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A spectrophotometric resin competition procedure to determine dissociation constants for metal ion-nucleotide complexes
ANALYTICAL BIOCHEMISTRY 145,362-366
(1985)
A Spectrophotometric Resin Competition Procedure to Determine Dissociation Constants for Metal Ion-Nucleotide Complexes’ W. TERRY JENKINS Department
of Chemistry,
Indiana
University,
Bloomington,
Indiana
47405
Received September 4, 1984 The resin competition method for determining the dissociation constants of metal ionnucleotide complexes was modified to take into account the fact that some metal nucleotide complexes are anionic and thus, like the free nucleotide, will bind to the resin. A simple, rapid spectrophotometric titration procedure is given for the determination of both the metal ionnucleotide complex dissociation constant and the ratio of the affinities of the nucleotide and its COmpkX for the resin. 0 1985 Academic Press, Inc. KEY WORDS: nucleotides; metal ions; bioenergetics; spectrophotometry; kinetics, enzyme; kinases.
where NP represents the nucleotide and MS NP and NP - resin its complexes with the metal ion and resin, respectively. If the free nucleotide and its metal ion complex have the same molar extinction coefficient (tM) then
For detailed kinetic studies of enzymes that use nucleotides and require divalent cations, such as magnesium, it is necessary to determine, to the highest degree of accuracy, the effective metal ion dissociation constant (Kh) for the nucleotide complex under conditions of buffer and ionic strength identical to those of the kinetic investigation. These dissociation constants cannot be calculated easily for they are markedly affected by both the ionic strength and the nature of the buffer. The method presented in this paper is based on the Schubert resin competition method ( l-3).
Total nucleotide in solution Resin-bound nucleotide
=
= K;(l
If one assumes ( 1,2) that nucleotide binding both to a cationic resin and to a metal cation are simple competing equilibria governed by the Law of Mass Action, then +NP] * resin]
VI
362 $3.00
Copyright 0 1985 by Academic Press. Inc. All rights of reproduction in any form reserved.
131
AJ/~M
[41
where A, is the absorbance before addition of metal ion. If the amount of resin is kept constant, plots of the left-hand side of Eq. [3] with respect to the free metal ion concentration ([MI) should yield straight lines that cut the ordinate at values of K’,, proportional to the reciprocal of the amount of resin used (K’,
[II
’ This work was supported in part by BRSG SO7 RR0703 1, awarded by the Biomedical Research Support Program, Division of Research Resources, National Institutes of Health. 0003-2697185
+ DflIKJ
WI = Ml - (A, -
and K, = [NP][resin]/[NP
[resin]
where A, and A0 are the absorbances with and without both resin and metal respectively and K’, = K,/[resin]. The “free” metal ion concentration [M] can be calculated (3) from that added ([M,]) by the expression
THEORY
K; = [NP][M]/[M
= Kdl + [WKd
A,
Ao - A,
DISSOCIATION
CONSTANTS
= K,/[resin]). The negative abscissa intercepts, corresponding to K>, should be independent of the amount of resin used (2). In many cases such straight lines are in fact obtained but in others a downward curvature is observed. This curvature arises when the complexes are anionic and also bind to the resin, either because the charge is not completely neutralized (e.g., Mg sATP2-) or, as with transition metals, because the metal ion binds both nucleotide and additional anionic Iigands in its open coordination sites (e.g., ML:- + ATF- = L2M.ATp+ 2L-). A more general formulation must, therefore, include a Mass Action equilibrium for the binding of the complex to the resin. K, = [MSNPj[resin]/[M.NP*resin] This results in a modified titration
equation
= (l/Am - (1 + UWIAolI&
[5J for the
Fl
where K:. = KJ[resin]. If the values of metal ion concentration ([MI) are known, this equation can also be plotted to yield a straight line of slope l/Kb and abscissa intercept (1 + l/Kc)/Ao. If the amount of resin is varied, a series of parallel lines should be obtained whose abscissa intercepts increase linearly with the amount of resin used, since l/K: = [resin]/&. The concentration of free metal can be calculated from the total added by the expression
[MI = Ml - &, - A,)(1 +
1/K)/cM.
