(S) + 7.90. lOh(

or negative

essays of

I:1 2:I 7:3

1.91 1.91 I 79

I:1 ‘:I 3:2

0.36 0.22 0.70

2:l 3:2

0.19 0.019

terms which have 11 or 01

rium in the binding of the enzyme with the substrate which is not disturbed by catalysis itself, the following rate equation is obtained: 7’k2(S) + %‘k,‘kL(S)’ I’ = v 1-q z2(j)+ 1Q1i2(s)2 where L’ =

'k,,,(E), and

0 =

“I\

2:.

‘kc.,,

I

I

50

75

IO<

( m hi-’ 1

Fig. 5. Lineweaver-Burk plots for the hydrolysis of p-nitrophenyl phosphate in presence of Tris: ( -~-•-- ) 0.1 M Tris. 1 = 2.0M. pH8.78. T= 25 C and O.O14~g~ml-’ of enzyme. (- -) 0.01 M Barbital. I = 2.0 M. pH 8.63 T= 25 C and 0.027 ~g~rnl~’ of enzyme. In both the range of substrate concentration was IO- ‘-IO-’ M.

(7)

Negative cooperativity in alkaline phosphatase from E. co/i

135

Table 5. Rate equations fitted according to the iterative program of Feraudi (Feraudi er al., 1977) for kinetic essays of hydrolysis of p-nitrophenyl phosphate. to study the effect of Tris with respect to Barbital

Conditions Barbital 0.01 M I = 2.0 M: pH 8.6 Tris 0.1 M I = 2.0M; pH 8.7

Data

Range of L (pmol.min-‘.mgE-‘)

10

50.41- 16.85

1:l

0.69

2:l 212

0.54 0.55

65.07-23.89

212

0.71

1:1 2:l 2:3 3:3

2.89 1.30 0.71 0.71

9

Best fitting equation

* Neither n:m fittings with negative terms nor those ,~:rn fittings which have n or m greater than 3 are included.

In this treatment, it has been assumed that the Michaelis-Menten equilibrium condition has been fulfilled. deliberately excluding the consideration of steady-state. With this last proposal, a 2:2 equation is also achieved. though with more complex parameter values. Equation (7) is thus more informative and is the one which will be used in this study. For this model, the cooperativity in the substrateenzyme binding may be calculated by the value of fj = ‘k2i1k2 and the cooperativity in the catalysis by the value of 6 = 21i,,,/‘k,.,,. Theoretical representations of equation (7) for different values of 6. ‘1\* and *li, result in the form of the different cooperatitity behaviour (C’adenas. 1978). The form which coincides best with our results is the one which corre-

0

with positive

o

or negative

terms

sponds to negative cooperativity in the binding (p < 1) and the absence of cooperativity in the catalysis (6 = 1). Regarding cooperativity in the binding (Q), it seems clear that it is negative, sjnce the doublereciprocal plot is concave-down. Less defined, however, is the degree of cooperativity in the catalysis (6). since the differences are less apparent. Nevertheless, it might be a reasonable assumption to admit non-cooperativity in the catalysis (6), because this is most normal in this polymeric enzyme. A double-reciprocal plot of equation (7) leads to the determination of all the parameters of the model ('k2, 'k2. V) from the limits o,f the polynomial function and its first derivative when (l/S) + 0 and when (l/S) -+ co. For the hydrolysis experiments at different ionic

25

75

11 [S]

Otter fittings*

100

(mhi-‘)

Fig. 6. Double-reciprocal plots for the hydrolysis of p-nitrophenyl phosphate in presence of NH;-NH, as a effector: (0) 0.1 M NH,CI and (0) 0.05 M NH,CI. Both of them were 0.01 M in Barbital and for all cases were pH 9.10, I = 2.0 M. T= 25 C. The enzyme of substrate concentration H<

14 2

I,

concentration was 0.042 pg.ml-’ was 10-‘-10-5 M.

and the range

A. DEL ARCS cr (11.

136 Table

6. Rate equations fitted according to the Iterative program of Feraudi (Feraudi er trl.. 1977) for ktnetic essays hydrolysis of p-nitrophenyl phosphate, to study the effect of the NH&NH, species (constituent of Tris).

