Eur. J. Biochem. 76, 513-520 (1977)

The Allosteric Inhibition by Calcium of Soluble and Partially Purified Adenylate Cyclase from Turkey Erythrocytes Emmanuel HANSKI, Nehama SEVILLA, and Alexander LEVITZKI Department of Biological Chemistry, The Hebrew University of Jerusalem (Received October 30, 1976/March, 19, 1977)

Adenylate cyclase from turkey erythrocyte membranes was solubilized in Lubrol-PX and partially purified (22-fold) by molecular sieve chromatography on Biogel A5M. The molecular weight of the enzyme was found to be 316000. The partially purified solubilized enzyme was found to retain all the kinetic and regulatory properties of the native membrane-bound enzyme except its sensitivity to bagonists. The enzyme responds to Mg2+in a positively cooperative fashion, with a Hill coefficient of n H = 2.0. The enzyme is inhibited by Ca2+ in a positively cooperative fashion with a Hill coefficient of n H = 2.0. The calcium effect is only on the kcatof the reaction and not on the binding and kinetic parameters of the enzyme towards the other ligands such as MgATP and M$+ . The Mn2+-supported adenylate cyclase is not inhibited by Caz+ as was found for the native membrane-bound enzyme. The essential role of metal ions in the activity of adenylate cyclase was originally discussed by Rall and Sutherland [l]. They pointed out that the substrate for the adenylate cyclase reaction is the complex MgATP. Free MgZ is also required for the adenylate cyclase activity and presumably binds to specific regulatory sites on the enzyme [2,3]. Mn2+ is able to substitute for Mg2+in the enzyme activity [4]. In some systems Mn2+ activates the enzyme to a lower specific activity than Mg2+, as in the cerebral cortex [5], whereas in other systems Mn2+ activates better than Mg2+ as in the case of adenylate cyclase from rabbit ventricular myocardium [ 5 ] . Calcium ions were found to be inhibitory to most of the adenylate cyclases [4,6]. It was therefore suggested [2] that Ca2+ may function as a regulator of adenylate cyclase. It was also found by these authors that Ca2+is a competitive inhibitor for Mg2+ in cardiac adenylate cyclase. In turkey erythrocyte membrane adenylate cyclase it is however shown that the inhibition of Ca2+is not in competition with Mg2+ but rather Ca2+ exerts its effect through a separate regulatory site [2]. The response to Ca2+ was found to be cooperative with a Hill coefficient of n H = 1.9 suggesting a minimum of two interacting Ca2+ sites. The inhibitory effect of Ca2+was found to be identical also for the enzyme in its highly active form, namely, in the presence of GuoPP(NH)P and l-epinephrine [S]. Calcium however does not interfere with the kinetic +

process of adenylate cyclase activation by GuoPP(NH)P and epinephrine [S]. The binding of Ca2+ to the enzyme was found not to alter the So.5 values for the substrate ATP, or for the Mg2+effector, nor does it alter the cooperative response or the enzyme towards Mg2+. The affinity of the P-receptor towards either agonists [7] or antagonists [9] also remains unchanged. All these observations taken together strongly indicate that the enzyme possesses a unique class of Ca2+ binding sites which affects directly the catalytic site of the enzyme upon Ca2+ binding. It should be emphasized that Ca2+ was found to inhibit the catecholamine-dependent adenylate cyclase activity in whole turkey red cells [lo] as well as in hormoneresponsive released ghosts [ 11]. In this study we present a detailed analysis of the Ca2+ inhibitory action on soluble and partially purified adenylate cyclase from turkey erythrocyte membranes.

MATERIALS AND METHODS

Membranes Turkey erythrocyte membranes were prepared according to published procedures [7] and stored in vials in liquid nitrogen.