I71
Since this equation involves the unknown K; it may be necessary first to evaluate KL by using Eq. [4] to estimate the free metal ion concentrations. However, if the resin binds free nucleotide tighter than it does the metal ion complex, then l/K:. must be less than l/K’, which is chosen to be about 2.0. Hence the additional correction for metal ion bound as nucleotide complex to the resin is small and it may not be necessary to
BY SPECTROPHOTOMETRY
363
correct for Kc; at most only one iteration cycle is necessary. MATERIALS
The buffers and ATP were obtained from Sigma. Solutions of reagent-grade metal salts were standardized by titration of an aliquot with base after removal of the cations by passage through a small column of a cationic exchange resin (4). Purified analytical-grade resins were obtained from Bio-Rad. Standard 0.1 M solutions of ZnClz were made in 2 mM HCl to avoid precipitation of Zn(OH)z. METHOD Step I. Analytical-grade anion exchange resin AGl-X2 (chloride, 200-325 mesh), is washed with water and then allowed to dry in air at room temperature. To 50 ml of the buffer of interest is added enough nucleotide (e.g., 80 /IM ATP) to give an absorbance (Ao) of about 1.2 at the absorption maximum or at a wavelength where the absorption of the buffer is minimal. A known amount of resin is then added, sufficient to absorb less than 50% of the nucleotide. After 5 min stirring on a magnetic stirrer, the absorbance (A,) is measured in a 5-ml aliquot after the resin is removed by centrifugation. This aliquot is then resuspended by vortex mixing and added back to the titration. Another aliquot of resin is added and the procedure repeated until more than 70% of the nucleotide has been adsorbed. Equation [3], in the absence of metal ion, can be written
(Ao/Ar - 1) = [resin]/Ki
WI
so that a plot of l/A, with respect to the amount of resin used should be a straight line intersecting the ordinate at l/A0 and having an abscissa intercept -K, Step 2. From the previous graph an amount of resin is chosen to absorb about 2/3 of the nucleotide ([resin]/& = l/K; == 0.5). After the addition of the nucleotide, this resin is titrated with small aliquots (20 ~1) of a
364
W. TERRY JENKINS
concentrated metal-ion salt solution (about 0.2 M) and the absorbances (A,) are measured as before. A graph is then constructed of (l/A, - l/A,)/[M] with respect to l/A,. For this initial graph the concentrations of free metal ([MI) are estimated with Eq. [4]. If necessary the data can be later refined using I
Eq. [71.
Controls. Important controls are to show that the resin equilibrates rapidly by studying the absorbance changes with time and to show that both l/K’, and l/K’, increase linearly with the amount of resin but that K& is independent of the amount of resin used. One should also confirm that the metal ion does not affect the absorbance of the nucleotide. RESULTS
Figure 1 shows titration data, plotted according to Eq. [3], for four metals in imidazole and N-Tris(hydroxymethyl)methyl-2aminoethane sulfonate (TES)2 buffers of the same pH and comparable ionic strength. Although the plots yield similar values for the x7, for Mn and Ca in the two buffers, it is clear that Eq. [3] is not valid for Zn and Co in TES buffers. Figure 2 shows the same data used to plot Fig. 1 graphed according to Eq. [6]. This yielded straight lines; and the abscissa intercepts, at points greater than I/&, = 0.82, indicated that not only the Co and Zn but also the Ca complexes with ATP bind to the resin in TES buffers. Table I summarizes the results obtained from the graphs in Fig. 2. The effect of imidazole is to increase the dissociation constants for Zn and Co, which is expected since they react with imidazole. Imidazole, however, also increases the selectivity for the free ligand with respect to the metal complex (Kc/K,). The ratio Kd- Kc/K, is the amount of metal ion required to form the resinbound complex from the resin-bound metal-
I 0.5
1 I 1.0 [METALI~M
L 0.5
t I 1.0
FIG. 1. Displacement of ATP from AGl-X2 anion exchange resin. Data plotted according to Eq. [3]. (A) 0.06 M Imidazole chloride, pH 7.45, containing 20 mM Na2S04, 128 mM NaCl; 4 mg resin/ml. (B) 0.06 M TES, pH 7.45, containing 20 mM Na,SO.,, 128 mM NaCI: 6.6 mg resin/ml.