Conditions

Data

NHJCIO.I M pH Y.00; I = 2.0 M

Y

NH,CI 0.05 M pH 9.00: I = 1.0 M

IO

Range of I; (htmol’min ’ mgE 40.67- I I. 14

43.53

* Neither n:m tittmgs with negative greater than 3 are included

II.50

terms

Best frttmg equatton

‘)

nor those

1’ =

1.66. lob(S) + 1.10, 10’(Sj2 ~~~~~ ~~~~~~ 1 + 5.23 IO”(S) + 1.47 Io’(s)2

0.63

t =

1.75’ lob(s) + 3.10’ 104(S)’ ~_~ ~~~~~~ _~ ~_~ _ ~ I + 5.46. 104(S) + 5.57’ IO’(St’

0.32

n:nt fittings

(Fig. 3). these parameters are shown in Table 7 where the following may be observed: (1) The binding constant of the second substrate molecule (‘k,) is always smaller than that of the first molecule ( ‘k2) (negative-cooperativity). except at high ionic strengths where both coincide in value (i, = 1) (non-cooperativity). (2) Both binding constants tend to approach each other in value parallel to the increase in ionic strength, the first (‘k2) decreasing, and the second (21\2) increasing. At an ionic strength of 2.0 M. both constants are equal at an intermediate value. A similar proposition was adopted by Simpson & Vallee (1970), who for p-nitrophenyl phosphate in 0.1 M Tris. pH 7.8, I = 0.05 M and using equilibrium dialysis with labelled phosphate found binding constants of 5.9’ IO’ and 3.3. IO” Mm ‘; in good agreewith our own results of 7.8. IO’ and ment 6.4.10” M ’ (Table 7). However. the differences are greater at higher iomc strength (I = I.0 M) where the same authors found binding constants of I .2. lo5 and 2.5. IO’ M ‘. our values under similar conditions being 9.8. IO’ and 2.4’ IO” M- ’ (Table 7) that is, their ‘I\, is some lOO-fold smaller than ours. though thetr ‘I\, is fairly similar. According to this, for Simpson & strengths

lkcat

(T

with posittve

or negative

terms

which

01

Otter fittings* I:1 2:l 3:z 3:3

1.88 0.64 0.64 0.63

I:1 2:l 3:3

I.85 0.43 0.30

have )I or rrt

Vallee (1970) the greater “Michaelian” nature seen in the kinetics at high ionic strength is due to the fact that the contribution of the second site would be negligible, while according to our own calculations. this effect would be due to the fact that the two sites would equalize their binding constants for the substrate as the ionic strength increased. With respect to the computer fitting. it has been seen that the most suitable one has in most cases been a polynomial quotient of 2:2 degree. which would agree wtth mechanism of the Fig. 7; only at high ionic strength does the 2:2 degree seem to be reduced to I : 1. and this is also in agreement with what has been reported above. Thus there existed the possibility of using the pi and y, coefficients of the polynomial tittings to determine the values of ‘k,, ‘li,. 0 and V of equation (7). too. This was carried out, and the values of these parameters are found to be in fair agreement with those established by the graphic method. However, excessive credit should not be given to the parameters of equation (7). since the fitting coefficients may not be taken as exact values, due to both statistical and calculational hypotheses of the computerized fitting method. However, what is completely valid is the algebraic form of these polynomial fittings.

zkcat

Fig. 7. Basic mechanism for a dtmeric enzyme with two equivalent binding sttes per molecule for a single substrate. The open circles represent free sttes and the solid ones are sttes occupied by substrate. It is assumed that there ts cooperativity both in the binding and in the catalysis.

