- Email: [email protected]
A method of estimating the amount of calcium bound to the metallochromic indicator arsenazo III
217
Biochimica et Biophysica Acta, 586 (1979) 217--230 © Elsevier/North-Holland Biomedical Press
BBA 28965
A METHOD OF ESTIMATING THE AMOUNT OF CALCIUM BOUND TO THE M E T A L L O C H R O M I C INDICATOR A R S E N A Z O III
S. TSUYOSHI OHNISHI
Biophysics Laboratory, Department of Anesthesiology and Department of Biological Chemistry, Hahnemann Medical College, Philadelphia, PA 19102 (U.S.A.) (Received October 30th, 1978)
Key words: Metallochromic indicator; Arsenazo IIl; Murexide method; Ca2+ binding assay
Summary As a metallochromic indicator for ionized calcium, arsenazo III is approximately 50 times more sensitive than murexide. However, because of the high binding constant for calcium, the following problems may occur: (a) a considerable a m o u n t of calcium is b o u n d to arsenazo III, thereby causing an error in estimating the concentration o f ionized calcium; (b) the amount of b o u n d calcium varies with the concentrations of calcium, arsenazo III, magnesium ion and monovalent cations; (c) the a m o u n t also varies with pH, (d) the relationship between the absorbance change and the concentration of ionized calcium is nonlinear; and (e) the binding constant of arsenazo III for calcium cannot be determined b y the conventional double reciprocal plot. A new experimental and theoretical m e t h o d is presented which copes with these problems.
Introduction Since calcium ions (Ca 2÷) are known to regulate many important biological reactions, such as muscle contraction, nerve conduction, excitation-contraction coupling, neurosecretion, transport, and cell growth, methods of determining Ca 2+ concentration in physiological media are extremely important. Ohnishi and Ebashi developed a direct spectrophotometric m e t h o d of measuring low concentrations of Ca 2+ in physiological solutions using a metallochromic indicator (murexide) and a dual-wavelength s p e c t r o p h o t o m e t e r [1--4]. The method was also used to measure the binding constant of protein for Ca 2÷, and a Abbreviations: EGTA, ethyleneglycol-bis(13-aminoethyl ether)-N,N'-tetraacetic acid; HEPES, N-2-hydroxy. ethyl piperazine-N'-2-ethanesulfonic acid; MES; 2-(N-morpholino) ethanesulfonic acid.
218
m e t h o d of analyzing a system with two classes of binding site was established [5]. The m e t h o d has been applied to various systems successfully [6--10]. Detailed experimental procedure, as well as theoretical characterization of the murexide m e t h o d , has been reported [ 5,11 ]. Recently, arsenazo III was introduced as a sensitive Ca 2÷ indicator [12--16] and has been widely used. However, m a n y investigators are using arsenazo III w i t h o u t considering the difference between a murexide type indicator and arsenazo III. For example, t h e y calibrate the absorbance signal by adding a known concentration of Ca 2+ to the reaction mixture containing arsenazo III. However, because of the high binding constant of arsenazo III for Ca 2÷ (104--10 s M-l), a significant a m o u n t of Ca 2÷ is bound to the indicator. This causes an error in estimating the concentration of ionized calcium in the reaction mixture. To make the situation more complicated, the a m o u n t of arsenazo IIIbound Ca 2÷ depends on the concentrations of Ca 2÷, other cations, arsenazo III itself, and on the pH as well. Another misunderstanding concerns the effect of Mg 2÷. In much of the literature it has been assumed that the effect of Mg 2÷ can be ignored by selecting the combination o f wavelengths in such a way that the absorbance difference of arsenazo III changes only with Ca 2+, but not with Mg 2÷. This is not true. Even though the absorbance difference is not directly influenced by Mg2*, the assay of Ca 2÷ is influenced by Mg 2÷ (since the Ca 2÷ binding of arsenazo III is competitively inhibited by Mg2+). The situation is entirely different from that o f murexide, where the indicator is practically insensitive to Mg2÷ in aqueous solution [ 11 ]. In order to solve these problems, a systematic m e t h o d of analyzing the binding characteristics of arsenazo III has to be established. In this paper, the experimental and theoretical bases of such a m e t h o d are described. The effect of concentrations of arsenazo III, Ca 2÷, Mg2÷ and monovalent cations as well as effect of pH are also discussed. Materials and Methods C h e m i c a l s Arsenazo III (Grade I), EDTA, EGTA and murexide were purchased from Sigma Chemical Co. (St. Louis, MO). HEPES, MES and tetraTITRATION ATTACHMENT Co-SOLUTION
INDCATER
SOLUTION
FILTER
LAMP
STIRRER~.~ '\" FILTER "PM I
I
I WATER
[
J JACKET
t
RECORDER
i DUAL WAVELENGTH SPECTROPHOTOME TER
Fig. i . Sehematie illustration of the automatic eaJeium titrator. Abbreviations: A, absorbance recording o n a r e c o r d e r ; AMP, a m p l i f i e r ; C, c u v e t t e ; L O G AMP, l o g a r i t h m i c a m p l i f i e r ; M, m i r r o r ; a n d PM, photo-
multiplier.
219 methyl murexide were obtained from Calbiochem (La Jolla, CA). Chelex 100 resin was purchased from Bio-Rad Laboratories (Richmond, CA). Calcium standard solution was purchased from Orion Research Laboratories (Cambridge, MA). The contaminating Ca 2÷ in arsenazo III stock solution was removed by passing it through a column of Chelex 100. Spectrophotometric measurements. Calcium titration was carried out by a Model CL dual-wavelength spectrophotometer by TCS Co. (P.O. Box 141, S o u t h a m p t o n , PA 18966) with an automatic titration attachment. Optical measurements were performed on a sample volume of 1 ml in a quartz cuvette (10 × 10 mm), and the temperature was kept constant (25 ± 0.1°C) by circulating water from the Lauda 2-k/R thermobath (A.H. Thomas, Philadelphia, PA) through the cuvette holder (See Fig. 1). Results I. Analysis o f the calcium titration curve o f arsenazo III In carrying out the Ca 2÷ titration of an arsenazo III solution (which contains buffer and salt), it would be best if the contaminating Ca 2÷ could be completely removed. However, it is tedious and time-consuming to remove the minute a m o u n t of contaminating Ca 2÷ from the buffer and salt solution by passing them through a Chelex 100 resin column. Therefore, we developed a m e t h o d of running the Ca2÷ titration without interference from such small a m o u n t of Ca 2÷. As shown in Fig. 2A, we first add 2 mM EGTA to the arsenazo III solution and record the decrease in absorbance. This 'EGTA drop' is registered as G, and the new level is defined as 0' (true Ca 2÷ zero level). The solution is discarded and the cuvette is filled with the new solution. Then the relation between the a m o u n t of added Ca 2÷ (denoted by [Ca]t i in Fig. 2B) and the absorbance change A is recorded by using the automatic Ca :÷ titrator attachment (Fig. 1). The volume of Ca 2÷ solution added during the titration is less than 10 t~l. After titration is finished, excess Ca 2÷ (10 mM) is added to the solution to record the Ca :÷ saturation value A~ (see Fig. 2B). The beginning portion of the titration curve is extrapolated downwards to hit the true Ca :÷ zero
~ 0.1 i
uJ0.05~
Titrotion
,-Y ....
/ /
G
r ....
|/0 0
/
.-
Io 10
Co
J
20 20
30 30
40 [co]~ 40 [co] t
(~M)
Fig. 2. A . Decrease in absorbanee caused b y 2 m M E G T A . B. Ca 2+ t i t r a t i o n o f arsenazo I l l solution. Condition: 4 0 m M H E P E S ( p H 7.0), 1 0 p M arsenazo I I I , 25~C. The ionic strength is adjusted t o 0 . ] w i t h See text for
KCI.
details.