free ligand. It is of interest that Ca is an order of magnitude less effective than either Co or Zn. Figure 3A shows a series of magnesium titrations in Tris buffers, pH 8.2, with different amounts of resin, plotted according to Eq. [3]. Reasonably straight lines were obtained that appeared to have a common intercept (Kd = 0.22 mM) on the abscissa as predicted by the equation. Closer examination shows the lines to have a downward curvature indicating that the MgATP2- complex adsorbs to the resin. When plotted according to Eq. [6] (Fig. 3B) a series of parallel lines was obtained with a lower Kd value (Kb = 0.15 mM). The inset in Fig. 3B shows that the abscissa intercepts (1 + [resin]/K,)/Ao when plotted with respect to the amount of resin yield a straight line cutting the ordinate at l/A, as predicted by the equation. The inset also shows that the reciprocals of the absorbances before the addition of metal ion I/(&) yield a straight line cutting the ordinate at l/A0 as predicted by Eq. [S]. The ratio of the slopes of the two lines (Kc/K1 = 7.1) in the inset gives the resin selectivity for ATI’over Mg . ATP’-. DISCUSSION
* Abbreviation: TES-N-Tris(hydroxymethyI)methyl-2aminoethane sulfonate.
The amount of resin required varies quite markedly with the particular buffer used and
DISSOCIATION
CONSTANTS
365
BY SPECTROPHOTOMETRY
FIG. 2. Experimental data of Fig. 1 replotted according to Eq. [6]. Since l/A0 = 0.82 any abscissa intercept greater than 0.82 indicates that the complex binds to the resin (i.e.. l/Kc > 0). TES buffer (0); imidazole buffer (X).
cited in the literature (4,5) are either inappropriate thermodynamic constants or estimates derived from approximate empirical equations for the effects of ionic strength and pH on these thermodynamic constants. The procedure in this paper differs from that of Walaas (2) in several important respects.
must be determined by trial. To avoid using very small amounts of resin it may be necessary to increase the ionic strength of the buffer. It should be noted that these dissociation constants are experimental constants because the “free” metal concentration is, by definition, the amount not complexed with the nucleotide effectively. Much of this metal ion is9 of course, not really free but is complexed with the buffer. However, the Mass Action Law is still valid because the amount of ion that is truly free is proportional to the total present. The important point is that it is these experimental I$ values that are required in enzymological investigations to determine the amounts of free nucleotide and metal nucleotide complex. The constants
(a) The time of equilibration with the resin is considerably shorter, so that a single titration vessel can be used, thus greatly improving the precision of the method. Walaas used an equilibration period of 3 h, but with AGI-X2 resin it can be shown experimentally that equilibration occurs in less than 3 min. (b) The assumption made in deriving Eq. [3] that no nucleotide complex binds to the
TABLE 1 BUFFER
Buffer”: Cation: Kd
(mM) K, Ongh-4
0.06
M
EFFECTS
ON K>, K, AND
K
0.06
TES
Mn
Ca
Zn
co
0.077 3.1
0.45 2.9
0.21 2.9
0.18 2.8
Mn
Ca
M
Imidazole Zn
co
0.070 2.1
0.45 2.0
1.58 2.2
0.32 2.0
Kc CWml)
cc'
38.0
7.4
UK,
m cc
13.1 5.9
2.6 0.55
8.7 3.1
co m
cc' K
05 rx,
ZI CL
0.56
cc
02
*
cc
0.076
0.57
1.16
0.92
Kd- KJK, Fd (rnM)b
CmM)
a All buffers pH 7.45, 2omM NazSOs, 128 mM NaCl. * Kb values from Fig. 1 used unweighted regression lines.
0.07
1
0.47
1.52
0.35
366
W. TERRY JENKINS
I
0.1 0.2 0.3 (Mgl
1.5
2
I/Am
mM
FIG. 3. Determination of Kb for Mg . ATP. 0.1 M T&chloride, pH 8.2, containing 60 mM NaCl and 30 mM Na$O+ Titrations were performed with 1, 2, and 3 mg resin/ml. (A) Data plotted according to Eq. [3]. The apparent Kb = 0.22 mix (B) Data plotted according to Eq. [6]. The parallel lines indicate K& = 0.15 mM. The figure inset shows the validity of Eqs. [8] and [6].