Negative Table

7. Hydrolysis

cooperativity

in alkaline

of p-nitrophenyl

phosphate

(Ml

PH

I (M)

0.02 0.01 0.0 I

9.0 8.83 8.63

0.02 1.0 2.0

Barbital

V (~mol.mln~‘.mgE-‘) 7.9 25.8 26.8

This previous mechanism (Fig. 7) nevertheless ,ippears somewhat simplified for an alkaline phosphatase. since it does not include aspects such as phosphorylation and dephosphorylation of the enzyme, inhibition by phosphate etc. It has been demonstrated that in some cases. the explicit formulation of mech,mism can lead to an increase in degree of the corre\ponding rate equation (Waight & Bardsley, 1977) and this aspect should be considered. A mechanism which does in fact consider all these steps is the one proposed by Waight et (I/. (1977); this mechanism is represented in Fig. 8 (Mechanism I), where Q is phosphate, P phenol and the rest are described according to normal symbolism. This six-noded mechanism corresponds to a 3:3 rate equation when resolved by a computer according to steady-state treatment. that is:

PI(S) + p2(W + p3(S)” Y,(S) + ‘]*(s)2 + q3(S)T

I‘= ‘/O +

where p, and ~1,are highly complex expressions of the individual constants of Mechanism I (Waight ef al., 1977). Experimental studies carried out by the same authors (Waight rt u/., 1977). showed that the kinetic data needed at least a 3:3 polynomial quotient in order to be fitted satisfactorily, in agreement with hIechamsm I. However. under similar experimental conditions. our results show that a 2:2 fitting seems to be sufficient and that a 3:3 degree does not improve the fitting appreciably. It is possible that our fitting programme converges slightly better than Waight‘s does and the good 2:2 fitting. found by us in this work, might therefore indicate that. under given conditions, the general 3: 3 equation from Mechanism I will be reduced to a 2:2 fitting and even to 1: 1 (at high ionic strengths and phosphate concentrations). Waight et u/. (1977) themselves have studied this reduction in degree in a number of reports and have established that these reductions are originated when the numerator and denominator of the function share a common linear factor and take place when the Silvaster resultants cancel out. Thus for a reduction from 3.3 to 2:2 the next resultant would have to be zero: Y3 ‘IZ ‘i 1 (10 0 0 q3 Y2 ‘/I 0 =

from E. m/i

in Barbital.

137

Determination

of the

substrate binding constants (‘L2. ‘k2) and of maximum rate (I/) (Mechanism Fig. 7). assuming non-cooperativity in catalysis (6 = 1I

enzyme

R,,

phosphatase

0

0

P3

P2

PI

0

P3

P2

PI

0

P3

P2

PI

0

0

=

@lIEI

-

E:2

)!p3.

But the fact that R. must be cancelled says nothing in molecular terms, since E, ,, E,~ and ei3 are parameters

‘A2 (M-I) 7.8 IO4 9.8 10“ 4.7, IO”

‘L>

Zkz (M-1)

of

(‘2 =

II, L

6.4.103 2.4. IO“ 4.7. lo4

0.082 0.246 1.0

which depend on the individual rate constants in so complex a manner that it IS not possible to reach an explanation in terms of one or two rate constants (Waight or ul.. 1977). Its only meaning is mathematical and in general, it is only wlhen any given values of the rate constants are concurrent. that the Silvester resultant can be made equal to zero. It would be necessary to make similar arguments to carry out reductions from 3:3 to I:1 or from 2:2 to 1:l. According to this, all changes in fittings and in the form of the curves can be explained in mathemattcal terms without it being IK~~~L~SSII~~~ that some type of cooperativity should have to disappear. A more intuitive treatment might be to approach the problem from a molecular point of view. Which steps of Mechanism I would be negligible under the experimental conditions of our study’! Does the elimination of these steps lead to a mechanism of 2:2 or I : 1 degree’? Let us begin by analyzing the studies in the absence of phosphate; these havje two important aspects which should be born in mind: (1) In all cases, initial rates have been measured: that is, not more than 3 5”(, of the reaction. (2) In the reaction medium. initially there were none of the products present at the end of the reaction (phosphate. phenol). Under these conditions. the general Mechanism I could be simplifed to Mechanism II (Fig. 8). That is. according to (2) the EEQ % SEEQ pathway has been completely eliminated. since in conditions of absence of phosphate the EEQ concentrations would be so low that the participation of such a pathway would be negligible compared with the rest. By the same cause, the utilization of the followmg direction EE --t EEQ + QEEQ is also negligible. Furthermore with respect to the pathways corresponding to EEQ + EES: XEQ + SEES; QEEQ+ .‘XEQ of Mechanism I have not been considered because p-nitrophenol (P) is not a good acceptor of inorganic phosphate and the extent of the reaction P + Q -+ S would be negligible. Mechanism II leads to a 2:2 degree rate equation when steady-state treatment is applied. In principle. this could explain well most of our 2:2 fittings. With respect to the reduction in degree from 2:2 to 1: 1 at very high ionic strength there could be two possible explanations: a very simple one could be that at very high strength, the cooperativity of the sites would disappear (Table 7). and a more complex one would be that, under these conditions, a reduction in degree might be due to the effect of the ionic strength on the values of the individual rate constants, meaning that, the Silvester resultant would be cancelled (cooperat-