220
level. Th e a m o u n t indicated by [Ca]in in Fig. 2B corresponds to the a m o u n t o f initial contaminating Ca 2+ in the arsenazo III solution. ([Ca]in is t he sum o f arsenazo III-bound Ca and free Ca 2+ in t he solution before the start o f the titration). Then total Ca 2+ ( d e n o t e d by S) in t he system is given by S = [Ca]i n + [Ca]t i
(1)
The reaction between Ca :+ and arsenazo III (denot ed by AZ) is given by AZ + Ca ~ AZ • Ca [AZ] = E - - p [Ca]f = S - - p
(2)
[AZ • Ca] = p where p stands for the c o n c e n t r a t i o n o f the com pl ex AZ • Ca and E stands for the total c o n c e n t r a t i o n o f arsenazo III. [Calf represents the c o n c e n t r a t i o n o f free Ca :+. The dissociation constant, K, is defined by g -
(E - - p ) ( S - - p )
(3)
P Let Ae be th e difference molar ext i nct i on coefficient o f arsenazo III at a particular c o m b i n a t i o n o f wavelength, t hen G+A =Ae-p
(4)
G+A~ =Ae'E from Eqn. 3 we have E_I -
+
K s-p
(5)
or by defining normalized values ¢, 9, t} and ~ by the following equations:
¢=p E
= G+A G+A+
S O=-E 5=0--¢-
normalized Az-bound Ca normalized total Ca
S--P E
K = -E
normalized free Ca normalized dissociation const ant
(6)
we can rewrite Eqn. 3 as
¢ 1+0_¢ 1+--~
(7)
Note th at there is a difference between this equation and the Dixon-Webbs e q u atio n (p. 67 Eqn. IV.15 in Ref. 18). In their equation
S>> p ;
orS--p-
S
(8)
221
is assumed according to the Michaelis-Menten t y p e enzyme kinetics, while our Eqn. 7 is valid without using this assumption. As pointed out already, this assumption is valid for murexide t y p e indicators, b u t n o t for arsenazo III [11]. Owing to the approximation shown b y Eqn. 8, the binding constant of murexide t y p e indicators for Ca 2÷ could be determined from a straight line of the double reciprocal plot without knowing the indicator concentration (see Ref. 11). However, as shown b y Eqns. 6, it is essential to k n o w the indicator concentration (E) to obtain a linear plot represented by Eqn. 7. A spectrophotometric method o f determining the indicator concentration is given in the Appendix. 2. D e t e r m i n a t i o n o f the dissociation c o n s t a n t
Solving Eqn. 3 or Eqn. 6, we have either p = (B -- (B 2 -- 4ES)1/2)/2;
B =E +S +K
(9)
or
=(fi_(fi2_40)l/2)/2;
~=1+0+~
(10)
The titration curve in Fig. 3 represents Eqn. 9 (using the t o p and right scales) and Eqn. 10 (using the b o t t o m and left scales). The d o t t e d line in the figure is a tangent drawn to the initial part of the curve *, and the straight solid line drawn from the origin with unity slope is the limiting titration curve (this is the limiting case of the titration with infinitely strong binding). In the same figure, a horizontal line is shown which intersects with the ordinate, the limiting titration curve and the actual titration curve, and the corresponding intersections are designated as U, V and W, respectively. Since U V = O U = p , and UW = S, the distance U V gives the concentration of indicatorb o u n d Ca 2÷ and V W gives that of free Ca 2÷. N o w the approximation made for the conventional Michaelis-Menten t y p e equation may be readily visualized. In their equation, free Ca 2* is estimated as UW instead of VW. When the dissociation constant is large (weak binding) or when the concentration S is far greater than E, this approximation is valid. However, in the case of Ca2+-arsenazo III binding, this approximation causes a serious error as may be seen in Fig. 3. From Fig. 3, the dissociation constant can be determined in two ways: (i) draw a horizontal line at p = E l 2 (in the illustrated example E = 40), and intersect with the unity~lope line and the titration curve (P and Q, respectively). Then, the distance PQ represents K; (ii) extrapolate the initial slope until it intersects with the t o p scale (p = E). The value of the abscissa at the intersection is E + K. Since the extrapolation of the initial slope is subjectively done, m e t h o d (i) is generally more accurate. The dissociation constant can also be obtained b y t w o other graphical representations where the data points are expressed b y a straight line [ 23--26]. Fig. * T h e r e is a m e t h o d o f d e t e r m i n i n g the c o n c e n t r a t i o n o f the i n d i c a t o r b y e x t r a p o l a t i n g t h e initial part o f the t i t r a t i o n c u r v e t o t h e l e v e l o f p = E ( m o l a r r a t i o m e t h o d [ 2 2 ] ) . H o w e v e r , this m e t h o d is v a l i d o n l y when E ~ K . F r o m E q n . 9 t h e i n i t i a l s l o p e is c a l c u l a t e d as E / ( E + K ) , T h e r e f o r e , t h e e x t r a p o l a t i o n o f t h e initial s l o p e i n t e r s e c t s w i t h the l e v e l o f p = E a t E + K , b u t n o t at E .
222
0
[Co]t
(,~M) 40
r ~z~ 0.5
E o1!.J,
-40 P (#M}
-20
o
0.5
1.5
I
e Fig. 3. A n a l y s i s o f t h e t i t r a t i o n curve. Solid curve, t i t r a t i o n curve; d o t t e d line, initial slope; solid line, l i m i t i n g t i t r a t i o n curve; K, d i s s o c i a t i o n c o n s t a n t ; [ C a l f , c o n c e n t r a t i o n o f free C a ; [ C a ] A Z , c o n c e n t r a t i o n o f i n d i c a t o r - b o u n d Ca. C o n d i t i o n s : 4 0 DM a r s e n a z o III, 4 0 m M H E P E S ( p H 7 . 0 ) , i o n i c s t r e n g t h 0 . 1 , 2 5 ° C.
4A shows an example of arzenazo III-Ca binding represented by the linear equation 7. The x-axis intercept gives (--~). Fig. 4B shows another representation o f the same data as Fig. 4A by the following equation:
¢ 5
-
1
(1 -- ~b)
(11)
where the slope gives the association constant (=1/~). Having derived all of the mathematical expressions, all portions of the data analysis were computerized to minimize human error. The procedures are as follows: using an arsenazo III solution of concentration E, perform the titration and obtain data for G, for A as a function of [Ca]ti, and for A~. First, calculate an approximate value for [Ca]in by linearly extrapolating the initial part of the titration downwards to hit the level of 0'. Then using [Ca]in, calculate S, and find the value for K which makes the best fit curve for the titration data. Then, using that best fit curve, re-estimate the value of [Ca]in. Repeating this
6t
A
3.0 L
B
i
o
o. 5
I,O
8 Fig. 4. T w o linear r e p r e s e n t a t i o n s o f data. T h e data are t a k e n f r o m the t i t r a t i o n curve o f Fig. 3, a n d a n a l y z e d a c c o r d i n g to the m e t h o d d e s c r i b e d in the t e x t .
223 iteration permits us to find the values for both [Ca]i n and the dissociation constant K. At pH 7.0 and the ionic strength 0.1 M, the dissociation constant of arsenazo III was estimated to be 17 pM (or the association constant: 5.9 • 104 M -I) and A(~(675__685nm)to be 1.29 • 104.
3. Determination o f the indicator-bound Ca When the concentration and the dissociation constant of arsenazo III are known, the concentrations of arsenazo III-bound Ca 2÷, [Ca]AZ, and free Ca 2÷, [Ca]f, can be determined by the following equations: [Ca]f = Kp/(E --p)
or
61= ~ / ( 1 -- ¢)
[Ca]A z = [Ca]t -- [Ca]f
or
(12)
~b = O -- ~
(13)
Fig. 5A shows the difference between murexide and arsenazo III. In Fig. 5A, the d o t t e d line shows an ideal case of no Ca-binding. The open circles show 1.4% binding for 50 pM murexide (Ref. 11), and the filled circles show 40 t~M arsenazo III. It is clear t h a t a considerable a m o u n t of Ca 2+ is bound, especially at low [Ca]t concentrations. For example, at [Ca]t = 5 pM, 76% of Ca 2+ is in the bound form. Fig. 5B shows the relationship between the ratio [Ca]f/[Ca]t and [Ca]t. From Eqn. 10 or 11, it was calculated that the ratio approaches K/(E + K) or K/(1 + K) at the limiting case o f [Ca]t -~ 0.
4. Effect o f pH on Ca-binding o f arsenazo III It was found that the dissociation constant of arsenazo III is pH dependent. As shown in Fig. 6A, the association constant K (= 1/K) increases with an increase of the pH. Fig. 6B demonstrates how the ratio of [Ca]f/[Ca] t changes over the pH range of 6.3 to 8.0. 5. Mg binding o f arsenazo III A unique feature of the murexide t y p e indicator was the extremely low sensitivity to Mg2÷ in aqueous solutions [11]. On the contrary, as already shown
4o. A t
,,/
~.0-
B
~%50~ M MX
/
""0.62
0.5"
Io"1 / o
~ I0
~
~40pM AZ
40~M
20
30
40
[Co']total
(~M)
0
I
e
3
4
Fig. 5 A . R e l a t i o n s h i p b e t w e e n t o t a l Ca a n d f r e e C a c o n c e n t r a t i o n s o f m u r e x i d e ( M X ) a n d a r s e n a z o III ( A Z ) . B. R e l a t i o n s h i p b e t w e e n t h e n o r m a l i z e d t o t a l C a c o n c e n t r a t i o n 0 and the ratio of [Ca]free / [ C a ] t o t at . D o t t e d l i n e s s h o w [ C a ] f r e e = [ C a ] t o t a 1. D a t a f o r m u r e x i d e a r e t a k e n f r o m R e f . 1 1 . C o n d i t i o n s : • . o 4 0 m M H E P E S ( p H 7 . 0 ) , l o m c s t r e n g t h 0 . 1 , 2 5 C.
224
/
IO 7~ T
]'0 1 . . . . . . . . . . . . . . . . . . .
0 5 ~
j ....
I I
I
I
6
7
8
0
I
B
F
2 0
pH
F i g . 6. A. R e l a t i o n s h i p b e t w e e n t h e p H a n d t h e a s s o c i a t i o n c o n s t a n t K ( = I / K ) o f a r s e n a z o III f o r Ca. B. E f f e c t o f p H o n t h e r e l a t i o n b e t w e e n t h e n o r m a l i z e d t o t a l Ca c o n c e n t r a t i o n a n d t h e r a t i o o f [ C a ] f r e e / [ C a ] t o t aI . C o n d i t i o n s : 1 7 . 8 / a M a r s e n a z o III, 4 0 m M H E P E S , i o n i c s t r e n g t h 0 . 1 , 25~C.
in Ref. 15, arsenazo III is somewhat sensitive to Mg 2+. In this study, Mg 2+ titration was performed in a similar fashion to that for Ca 2+ and the dissociation constant was estimated as 837 pM (or the association constant: 1.2 • 103 M-') and Ae(675_685nm) as 4.36 • 103 at pH 7.0, ionic strength 0.1 and 25°C. If we define the sensitivity by A/S, the highest sensitivity will be the initial slope of the titration curve, which may be derived from Eqns. 4 and 9
A S
AcE E+K
(14)
In the murexide t y p e indicators, the term E in the denominator of Eqn. 14 could be neglected due to their high dissociation constant [11]. As shown in Table I, Ca/Mg sensitivity ratio of arsenazo III was 39, a value much lower than those for murexide type indicators. 6. Effect o f salts on Ca-binding o f arsenazo III Assume that cation I competitively binds to arsenazo III with the dissociaTABLE I S E N S I T I V I T I E S O F I N D I C A T O R S T O C a A N D Mg C o n c e n t r a t i o n o f i n d i c a t o r s is 50 p M . T h e s e n s i t i v i t y A / S is c a l c u l a t e d f r o m E q n . 14. D a t a f o r m u r e x i d e a n d t e t r a m e t h y l m u r e x i d e a r e t a k e n f r o m Ref. 11. C o n d i t i o n s : p H 7 . 0 , i o n i c s t r e n g t h 0 . 1 , 2 5 ° C . Ca K X 10 6
A/S
Ae X 10 -6
129
17
9630
153
3570
180
2780
Ae X 1 0 -6 A r s e n a z o III (675--685 nm) Murexid e (500--544 nm) Tetramethyl murexide (507--554 nm)
Mg
* R a t i o o f t h e Ca s e n s i t i v i t y to Mg s e n s i t i v i t y .