Activation of the Adenylate Cycluse Abbreviation. GuoPP(NH)P, guanosine 5'-03-(1,2-p-imido)The turkey red cell membranes were triphosphate; EGTA, ethyleneglycol bis(2-aminoethyl)-N,N,Nr,N'tetra-acetic acid. suspended in Tris-HC1 buffer 50 mM pH

thawed and 7.4 contain-

514

ing 1 mM EDTA, 2 mM MgC12,0.5 mM dithiothreitol and 10 pM diisopropylphosphofluoridate. Then the membranes were centrifuged at 28000 x g for 10 min. The washing was repeated three times, then the membrane adenylate cyclase was activated with 2.0 pM [3H]GuoPP(NH)P(400 counts x min-' x pmol-') and 0.1 mM l-epinephrine in the above buffer, at 37 "C for 30 min. The protein concentration in the incubation mixture was 5 mg/ml and the final volume was 25 ml. Then the excess [3H]GuoPP(NH)P and epinephrine were washed four times by centrifugation in the above buffer.

So lubiliza t ion Solubilization was conducted essentially according to Pfeuffer and Helmreich [12]. Preactivated membranes in a final concentration of 5 mg/ml were incubated with 1.2 % (w/v) [14C]Lubrol-PX (44 counts x min-l x pg-') and 0.25 M sucrose in 50 mM TrisHCl pH 7.4 containing 1 mM EDTA, 2 mM MgC12, 0.5 mM dithiothreitol and 10 pM diisopropylphosphofluoridate, (buffer 1) at 4 "C for 30 min. The mixture was centrifuged at 105000 x g for 60 min at 4 "C. The supernatant was concentrated to a final volume of 1.5 to 2.0 ml by vacuum dialysis. Gel Chromatography

The concentrated solubilized cyclase was loaded on a Biogel A5M column (2 x 30 cm) preequilibrated with the same buffer or with a buffer that included 50 mM Tris-HC1 pH 7.4, 1 mM MgC12, 10 pM diisopropylphosphofluoridate, 0.5 mM dithiothreitol, (buffer 11) at 4 "C. The column was eluted using buffer I or buffer I1 at a flow rate of 12 ml/h and 2-ml fractions were collected. We used buffer I1 to control the accurate concentration of the metal ions in our system. As can be seen buffer I1 does not contain EDTA or EGTA.

The Allosteric Inhibition by Calcium of Adenylate Cyclase

tion. The specific radioactivity of the ['4C]Lubrol-PX was found to be 44 counts x min-' x yg-'. Det.ermination of Molecular Weights

Molecular weight determination of the eluted peaks from the Biogel A5M column was performed according to standard procedures. The column was calibrated using the following markers ; blue dextran (2000000), 8-galactosidase (521 000), urease (450000), catalase (250000), pyruvate-phosphate dikinase (160000), and hexokinase (1 10000). All these enzyme markers and the blue dextran were solubilized in 2.2 ml of I0 mM imidazole buffer pH 7.5 containing 0.5 mM dithiothreitol and 100 mM NaC1. Determination of ATPase

The assay mixture for ATPase contained 2 mM [Y-~~P]AT (8Pcounts x min-l x pmol-'), 0.4 mg/ml theophylline and 10 mM MgC12 in 50 mM Tris-HC1 pH 7.4. The protein sample was 20-60 yg per assay in the case of membranes and 2- 10 pg protein in the case of solubilized protein. The final volume of the assay mixture was 150 p1. The assay was performed by introducing the protein sample into the reaction mixture preequilibrated for 5 min at 37 "C. Samples of 50 yl were withdrawn at different time intervals and transferred into 0.85 ml suspension of 5 % (w/v) Norit A in 20 mM sodium phosphate buffer pH 7.0 at 0 "C. The suspension was centrifuged at 12000 x g for 5 min. 50-pl or 100-pl samples were withdrawn from the supernatant and counted for radioactivity in scintillation counter. A blank [ Y - ~ ~ P I A T sample P yielded 2.1 "/, of the radioactivity introduced. RESULTS Solubilization and Chromatography of Adenylate Cyclase

Adenylate Cyclase

The activity of adenylate cyclase was measured according to Salomon et al. [13]. Protein Determination

Protein was determined according to Lowry et al. [14] and also by the determination of the absorbance at 280nm. It was found that one absorbance unit corresponds to 0.67 mg/ml of solubilized protein. [14C]Lubrol PX