138

A. DEI ARCO CI d

k +B

k IP

Mechanism

I

k+B

Mechanism

EES

EEO

k +1

\J k +I

II

k ,6

k -5 (01

SEE

k_,tO

2k+e

(S’ k-6 OEEQ

*+T

Met

honism

IIf

0

FIN. 8. Mechanisms proposed for E. ~oli alkaline phosphatase: (I) Two sited cooperatively linked PingPong Uni-Bi-mechanism from Waight cf trl. (1977). (II) Ping-Pong Uni-Bi-mechanism ohtained by stmplifying Mechanism (I). proposed as valid uhen there are negligtble amounts of the final products p-nitrophenol (PI and phosphate (Q) in the reaction medium. IllI) Ping-Pong lint-Bi-mechanism obtained by simplificatton of Mechanism (1) proposed as valtd when the reaction takes place in the presence of high phosphate concentration (Qt. In all schemes. EE represents the enzyme with its two sites. S represents p-nitrophenyl phosphate. and EES. SEE. EEQ.. represent the different states the (1) habe not enzyme may be found tn. The pathways correspondtng to !, + L, and I\_, of Mechanism been considered in Mechanisms (II) and (III) because p-mtrophcnol (P) is not a good acceptor of Inorganic phosphate since tt has been shown that the extent of the reaction P + Q-S uould he negltgible.

ivity does exist but IS hidden).

In support

of this latter

hypothesis is the fact that at the same ionic strength (2.0 M) but in the presence of Tris or NH:-NH, buffer, double-reciprocal concave-down curves appear in the plots though there also exists the alternative possibility that Tris and NH;-NH, might act as true allosteric effecters.

With respect to the studies in the presence of phosphate. we feel that the general Mechanism 1 could in reality be transformed into Mechanism III (Fig. 8) in which the EES 2 SEES 2 SEEQ loops have been eliminated on considering that it would be of little importance in a system of appreciable initial phosphate concentration. where it is expected that part

Negative

cooperativity

in alkaline

of the flow of the reaction should follow the EE z EEQ e SEEQ+ QEEQ and as the substrate concentration increases the EE G EES I SEEQ s EEQ and EE F? EES - EEQ loops will be of greater importance. This Mechanism III also leads to a 2:2 degree rate equation when steady-state treatment is applied so that the 2:2 fittings found by us for phosphate concentration of less than 5.10--j M nould also be explained. The participation of these pathways at increasing substrate concentrations does not necessarily mean that there must be sigmoid behaviour in the rate vs substrate plots. as has been proposed by Waight et rrl. (1977), but that there might also be non-Michaelian hyperbolic behaviour with concave-down double-reciprocal plots (Fig. 4). The reduction in degree from 2:2 to 1: 1 seen in our own experiments on increasing the phosphate concentration from IO-” to 5. IO- 3 M (Fig. 4) might merely bc due to a mathematical reduction of the kind that h,ls already been reported (null-Silvester resultant) due to influence on the phosphate concentration of the parameters of the polynomial quotient, since those parameters depend on (Q).