(Ca/Mg) * K X 10 6
A/S
43.6
830
247
211
2.9
125 000
318
7.8
62 500
0.115 0.62
39 1840 513
225 tion constant KI, then we have AZ+I=AZ'I;
or
K1 =
(E -- q)(i -- q)
(15)
q
where concentrations of the cation and arsenzao III-bound cation are given by i and q, respectively. From Eqns. 3 and 15, we can derive --=1+---p
1+
S--p
or
'
=1
+
(16)
where ¢o = ( i - q ) / E and ~ = K I / E . These equations look similar to the Michaelis-Menten equation for competitive inhibition (Ref. 18), but t h e y are solved w i t h o u t the conventional approximation of Eqn. 8 as well as i -- q - i. Eqn. 16 implies that in the presence of cations the apparent dissociation constant Kapp is expressed by gap p =
K(1 + (i - - q ) / g l )
(17)
If we define the corresponding association constants by K, Kapp and K~, we have K --=
1 + ( i - - q ) KI
(18)
Kapp
From the plot of K/Kapp vs. ( i - - q ) , Kx can be obtained as an inverse of the x-axis intercept. Fig. 7A shows such plots for Mg 2÷, K ÷ and Na ÷. It is obvious that these salts considerably decrease the association constant of arsenazo III for Ca 2÷. From the x-axis intercepts, the association constants of arsenazo III for these salts are estimated to be 1.1 • 103 for Mg2÷, 6.0 for K ÷ and 4.5 for Na ÷ (all in M-I). The value o f the association constant for Mg2÷ obtained by this m e t h o d is in good agreement with the value determined by the direct titration in the above section (1.2 • 103). Fig. 7B demonstrates t h a t the ratio of [Ca]free/[Ca]totaI also changes in the
~ .
o
. . . .
.~ .Mg . . . <,'nMp)
,5'-[
../S
0.5 ~ /
O~ M NoCI \CONTROL
B 0
0.5
I
NoCI or KCI (M)
Fig. 7. A. E f f e c t o f salts o n t h e r a t i o o f a s s o c i a t i o n c o n s t a n t ( K ) / a p p a r e n t a s s o c i a t i o n c o n s t a n t ( K a p p ) . B. E f f e c t o f salts o n the r e l a t i o n b e t w e e n the n o r m a l i z e d t o t a l C a c o n c e n t r a t i o n 0 a n d the ratio o f o [ C a ] f r e e / [ C a ] t o t a l . C o n d i t i o n s ; 1 3 . 6 / ~ M a x s e n a z o III, 4 0 m M H E P E S ( p H 7 . 0 ) , i o n i c s t r e n g t h 0 . 1 , 2 5 C.
226 presence o f salts, which is a n o t h e r problem o f the arsenazo III m e t h o d in determining ionized Ca c o n c e n t r a t i o n .
Discussion Arsenazo III is a sensitive metallochromic indicator useful for monitoring physiologic co n cent r a t i ons o f Ca 2+. However, various problems are created by t h e high Ca 2÷ binding constant o f arsenazo III. First o f all, for the measurement o f a low c o n c e n t r a t i o n o f Ca 2+, for which arsenazo III is most useful, the ratio o f b o u n d Ca2+/total Ca 2÷ becomes very high. In some cases, m ore than 80% of the total Ca 2+ is b o u n d t o the indicator itself. Therefore, w i t h o u t knowing this ratio, it is impossible to measure the c o n c e n t r a t i o n of ionized calcium. Secondly, this ratio changes with changes in the c o n c e n t r a t i o n o f arsenazo III, total Ca 2÷ and o t h e r salts in t he assay solution. Thirdly, the ratio changes with pH. Because o f these problems, the following parameters should be know n in applying arsenazo III for the m e a s ur e m ent o f ionized calcium concent rat i on in a solution: (a) the c o n c e n t r a t i o n o f arsenazo III, (b) the c o n c e n t r a t i o n of contaminating Ca 2÷ (which is derived from arsenazo III itself, buffer and salts), and (c) the Ca 2+ binding constant o f arsenazo III in the solution (the constant varies depending on t he concentrations o f buffer and salts as well as on the pH). A p r o b lem associated with knowing t he c o n c e n t r a t i o n o f arsenazo III is t hat commercial arsenazo III is n o t pure. According t o s p e c t r o p h o t o m e t r i c assay o f arsenazo III (~ee t he Appendix), Sigma's arsenazo III (Grade I) was found to be 90% pure, and that from a n o t h e r c o m p a n y has a purity of less than 25%. T h e r e f o r e , t h e first step in the e x p e r i m e n t is to determine the exact concentration o f arsenazo III. Contaminating Ca 2+ may not present a serious problem as long as it is removed from t he arsenazo III by Chelex 100 resin. The a m o u n t of contaminating Ca 2+ in the solution may be det erm i ned by adding E G T A (see Fig. 2A). The n e x t step in the e x p e r i m e n t is t o det erm i ne the Ca 2÷ binding constant o f arsenazo III in the solution. A titration of the solution with Ca 2+ (see Figs. 1 and 2) and a pr oper mathematical t r e a t m e n t are needed to determine the constant. A graphical m e t h o d o f determining the binding constant is described in Fig. 3. The procedure can also be computerized. If arsenazo III is used for determining t he total a m o u n t of Ca 2+ sequestered by or released f r o m cell organelles (and if a knowledge o f the c o n c e n t r a t i o n of ionized calcium in the solution is n o t required), the situation may be different. In this case, th e conventional m e t h o d o f calibrating the absorbance signal by adding a k n o wn a m o u n t o f Ca 2÷ may be e m p l o y e d , since the size of the absorbance signal p r o d u c e d by the addition o f t h e external Ca 2+ is the same as that p r o d u c e d by the change o f Ca 2÷ c o n c e n t r a t i o n caused by either sequestration or release. However, in this t y p e o f exper i ment , it is necessary to confirm that arsenazo III does n o t interfere with t he Ca 2+ binding capacity o f the cell orgahelle. It was f o u nd that the Ca 2+ binding of arsenazo III is so strong that it removed Ca 2÷ from m i t o c h o n d r i a when the Ca ~+ uptake reaction is inhibited by r u t h e n i u m red (murexide t ype indicators did n o t remove Ca 2+ under the same condition) [27].
227 Another problem with arsenazo III, is the low ratio of Ca/Mg sensitivity. For the measurement of ionized calcium in physiological media, it is always advantageous to have a high Ca/Mg sensitivity ratio. The Ca/Mg sensitivity ratio of arsenazo III was f o u n d to be 39, a value which is much lower than that for murexide t y p e indicators (513--1840). All these properties of arsenazo III make this indicator much more complicated to use than a new pH insensitive indicator, tetramethyl murexide [11]. However, arsenazo III has the following distinctly advantageous features compared with the murexide t y p e indicators: (i) High sensitivity. The Ca sensitivity of arsenazo III is approximately 30 times higher than that of tetramethyl murexide and 50 times higher than that of murexide (Table I). A minimum detectable concentration of ionized Ca with arsenazo III is about 0.05 ~M. (There exists a dilemma with the use of arsenazo III: in order to have a sufficient absorbance change, it is necessary to use a high concentration of arsenazo III, but the high arsenazo III concentration makes the ratio of bound Ca/total Ca 2÷ very high so t h a t the assay of ionized Ca becomes inaccurate.) (ii) Low scattering effect. Since scattering is proportional to the (wavelength) -4, the scattering effect of a turbid suspension in dual-wavelength spectrophotometry may be estimated by (k~ 4 --k~4), where XI and X2 are the pair of wavelengths used for the Ca 2÷ assay. Arsenazo III is superior to the murexide type indicators for two reasons: one, longer wavelengths are used; and two, there is a smaller wavelength difference. Using the pair of wavelengths shown in Table I, the scattering effect of t e t r a m e t h y l murexide is estimated as 4.51 • 10 -12 nm -4, while that of arsenazo III is 0.275 • 10 -12, a value which is approximately 16 times smaller than that obtained with tetramethyl murexide. (iii) High stability. Although tetramethyl murexide is much more stable than murexide, it is still susceptible to oxidants and reductants (Ohnishi, S.T., unpublished results). However, arsenazo III is stable against such reagents. (iv) Low permeability to membranes. Arsenazo III is much less permeable to biological membranes than murexide type indicators [27]. Therefore, with the understanding of the problems and with proper methods of analysis, arsenazo III is a very useful indicator for ionized calcium. In order to minimize the interference caused by the indicator-bound Ca 2÷, it is recommended that a low concentration of arsenazo III (below 5 pM) be used (which requires a high sensitivity spectrophotometer with a full scale of at least 0.05 absorbance.) The m e t h o d developed in this paper to analyze a strong binding reaction without conventional approximations could also be applied to the kinetic analysis of certain enzyme reactions. If K m (Michaelis constant) is small, or if the concentration of an enzyme is not negligibly small compared with that of the substrate, this analysis is readily applicable to the study of the enzyme reaction by redefining ~bin Eqn. 6 as v/V, where v is the rate of the enzyme reaction. Appendix
Determination o f the concentration o f arsenazo HI. The continuous variation m e t h o d [ 19--21] was modified and used for the spectrophotometric deter-
228 m i n a t i o n o f arsenazo III c o n c e n t r a t i o n . First, it is assumed t h a t t h e c o n c e n t r a t i o n o f a s t o c k s o l u t i o n o f arsenazo III is k n o w n . B y keeping t h e sum o f t h e c o n c e n t r a t i o n s o f Ca 2÷ and arsenazo III c o n s t a n t , i.e., ,
Sj + E i = c o n s t a n t = L ,
(A1)
we measure t h e relation b e t w e e n Aj ( a b s o r b a n c e change o f arsenazo III solut i o n with c o n c e n t r a t i o n Ej) and Sj. Since Ai = A e . p, we can d r a w t h e relationship b e t w e e n p and Si as s h o w n b y Fig. 8A. Since Eqn. 3 can b e r e w r i t t e n as (A2)
p2 _ ( S + E + K ) p + E S = 0
the relationship b e t w e e n p and Sj is o b t a i n e d f r o m Eqns. A1 and A2 as
p = ½((L + K) -- ((n + K)2 -- 4(L --Sj)Sj)),/2
(A3)
The curve reaches the maximum at Sj = L/2, and the peak valuePm is given by K ((I + ~ - ) '/2 -- 1) Pm = L ~--~ .