[14C]Lubrol was synthesized according to Gaylor and Delwiche [15] and used for the enzyme solubiliza-

The solubilized membrane preparation which contains adenylate cyclase and the [3H]GuoPP(NH)P binding proteins cannot be checked for the yield of adenylate cyclase solubilized, since Lubrol-PX strongly inhibits the cyclase activity (Fig. 1). Thus the first step in which the yield of cyclase solubilized can be examined is only subsequent to gel chromatography. The yield of cyclase subsequent to gel chromatography on Biogel A5M was found to be 40% of the original membrane activity. 12 % of the membrane protein was found to be solubilized and over 90% of the [3H]GuoPP(NH)P bound to the membranes were found in the solubilized protein. The Lubrol-solubilized enzyme loses 50 % of its cyclase activity after 3 days and 90 % after 7 days upon storage at 4 "C. The chromatographic pattern of the solubilized membranes is shown

51 5

E. Hanski, N. Sevilla, and A. Levitzki

-

;'

0 (I

in Fig.2. Three major protein fractions can be identified in the chromatographic pattern. The chromatographic pattern can be divided to three major fractions designated I, I1 and 111. The properties of the maxima of these peaks is summarized in Table 1.

I

750

h

The E f J c t of Ligands on the Solubilized Enzyme

0.25 0.50 Lubrol- PX concentration

0

(%,

0.75

in assay

w/v)

Fig. 1. Dependence ofthe adenylaie cyclase activity on Luhrol-PX concentration. Membranes were preincubated in the presence on 0.1 inM GuoPP(NH)P and 0.1 mM 1-epinephrine for 30 min at 37 "C at a final protein concentration of 5 mgjml, in 50 mM Tris-HCI pH 7.4 containing 1 mM EDTA, 2 mM MgClz and 0.5 mM dithiothreitol. Enzyme samples were assayed in the usual system containing 10 pM DL-propranolol and increasing concentrations of Lubrol-PX as depicted in the figure

The adenylate cyclase activity in fraction I1 is not stimulated further by either hormone, GuoPP(NH)P or their combination. Fluoride ions at 10 mM, however inhibit the enzyme activity to the extent of 40% (from specific activity of 16000 pmol x mg-' x min-' to 9650 pmol x mg-' x min-'). The Molecular Weight of the Separated Components

The apparent molecular weight of adenylate cyclase and [3H]GuoPP(NH)P binding proteins were determined from their position in the elution profile of the calibrated Biogel A5M column. The position

240

.

200

07

- 160 ._ j .

t

.a.l

g

120

80

40 0 Elution volume ( m l )

Fig. 2. The chromatography pattern on Biogel ASM. The activation of the membrane enzyme by GuoPP(NH)P and epinephrine and the solubilization were conducted as described in the Materials and Methods section. The solubilized protein sample was loaded on the Biogel A5M column (2 x 30 cm) and the chromatography was run at 4 "C using 50 mM Tris-HC1 pH 7.4 containing 1 mM EDTA, 2 mM MgC12, I0 pM diisopropylphosphofluoridate and 0.5 mM dithiothreitol as the elution buffer. The flow rate was 12 ml per hour. Protein adenylate cyclase activity, [3H]GuoPP(NH)Pbinding, [14C]Lubrol-PXbinding and ATPase activity were all assayed as described in Materials and Methods. (0)Protein; (A)cyclase activity; (A) ['4C]Lubrol; (0)[3H]GuoPP(NH)P bound Table 1 . Properties of major protein fractions from the Biogel-ASM column Experimental details are given in the text. It can be seen that the enzyme peak possesses 0.0052% detergent and the [3H]GuoPP(NH)P binding peak 0.26% detergent compared to 1.2% in the sample originally loaded Fraction

