ANALYTICALBIOCHEMISTRY

186,31-40

(1990)

Complexometric Titrations of Protein-Bound Metal Ions: A Method for Determining Binding Constants James

A. Roe’ and Joan Selverstone

Valentine

Departments of Chemistry and Biochemistry and The Molecular University of California, Los Angeles, California 90024

Received

July

Biology Institute,

26,1989

A method for quantifying the affinity of proteins for specific metal ions has been developed. Both the stoichiometry and the binding constants of the protein-bound metal ion can be determined by titrating protein-bound metal ions with complexometric reagents and observing electrochemically the change in free metal ion concentration. The technique is limited to cases where the affinity of the macromolecule for the metal ion is less than or similar to the affinity of the complexometric reagent for the metal ion. The method has been employed successfully in the study of both Cu(I1) and Ag(1) binding to the apoprotein of bovine cuprozinc superoxide dismutase. CC)1990 Academic Press. Inc.

Interactions between metal ions and biomolecules continue to interest biochemists and molecular biologists, especially in light of recent evidence that metal ions play crucial roles in gene regulation. Some gene regulation mechanisms may be triggered by the binding of a metal ion to a domain of a gene effector and thus depend on the affinity of that effector for the metal ion. Examples include the interactions between Hg(I1) and the MerR protein (l), and Zn(I1) and “zinc fingers” (2). In addition, metal ion binding to proteins is important in metal ion transport as in the cases of ceruloplasmin and transferrin and in metal ion storage as in the case of ferritin (3-5). There are two important aspects of the binding of a metal ion to a biomolecule. The first is the effect of the metal ion on the structure of the biomolecule. For example, zinc-finger structures are presumably induced by the binding of zinc which causes a structural reorganization of a protein domain. The second con’ Current address: Department stitute of Scripps Clinic, 10666 92037.

of Molecular Biology, N. Torrey Pines Road,

0003-2697/90 $3.00 Copyright Q 1990 by Academic Press, Inc. All rights of reproduction in any form reserved.

Research La Jolla,

InCA

terns the magnitude of the binding affinity and its dependence on solution conditions, which include pH and ionic strength. It is to the binding affinity that this paper is addressed. Methods of quantifying metal-binding constants of biomolecules include equilibrium dialysis as well as direct titrations of biomolecules with metal ions. An example of the use of equilibrium dialysis is a study by Hirose et al. (6), in which the binding affinities of Cu(I1) to the well-characterized metal-binding sites of bovine cuprozinc superoxide dismutase (SOD)’ were determined by dialyzing the protein, to which the metal ion had been bound, against a known concentration of a complexometric reagent, picolinic acid (pa). The amount of protein-bound metal and the corresponding aqueous metal ion concentration were calculated from analysis by atomic absorption spectrometry (AAS) of the protein solutions and the dialysates for total metal content. These authors were able to determine the binding constants by carrying out a series of these dialyses and varying the concentration of the complexometric reagent. As a general method, however, equilibrium dialysis has several drawbacks, including the need for multiple experiments in order to determine a binding constant with a high degree of precision and the requirement for a lengthy period of equilibration time. In the study by Hirose et al. (6), approximately 10 to 20 days was needed for each dialysis experiment to reach equilibrium. In addition, the

* Abbreviations used: SOD, superoxide dismutase; pa, picolinic acid; AAS, atomic absorption spectrometry; ISE, ion-selective electrode; en, ethylenediamine; RT, room temperature. CuzZn,SOD represents the native form of cuprozinc superoxide dismutase as isolated from bovine liver. In general, X,Y,SOD signifies those derivatives of the native protein in which the metal ions X and Y have been substituted for the native CL?+ and Zn*+, respectively (X and Y may be the same: E = empty). On occasion, the XYSOD,,b is used to represent one of the identical subunits. All metal ions are assumed to be 2+ unless noted otherwise, except for silver which has an oxidation state of l+. 31