(A4)
As shown in the figure, if we draw two tangents to the curve at Sj = 0 and L (dotted lines), they meet also at Sj = L]2 as indicated by t. At Si = L/2, add excess Ca2+ to the arsenazo Ill solution to obtain the saturation value too.Then, the distance between t~o and Pm is given by
d =~
((1+
(A5)
--
R e w r i t i n g this e q u a t i o n , we have an expression for K as g -
2d 2
(A6)
L - - 2d
A p r o b l e m arises as t o h o w this e x p e r i m e n t be d o n e if the e x a c t c o n c e n t r a t i o n o f arsenazo III is n o t k n o w n . Let t h e c o n c e n t r a t i o n o f arsenazo III calculated f r o m t h e m o l e c u l a r weight be E w and t h e t r u e c o n c e n t r a t i o n be E Ea, i.e., (A7)
E a = rE w
w h e r e r is t h e ratio t o be d e t e r m i n e d . A series o f e x p e r i m e n t s m a y be r u n u n d e r t h e c o n d i t i o n t h a t Ew + Sj = L = c o n s t a n t . H o w e v e r , since t h e t r u e c o n c e n t r a t i o n o f arsenazo IH is Ea, the results f o l l o w t h e curve given b y p2__ ((1 - - r ) S i + rL + K ) p + r ( L - - S i ) S i = 0
(A8)
E q u a t i o n s o f t w o tangents ( d o t t e d lines) and a line d r a w n c o n n e c t i n g S i = L / 2 and t h e intersecting p o i n t o f t w o tangents ( b r o k e n line) are given in Fig. 8B). T h e peak o f t h e curve lies o n t h e b r o k e n line, and the position (Sin, Pro) is given by S,~ = R L + (1 -- r ) K Q / ( 1 + r)2; R=r/(l
+r),
Q=(I
P m = R L - - 2 r K Q / ( 1 + r) 2
+L(1 +r)/K)'J2--1
(A9)
229 (A)
p 3o-~ /
r=
(B)
t=j LSi ] ' )
UL-Sj)
,o4 \ V,, ,\L I
%/
0
r=0.6 r(I-2Sj
P" / I - r
,J
30 Si
60 (]aM)
\i
\ ! /
rLSi \ ~ rL(L- Si) P=L--~---~/ r \ ~p= rL*K
0
30
60 Si
Fig. 8. A m e t h o d o f d e t e r m i n i n g t h e c o n c e n t r a t i o n o f a r s e n a z o n I ( A Z ) . ( A ) r = 1, a n d (B) r = 0 . 6 . T h e c o n d i t i o n s : [ A Z ] + [ C a ] = 6 0 / ~ M , 4 0 m M H E P E S ( p H 7 . 0 ) , 2 5 ° C . T h e i o n i c s t r e n g t h is 0.1 M. See a p p e n dix for details.
The position of the intersection of two tangents (St, Pt) is given by S t = L ( r L + K)/((1 + r ) L + 2K);
P t = r L 2 / ( ( 1 + r ) L + 2K)
(A10)
As shown later, the value for K is of the order of 10 -s M. If we choose L to be 10 -4 M, r could be approximately estimated from St as r = St/(L
--St)
(All)
Based upon this value of r, Ea is estimated according to Eqn. A7. Then another series of experiments is run keeping the sum of E a + Sj constant. After repeating this procedure for a few times, the resuIt of r = 1 is obtained, as shown in Fig. 8A. This means t h a t the assumed concentration was correct. It is tedious to run these experiments each time. Therefore, the extinction coefficient of arsenazo III was determined when the correct concentration was known. According to our result, in a solution containing 20 mM HEPES and 1 mM EDTA (pH 7.0, 25°C), the molar extinction coefficient was 1 . 1 0 - l 0 s (in 10 mm optical path) at the peak wavelength (538 nm).
Acknowledgement This work was supported in part by NIH grant 15799.
References 1 0 h n i s h i , T. a n d E b a s h i , S. ( 1 9 6 3 ) J. B i o c h e m . 5 4 , 5 0 6 - - 5 1 1 2 O h n i s h i , T. a n d E b a s h i , S. ( 1 9 6 4 ) J. B i o c h e m . 5 5 , 5 9 9 - - 6 0 3 3 O h n i s h i , T. ( 1 9 6 4 ) J. B i o c h e m . 5 5 , 1 7 2 - - 1 7 7 4 O h n i s h i , T. a n d E b a s h i , S. ( 1 9 6 5 ) A b s t r a c t o f t h e 6 t h I n t e r n a t i o n a l C o n f e r e n c e o n M e d i c a l E l e c t r o nics and Biological Engineering, pp. 620--621, Japan Society of Medical Electronics and Biological Engineering, Tokyo 5 0 h n i s h i , T., M a s o r o , E . J . , B e r t r a n d , H . A . a n d Y u , B.P. ( 1 9 7 2 ) B i o p h y s . J. 1 2 , 1 2 5 1 - - 1 2 6 5 6 J S b s i s , F . F . a n d O ' C o n n o r , M.J. ( 1 9 6 6 ) B i o c h e m . B i o p h y s . Res. C o m m u n . 2 5 , 2 4 6 - - 2 5 2 7 M e l a , L. a n d C h a n c e , B. ( 1 9 6 6 ) B i o c h e m i s t r Y 7 , 4 0 5 9 - - 4 0 6 3 8 C i t t a d i n i , A., S c a r p a , A. a n d C h a n c e , B. ( 1 9 7 1 ) F E B S L e t t . 1 8 , 9 8 - - 1 0 2 9 S c a r p a , A. ( 1 9 7 2 ) in M e t h o d s i n E n z y m o l o g y ( S a n P i e t r o , A., e d . ) , Vol. 2 4 , p p . 3 4 3 - - 3 5 1 , A c a d e m i c Press, N e w Y o r k 1 0 Inesi, G. a n d S c a r p a , A. ( 1 9 7 2 ) B i o c h e m i s t r Y 1 1 , 3 5 6 - - 3 5 9 11 O h n i s h i , S.T. ( 1 9 7 8 ) A n a l . B i o c h e m . 6 5 , 1 6 5 - - 1 7 9
230 12 Michaylova, V. and Ilkova, P, (1971) Anal. Chim. Acta 53, 194--198 13 Michaylova, V.Y. and Kouleva, N.K. (1972) C.R. Acad. Bulg. Sei. 25, 949--952 14 Burger, K. (1973) International Series of Monographs in Analytical Chemistry, Vol, 54, Pergamon Press, Oxford 15 Dipolo, R., Reguena, J., Brinley, F.J., Mullins, L.J., Scarpa, A. and Tiffert, T. (1976) J. Gen. Physiol. 67,433--467 16 Scarpa, A., Tiffert, T. and Brinley, F.J. (1976) in Biochemistry of Membrane Transport (Semenza, G. and Carafoli, E., eds.), pp. 552-~566, Springer Verlag, New York 17 Ohnishi, S.T. (1978) A n n . N.Y. Acad. Sci. 3 0 7 , 2 1 3 - - 2 1 6 18 Dixon, M. and Webb, E.C. (1964) in Enzymes, 2nd Edn., p. 67, Academic Press, New York 19 Job, P. (1936) Ann. Chim. [11] 6, 97--144 20 Vosburg, W.C., Cooper, G.R. (1941) J. Am. Chem. Soe. 6 3 , 4 3 7 - - 4 4 2 21 Chberek, S., Marten, A.E. (1959) in Organic Sequestering Agents, p. 78, J ohn Wiley and Sons, New York 22 Yoe, J.H., Jones, A.L. (1944) Ind. Eng. Chem. Anal. Ed. 16° 111--117 23 Scatchard, G. (1949) Ann. N.Y. Acad. Sci. 51° 660--672 24 Lineweaver, H. and Burk, D. (1934) J. Am. Chem. Soc. 56,658---666 25 Klotz, I.M. (1946) Arch. Biochem. 9 , 1 0 9 - - 1 1 7 26 Klotz, I.M. (1953) in Proteins, Vol. 2 (Neurath, H. and Baily, K., eds.), Academic Press, New York 27 Ohnishi, S.T. (1979) Biochim. Biophys. Acta 5 8 5 , 3 1 5 - - 3 1 9
Biochimica et Biophysica Acta, 586 (1979) 217--230 © Elsevier/North-Holland Biomedical Press
BBA 28965
A METHOD OF ESTIMATING THE AMOUNT OF CALCIUM BOUND TO THE M E T A L L O C H R O M I C INDICATOR A R S E N A Z O III
S. TSUYOSHI OHNISHI
Biophysics Laboratory, Department of Anesthesiology and Department of Biological Chemistry, Hahnemann Medical College, Philadelphia, PA 19102 (U.S.A.) (Received October 30th, 1978)
Key words: Metallochromic indicator; Arsenazo IIl; Murexide method; Ca2+ binding assay
Summary As a metallochromic indicator for ionized calcium, arsenazo III is approximately 50 times more sensitive than murexide. However, because of the high binding constant for calcium, the following problems may occur: (a) a considerable a m o u n t of calcium is b o u n d to arsenazo III, thereby causing an error in estimating the concentration o f ionized calcium; (b) the amount of b o u n d calcium varies with the concentrations of calcium, arsenazo III, magnesium ion and monovalent cations; (c) the a m o u n t also varies with pH, (d) the relationship between the absorbance change and the concentration of ionized calcium is nonlinear; and (e) the binding constant of arsenazo III for calcium cannot be determined b y the conventional double reciprocal plot. A new experimental and theoretical m e t h o d is presented which copes with these problems.