I I1 111 Preactivated membranes prior to solubilization

Adenylate cyclase activity

[3H]GuoPP(NH)Pbinding

[14C]Lubrol binding

pmol x mg-' x min-'

pmol/mg

mg detergent/mg protein

16050 0

510 2 360

0.52 12.1

750

60

516

The Allosteric Inhibition by Calcium of Adenylate Cyclase

900 000 L

700000

.m $ L

500 Oo0

!I

7 --a_-

p-Galactosidase ( 5 2 1 000) Adenyl c y c l a s k s e ( 4 5 0 000)

400000

1

Dikinase

-

c

-01

100 000

1.o

1.5

2

.o

2.5

o

'

.Y

10-5

10-4

10-3

[CaZ'ltot.~ ( M )

vE/VO

Fig. 3. The determinution ofthe moleculur weight of udenylute cyclase and (3H]GuoPP(NH) P binding protein. The Biogel A5M column was calibrated using /3-galactosidase, catalase, urease, pyruvate phosphate dikinase and hexokinase as the molecular weight markers. Blue dextran was used to measure the void volume. Further details are given in Materials and Methods. The molecular weight of the adenylate cyclase and of the [3HJGuoPP(NH)Pbinding protein are depicted on the figure

Fig.4. The efyect of Cu" on udenylute cyclase activity in the presence ofMg" and M n z t . Solubilized preparation of adenylate cyclase was prepared as described in Materials and Methods. The gel chromatography was performed in buffer I1 to control the accurate concentrations of the metals ions in the assay system. (0)Adenylate cyclase activity in the presence of 10 mM Mgz+.(0) Adenylate cyclase activity in the presence of 10 mM Mn2+

of the adenylate cyclase peak corresponds to a molecular weight of 480000 whereas the [3H]GuoPP(NH)P binding peak corresponds to a molecular weight of 220000 (Fig. 3). From the Lubrol content in the enzyme peak and in the GuoPP(NH)P binding peak, one can calculate the contribution of the Lubrol to the molecular weight and thus obtain the corrected values. The values obtained are: 316000 for the adenylate cyclase and 19000 for the GuoPP(NH)P binding protein.

is expressed only when the enzyme is assayed in the presence of 10 mM Mg2+ but has no effect when the enzyme is supported by Mn2+ instead of Mg2+. In order to calculate the inhibitory response to Ca2 as a function of free Ca2+concentration the following equilibria were considered : +

+ Mg2+aATPMg ATP + C ~ ~ + & A T P C ~

ATP

(1) (2)

and the following conservation formulas were used : ATPuse Activity

ATPase activity was determined under similar conditions to those used for the adenylate cyclase assay (see Materials and Methods). It was also found that Ca2+ has no effect on the ATPase activity. The ATPase specific activity measured in the membrane preparation was found to be 54000 pmol x mg-' x min-l whereas at the peak of the adenylate cyclase activity (fraction I1 on the Biogel ASM chromatography) the specific activity found was 42000 pmol x mg-' x min- At the same time however the specific activity of adenylate cyclase was increased 22-fold. One can therefore calculate that the ratio of ATPase activity to adenylate cyclase activity decreased from 54 : 1 to 3 : 1. This observation enabled us to omit the ATP regenerating system from experiments performed on the solubilized and partially purified adenylate cyclase.

'.

The Inhibitory Eflect of Cu2'

Calcium inhibits the adenylate cyclase activity of the solubilized and partially purified enzyme. It can be seen from Fig.4 that the inhibitory effect of Ca2+

+ [ATPMgl + [ATPCal [Mg2 = [Mg2+]free + [MgATP] + [CaATP]. [Ca2+]totai= [Ca2+]free [ATPltota~ = [ATPIf,,, +]total

(3) (4)

(5) The dependence of adenylate cyclase activity as a function of free Ca2+ is shown in Fig. S and the Hill plot of the same data in Fig.6. The Hill coefficient calculated for the Ca" effect is 2.0. The Eflect of Cu2' on the Dependence of Enzyme Activity on M g 2 +