32

ROE

AND

results of Hirose et al. were dependent on the accuracy and suitability of the literature values for the metalbinding constant of the complexing agent used in the equilibrium dialysis. Another technique for quantifying biomolecule-metal interactions is that of direct titration, wherein a metalfree protein is titrated with a specific metal ion. In theory one can calculate the binding constants from data measured in a single experiment if one can monitor the aqueous metal ion concentration constantly throughout the titration. Avdeef et al. (7) determined Cd(II)-binding constants of metallothionein by such an approach by titrating the protein with Cd(I1) and monitoring the aqueous Cd(B) concentration by a Cd(I1) ion-selective electrode USE). However, there are also drawbacks inherent in this direct titration method. Large amounts of protein are required in order to make the metal ion concentration large enough to ensure that the response time of the electrode is reasonable. However, proteins in relatively high concentration (mM) adhere to the surface of electrodes and they themselves, therefore, frequently interfere with the response of the electrode. This is especially true if the total metal ion concentration is low, as it would be at the beginning of a direct titration of a protein that is a tight binder of a metal ion. In addition, there are reports that free sulfhydryl groups of sulfurrich proteins interfere with the determination of metal ion concentrations by Ag,S-based ISEs (8). Fortunately, there are no free thiol groups on bovine SOD. In this paper, we introduce a method for determining metal ion-protein-binding constants by titrating the SOD-bound metal ion with a complexometric reagent, such as pa, and following the aqueous metal ion concentrations with metal sulfide ISEs. We apply this method in the quantitative removal of Ag( I) from Ag,Ag,SOD by complexation with I- and CN- and extend it to nearquantitative removal of Cu(I1) from Cu.J&SOD by complexation with pa and ethylenediamine (en).

MATERIALS

AND

METHODS

Reagents The metal ion sources were commercially available standard solutions: 100 InM Cu(NO& from Orion, and 1000 ppm AgNOB from Fisher. All other reagents were AR grade and used without purification. Triply deionized water (Millipore) was used exclusively throughout the study. The concentrations of the complexometric titers (CN-, II, pa, and en) were determined by titration against the commercial metal ion standards and monitored by ISE. In particular the methods of Asplund (9) were followed in the titration of NaCN. Typically, I- solutions were ca. 5 mM, and those of the other titers ca. 10 mM.

VALENTINE

Protein Manipulation

and Preparation of Derivatives

Bovine liver CuzZnzSOD (SOD) was obtained from Diagnostic Data, Inc. (Mountain View, CA), as a lyophilized powder. Protein concentrations were determined spectrophotometrically, with 6258 nm= 10,300 and 2920 M-l cm-’ for the native SOD and the apoprotein, respectively. The preparation of the apoprotein has been described elsewhere (10). Metal-substituted derivatives were prepared by the direct addition of stoichiometric amounts of apoprotein to a dilute solution (ca. 8 X 10d2mM) of the metal ion made by the dilution of the commercial standard in the appropriate buffer. Measurement of Free Metal Ion Activity ISE measurements were performed with an Orion 901 digital ion analyzer equipped with a Model 605 electrode switch at RT (1%22°C). Metal ion activities were determined either by an Orion (94-15a) Ag,S ISE for Ag+ or by a Cu2+-doped Ag,S ISE for Cu2+ (Orion Model 9429a), referenced against a single junction electrode (Orion Model 9001) filled with a 0.5 M silver-saturated solution of KCl. Prior to use the electrodes were prepared in the manner of Avdeef et al. (11). A chart recorder (Houston Instruments Model 200) which was adjusted to measure millivolts vs time was connected to the ion analyzer in order to observe the time course of electrode equilibration. ISE Calibration The Cu ISE was calibrated against ethylenediaminel Cu2+ buffers after the method of Avdeef et al. (11). In some cases, calibration was carried out against cupric ion buffers consisting of pa at appropriate pHs based on the binding constants reported by Aderegg (12). The silver ISE was calibrated from pAg = 3 to 15 against a series of Ag’-saturated solutions in which the free metal ion concentration was buffered by NaI, KSCN, or NaCl, as well as against unbuffered AgNOB solutions at pAg = 3, 4, and 5.3 The solubility products used for calculating the free silver concentration in the buffers were taken from Ref. (13). The ionic strength of all standards and titration solutions was adjusted to 100 mM with NaN03. Complexometric Titrations of Protein-Bound Ag+ and Cu” A typical titration was carried out in the following manner. A solution of the metal ion-protein derivative 3 Aqueous metal ion concentrations are given as pM, which we define as pH is defined; i.e., pM = -log[M](.,,. In this study M = Cuzc (PCU)

or&+

(p&L

COMPLEXOMETRIC

TITRATIONS

OF PROTEIN-BOUND

METAL

IONS

33

was prepared by the addition of the protein to a dilute solution of the metal ion of interest. The total volume of the solution was typically 25 ml and contained ca. 2 pmol of metal ion. A total of ca. 0.5 pmol of apo-SOD was added to the metal ion solution. The protein-metal ion solution was allowed to equilibrate before complexometric reagents were added. Equilibration was monitored by ISE. Equilibrium was defined as that point when the millivolt reading changed less than 0.5 mV/h. Upon equilibration, which typically was reached in 30 min, the metal ions bound to the protein were titrated with the appropriate complexometric reagent. Iodide and cyanide were used to titrate Ag’, and en and pa to titrate CL?‘. In addition, an identical protein-free solution was titrated for metal content, and this titration served as a control for the protein titration (vide infra).