anion exchanger is, on both theoretical and experimental grounds, clearly invalid for certain nucleotides in certain buffers. Because the lines of plots based on Eq. [3] may be slightly curved downwards, the K& values may be overestimated by a considerable amount if linear regression lines are drawn (Table 1 and Fig. 3). Equation [6] suffers from the disadvantage that the K& value depends upon differences between numbers of comparable magnitude so that the precision is very dependent upon an accurate value for A,. Equation [3] is, therefore, preferable for the determination of K& when there is no evidence for the resin binding the complex (i.e., l/K, = 0). (c) Many workers have failed to estimate the amount of free metal ion, whereas others have estimated it from the curved plots based on Eq. [3] by a mathematical reiteration procedure designed to give straight lines (4). This procedure is invalid if the curvature is ascribed to the affinity of the complex for the resin. The ratio of K',/Kc = K,/K, is a measure of the selectivity of the resin for the free nucleotide over the metal complex. With transition metals in imidazole buffers, it was found that K, /Kc = 0 and Kb was much increased, indicating that imidazole prevents both the formation of the complex and com-
plex binding to the resin. With TES buffers the ratio for Co was 0.32, indicating that TES favors binding of the metal ion complex to the resin. This may be due to TES anions occupying the open coordination sites on the metal. The selectivity of AGl-X2 resin may be a useful experimental parameter for a comparison of different nucleotides and metal ions. This same procedure could also be used to determine the relative affinities of metal ion complexes and free nucleotides for enzymatic active sites. Thermodynamically, the ion selectivity (K,/K,) is a measure of the energy contribution by the metal ion to the dissociation of the ionic ligand. This ion exchange type of ion selectivity may thus be an important factor in understanding the role of metal ions in enzyme bioenergetics (3). REFERENCES 1. Schubert, J. ( 1956) in Methods of Biochemical Analysis (Click, D., ed.), Vol. 3, pp. 247-263, Interscience, New York. 2. WaIaas, E. (1958) Acta Chem. Stand. 12, 528-536. 3. Jenkins, W. T., Marshall, M. M., and Lewin, A. S. (1984)
Arch.
Biochem.
Biophys.
232, 496-504.
4. O’Sullivan, W. J., and Smithers, G. W. (1979) in Methods in Enzymology (Purich, D. L., ed.), Vol. 63, pp. 294-336, Academic Press, New York. 5. Tu, A. T., and Heller, M. J. (1974) in Metal Ions in Biological Systems (Sigel, H., ed.), Vol. 1, pp. I49, Dekker, New York.
(1985)
A Spectrophotometric Resin Competition Procedure to Determine Dissociation Constants for Metal Ion-Nucleotide Complexes’ W. TERRY JENKINS Department
of Chemistry,
Indiana
University,
Bloomington,
Indiana
47405
Received September 4, 1984 The resin competition method for determining the dissociation constants of metal ionnucleotide complexes was modified to take into account the fact that some metal nucleotide complexes are anionic and thus, like the free nucleotide, will bind to the resin. A simple, rapid spectrophotometric titration procedure is given for the determination of both the metal ionnucleotide complex dissociation constant and the ratio of the affinities of the nucleotide and its COmpkX for the resin. 0 1985 Academic Press, Inc. KEY WORDS: nucleotides; metal ions; bioenergetics; spectrophotometry; kinetics, enzyme; kinases.
where NP represents the nucleotide and MS NP and NP - resin its complexes with the metal ion and resin, respectively. If the free nucleotide and its metal ion complex have the same molar extinction coefficient (tM) then
For detailed kinetic studies of enzymes that use nucleotides and require divalent cations, such as magnesium, it is necessary to determine, to the highest degree of accuracy, the effective metal ion dissociation constant (Kh) for the nucleotide complex under conditions of buffer and ionic strength identical to those of the kinetic investigation. These dissociation constants cannot be calculated easily for they are markedly affected by both the ionic strength and the nature of the buffer. The method presented in this paper is based on the Schubert resin competition method ( l-3).
Total nucleotide in solution Resin-bound nucleotide
=
= K;(l
If one assumes ( 1,2) that nucleotide binding both to a cationic resin and to a metal cation are simple competing equilibria governed by the Law of Mass Action, then +NP] * resin]
VI
362 $3.00
Copyright 0 1985 by Academic Press. Inc. All rights of reproduction in any form reserved.