The aim of this experiment was to determine whether Ca2 functions as a competitive inhibitor for Mg2+ or whether it functions through an independent regulatory site. To examine this point the dependence of enzyme activity on Mg2' concentration was examined at different concentrations of Ca2+ (Fig. 7 and 8). The concentration of free Mg2+ was calculated using Eqns (1) through (5) (for details see the Appendix) and thus the dependence of adenylate cyclase activity on free Mg2+ concentration could be deter+

517

E. Hanski, N. Sevilla, and A. Levitzki

p 1

-0

I

o

10.~

10-4 [Ca2'lfree

x

10-3

(MI

[Mg2'lfree ( m M )

Fig. 5. The inhibitory eflect qfCuz' on udenylute cyclase us u,function o f f r e e calcium. The concentration of free CaZ+ was calculated as described in the text and the Appendix. The data used was taken from Fig. 4

o.2

Fig. 7. The dependence of udenylute cyclase activity on free M g z + concentration in the presence of C u z + . Solubilized preparate of adenylate cyclase was prepared as described in Materials and Methods. The chromatography was done in buffer 11. (0) [Ca*+] = 0; (A) [Ca2+]= 70 FM; (0) [Ca"] = 0.2 mM; (A) = 0.4 mM

I

0.1

0.2

10.~

0.40.6

Fig.6. Hillplot of C a z t inhibition. The hill plot of Ca" was calculated according to the data in Fig. 5

1

2

[Mg2+Ifree

[Ca2+lfrae ( M I

inhibition

(mM)

Fig. 8. The Hill plot ,for M g 2 + uctivution. The data of Fig. 7 were plotted according to the Hill equation: = log K + log [Mg2+]f,,,. I-Y ( 0 ) [Ca2+]= 0 ; (A) [CaZ+]= 70 pM; (0) [Ca2+]= 0.02 mM; (A) [CaZ+]= 0.04 mM

log

mined (Fig.7). It can be immediately seen that the cooperative response towards Mg2+ remains essentially identical at different Ca2 concentrations with a Hill coefficient of about 2.0 and the So.5 values increase only slightly as a function of the extent of enzyme inhibition (Table 2). A Hill coefficient of 3.0 0.1 for the Mg2+ dependency is found when in the Hill plot the total Mg2 concentration rather than the free Mg2+ concentration. This value is identical to that reported for the unpurified native membrane bound enzyme [7].

3 4 5 6 8 10

~~

+

of its Mg2+ activity (Table 3). The Mn2+ adenylate cyclase is not inhibited by Ca2+ (Table 3) as was also found for the crude membrane-bound enzyme [7].

+

Properties of the Mn2 +-Activated Enzyme

When the soluble enzyme is assayed in the presence of Mn2+ instead of Mg2+ the enzyme exhibits 50%

DISCUSSION The adenylate cyclase from turkey erythrocyte membranes is inhibited by Ca2+ where the Ca2+ ion interacts with specific inhibitory sites. A detailed kinetic study on the effects of Ca" on membranebound adenylate cyclase revealed that the binding parameters for agonist [7] and antagonist [9] remain

The Allosteric Inhibition by Calcium of Adenylate Cyclase

518 Table 2. Kinetic parameters for M g 2 + at dij'ferent C a z + concentrations Preparation of the soluble and partially purified enzyme was performed according to the experimental details described in the text. Due to the low ATPase activity in the partially purified soluble adenylate cyclase, no ATP-regenerating system was found to be necessary. The enzyme assays were performed for 10 min at 37 "C [CaZ+],,,,,