of buffer-bound and free metal ion and can be related to Mb

Evaluation of Titration Data

where B is the uncomplexed buffer concentration. Since we choose conditions for our experiment so that the total buffer concentration, B,,, is much greater than the total metal ion concentration, M,,, we can approximate B in Eq. [5] by B0 and (B,)” is therefore a constant. Typically, in our experiments, B0 is 100 mM and M0 is less than 0.1 mM. The apparent buffer-binding constant, which appears in Eq. [3], is defined, then, as

In the complexometric titration of protein-bound metal ions, the observables are pM and the amount or total concentration of added complexometric titer, Lo, which is incremented in the course of the titration. The constants are the total amounts, or initial concentrations, of the added protein and metal ion, which we designate by POand MO. From these quantities, it is possible under specific conditions to calculate the concentration and change in concentration of protein-bound metal ion, [MP], and to obtain the useful quantity R, which is called the protein metal content, and is defined as

PI

R = [MP]/P,.

This quantity is functionally dependent on pM. An analysis of this functionality leads to an understanding of the behavior of the protein metal binding. A good example of such an analysis is the study carried out by Hirose et al. (6) on the binding of Cu2+ to apo-SOD. To evaluate R for each value of pM, we need to determine [MP], the concentration of bound metal ion. We can express [MP] as [MP] = M,, - M - [ML,]

- [MB,],

Kb = [MB,]/M and thus we obtain [MB,] [MB,]

[31

as = M-K&.

[41

Equation [4] is derived in the following manner. Complex MB,,, is formed when m molecules of some buffer binds the metal ion. This equilibrium is characterized by the constant KB. It can be shown that the concentration of the metal ion-buffer complex can be calculated with the expression [MB,]

= Ke.M.Bm,

K;s = KB. (B,)“.

[51

[61

Thus, the amount of metal ion complexed by the buffer can be related simply to the observable M and calculated Eq. [41. In addition to [MB,], we are also required to determine [ML,] in order to solve Eq. [2] for the proteinbound metal ion concentration, [MP]. There are three casesto consider in obtaining values for [ML,]. The first case arises when the metal-binding constant of the protein is much greater than that of the complexometric reagent. We will not discuss this case as it would be impractical to carry out the titration in those circumstances. The second case arises when the complexometric reagent quantitatively removes the metal from the protein and this reaction can be approximated by

PI MP+nL-tML,+P.

where M, [ML,], and [MB,] are, respectively, the “free” or aqueous, reagent-complexed, and buffer-complexed metal ion concentrations. M is measured as pM, but it is usually insignificant compared to the other quantities except at large values of R, that is, when the metal-binding sites are saturated. [MB,,,] can be determined by a metal ion titration of the buffer alone in order to obtain the apparent buffer-binding constant Ka . This remains a constant only under the condition that the concentration of the buffer is much greater than the concentration

I71

If n = 1, then this quantitative removal would be stoichiometric under all conditions as well. Even when n > 1, there exist pM ranges where the complexation is stoichiometric and in such ranges, ML, = Lo/n. Thus, in this case where the metal ion is removed from the protein both quantitatively and stoichiometrically, we can calculate the concentration of the protein-bound metal ion, [MP], and R for every value of pM except at the equivalence point, where the approximation inherent in

34

ROE

AND

I6..a

12..

I a

.’ .=’ d

4 .’ 1 0

5

. 4 15

10 x

La

15

10

20

25

5M

A

0

2

4

6

e

lb

1.2

lb

VALENTINE

which binds the metal ion in a 1:l ratio (n = 1 in Eq. [7]) and Fig. 1B shows the case where n = 2. The control titrations are also simulated in the figure. The titration of the protein-bound metal ion can be considered quantitative if the equivalence points of both the protein titration and the control titration coincide and correspond correctly to the total amount of metal ion present in the solutions (cf. Figs. 1A and 1B). The titration of the protein-bound metal ion can be considered stoichiometric when no break in the titration curve is observed except at the equivalence point (cf. Fig. 1). The third case involves the use of a complexometric reagent for which the metal ion-binding affinity is comparable or slightly greater than the affinity of the protein and where the control titration (i.e., in the absence of protein) is essentially quantitative. Figures 2A and 2B depict computer simulations of such titrations for the cases where n = 1 and n = 2. Note that there are no apparent equivalence points for the simulated protein titrations and that only at large values of L,, do the two