131
AJ/~M
[41
where A, is the absorbance before addition of metal ion. If the amount of resin is kept constant, plots of the left-hand side of Eq. [3] with respect to the free metal ion concentration ([MI) should yield straight lines that cut the ordinate at values of K’,, proportional to the reciprocal of the amount of resin used (K’,
[II
’ This work was supported in part by BRSG SO7 RR0703 1, awarded by the Biomedical Research Support Program, Division of Research Resources, National Institutes of Health. 0003-2697185
+ DflIKJ
WI = Ml - (A, -
and K, = [NP][resin]/[NP
[resin]
where A, and A0 are the absorbances with and without both resin and metal respectively and K’, = K,/[resin]. The “free” metal ion concentration [M] can be calculated (3) from that added ([M,]) by the expression
THEORY
K; = [NP][M]/[M
= Kdl + [WKd
A,
Ao - A,
DISSOCIATION
CONSTANTS
= K,/[resin]). The negative abscissa intercepts, corresponding to K>, should be independent of the amount of resin used (2). In many cases such straight lines are in fact obtained but in others a downward curvature is observed. This curvature arises when the complexes are anionic and also bind to the resin, either because the charge is not completely neutralized (e.g., Mg sATP2-) or, as with transition metals, because the metal ion binds both nucleotide and additional anionic Iigands in its open coordination sites (e.g., ML:- + ATF- = L2M.ATp+ 2L-). A more general formulation must, therefore, include a Mass Action equilibrium for the binding of the complex to the resin. K, = [MSNPj[resin]/[M.NP*resin] This results in a modified titration
equation
= (l/Am - (1 + UWIAolI&
[5J for the
Fl
where K:. = KJ[resin]. If the values of metal ion concentration ([MI) are known, this equation can also be plotted to yield a straight line of slope l/Kb and abscissa intercept (1 + l/Kc)/Ao. If the amount of resin is varied, a series of parallel lines should be obtained whose abscissa intercepts increase linearly with the amount of resin used, since l/K: = [resin]/&. The concentration of free metal can be calculated from the total added by the expression
[MI = Ml - &, - A,)(1 +
1/K)/cM.
I71
Since this equation involves the unknown K; it may be necessary first to evaluate KL by using Eq. [4] to estimate the free metal ion concentrations. However, if the resin binds free nucleotide tighter than it does the metal ion complex, then l/K:. must be less than l/K’, which is chosen to be about 2.0. Hence the additional correction for metal ion bound as nucleotide complex to the resin is small and it may not be necessary to
BY SPECTROPHOTOMETRY
363
correct for Kc; at most only one iteration cycle is necessary. MATERIALS
The buffers and ATP were obtained from Sigma. Solutions of reagent-grade metal salts were standardized by titration of an aliquot with base after removal of the cations by passage through a small column of a cationic exchange resin (4). Purified analytical-grade resins were obtained from Bio-Rad. Standard 0.1 M solutions of ZnClz were made in 2 mM HCl to avoid precipitation of Zn(OH)z. METHOD Step I. Analytical-grade anion exchange resin AGl-X2 (chloride, 200-325 mesh), is washed with water and then allowed to dry in air at room temperature. To 50 ml of the buffer of interest is added enough nucleotide (e.g., 80 /IM ATP) to give an absorbance (Ao) of about 1.2 at the absorption maximum or at a wavelength where the absorption of the buffer is minimal. A known amount of resin is then added, sufficient to absorb less than 50% of the nucleotide. After 5 min stirring on a magnetic stirrer, the absorbance (A,) is measured in a 5-ml aliquot after the resin is removed by centrifugation. This aliquot is then resuspended by vortex mixing and added back to the titration. Another aliquot of resin is added and the procedure repeated until more than 70% of the nucleotide has been adsorbed. Equation [3], in the absence of metal ion, can be written
(Ao/Ar - 1) = [resin]/Ki
WI
so that a plot of l/A, with respect to the amount of resin used should be a straight line intersecting the ordinate at l/A0 and having an abscissa intercept -K, Step 2. From the previous graph an amount of resin is chosen to absorb about 2/3 of the nucleotide ([resin]/& = l/K; == 0.5). After the addition of the nucleotide, this resin is titrated with small aliquots (20 ~1) of a
364
W. TERRY JENKINS
concentrated metal-ion salt solution (about 0.2 M) and the absorbances (A,) are measured as before. A graph is then constructed of (l/A, - l/A,)/[M] with respect to l/A,. For this initial graph the concentrations of free metal ([MI) are estimated with Eq. [4]. If necessary the data can be later refined using I
Eq. [71.