Introduction Since calcium ions (Ca 2÷) are known to regulate many important biological reactions, such as muscle contraction, nerve conduction, excitation-contraction coupling, neurosecretion, transport, and cell growth, methods of determining Ca 2+ concentration in physiological media are extremely important. Ohnishi and Ebashi developed a direct spectrophotometric m e t h o d of measuring low concentrations of Ca 2+ in physiological solutions using a metallochromic indicator (murexide) and a dual-wavelength s p e c t r o p h o t o m e t e r [1--4]. The method was also used to measure the binding constant of protein for Ca 2÷, and a Abbreviations: EGTA, ethyleneglycol-bis(13-aminoethyl ether)-N,N'-tetraacetic acid; HEPES, N-2-hydroxy. ethyl piperazine-N'-2-ethanesulfonic acid; MES; 2-(N-morpholino) ethanesulfonic acid.
218
m e t h o d of analyzing a system with two classes of binding site was established [5]. The m e t h o d has been applied to various systems successfully [6--10]. Detailed experimental procedure, as well as theoretical characterization of the murexide m e t h o d , has been reported [ 5,11 ]. Recently, arsenazo III was introduced as a sensitive Ca 2÷ indicator [12--16] and has been widely used. However, m a n y investigators are using arsenazo III w i t h o u t considering the difference between a murexide type indicator and arsenazo III. For example, t h e y calibrate the absorbance signal by adding a known concentration of Ca 2+ to the reaction mixture containing arsenazo III. However, because of the high binding constant of arsenazo III for Ca 2÷ (104--10 s M-l), a significant a m o u n t of Ca 2÷ is bound to the indicator. This causes an error in estimating the concentration of ionized calcium in the reaction mixture. To make the situation more complicated, the a m o u n t of arsenazo IIIbound Ca 2÷ depends on the concentrations of Ca 2÷, other cations, arsenazo III itself, and on the pH as well. Another misunderstanding concerns the effect of Mg 2÷. In much of the literature it has been assumed that the effect of Mg 2÷ can be ignored by selecting the combination o f wavelengths in such a way that the absorbance difference of arsenazo III changes only with Ca 2+, but not with Mg 2÷. This is not true. Even though the absorbance difference is not directly influenced by Mg2*, the assay of Ca 2÷ is influenced by Mg 2÷ (since the Ca 2÷ binding of arsenazo III is competitively inhibited by Mg2+). The situation is entirely different from that o f murexide, where the indicator is practically insensitive to Mg2÷ in aqueous solution [ 11 ]. In order to solve these problems, a systematic m e t h o d of analyzing the binding characteristics of arsenazo III has to be established. In this paper, the experimental and theoretical bases of such a m e t h o d are described. The effect of concentrations of arsenazo III, Ca 2÷, Mg2÷ and monovalent cations as well as effect of pH are also discussed. Materials and Methods C h e m i c a l s Arsenazo III (Grade I), EDTA, EGTA and murexide were purchased from Sigma Chemical Co. (St. Louis, MO). HEPES, MES and tetraTITRATION ATTACHMENT Co-SOLUTION
INDCATER
SOLUTION
FILTER
LAMP
STIRRER~.~ '\" FILTER "PM I
I
I WATER
[
J JACKET
t
RECORDER
i DUAL WAVELENGTH SPECTROPHOTOME TER
Fig. i . Sehematie illustration of the automatic eaJeium titrator. Abbreviations: A, absorbance recording o n a r e c o r d e r ; AMP, a m p l i f i e r ; C, c u v e t t e ; L O G AMP, l o g a r i t h m i c a m p l i f i e r ; M, m i r r o r ; a n d PM, photo-
multiplier.
219 methyl murexide were obtained from Calbiochem (La Jolla, CA). Chelex 100 resin was purchased from Bio-Rad Laboratories (Richmond, CA). Calcium standard solution was purchased from Orion Research Laboratories (Cambridge, MA). The contaminating Ca 2÷ in arsenazo III stock solution was removed by passing it through a column of Chelex 100. Spectrophotometric measurements. Calcium titration was carried out by a Model CL dual-wavelength spectrophotometer by TCS Co. (P.O. Box 141, S o u t h a m p t o n , PA 18966) with an automatic titration attachment. Optical measurements were performed on a sample volume of 1 ml in a quartz cuvette (10 × 10 mm), and the temperature was kept constant (25 ± 0.1°C) by circulating water from the Lauda 2-k/R thermobath (A.H. Thomas, Philadelphia, PA) through the cuvette holder (See Fig. 1). Results I. Analysis o f the calcium titration curve o f arsenazo III In carrying out the Ca 2÷ titration of an arsenazo III solution (which contains buffer and salt), it would be best if the contaminating Ca 2÷ could be completely removed. However, it is tedious and time-consuming to remove the minute a m o u n t of contaminating Ca 2÷ from the buffer and salt solution by passing them through a Chelex 100 resin column. Therefore, we developed a m e t h o d of running the Ca2÷ titration without interference from such small a m o u n t of Ca 2÷. As shown in Fig. 2A, we first add 2 mM EGTA to the arsenazo III solution and record the decrease in absorbance. This 'EGTA drop' is registered as G, and the new level is defined as 0' (true Ca 2÷ zero level). The solution is discarded and the cuvette is filled with the new solution. Then the relation between the a m o u n t of added Ca 2÷ (denoted by [Ca]t i in Fig. 2B) and the absorbance change A is recorded by using the automatic Ca :÷ titrator attachment (Fig. 1). The volume of Ca 2÷ solution added during the titration is less than 10 t~l. After titration is finished, excess Ca 2÷ (10 mM) is added to the solution to record the Ca :÷ saturation value A~ (see Fig. 2B). The beginning portion of the titration curve is extrapolated downwards to hit the true Ca :÷ zero
~ 0.1 i
uJ0.05~
Titrotion
,-Y ....
/ /
G
r ....
|/0 0
/
.-
Io 10
Co
J
20 20
30 30
40 [co]~ 40 [co] t
(~M)
Fig. 2. A . Decrease in absorbanee caused b y 2 m M E G T A . B. Ca 2+ t i t r a t i o n o f arsenazo I l l solution. Condition: 4 0 m M H E P E S ( p H 7.0), 1 0 p M arsenazo I I I , 25~C. The ionic strength is adjusted t o 0 . ] w i t h See text for
KCI.
details.