lb

FIG. 1. Simulations of quantitative complexometric titrations of metal ion M. Solid curves are simulations of titrations by ligand L of 8 X lo-’ mM metal ion solutions, which contain no protein and which are buffered; broken curves represent titrations of 8 X lo-’ mM of protein-bound metal ion by ligand L in an identically buffered solution as the protein-free solution. Protein concentration is assumed to be 8 X lo-’ mM and to contain one metal ion-binding site, which has a binding constant I&. The solid curves were calculated on the basis of the simple ligand-metal ion coordination reactions which are characterized by the stability constant /3i for the binding of the metal ion by a single equivalent of L for panel A, and & and pz for the sequential coordination of the metal ion by the first and second equivalents of L for panel B. In addition, L, = 8 X 10m2 mM for panel A and 16 X 10m5 M for panel B (see text). The apparent metal ion-buffer-binding constant is given as Kb (see text for Eq. [6]). (A) Log pi = 14, log Kp = 10.5, and log Kb = 3; (B) log & = 11, log p2 = 20, log K, = 10, and log Kb = 0.4.

Eq. [7] breaks down, namely that the titration is quantitative. In order to ascertain whether the complexometric titration of protein-bound metal ion is quantitative, a control titration of a protein-free solution identical in all other ways to the composition of the protein titration solution should be carried out in parallel. Figure 1 contains computer simulations of quantitative and stoichiometric titrations of a protein-bound metal by a complexing reagent. Figure IA depicts titration by some reagent

I

0

b

0

l

2

4

.

6 Lox

L,

%

.

10

12

14

16

105H

FIG. 2. Simulations of near-quantitative complexometric titrations of metal ion M. Please see the legend to Fig. 1 for a complete description. (A) Log & = 11, log Kp = 10.5, and log Kb = 3; (B) log P1 = 10, log flz = 19, log K, = 14, and log Kb = 5.

COMPLEXOMETRIC

TITRATIONS

curves merge into each other, indicating the completion of the titration. Now, in order to determine [ML,] for use in Eq. [Z], we must determine L, the free ligand concentration, and subtract its value from the total concentration of added ligand, Lo. Three procedures may be adopted in order to determine L. (i) At points during the titration, the free ligand concentration may be measured by some method, such as ultrafiltration of the sample followed by titration of the filtrate by the metal ion for L. This protocol may be accurate, but it is time consuming and again reduces the determination of protein-metal ion-binding constants to a series of experiments, rather than one. (ii) At each point during a titration, L may be calculated on the basis of published stability constants and the values of Lo and pM, as well as ionic strength and pH. This method requires that the constants, the temperature, and the solution conditions are known accurately or else errors will accumulate in the calculation of L. (iii) At each point during the course of the titration of protein-bound metal L, the free ligand concentration, may be determined by comparison with a control titration. The control titration is carried out under conditions identical to those of the protein titration (i.e., the same volume, solution composition, and metal ion concentration) except that no protein is added. In this way reliance on published stability constants is obviated. We chose this method for determining the free ligand concentration during the titrations (vide infra). Determination

of the Free Ligand Concentration

As discussed above, we chose the comparison between a control titration, where the free ligand concentration is known, and the titration of the protein-bound metal ion to determine [MP] which is necessary for the calculation of the metal ion content, R. Figures 2A and 2B depict simulated curves of both the control titrations and the titrations of the protein-bound metal ion by some complexometric reagent (see figure legend for specifics). These simulations are presented as pM vs the total concentration of added ligand, Lo. We define the equivalence point of a control titration as L,, which is equal to nMo, where M0 is the total concentration of metal ion in the solution and n is defined as in Eq. [7]. As we demonstrate below for three cases, we can calculate the concentration of the free ligand during the course of the complexometric titration of protein-bound metal ion from the total concentrations of added ligand in the protein titration, (Lo),, and the control titration, (L,), , at each value of pM, when the control and the protein titrations are carried out identically. As can be seen from Fig. 2, the values of (L,), in the regions of interest are greater than L,. The free ligand concentrations at the same pM in the protein solution and the control

OF

PROTEIN-BOUND

METAL

35

IONS

titrations will differ until all of the protein-bound metal ion has been removed and complexed. We define the free ligand concentration in the protein solution as L,, and L, for the control. Finally since the ligand binds essentially quantitatively to the free metal ion, we note.that when &I), ’ L, (L,),

WI

= L, + L, = nMo + L,

and (L,), = n[ML,]

+ L, = nM, - [MP]

+ L,.