Controls. Important controls are to show that the resin equilibrates rapidly by studying the absorbance changes with time and to show that both l/K’, and l/K’, increase linearly with the amount of resin but that K& is independent of the amount of resin used. One should also confirm that the metal ion does not affect the absorbance of the nucleotide. RESULTS
Figure 1 shows titration data, plotted according to Eq. [3], for four metals in imidazole and N-Tris(hydroxymethyl)methyl-2aminoethane sulfonate (TES)2 buffers of the same pH and comparable ionic strength. Although the plots yield similar values for the x7, for Mn and Ca in the two buffers, it is clear that Eq. [3] is not valid for Zn and Co in TES buffers. Figure 2 shows the same data used to plot Fig. 1 graphed according to Eq. [6]. This yielded straight lines; and the abscissa intercepts, at points greater than I/&, = 0.82, indicated that not only the Co and Zn but also the Ca complexes with ATP bind to the resin in TES buffers. Table I summarizes the results obtained from the graphs in Fig. 2. The effect of imidazole is to increase the dissociation constants for Zn and Co, which is expected since they react with imidazole. Imidazole, however, also increases the selectivity for the free ligand with respect to the metal complex (Kc/K,). The ratio Kd- Kc/K, is the amount of metal ion required to form the resinbound complex from the resin-bound metal-
I 0.5
1 I 1.0 [METALI~M
L 0.5
t I 1.0
FIG. 1. Displacement of ATP from AGl-X2 anion exchange resin. Data plotted according to Eq. [3]. (A) 0.06 M Imidazole chloride, pH 7.45, containing 20 mM Na2S04, 128 mM NaCl; 4 mg resin/ml. (B) 0.06 M TES, pH 7.45, containing 20 mM Na,SO.,, 128 mM NaCI: 6.6 mg resin/ml.
free ligand. It is of interest that Ca is an order of magnitude less effective than either Co or Zn. Figure 3A shows a series of magnesium titrations in Tris buffers, pH 8.2, with different amounts of resin, plotted according to Eq. [3]. Reasonably straight lines were obtained that appeared to have a common intercept (Kd = 0.22 mM) on the abscissa as predicted by the equation. Closer examination shows the lines to have a downward curvature indicating that the MgATP2- complex adsorbs to the resin. When plotted according to Eq. [6] (Fig. 3B) a series of parallel lines was obtained with a lower Kd value (Kb = 0.15 mM). The inset in Fig. 3B shows that the abscissa intercepts (1 + [resin]/K,)/Ao when plotted with respect to the amount of resin yield a straight line cutting the ordinate at l/A, as predicted by the equation. The inset also shows that the reciprocals of the absorbances before the addition of metal ion I/(&) yield a straight line cutting the ordinate at l/A0 as predicted by Eq. [S]. The ratio of the slopes of the two lines (Kc/K1 = 7.1) in the inset gives the resin selectivity for ATI’over Mg . ATP’-. DISCUSSION
* Abbreviation: TES-N-Tris(hydroxymethyI)methyl-2aminoethane sulfonate.
The amount of resin required varies quite markedly with the particular buffer used and
DISSOCIATION
CONSTANTS
365
BY SPECTROPHOTOMETRY
FIG. 2. Experimental data of Fig. 1 replotted according to Eq. [6]. Since l/A0 = 0.82 any abscissa intercept greater than 0.82 indicates that the complex binds to the resin (i.e.. l/Kc > 0). TES buffer (0); imidazole buffer (X).
cited in the literature (4,5) are either inappropriate thermodynamic constants or estimates derived from approximate empirical equations for the effects of ionic strength and pH on these thermodynamic constants. The procedure in this paper differs from that of Walaas (2) in several important respects.