Adenylate cyclase activity

[MgZ+Ifree at 50% maximal velocity

Hill coefficient

s0.5

PM

%

mM

0 10 200 200

100 78 51 36

0.80 1.75 2.25 & 2.50 &

0.10 0.10 0.10 0.10

2.13 0.10 1.94 i 0.10 1.85 i 0.10 1.94 2 0.10

is not inhibited by Ca2+(Fig. 4). All of these properties are identical to those observed in the crude membranebound enzyme. It follows then that the adenylate cyclase in the solubilized state retains its regulatory CaZ+sites. The number of Ca2+sites is at least two and they act in a cooperative fashion. The soluble enzyme also possesses at least two M 2 + sites which act in a cooperative fashion. There is no overlap between the Mg2+ sites and the Ca2+ sites since the Ca2+ inhibition is not competitive with Mg2+ as in the cardiac adenylate cyclase [2]. Since in all experiments the enzyme concentration used was in the picomolar range, the concentration of bound metal to the enzyme could be neglected. The calculation was performed as further explained in the Appendix. The inhibitory response of adenylate cyclase towards Ca2 as a function of the free calcium concentrations is depicted in Fig. 5. Fig. 6 depicts the Hill plot of the data in Fig.5. The Hill coefficient for the Ca2+ inhibitory effect was found to be nn = 2.1 and the SO5 value (50 % inhibition value) was found to be So 5 = 76 x [Ca2+If,,,pM. The adenylate cyclase activity was found to be linear as a function of time at each of the Ca2+concentrations determined. This was found to be the case in the presence and in the absence of an ATP-regenerating system. These experiments exclude the possibility that Ca2+ acts by activating an inhibitory mechanism such as phosphorylation [16]. If that were the case non-linear dependence of the adenylate cyclase activity on time would be expected in the presence of Ca". Similar results were obtained for the membrane preparation both in the presence of 1-epinephrine + GuoPP(NH)P (activated state) and 1-epinephrine. The regulatory Ca" ion also does not alter the K, for ATP. At this stage it is sufficient to say that the partially purified Lubrol-solubilized adenylate cyclase possesses kinetic properties and an allosteric behaviour identical to that reported [7] for the native membranebound enzyme. The only difference between the partially purified enzyme and the native membrane-bound enzyme is the insensitivity of the former to hormone. With the aid of the newly synthesized p-receptor affinity label [17,18] presently attempting to localize the /3-receptor moiety in the chromatographic pattern of the solubilized membranes. The molecular weight of the detergent-free adenylate cyclase is 316000 (Fig.3) and is therefore probably composed from a number of subunits. It is clear that the enzyme possesses at least three types of sites: sites for the substrate MgATP, sites for the positive effector Mg2+and sites for the negative effector Ca". It is not clear yet whether the 316 000 molecular weight of adenylate cyclase species still possesses GuoPP(NH)P regulatory sites. Further purification of the enzyme is needed in order to elucidate the subunit structure of the enzyme +

Table 3. Properties o f M n 2 +adenylate cyclase The experimental details are identical to those described in Table 2 [Mg"] in assay

[Mn*+] in assay

[Ca"] in assay

pmoI x mg-' x min-'

mM 10 10 10 -

Adenylate cyclase activity

-

-

-

1.0

1.o 10 10

-

1.o

11200 820 11200 5620 5560

i 100 f 80 i 100 & 60 60

100 7.3 100 50.5 50.5

unchanged in the presence of Ca2+.Also, it was found that Ca2+ does not affect the So.svalues for the substrate Mg-ATP and the activating ion Mg2+ [7]. Ca2+ was also found to be without any effect on the activation of the enzyme by guanyl nucleotides and hormone [S]. These results on the crude native membraneous enzyme induced us to examine whether the Ca2+regulatory sites reside on the same protein as the adenylate cyclase activity. For this purpose we have solubilized the erythrocyte membranes partially purified (22-fold) the enzyme and separated it from the major [3H]GuoPP(NH)P binding proteins (Fig. 2). Upon examination of the soluble and partially purified enzyme it was found that the enzyme retains its Ca2+ sensitivity. Furthermore, a detailed kinetic analysis of the Ca2+-inhibitoryeffect revealed the following properties of this calcium inhibition. Firstly the inhibition of the enzyme by Ca2+ is cooperative with a Hill coefficient of n H = 2.1. Secondly, the CaZ ion does not compete for the Mg2+ binding sites on the enzyme since the So.svalue for the Mg2+ activation increases only slightly. (Table 2). Also, cooperativity of the Mg2+- Mg2+ interaction remains unchanged where the coefficient for the Mg2+ dependence is identical in the presence and in the absence of Ca2+ (Fig. 8). Thirdly, the Mn2+-supported enzyme which possesses 50 % of the activity in the presence of Mg2 +