[Bb]

Equations [Ba] and [Bb] only hold true when (L,), > L,. We now consider three cases of complexation: (i) the complexometric reagent precipitates out the metal ion in a 1:l complex, (ii) the reagent complexes the metal ion in a 1:l ratio and remains in solution, and (iii) two equivalents of reagent complex the metal ion which remains in solution. The first case is depicted by MP + L ti MLCppt, + P,

PI

where MP is the protein-bound metal ion, L is the free ligand, ML is the insoluble complex, and P is the free protein. The insoluble complex is characterized by a solubility product so that Ma L = constant. This is true for both titrations, so that at a given value of M, the aqueous metal concentration, the free ligand concentrations are the same; i.e., L, = L,, assuming that the solution is saturated in metal ion. It can be shown then from Eqs. [Sal and [Bb] that W’l

DOI

= (Lo), - (LoA,

where (L,), and (L,), are the total added ligand concentrations in the control and protein titrations, respectively. Equation [lo] only holds true beyond the equivalence point of the control titration where ML are MP are the major species in solution and MB and M are insignificant by comparison, In a similar manner, [ MP] may be calculated from the values of (Lo), and (L,), for a given pM when the reagent complexes the metal ion in a one-to-one soluble complex. This reaction may be written as

Ull

MP+L+ML+P. The metal written as

ion/ligand

binding

M+LsML,

reaction

itself

may be

WI

36 where

ROE

& is the equilibrium

constant

AND

and is defined by

p = [ML1 ’

VALENTINE

construct the quantitative relationship between R or [MP] and the free metal ion concentration and thus to determine the binding constants.

M-L’

Experimental At a given value of M, L, and L, can be related by

M _ (ML), _ (ML), L*P1 Lt.& ’

D41

where (ML), and (ML), represent the concentrations of the metal ion complex in the control and protein titrations, respectively. Since the titration has been carried beyond the equivalence point of the control titration, only ML is the major metal ion species in the control solution, and only ML and MP are major species in the protein titration. Thus, we can approximate (ML), by MO and (ML), by MO - [MP]. By substitution of (ML), = MO and (ML), = MO - [MP] into Eq. [14] and by use of Eqs. [8a] and [8b] where n = 1, we can solve for [MP]. The result is

Mp = MO- {(Lo), - (Lo),} (Lo), * Figure 2A depicts a simulation where a complexometric reagent removes protein-bound metal ion in a one-toone fashion, but not quantitatively. Equation [ 151 would be appropriate in such a case. In the same manner, a relationship for [MP] can be derived in the third case, where two equivalents of complexometric reagent are required to remove a metal ion from the protein as a soluble complex, ML2. As done above for the simpler case (Eq. [14]), L, and L, can be related at a specific value of pM by

MO_ MO- W’l L,‘L,2

.

By algebra we obtain

WPI = M, - {&,)t - A}/%

P71

where

A={(Lo), - 2Mo)’ 4Mo

(Lo),

8Mo ((Lo), - 2Mo}’

This last case formulated by Eq. [18] is specifically depicted in Fig. 2B. Thus we have shown that in three cases where the affinity of the complexometric reagent is not enough relative to the protein-binding constant to remove protein-bound metal quantitatively, it is still possible to obtain enough information from the titration to

Design

There are several conditions which must be met in the design of an experiment to measure the affinity of a macromolecule for a metal ion by complexometric titration. First, the metal ion binding to the macromolecule must be shown to be freely reversible. Second, it must be shown that an equilibrium among the macromolecule, the metal ion, and the complexometric reagents can be reached in some reasonable time (i.e., less than a day). Finally, it must be shown that the complexometric reagent retains a specific binding stoichiometry over the pM range studied. This final point is taken up in more detail below. The selection of the appropriate complexometric reagent is perhaps the most important detail in the design a complexometric titration of protein-bound metal ions. Ideally, the reagent should quantitatively remove the metal ion from the macromolecule in a 1:l ratio. This would be the easiest to evaluate. However, as long as the complexometric reagent can stoichiometrically complex the protein-bound metal ion in a reasonably strong fashion (i.e., the total concentration of metal concentration is complexed entirely by only one or two times excess of ligand), the methods discussed above may be used. In addition, it is very important that the complexometric reagent complex the metal ion in the control titrations quantitatively. For example, in this study we selected NaI as the 1:l complexometric reagent of protein-bound silver at low pHs. This is a perfect choice in that it satisfies the requirements stated above and that it is a very strong 1:l complexer of Ag+, giving both quantitative control titrations and titrations of the protein-bound metal ion. We also employed CN- as the complexer of Agf at higher pH. It can be shown that in the pM ranges of the experiments carried out cyanide binds silver in a 2: 1 ratio. This can be demonstrated mathematically using published values for the constants describing the binding of CN- to Ag+. Similarly, it can been shown that en and pa complex Cu2+ in a 2:l fashion over the pCu range studied. We will derive below a general expression to evaluate under what experimental conditions a particular complexometric reagent would bind some metal ion essentially stoichiometrically in a 2:l manner, rather than a 1:l complex or as a 1:l precipitate (i.e., AgCN). Complexes of a higher ligand-to-metal ion stoichiometry are ignored in this treatment. In fact, in the experimental systems studied in this work, complexes of stoichiometry greater than 2 are negligible. Assume that f(2) is the fraction of total complexed metal which is complexed in a 2:l ligand-to-metal ion ratio. This may be expressed by