must be determined by trial. To avoid using very small amounts of resin it may be necessary to increase the ionic strength of the buffer. It should be noted that these dissociation constants are experimental constants because the “free” metal concentration is, by definition, the amount not complexed with the nucleotide effectively. Much of this metal ion is9 of course, not really free but is complexed with the buffer. However, the Mass Action Law is still valid because the amount of ion that is truly free is proportional to the total present. The important point is that it is these experimental I$ values that are required in enzymological investigations to determine the amounts of free nucleotide and metal nucleotide complex. The constants
(a) The time of equilibration with the resin is considerably shorter, so that a single titration vessel can be used, thus greatly improving the precision of the method. Walaas used an equilibration period of 3 h, but with AGI-X2 resin it can be shown experimentally that equilibration occurs in less than 3 min. (b) The assumption made in deriving Eq. [3] that no nucleotide complex binds to the
TABLE 1 BUFFER
Buffer”: Cation: Kd
(mM) K, Ongh-4
0.06
M
EFFECTS
ON K>, K, AND
K
0.06
TES
Mn
Ca
Zn
co
0.077 3.1
0.45 2.9
0.21 2.9
0.18 2.8
Mn
Ca
M
Imidazole Zn
co
0.070 2.1
0.45 2.0
1.58 2.2
0.32 2.0
Kc CWml)
cc'
38.0
7.4
UK,
m cc
13.1 5.9
2.6 0.55
8.7 3.1
co m
cc' K
05 rx,
ZI CL
0.56
cc
02
*
cc
0.076
0.57
1.16
0.92
Kd- KJK, Fd (rnM)b
CmM)
a All buffers pH 7.45, 2omM NazSOs, 128 mM NaCl. * Kb values from Fig. 1 used unweighted regression lines.
0.07
1
0.47
1.52
0.35
366
W. TERRY JENKINS
I
0.1 0.2 0.3 (Mgl
1.5
2
I/Am
mM
FIG. 3. Determination of Kb for Mg . ATP. 0.1 M T&chloride, pH 8.2, containing 60 mM NaCl and 30 mM Na$O+ Titrations were performed with 1, 2, and 3 mg resin/ml. (A) Data plotted according to Eq. [3]. The apparent Kb = 0.22 mix (B) Data plotted according to Eq. [6]. The parallel lines indicate K& = 0.15 mM. The figure inset shows the validity of Eqs. [8] and [6].
anion exchanger is, on both theoretical and experimental grounds, clearly invalid for certain nucleotides in certain buffers. Because the lines of plots based on Eq. [3] may be slightly curved downwards, the K& values may be overestimated by a considerable amount if linear regression lines are drawn (Table 1 and Fig. 3). Equation [6] suffers from the disadvantage that the K& value depends upon differences between numbers of comparable magnitude so that the precision is very dependent upon an accurate value for A,. Equation [3] is, therefore, preferable for the determination of K& when there is no evidence for the resin binding the complex (i.e., l/K, = 0). (c) Many workers have failed to estimate the amount of free metal ion, whereas others have estimated it from the curved plots based on Eq. [3] by a mathematical reiteration procedure designed to give straight lines (4). This procedure is invalid if the curvature is ascribed to the affinity of the complex for the resin. The ratio of K',/Kc = K,/K, is a measure of the selectivity of the resin for the free nucleotide over the metal complex. With transition metals in imidazole buffers, it was found that K, /Kc = 0 and Kb was much increased, indicating that imidazole prevents both the formation of the complex and com-
plex binding to the resin. With TES buffers the ratio for Co was 0.32, indicating that TES favors binding of the metal ion complex to the resin. This may be due to TES anions occupying the open coordination sites on the metal. The selectivity of AGl-X2 resin may be a useful experimental parameter for a comparison of different nucleotides and metal ions. This same procedure could also be used to determine the relative affinities of metal ion complexes and free nucleotides for enzymatic active sites. Thermodynamically, the ion selectivity (K,/K,) is a measure of the energy contribution by the metal ion to the dissociation of the ionic ligand. This ion exchange type of ion selectivity may thus be an important factor in understanding the role of metal ions in enzyme bioenergetics (3). REFERENCES 1. Schubert, J. ( 1956) in Methods of Biochemical Analysis (Click, D., ed.), Vol. 3, pp. 247-263, Interscience, New York. 2. WaIaas, E. (1958) Acta Chem. Stand. 12, 528-536. 3. Jenkins, W. T., Marshall, M. M., and Lewin, A. S. (1984)
Arch.
Biochem.
Biophys.
232, 496-504.
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