220
level. Th e a m o u n t indicated by [Ca]in in Fig. 2B corresponds to the a m o u n t o f initial contaminating Ca 2+ in the arsenazo III solution. ([Ca]in is t he sum o f arsenazo III-bound Ca and free Ca 2+ in t he solution before the start o f the titration). Then total Ca 2+ ( d e n o t e d by S) in t he system is given by S = [Ca]i n + [Ca]t i
(1)
The reaction between Ca :+ and arsenazo III (denot ed by AZ) is given by AZ + Ca ~ AZ • Ca [AZ] = E - - p [Ca]f = S - - p
(2)
[AZ • Ca] = p where p stands for the c o n c e n t r a t i o n o f the com pl ex AZ • Ca and E stands for the total c o n c e n t r a t i o n o f arsenazo III. [Calf represents the c o n c e n t r a t i o n o f free Ca :+. The dissociation constant, K, is defined by g -
(E - - p ) ( S - - p )
(3)
P Let Ae be th e difference molar ext i nct i on coefficient o f arsenazo III at a particular c o m b i n a t i o n o f wavelength, t hen G+A =Ae-p
(4)
G+A~ =Ae'E from Eqn. 3 we have E_I -
+
K s-p
(5)
or by defining normalized values ¢, 9, t} and ~ by the following equations:
¢=p E
= G+A G+A+
S O=-E 5=0--¢-
normalized Az-bound Ca normalized total Ca
S--P E
K = -E
normalized free Ca normalized dissociation const ant
(6)
we can rewrite Eqn. 3 as
¢ 1+0_¢ 1+--~
(7)
Note th at there is a difference between this equation and the Dixon-Webbs e q u atio n (p. 67 Eqn. IV.15 in Ref. 18). In their equation
S>> p ;
orS--p-
S
(8)
221
is assumed according to the Michaelis-Menten t y p e enzyme kinetics, while our Eqn. 7 is valid without using this assumption. As pointed out already, this assumption is valid for murexide t y p e indicators, b u t n o t for arsenazo III [11]. Owing to the approximation shown b y Eqn. 8, the binding constant of murexide t y p e indicators for Ca 2÷ could be determined from a straight line of the double reciprocal plot without knowing the indicator concentration (see Ref. 11). However, as shown b y Eqns. 6, it is essential to k n o w the indicator concentration (E) to obtain a linear plot represented by Eqn. 7. A spectrophotometric method o f determining the indicator concentration is given in the Appendix. 2. D e t e r m i n a t i o n o f the dissociation c o n s t a n t
Solving Eqn. 3 or Eqn. 6, we have either p = (B -- (B 2 -- 4ES)1/2)/2;
B =E +S +K
(9)
or
=(fi_(fi2_40)l/2)/2;
~=1+0+~
(10)
The titration curve in Fig. 3 represents Eqn. 9 (using the t o p and right scales) and Eqn. 10 (using the b o t t o m and left scales). The d o t t e d line in the figure is a tangent drawn to the initial part of the curve *, and the straight solid line drawn from the origin with unity slope is the limiting titration curve (this is the limiting case of the titration with infinitely strong binding). In the same figure, a horizontal line is shown which intersects with the ordinate, the limiting titration curve and the actual titration curve, and the corresponding intersections are designated as U, V and W, respectively. Since U V = O U = p , and UW = S, the distance U V gives the concentration of indicatorb o u n d Ca 2÷ and V W gives that of free Ca 2÷. N o w the approximation made for the conventional Michaelis-Menten t y p e equation may be readily visualized. In their equation, free Ca 2* is estimated as UW instead of VW. When the dissociation constant is large (weak binding) or when the concentration S is far greater than E, this approximation is valid. However, in the case of Ca2+-arsenazo III binding, this approximation causes a serious error as may be seen in Fig. 3. From Fig. 3, the dissociation constant can be determined in two ways: (i) draw a horizontal line at p = E l 2 (in the illustrated example E = 40), and intersect with the unity~lope line and the titration curve (P and Q, respectively). Then, the distance PQ represents K; (ii) extrapolate the initial slope until it intersects with the t o p scale (p = E). The value of the abscissa at the intersection is E + K. Since the extrapolation of the initial slope is subjectively done, m e t h o d (i) is generally more accurate. The dissociation constant can also be obtained b y t w o other graphical representations where the data points are expressed b y a straight line [ 23--26]. Fig. * T h e r e is a m e t h o d o f d e t e r m i n i n g the c o n c e n t r a t i o n o f the i n d i c a t o r b y e x t r a p o l a t i n g t h e initial part o f the t i t r a t i o n c u r v e t o t h e l e v e l o f p = E ( m o l a r r a t i o m e t h o d [ 2 2 ] ) . H o w e v e r , this m e t h o d is v a l i d o n l y when E ~ K . F r o m E q n . 9 t h e i n i t i a l s l o p e is c a l c u l a t e d as E / ( E + K ) , T h e r e f o r e , t h e e x t r a p o l a t i o n o f t h e initial s l o p e i n t e r s e c t s w i t h the l e v e l o f p = E a t E + K , b u t n o t at E .
222
0
[Co]t
(,~M) 40
r ~z~ 0.5
E o1!.J,
-40 P (#M}
-20
o
0.5
1.5
I
e Fig. 3. A n a l y s i s o f t h e t i t r a t i o n curve. Solid curve, t i t r a t i o n curve; d o t t e d line, initial slope; solid line, l i m i t i n g t i t r a t i o n curve; K, d i s s o c i a t i o n c o n s t a n t ; [ C a l f , c o n c e n t r a t i o n o f free C a ; [ C a ] A Z , c o n c e n t r a t i o n o f i n d i c a t o r - b o u n d Ca. C o n d i t i o n s : 4 0 DM a r s e n a z o III, 4 0 m M H E P E S ( p H 7 . 0 ) , i o n i c s t r e n g t h 0 . 1 , 2 5 ° C.
4A shows an example of arzenazo III-Ca binding represented by the linear equation 7. The x-axis intercept gives (--~). Fig. 4B shows another representation o f the same data as Fig. 4A by the following equation:
¢ 5
-
1
(1 -- ~b)
(11)
where the slope gives the association constant (=1/~). Having derived all of the mathematical expressions, all portions of the data analysis were computerized to minimize human error. The procedures are as follows: using an arsenazo III solution of concentration E, perform the titration and obtain data for G, for A as a function of [Ca]ti, and for A~. First, calculate an approximate value for [Ca]in by linearly extrapolating the initial part of the titration downwards to hit the level of 0'. Then using [Ca]in, calculate S, and find the value for K which makes the best fit curve for the titration data. Then, using that best fit curve, re-estimate the value of [Ca]in. Repeating this
6t
A
3.0 L
B
i
o
o. 5
I,O
8 Fig. 4. T w o linear r e p r e s e n t a t i o n s o f data. T h e data are t a k e n f r o m the t i t r a t i o n curve o f Fig. 3, a n d a n a l y z e d a c c o r d i n g to the m e t h o d d e s c r i b e d in the t e x t .
223 iteration permits us to find the values for both [Ca]i n and the dissociation constant K. At pH 7.0 and the ionic strength 0.1 M, the dissociation constant of arsenazo III was estimated to be 17 pM (or the association constant: 5.9 • 104 M -I) and A(~(675__685nm)to be 1.29 • 104.
3. Determination o f the indicator-bound Ca When the concentration and the dissociation constant of arsenazo III are known, the concentrations of arsenazo III-bound Ca 2÷, [Ca]AZ, and free Ca 2÷, [Ca]f, can be determined by the following equations: [Ca]f = Kp/(E --p)
or
61= ~ / ( 1 -- ¢)
[Ca]A z = [Ca]t -- [Ca]f
or
(12)
~b = O -- ~
(13)
Fig. 5A shows the difference between murexide and arsenazo III. In Fig. 5A, the d o t t e d line shows an ideal case of no Ca-binding. The open circles show 1.4% binding for 50 pM murexide (Ref. 11), and the filled circles show 40 t~M arsenazo III. It is clear t h a t a considerable a m o u n t of Ca 2+ is bound, especially at low [Ca]t concentrations. For example, at [Ca]t = 5 pM, 76% of Ca 2+ is in the bound form. Fig. 5B shows the relationship between the ratio [Ca]f/[Ca]t and [Ca]t. From Eqn. 10 or 11, it was calculated that the ratio approaches K/(E + K) or K/(1 + K) at the limiting case o f [Ca]t -~ 0.
4. Effect o f pH on Ca-binding o f arsenazo III It was found that the dissociation constant of arsenazo III is pH dependent. As shown in Fig. 6A, the association constant K (= 1/K) increases with an increase of the pH. Fig. 6B demonstrates how the ratio of [Ca]f/[Ca] t changes over the pH range of 6.3 to 8.0. 5. Mg binding o f arsenazo III A unique feature of the murexide t y p e indicator was the extremely low sensitivity to Mg2÷ in aqueous solutions [11]. On the contrary, as already shown
4o. A t
,,/
~.0-
B
~%50~ M MX
/
""0.62
0.5"
Io"1 / o
~ I0
~
~40pM AZ
40~M
20
30
40
[Co']total
(~M)
0
I
e
3
4
Fig. 5 A . R e l a t i o n s h i p b e t w e e n t o t a l Ca a n d f r e e C a c o n c e n t r a t i o n s o f m u r e x i d e ( M X ) a n d a r s e n a z o III ( A Z ) . B. R e l a t i o n s h i p b e t w e e n t h e n o r m a l i z e d t o t a l C a c o n c e n t r a t i o n 0 and the ratio of [Ca]free / [ C a ] t o t at . D o t t e d l i n e s s h o w [ C a ] f r e e = [ C a ] t o t a 1. D a t a f o r m u r e x i d e a r e t a k e n f r o m R e f . 1 1 . C o n d i t i o n s : • . o 4 0 m M H E P E S ( p H 7 . 0 ) , l o m c s t r e n g t h 0 . 1 , 2 5 C.
224
/
IO 7~ T
]'0 1 . . . . . . . . . . . . . . . . . . .
0 5 ~
j ....
I I
I
I
6
7
8
0
I
B
F
2 0
pH
F i g . 6. A. R e l a t i o n s h i p b e t w e e n t h e p H a n d t h e a s s o c i a t i o n c o n s t a n t K ( = I / K ) o f a r s e n a z o III f o r Ca. B. E f f e c t o f p H o n t h e r e l a t i o n b e t w e e n t h e n o r m a l i z e d t o t a l Ca c o n c e n t r a t i o n a n d t h e r a t i o o f [ C a ] f r e e / [ C a ] t o t aI . C o n d i t i o n s : 1 7 . 8 / a M a r s e n a z o III, 4 0 m M H E P E S , i o n i c s t r e n g t h 0 . 1 , 25~C.
in Ref. 15, arsenazo III is somewhat sensitive to Mg 2+. In this study, Mg 2+ titration was performed in a similar fashion to that for Ca 2+ and the dissociation constant was estimated as 837 pM (or the association constant: 1.2 • 103 M-') and Ae(675_685nm) as 4.36 • 103 at pH 7.0, ionic strength 0.1 and 25°C. If we define the sensitivity by A/S, the highest sensitivity will be the initial slope of the titration curve, which may be derived from Eqns. 4 and 9
A S
AcE E+K
(14)
In the murexide t y p e indicators, the term E in the denominator of Eqn. 14 could be neglected due to their high dissociation constant [11]. As shown in Table I, Ca/Mg sensitivity ratio of arsenazo III was 39, a value much lower than those for murexide type indicators. 6. Effect o f salts on Ca-binding o f arsenazo III Assume that cation I competitively binds to arsenazo III with the dissociaTABLE I S E N S I T I V I T I E S O F I N D I C A T O R S T O C a A N D Mg C o n c e n t r a t i o n o f i n d i c a t o r s is 50 p M . T h e s e n s i t i v i t y A / S is c a l c u l a t e d f r o m E q n . 14. D a t a f o r m u r e x i d e a n d t e t r a m e t h y l m u r e x i d e a r e t a k e n f r o m Ref. 11. C o n d i t i o n s : p H 7 . 0 , i o n i c s t r e n g t h 0 . 1 , 2 5 ° C . Ca K X 10 6
A/S
Ae X 10 -6
129
17
9630
153
3570
180
2780
Ae X 1 0 -6 A r s e n a z o III (675--685 nm) Murexid e (500--544 nm) Tetramethyl murexide (507--554 nm)
Mg
* R a t i o o f t h e Ca s e n s i t i v i t y to Mg s e n s i t i v i t y .