+

E. Hanski, N. Sevilla, and A. Levitzki

519

and the nature of the different binding sites for the different ligands. It is interesting to note that the cooperativity in the response of the enzyme towards MgZt remains unchanged at different degrees of Ca2+inhibition. This is probably due to the fact that Ca2+ is a pure k,,,-effector and its interaction with the enzyme has no effect on the binding parameters for any of the ligands involved in the adenylate cyclase reaction or regulation. Throughout the analysis of the Ca2+ effect it was assumed that the saturation function describing the binding of Ca2+ to its regulatory site is given by = u/V where u is the specific activity of the enzyme in the presence of a certain Ca2+concentration and V

r

is the specific activity of the enzyme in the absence of Ca2+. It is assumed that u/V measures the degree of at the regulatory site. It was Caz+ occupancy already pointed out that in those cases in which was obtained from both direct binding experiments and kinetic experiments v / V was found to be a reliable measure for Y [18]. Theoretically, of course, it is certainly possible to have v/V quite different from Y. As eukaryotic adenylate cyclases are not available in a pure form, direct Ca2+ binding experiments cannot be performed at the present time.

(r)

ATPCa

5 ATP + Ca2+

(2) (3)

(4)

and the conservation relationships are : [ATPItotal

=

[ATPIfree

+ [ATPMgl + [ATPCal

(5)

+ = [Ca2+]free+ [CaATPl.

[Mg2+]total= [Mg2+]free [MgATP]

(6)

[Ca2+ ]total

(7)

From Equations (2) to (7) it follows that:

By dividing Eqn (4) by Eqn (3) one obtains:

r

and from Eqns (5) to (7) it follows that Eqn (9) obtains the form :

The Possible Physiological Role of Ca2+

Ca2+ is known to activate adenosine 3': 5'-monophosphate phosphodiesterase [19] and is also known to be the second messenger for a-adrenergic receptors. Thus, it has been shown that the primary biochemical action of an a-agonist is the introduction of extracellular Ca" into the target cell. The CaZ+then triggers other effects, such as K + release and water secretion from the parotid gland [20]. One can postulate that in target cells which possess both a and fi-receptors, Ca2+not only functions as the second messenger for the &-receptor,but also as an inhibitor of fi-receptor activity. This hypothesis may be attractive since in tissues which possess both cx and fi-receptors, the a and the b-receptors function in an antagonistic fashion.

Using these definitions Eqn (10) obtains the form:

Therefore : Y =

xu zj--cx-=.

(12)

Introducing Eqn (12) into Eqn (8) one obtains:

Part of this work was carried out by E.H. in partial fulfilment

Rewriting Eqn ( 1 3 ) one obtains the polynom :

of an M. Sc. degree of the Hebrew University of Jerusalem.

+ (b-c+K2-22b)x2 + (Kba-Kbc-2KKzb+K2b+KbZ)x+KKzb

(K-l)x3

APPENDIX The Calculation of (Ca2+]Freein a Solution Containing ATP, M g 2 + and Ca2+

In the presence of ATP, Mg2+ and Ca2+ the following equilibria hold : ATPMg 5 ATP

+ Mg2+

(1)

=

0. (14)

Solving Eqn (14) for x [Ca2+Ifree one obtains for each set of experimental conditions [ATPItotal,[Ca2+]total and [Mg2+Itotal the value of [Ca2+Ifree in the system.

E. Hanski, N. Sevilla, and A. Levitzki : The Allosteric Inhibition by Calcium of Adenylate Cyclase

520

This polynom (Eqn 14) was solved according to the Nuan procedure of the Hebrew University computing center using Getpol program.

This polynom was solved according to the Nuan procedure of the Hebrew University computing center using Getpol program. REFERENCES

The Calculation of M?' Free in a Solution Containing ATP, M g 2 + and Ca2+ From Eqns (1) to (4) one can show that:

Using the definitions given above one obtains: x Q-Y) Y (a - 4

K

=

=

z;-r+