COMPLEXOMETRIC

TITRATIONS

OF

PROTEIN-BOUND

P2.L f(2) = p1+ p,&

s

METAL

37

IONS

B

E

where all the terms have been defined above. The stoichiometry of the binding then is an explicit function of the free ligand concentration, L. If we stipulate that the fraction of ligand-bound metal ion bound in a 2:l ratio must exceed 90% (i.e., essentially stoichiometric), then it follows from Eq. [ 191 that

a

E

a

E

a

0 a

0

0

0

0

0

E

0

0

0

0

*- E

a 0 0

a

a

L>9.$

f

2

0

5

10

15

20

(La)

When this condition is fulfilled the ligand will bind the metal ion in a ratio of 2:l. It is more useful to determine at what pM value Eq. [20] would hold true. This is dependent on the specific experimental conditions, i.e., the total concentration of metal ion present in the solution and what fraction is bound by the ligand. The free concentration of the metal ion, M, can be expressed as

M=

WLlo /3,-L + ,&.L2’

P21

x

30

3.5

40

10 5M

16

0

[23

where [ML&, in this instance is the total concentration of metal ion bound by the ligand. By substituting Eq. [20] into Eq. [21] we obtain the condition for M which will lead to greater than 90% stoichiometry of two ligand molecules per metal ion:

25

o”O

0oaOa

4

I1

0

a0

O0

a0

,

10

5

0

CL.1

FIG.

15 x

3. Complexometric titrations X lo-* mM Ag+ or Cu*+ in the presence sence of (open symbols) 1.8 X lo-’ mM of Ag+ in 50 mM borate buffer, pH 9.3; of Cu2+ in 50 mM borate buffer, pH 10.1. Figs. 1B and 3A and Figs. 2B and 3B.

20

25

10 St4 of solutions containing 7.4 of (filled symbols) or the abapo-SOD: (A) NaCN titration (B) ethylenediamine titration Note the similarities between

Finally we obtain the lower limit of pM for which the stoichiometry is 2:I as pM > -log[ML,],, pM > 2 - log[ ML,&, + 2 log ,6i - log & .

[231

Assuming that the complexometric reagent does not significantly coordinate the metal ion in ratios greater than 2:1, then, when Eq. [23] is satisfied by the experimental conditions, the complexometric titration can be considered stoichiometric with a ligand-to-metal ion ratio of 2: 1. This same information may be garnered less quantitatively by inspection of the control titrations as to where the break points and the buffer ranges occur. This will be discussed under Results and Discussion. Similar reasoning as above leads to the derivation of an equation which sets the lower limit for pM to ensure that 90% of a complexed metal ion is in the soluble ML2 rather than as the precipitate ML,,, . The lower limit is expressed as

+ 2 log KsP- log ,&,

1241

where KS,,is defined as the solubility constant of the 1:l precipitate. RESULTS

AND

DISCUSSION

The Complexometric Titration of SOD-Bound Ag’ Figure 3A depicts the titration of both 2 pmol of free Ag+ (control) and 2 pmol of protein-bound Ag+ by CNin 27 ml of 50 mM borate buffer, pH 9.3. We note that the equivalence points of each titration coincide, indicating that the protein titration was quantitative (cf. Fig. 1B). The final stoichiometry of the titration of the proteinbound Ag+ was two ligand molecules per metal ion. In addition the stoichiometry was 2:l at each point of the titration of the protein-bound Ag+. This last point may be demonstrated by Eq. [24] which will show that under