phosphatase

from E. co/i

139

Michaelian kinetics) and the reduction in degree from 2:2 to 1: 1 (Michaelis-Menten kinetics). The results have also been analysed in terms of a more general six-node mechanism which explicitly includes the step of phosphorylation and dephosphorylation of the enzyme together with all the combinations in the binding of the substrate or of the inorganic phosphate to the enzyme. This mechanism had been proposed by Waight et cd.(1977) in order to explain their 3:3 degree empirical rate equation. On the basis of our experimental conditions, we propose with this mechanism a possible explanation for the reduction in degree from 3:3 to 2:2 which we have observed in most of our experiments, and also for the reduction from 2:2 to 1: 1 found at high ionic strength and high phosphate concentration. Aclinowlrd~emenrs -We Feraudi (Medizinische Germany) for carrying discusslons.

are grateful to Professor M. Poliklinic. Heidelberg University. out the fitting tests and for fruitful

REFERENCES SUMMARl

A series of steady-state kinetic studies have been carried out with the alkaline phosphatase from E. co/i, using p-nitrophenyl phosphate as substrate. The experiments involved different pH conditions (6.3tX9.00). temperatures (10.3-39.8 C). ionic strengths (OS2.0 M) and phosphate concentration ( 10s4-5. lo- 3 M) using sodium Barbital as buffer. Kinetic studies were also carried out in the presence of Tris. NH;-NH, and methanol. In most cases studied, kinetics were non-MicGelian and a Michaelian behaviour was only found under the following two conditions: (A) at very high ionic strength (1 = 2.0 M): and (B) at high phosphate concentrations (5’ 10-j ML The kinetics were analysed first from the corresponding Lineweaver-Burk plots, the curves being concave-down in most cases. This could refer to effects of negative cooperativity in the enzyme. Apart from the graphic method, a computer statistical fitting method was also used successfully. evaluating rate vs substrate concentration data. This gave polynomial quotients type of degree n:m. In this way it has been possible to show that a 2:2 degree fitting is sufficient to analyse satisfactorily in mathematical terms most of our steady-state data, without 3:3 degree fittings and above implying an appreciable improvement of the goodness of fitting. It has also been shown that the kinetic studies which had linear Lineweaver-Burk plots had 1: 1 fittings of appreciable goodness. Our results differ from those obtained in similar conditions by Waight et cl/. (1977). who reported that all their steady-state data with alkaline phosphatase from E. c~li may be conveniently fitted by a 3:3 degree equation. These difference with respect to the degree of the polynome quotient could be due to a different convergence of the fitting programme used in the respective studies. 4 simple four-node mechanism. with cooperativity of binding and of catalysis has initially been proposed. explaining our 2:2 degree rate equations (non-

ALLEN

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140

A. DEL ARCO el ul.

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CWIVFRA

Ko S. H. D. & KEZDY F. J. (1967) The kinetrcs of the E. co/i alkaline phosphatase catalyzed hydrolysis of 2,4_dinitropheriyl phosphate. J. Am. ckem. SM. 89, 7139%7140. LALDL’NSKI

C.,

Pt7iT(UR(.

C..

CHAPPtLFT

LA~DUNSKI M.. PETITC.LI:K( DLJNSKI C. (1971) Flip-Flop

&

LA/-

model:

the alkaline

C..

CffAf+‘tLtT

D.

&

LAI-

mechanism m en.?ymology. A phosphatase of E. co/i. Eur. J. Bw-

c~/lum. 20( I ). 1’4. 139. MALAMY Y. M. H. & Hofmxf-.ft

and crystallization of the alkaline Bio~‘hcnlistr~~ 3, 1893-1897.

B. L. (1964) Purlticatlon phosphatase of E. &i.

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content

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ROIG M. G. (1981) Doctoral Thesis. Faculty of Science\. Llni\eraltj of Salamanca. Spaln. ROTHMA\ F. & BYRNE R. (1063) Fingrrprmt analysis of alkaline phosphatase of E. c,o/i K-12 J n~~~/r~~. Rio/. 6. 330 340. S~HLLSINGEH M. J. & BARKtTr K. 11965) Re\cralble dfasocfatfon of the alkaline phosphatase of E. W/I. I Formatlon and reactivation of subunits. J. ho/. C/IHH 240,

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allosterlc

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D

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state