(Ca/Mg) * K X 10 6
A/S
43.6
830
247
211
2.9
125 000
318
7.8
62 500
0.115 0.62
39 1840 513
225 tion constant KI, then we have AZ+I=AZ'I;
or
K1 =
(E -- q)(i -- q)
(15)
q
where concentrations of the cation and arsenzao III-bound cation are given by i and q, respectively. From Eqns. 3 and 15, we can derive --=1+---p
1+
S--p
or
'
=1
+
(16)
where ¢o = ( i - q ) / E and ~ = K I / E . These equations look similar to the Michaelis-Menten equation for competitive inhibition (Ref. 18), but t h e y are solved w i t h o u t the conventional approximation of Eqn. 8 as well as i -- q - i. Eqn. 16 implies that in the presence of cations the apparent dissociation constant Kapp is expressed by gap p =
K(1 + (i - - q ) / g l )
(17)
If we define the corresponding association constants by K, Kapp and K~, we have K --=
1 + ( i - - q ) KI
(18)
Kapp
From the plot of K/Kapp vs. ( i - - q ) , Kx can be obtained as an inverse of the x-axis intercept. Fig. 7A shows such plots for Mg 2÷, K ÷ and Na ÷. It is obvious that these salts considerably decrease the association constant of arsenazo III for Ca 2÷. From the x-axis intercepts, the association constants of arsenazo III for these salts are estimated to be 1.1 • 103 for Mg2÷, 6.0 for K ÷ and 4.5 for Na ÷ (all in M-I). The value o f the association constant for Mg2÷ obtained by this m e t h o d is in good agreement with the value determined by the direct titration in the above section (1.2 • 103). Fig. 7B demonstrates t h a t the ratio of [Ca]free/[Ca]totaI also changes in the
~ .
o
. . . .
.~ .Mg . . . <,'nMp)
,5'-[
../S
0.5 ~ /
O~ M NoCI \CONTROL
B 0
0.5
I
NoCI or KCI (M)
Fig. 7. A. E f f e c t o f salts o n t h e r a t i o o f a s s o c i a t i o n c o n s t a n t ( K ) / a p p a r e n t a s s o c i a t i o n c o n s t a n t ( K a p p ) . B. E f f e c t o f salts o n the r e l a t i o n b e t w e e n the n o r m a l i z e d t o t a l C a c o n c e n t r a t i o n 0 a n d the ratio o f o [ C a ] f r e e / [ C a ] t o t a l . C o n d i t i o n s ; 1 3 . 6 / ~ M a x s e n a z o III, 4 0 m M H E P E S ( p H 7 . 0 ) , i o n i c s t r e n g t h 0 . 1 , 2 5 C.
226 presence o f salts, which is a n o t h e r problem o f the arsenazo III m e t h o d in determining ionized Ca c o n c e n t r a t i o n .
Discussion Arsenazo III is a sensitive metallochromic indicator useful for monitoring physiologic co n cent r a t i ons o f Ca 2+. However, various problems are created by t h e high Ca 2÷ binding constant o f arsenazo III. First o f all, for the measurement o f a low c o n c e n t r a t i o n o f Ca 2+, for which arsenazo III is most useful, the ratio o f b o u n d Ca2+/total Ca 2÷ becomes very high. In some cases, m ore than 80% of the total Ca 2+ is b o u n d t o the indicator itself. Therefore, w i t h o u t knowing this ratio, it is impossible to measure the c o n c e n t r a t i o n of ionized calcium. Secondly, this ratio changes with changes in the c o n c e n t r a t i o n o f arsenazo III, total Ca 2÷ and o t h e r salts in t he assay solution. Thirdly, the ratio changes with pH. Because o f these problems, the following parameters should be know n in applying arsenazo III for the m e a s ur e m ent o f ionized calcium concent rat i on in a solution: (a) the c o n c e n t r a t i o n o f arsenazo III, (b) the c o n c e n t r a t i o n of contaminating Ca 2÷ (which is derived from arsenazo III itself, buffer and salts), and (c) the Ca 2+ binding constant o f arsenazo III in the solution (the constant varies depending on t he concentrations o f buffer and salts as well as on the pH). A p r o b lem associated with knowing t he c o n c e n t r a t i o n o f arsenazo III is t hat commercial arsenazo III is n o t pure. According t o s p e c t r o p h o t o m e t r i c assay o f arsenazo III (~ee t he Appendix), Sigma's arsenazo III (Grade I) was found to be 90% pure, and that from a n o t h e r c o m p a n y has a purity of less than 25%. T h e r e f o r e , t h e first step in the e x p e r i m e n t is to determine the exact concentration o f arsenazo III. Contaminating Ca 2+ may not present a serious problem as long as it is removed from t he arsenazo III by Chelex 100 resin. The a m o u n t of contaminating Ca 2+ in the solution may be det erm i ned by adding E G T A (see Fig. 2A). The n e x t step in the e x p e r i m e n t is t o det erm i ne the Ca 2÷ binding constant o f arsenazo III in the solution. A titration of the solution with Ca 2+ (see Figs. 1 and 2) and a pr oper mathematical t r e a t m e n t are needed to determine the constant. A graphical m e t h o d o f determining the binding constant is described in Fig. 3. The procedure can also be computerized. If arsenazo III is used for determining t he total a m o u n t of Ca 2+ sequestered by or released f r o m cell organelles (and if a knowledge o f the c o n c e n t r a t i o n of ionized calcium in the solution is n o t required), the situation may be different. In this case, th e conventional m e t h o d o f calibrating the absorbance signal by adding a k n o wn a m o u n t o f Ca 2÷ may be e m p l o y e d , since the size of the absorbance signal p r o d u c e d by the addition o f t h e external Ca 2+ is the same as that p r o d u c e d by the change o f Ca 2÷ c o n c e n t r a t i o n caused by either sequestration or release. However, in this t y p e o f exper i ment , it is necessary to confirm that arsenazo III does n o t interfere with t he Ca 2+ binding capacity o f the cell orgahelle. It was f o u nd that the Ca 2+ binding of arsenazo III is so strong that it removed Ca 2÷ from m i t o c h o n d r i a when the Ca ~+ uptake reaction is inhibited by r u t h e n i u m red (murexide t ype indicators did n o t remove Ca 2+ under the same condition) [27].
227 Another problem with arsenazo III, is the low ratio of Ca/Mg sensitivity. For the measurement of ionized calcium in physiological media, it is always advantageous to have a high Ca/Mg sensitivity ratio. The Ca/Mg sensitivity ratio of arsenazo III was f o u n d to be 39, a value which is much lower than that for murexide t y p e indicators (513--1840). All these properties of arsenazo III make this indicator much more complicated to use than a new pH insensitive indicator, tetramethyl murexide [11]. However, arsenazo III has the following distinctly advantageous features compared with the murexide t y p e indicators: (i) High sensitivity. The Ca sensitivity of arsenazo III is approximately 30 times higher than that of tetramethyl murexide and 50 times higher than that of murexide (Table I). A minimum detectable concentration of ionized Ca with arsenazo III is about 0.05 ~M. (There exists a dilemma with the use of arsenazo III: in order to have a sufficient absorbance change, it is necessary to use a high concentration of arsenazo III, but the high arsenazo III concentration makes the ratio of bound Ca/total Ca 2÷ very high so t h a t the assay of ionized Ca becomes inaccurate.) (ii) Low scattering effect. Since scattering is proportional to the (wavelength) -4, the scattering effect of a turbid suspension in dual-wavelength spectrophotometry may be estimated by (k~ 4 --k~4), where XI and X2 are the pair of wavelengths used for the Ca 2÷ assay. Arsenazo III is superior to the murexide type indicators for two reasons: one, longer wavelengths are used; and two, there is a smaller wavelength difference. Using the pair of wavelengths shown in Table I, the scattering effect of t e t r a m e t h y l murexide is estimated as 4.51 • 10 -12 nm -4, while that of arsenazo III is 0.275 • 10 -12, a value which is approximately 16 times smaller than that obtained with tetramethyl murexide. (iii) High stability. Although tetramethyl murexide is much more stable than murexide, it is still susceptible to oxidants and reductants (Ohnishi, S.T., unpublished results). However, arsenazo III is stable against such reagents. (iv) Low permeability to membranes. Arsenazo III is much less permeable to biological membranes than murexide type indicators [27]. Therefore, with the understanding of the problems and with proper methods of analysis, arsenazo III is a very useful indicator for ionized calcium. In order to minimize the interference caused by the indicator-bound Ca 2÷, it is recommended that a low concentration of arsenazo III (below 5 pM) be used (which requires a high sensitivity spectrophotometer with a full scale of at least 0.05 absorbance.) The m e t h o d developed in this paper to analyze a strong binding reaction without conventional approximations could also be applied to the kinetic analysis of certain enzyme reactions. If K m (Michaelis constant) is small, or if the concentration of an enzyme is not negligibly small compared with that of the substrate, this analysis is readily applicable to the study of the enzyme reaction by redefining ~bin Eqn. 6 as v/V, where v is the rate of the enzyme reaction. Appendix
Determination o f the concentration o f arsenazo HI. The continuous variation m e t h o d [ 19--21] was modified and used for the spectrophotometric deter-
228 m i n a t i o n o f arsenazo III c o n c e n t r a t i o n . First, it is assumed t h a t t h e c o n c e n t r a t i o n o f a s t o c k s o l u t i o n o f arsenazo III is k n o w n . B y keeping t h e sum o f t h e c o n c e n t r a t i o n s o f Ca 2÷ and arsenazo III c o n s t a n t , i.e., ,
Sj + E i = c o n s t a n t = L ,
(A1)
we measure t h e relation b e t w e e n Aj ( a b s o r b a n c e change o f arsenazo III solut i o n with c o n c e n t r a t i o n Ej) and Sj. Since Ai = A e . p, we can d r a w t h e relationship b e t w e e n p and Si as s h o w n b y Fig. 8A. Since Eqn. 3 can b e r e w r i t t e n as (A2)
p2 _ ( S + E + K ) p + E S = 0
the relationship b e t w e e n p and Sj is o b t a i n e d f r o m Eqns. A1 and A2 as
p = ½((L + K) -- ((n + K)2 -- 4(L --Sj)Sj)),/2
(A3)
The curve reaches the maximum at Sj = L/2, and the peak valuePm is given by K ((I + ~ - ) '/2 -- 1) Pm = L ~--~ .