38

ROE

AND

these conditions, 2 eq of cyanide binds each complexedsilver ion. For the cyanide binding of Ag+ the relevant constants at pH 9.3 are log KsP = -15 and log & = 20. If we assume that l/10 of the available Ag+ in the experiment is complexed by 2 eq of cyanide (i.e., [AgCN;] = 7.4 X low6 M), we obtain that pAg must be greater than 4.9. Figure 3A clearly shows that at no point during the titration did pAg dip below 8, indicating that no significant amount of AgCN(,, should have formed during the titration. Alternatively, the observation that only a single break in the protein-bound metal ion titration occurs at the 2:l ligand/metal ion equivalence point indicates that the titration was essentially stoichiometric. A break at the 1:l ligand/metal ion ratio would be expected if the ligand binding was sequential (cf. simulated control titrations in Figs. 1B and 2B). In addition, we also found the titration of SOD-bound silver at pH 5.5 by NaI to be quantitative (data not shown). The stoichiometry in the case of iodide binding of silver was found to be 1:l over the pAg range of 4 to 11. Figure 4A contains plots of R (the protein metal content) vs pAg for the cyanide titration of protein-bound silver ion and the iodide titration. The solid curves drawn through the data are theoretical fits of the data to a 4-eq binding function, which has been described in more detail elsewhere (14). Explicitly, the function is written as

R=

2K1M + 4K, K,M2 1+K1M+K1K2M2’

VALENTINE

4

3

\ 0 mh\. 0

0

R 2

0

a

0

5

0

7

9

11

13

0

i 15

PCU

P51

This equation describes the binding up to 4 eq of metal ion per dimer of protein in two distinct binding sites. In addition the occupancy of the second type of site is assumed to be dependent on the occupancy of the first site; that is, the mode of binding is sequential. In Eq. [25], M is the free metal ion concentration and Kl and K2 are the pH-dependent conditional binding constants which describe the metal ion binding to the respective sites on the protein. The fitting procedure consisted of minimizing the sum of the squared error between observed values of R and those calculated from Eq. [25]. Best-guess values were made for Kl and K2 and then the value of each constant was varied independently and sequentially until the sum of the squared errors had been minimized. The search increment for this procedure was chosen to be 0.05 log unit. We estimated by nonlinear least-squares methods (15) the uncertainty in the values of the binding constants to be approximately kO.10 log unit. The binding of Ag+ at pH 5.5 is clearly biphasic with a break at R = 2. The fit gave log Kl = 10.3 and log Kz = 6.2 within the increment of search of 0.05 log unit. By contrast, the silver-binding behavior of SOD at pH 9.3 did not exhibit a break at R = 2. This observation sug-

FIG. 4. Equivalents of protein-bound metal ion per dimer of SOD (R) as functions of pM. Solid curves are fits to the binding model described by Eq. [%I. (A) Ag+ binding by apo-SOD in a 100 mM acetate buffer, pH 5.5 (open symbols), and at pH 9.3 in a 50 mM borate buffer (filled symbols). (B) Cu*+ binding by apo-SOD in a 100 mM acetate buffer, pH 5.5 (circles), and at pH 10.1 in a 50 mM borate buffer (squares). The solid symbols in panel B were calculated from atomic absorption measurements.

gests that at this pH the affinity of each of the two distinct types of metal-binding sites for Ag+ is nearly equal. In fact the fit gave values of 10.8 for log Kl and 9.7 for log K2 within the search increment of 0.05 log unit, a difference of only one order of magnitude. The Complexometric

Titration

of SOD-Bound

CL?’

Figure 3B depicts the titration of Cu2+ bound to SOD by en at pH 10.1, as well as the control titration. In contrast to the silver titration curves, the copper curves (experimental and control) do not have identical equivalence points. In fact, there is no clear equivalence point in the titration of Cu2Cu2SOD. By inspection (cf. Fig. 2B), we determined that this titration of copper bound to SOD by en is not quantitative and are required to use Ea. ~ ~. 1171 Lo ~ to calculate the metal content at each value of