(A4)
As shown in the figure, if we draw two tangents to the curve at Sj = 0 and L (dotted lines), they meet also at Sj = L]2 as indicated by t. At Si = L/2, add excess Ca2+ to the arsenazo Ill solution to obtain the saturation value too.Then, the distance between t~o and Pm is given by
d =~
((1+
(A5)
--
R e w r i t i n g this e q u a t i o n , we have an expression for K as g -
2d 2
(A6)
L - - 2d
A p r o b l e m arises as t o h o w this e x p e r i m e n t be d o n e if the e x a c t c o n c e n t r a t i o n o f arsenazo III is n o t k n o w n . Let t h e c o n c e n t r a t i o n o f arsenazo III calculated f r o m t h e m o l e c u l a r weight be E w and t h e t r u e c o n c e n t r a t i o n be E Ea, i.e., (A7)
E a = rE w
w h e r e r is t h e ratio t o be d e t e r m i n e d . A series o f e x p e r i m e n t s m a y be r u n u n d e r t h e c o n d i t i o n t h a t Ew + Sj = L = c o n s t a n t . H o w e v e r , since t h e t r u e c o n c e n t r a t i o n o f arsenazo IH is Ea, the results f o l l o w t h e curve given b y p2__ ((1 - - r ) S i + rL + K ) p + r ( L - - S i ) S i = 0
(A8)
E q u a t i o n s o f t w o tangents ( d o t t e d lines) and a line d r a w n c o n n e c t i n g S i = L / 2 and t h e intersecting p o i n t o f t w o tangents ( b r o k e n line) are given in Fig. 8B). T h e peak o f t h e curve lies o n t h e b r o k e n line, and the position (Sin, Pro) is given by S,~ = R L + (1 -- r ) K Q / ( 1 + r)2; R=r/(l
+r),
Q=(I
P m = R L - - 2 r K Q / ( 1 + r) 2
+L(1 +r)/K)'J2--1
(A9)
229 (A)
p 3o-~ /
r=
(B)
t=j LSi ] ' )
UL-Sj)
,o4 \ V,, ,\L I
%/
0
r=0.6 r(I-2Sj
P" / I - r
,J
30 Si
60 (]aM)
\i
\ ! /
rLSi \ ~ rL(L- Si) P=L--~---~/ r \ ~p= rL*K
0
30
60 Si
Fig. 8. A m e t h o d o f d e t e r m i n i n g t h e c o n c e n t r a t i o n o f a r s e n a z o n I ( A Z ) . ( A ) r = 1, a n d (B) r = 0 . 6 . T h e c o n d i t i o n s : [ A Z ] + [ C a ] = 6 0 / ~ M , 4 0 m M H E P E S ( p H 7 . 0 ) , 2 5 ° C . T h e i o n i c s t r e n g t h is 0.1 M. See a p p e n dix for details.
The position of the intersection of two tangents (St, Pt) is given by S t = L ( r L + K)/((1 + r ) L + 2K);
P t = r L 2 / ( ( 1 + r ) L + 2K)
(A10)
As shown later, the value for K is of the order of 10 -s M. If we choose L to be 10 -4 M, r could be approximately estimated from St as r = St/(L
--St)
(All)
Based upon this value of r, Ea is estimated according to Eqn. A7. Then another series of experiments is run keeping the sum of E a + Sj constant. After repeating this procedure for a few times, the resuIt of r = 1 is obtained, as shown in Fig. 8A. This means t h a t the assumed concentration was correct. It is tedious to run these experiments each time. Therefore, the extinction coefficient of arsenazo III was determined when the correct concentration was known. According to our result, in a solution containing 20 mM HEPES and 1 mM EDTA (pH 7.0, 25°C), the molar extinction coefficient was 1 . 1 0 - l 0 s (in 10 mm optical path) at the peak wavelength (538 nm).
Acknowledgement This work was supported in part by NIH grant 15799.
References 1 0 h n i s h i , T. a n d E b a s h i , S. ( 1 9 6 3 ) J. B i o c h e m . 5 4 , 5 0 6 - - 5 1 1 2 O h n i s h i , T. a n d E b a s h i , S. ( 1 9 6 4 ) J. B i o c h e m . 5 5 , 5 9 9 - - 6 0 3 3 O h n i s h i , T. ( 1 9 6 4 ) J. B i o c h e m . 5 5 , 1 7 2 - - 1 7 7 4 O h n i s h i , T. a n d E b a s h i , S. ( 1 9 6 5 ) A b s t r a c t o f t h e 6 t h I n t e r n a t i o n a l C o n f e r e n c e o n M e d i c a l E l e c t r o nics and Biological Engineering, pp. 620--621, Japan Society of Medical Electronics and Biological Engineering, Tokyo 5 0 h n i s h i , T., M a s o r o , E . J . , B e r t r a n d , H . A . a n d Y u , B.P. ( 1 9 7 2 ) B i o p h y s . J. 1 2 , 1 2 5 1 - - 1 2 6 5 6 J S b s i s , F . F . a n d O ' C o n n o r , M.J. ( 1 9 6 6 ) B i o c h e m . B i o p h y s . Res. C o m m u n . 2 5 , 2 4 6 - - 2 5 2 7 M e l a , L. a n d C h a n c e , B. ( 1 9 6 6 ) B i o c h e m i s t r Y 7 , 4 0 5 9 - - 4 0 6 3 8 C i t t a d i n i , A., S c a r p a , A. a n d C h a n c e , B. ( 1 9 7 1 ) F E B S L e t t . 1 8 , 9 8 - - 1 0 2 9 S c a r p a , A. ( 1 9 7 2 ) in M e t h o d s i n E n z y m o l o g y ( S a n P i e t r o , A., e d . ) , Vol. 2 4 , p p . 3 4 3 - - 3 5 1 , A c a d e m i c Press, N e w Y o r k 1 0 Inesi, G. a n d S c a r p a , A. ( 1 9 7 2 ) B i o c h e m i s t r Y 1 1 , 3 5 6 - - 3 5 9 11 O h n i s h i , S.T. ( 1 9 7 8 ) A n a l . B i o c h e m . 6 5 , 1 6 5 - - 1 7 9
230 12 Michaylova, V. and Ilkova, P, (1971) Anal. Chim. Acta 53, 194--198 13 Michaylova, V.Y. and Kouleva, N.K. (1972) C.R. Acad. Bulg. Sei. 25, 949--952 14 Burger, K. (1973) International Series of Monographs in Analytical Chemistry, Vol, 54, Pergamon Press, Oxford 15 Dipolo, R., Reguena, J., Brinley, F.J., Mullins, L.J., Scarpa, A. and Tiffert, T. (1976) J. Gen. Physiol. 67,433--467 16 Scarpa, A., Tiffert, T. and Brinley, F.J. (1976) in Biochemistry of Membrane Transport (Semenza, G. and Carafoli, E., eds.), pp. 552-~566, Springer Verlag, New York 17 Ohnishi, S.T. (1978) A n n . N.Y. Acad. Sci. 3 0 7 , 2 1 3 - - 2 1 6 18 Dixon, M. and Webb, E.C. (1964) in Enzymes, 2nd Edn., p. 67, Academic Press, New York 19 Job, P. (1936) Ann. Chim. [11] 6, 97--144 20 Vosburg, W.C., Cooper, G.R. (1941) J. Am. Chem. Soe. 6 3 , 4 3 7 - - 4 4 2 21 Chberek, S., Marten, A.E. (1959) in Organic Sequestering Agents, p. 78, J ohn Wiley and Sons, New York 22 Yoe, J.H., Jones, A.L. (1944) Ind. Eng. Chem. Anal. Ed. 16° 111--117 23 Scatchard, G. (1949) Ann. N.Y. Acad. Sci. 51° 660--672 24 Lineweaver, H. and Burk, D. (1934) J. Am. Chem. Soc. 56,658---666 25 Klotz, I.M. (1946) Arch. Biochem. 9 , 1 0 9 - - 1 1 7 26 Klotz, I.M. (1953) in Proteins, Vol. 2 (Neurath, H. and Baily, K., eds.), Academic Press, New York 27 Ohnishi, S.T. (1979) Biochim. Biophys. Acta 5 8 5 , 3 1 5 - - 3 1 9