COMPLEXOMETRIC

TITRATIONS

pCu. Note that the stoichiometry (2:l) remained the same over the entire pCu range studied (10.5 to 14.5). By substituting into Eq. [23] the values for log & and log & at pH 10.1 (10.3 and 19.1, respectively) and assuming that [ML,lo is l/10 of the total concentration of cupric ion (i.e., 7.4 X lop6 M), we obtain as the lower limit of pCu, where the stoichiometry of at least 90% of binding is 2 en/Cu’+, 8.6, which is significantly smaller than the minimum titration pCu value of 10.5. CuaCuzSOD was also titrated by pa at pH 5.5 over a pCu range of 5 to 9.5. Below pCu 7, however, Eq. [23] indicates that a significant fraction of the bound species was the monocoordinated complex (pCu 6: f(1) = 40%). This led to a point by point calculation of the value of the free ligand for data points measured in the pCu range of 5 to 7 in Fig. 3B. This calculation is easily made as the solution of a quadratic equation on the basis of the equilibrium constants. The first datum point in Fig. 4B, however, was calculated from the direct measurement of unbound Cu’+, when no complexometric reagent had been added. We found the titration similar to the en titration in that it was not quantitative so that Eq. [17] was required for the calculation of [MP] and the metal content, R, at pCu greater than 7. Figure 4B contains plots of metal ion content vs pCu at each pH studied. These results are very similar to the silver results in that at the lower pH biphasic behavior is observed in copper binding with a break at R = 2 and that the affinities of both types of binding sites increased with higher pH. In addition, similar to the silver-binding behavior, no clear break is observed at R = 2 in the high pH copper-binding curve, indicating that the affinity of both sites for cupric ions is similar. The binding constants obtained by the fitting procedure were log K1 = 8.95 and log K2 = 4.95 at pH 5.5 and log KI = 14.45 and log K2 = 11.8 at pH 10.1, within the search increment of 0.05 log unit. Unfortunately, no previous study has quantified the affinity of SOD for Ag+, and therefore no comparison can be made with our results. On the other hand, Hirose et al. (6) have carried out an elegant equilibrium dialysis study of the binding of Cu2+ to SOD and have reported conditional binding constants over a large range of pH. Because they assumed that each of the metal-binding sites on the dimer was sequentially occupied and had different affinities for Cu2+ , they reported four constants compared to the two we report. For comparison purposes we quote Hirose et al’s results as K1 and K2, which are averages of their KI and K2 values and of their K3 and K4 values, respectively. At pH 5.5, they reported log KI = 11.8 and at pH 5.4, log K2 = 6.0. At pH 5.5, we obtained values of 8.95 and 4.95 for log KI and log K2. At pH of 10.0, they reported 15.75 and 14.85 for log KI and log K2, whereas we obtained values of 14.5 and 11.8 at pH 10.1. The binding constants calculated in our study are consistently lower than the values quoted from the work of

OF

PROTEIN-BOUND

METAL

IONS

39

Hirose et al. These differences suggest that some systematic error has occurred in either our method or that of Hirose et al. We point out that the values of the binding constants determined by Hirose et al. were calculated relative to the magnitudes of the binding constants of the competitive binder which they employed in the equilibrium dialysis experiments, namely pa. The authors used those values reported by Anderegg (12) for the complexation of Cu” by pa. However, Anderegg determined these stability constants at 25°C and Hirose et al. carried out their experiments at 4°C a significant difference in temperature. In addition, the temperature dependence of the metal ion-binding behavior of SOD is not known. Consequently, the temperature difference between our experimental protocol and that of Hirose et al. may be enough to explain the difference between our results. However, in order to confirm that our treatment was accurate at excess of free ligand (ca. 2:l excess of free pa or en to total metal ion present in solution), the final point on both curves in Fig. 4B was calculated after AAS determination of protein-bound copper. This determination was carried out by measuring the copper concentration of the protein solution and the proteinfree filtrate, which was obtained by ultrafiltration at 5000g (Amicon). The difference between the metal ion concentration of the protein solution and that of the filtrate was [MP]. The pCu value was measured by ISE. Note that the AAS data fall nicely on the curves in Fig. 4B, supporting the conclusions that our method is reliable in the presence of excess of ligand and that our values for the binding constants are accurate. In any case, this example nicely underscores one of the advantages of our method, that it is essentially independent of literature values of the metal-binding constants of complexometric reagents such as pa.

SUMMARY

We have described here a method for measuring metal-binding constants of macromolecules, which is much faster than equilibrium dialysis, is independent of literature values of metal ion-binding constants of complexing agents, and is resistant to macromolecular interference with the monitoring electrode. The method consists of titrating metal ions bound to some protein or other macromolecule with a complexometric reagent, such as ethylenediamine, and monitoring the free metal ion activity throughout the titration by ISE. We have demonstrated the efficacy of the method by determining the cupric and argentous binding constants of the apoprotein of bovine Cu,Zn-superoxide dismutase at both low and high pHs. The Ag’ titrations were found to be quantitative, the titrations of SOD-bound CuZt were not quantitative, and interpretation of the data therefore required comparison with protein-free control titrations.

40

ROE AND VALENTINE

ACKNOWLEDGMENTS The advice from A. Avdeef is greatly appreciated. supported by USPHS Grant GM28222 (J.S.V.).

This

work

was

7. Avdeef, A., Zelazowski, 24,1928-1933. 8. D’Orazio, 9. Asplund,

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