604
J. Phys. Chem. B 2008, 112, 604-611
Determining Thermodynamic Parameters from Isothermal Calorimetric Isotherms of the Binding of Macromolecules to Metal Cations Originally Chelated by a Weak Ligand† Lian Hong, William D. Bush, Lanying Q. Hatcher, and John Simon* Department of Chemistry, Duke UniVersity, Durham, North Carolina 27708 ReceiVed: July 22, 2007; In Final Form: September 13, 2007
An accurate data analysis method for determining stoichiometry and thermodynamic parameters from isothermal titration calorimetry data for the binding of macromolecules to metal cations that are solubilized through an association with a weak ligand is presented. This approach is applied to determine the binding constant for the association of Cu(II) to the first 16 residues of the Alzheimer’s amyloid β peptide, Aβ(1-16) under conditions where Cu(II) is rendered soluble through weak binding to glycine. At pH 7.2 and 37°C, a binding constant of 1.5 × 109 M-1 (Kd ) 0.7 nM) is determined for the association of Cu(II) with Aβ(1-16).
Introduction Isothermal titration calorimetry (ITC) is an ultrasensitive technique monitoring precise changes in heat for a chemical reaction and can resolve the binding stoichiometry, binding heat, and binding constant in one experiment. In determining these thermodynamic parameters, one compound in solution is generally added in small increments to a solution containing its binding partner, and the heat change is measured for each addition of the compound solution. Determination of accurate thermodynamic parameters from such ITC data requires that the experimental isotherms be modeled in terms of the chemical processes that occur upon mixing the two solutions, taking into account how each process contributes to the measured heat.1-5 ITC has the advantage that detection of the binding properties requires no modification of the compounds to be studied, and thereby it is possible to determine the binding parameters of biological macromolecules in their natural state. Owing to these unique strengths, ITC has been widely used to quantify the interactions of ligands and biological macromolecules.6-23 One area of current interest is the determination of binding constants of metals (e.g., Ca(II), Cu(II) and Fe(III)) to biological macromolecules.10,12,16,18,21,22,24-30 In analyzing ITC data from such experiments, there is one important issue that has not been quantitatively addressed, but needs to be in order to obtain accurate thermodynamic parameters. Specifically, metal cations such as Cu(II) and Fe(III) are poorly soluble in aqueous solutions at physiological pH.31 Thus, in order to achieve the millimolar concentration levels that are generally required for ITC, a weak ligand is added to the solution to solubilize the metal cation.5,18,21 The binding between the metal cation and this solubilizing ligand is generally not taken into account in modeling the ITC data. However, it is the case that the measured apparent binding constant depends on both the binding constant of the metal to the biological system of interest and the binding constant of the metal to the weak ligand. In such cases, there have been efforts to determine the desired binding constant, K, from the measured apparent binding †
Part of the “James T. (Casey) Hynes Festschrift”. * Corresponding author. Address: Duke University, Box 90034, Durham, North Carolina 27708. Phone: (919) 660-0330. Fax: (919) 684-4421. E-mail:
[email protected].
constant, Kapp.10,17,32,33 Thompsett and Zerovnik suggested correcting the apparent binding constant by direct multiplication of the metal-ligand binding constant.10,17 However, it is not quite this simple; it has been shown that a competitive binding reaction in ITC gives Kapp ) K/(1+KL[L]), where KL and [L] are the binding constant of the weak ligand to the metal, and the concentration of unbound weak ligand, respectively.32 Thus, the deconvolution of Kapp needs both KL and [L], the latter of which varies during the course of the ITC experiment. One possible way to overcome the variable nature of [L] is to use an excess amount of weak ligand, such as choosing a buffer that weakly chelates the metal ion of interest. The buffer is then present in both the injectant and reaction cell solutions and is in excess compared to the metal. Therefore the concentration of unbound ligand will remain essentially constant during the titration. As an example, Zhang et al. studied the interaction of Cu(II) to bovine serum albumin (BSA) using Tris as both a buffer and a weak ligand stabilizing Cu(II).33 The binding constant obtained for Cu(II) binding to BSA by this method was shown to be similar to other values obtained by techniques other than ITC. Thus, this particular approach can provide an accurate determination of the binding constants. However, one does not want to be constrained to studying metal-biological interactions in specific buffer solutions that guarantee the solubilization of metals and the need to use these buffers in excess so that the thermodynamic models can be simplified. To broadly address this issue, this paper develops a comprehensive approach that accounts for the general case in which the concentration of free ligand is directly taken into account. This work then opens up the ability to use ITC to study the interactions between metal-chelates and macromolecules and, from the data, determine the specific binding parameters for the metal to the macromolecule. Theory For a typical ITC experiment design, the macromolecule (P) in the reaction cell is to be titrated with metal cations (M) from the injecting syringe:
P + M T PM
10.1021/jp075747r CCC: $40.75 © 2008 American Chemical Society Published on Web 11/21/2007
(1)
Thermodynamics of Macromolecule-Metal Chelate Binding If P has a single set of identical binding sites for the metal M, then the subsequent binding constant (K) of M to P can be defined as
J. Phys. Chem. B, Vol. 112, No. 2, 2008 605 Thus the total amount of weak ligand [L]T, which can be calculated for each injection, is n
K)
Θ (1 - Θ)[M]
(2)
where Θ is the fraction of sites in the macromolecules occupied by metal ions, and [M] is the concentration of unbound metal ions. It can be deduced from eq 2 that
Θ)
K[M] 1 + K[M]
(
j × [MLj] ) [L] + ∑ j)1
[M]T - nP × [P]T ×
(4)
where nP is the number of sites in one macromolecule, and [P]T is the total concentration of macromolecule. When a weak chelator (L) is added, the solubilization of the metal by the ligand (L, with a 1:n stoichiometry) is represented by
1 + K[M]
)
n
×
j × Fj ∑ j)1
(11)
n
[M]T ) [M] + [PM] +
K[M] 1 + K[M]
K[M]
and the total amount of metal ion [M]T, which can be calculated for each injection, is
(3)
Thus, the concentration of sites in macromolecules that are bound with metal ions, or the concentration of metal cations that are bound with the macromolecules (PM) can be represented as
[PM] ) nP × [P]T ×
[L]T ) [L] +
K[M] 1 + K[M]
(
[MLj] ) [M] + nP × [P]T × ∑ j)1
+ [M]T - nP × [P]T ×
K[M] 1 + K[M]
)
n
Fj ∑ j)1
(12)
From eq 11, the fraction of occupied sites in the macromolecules, Θ, can be written as a function of [L],
Θ)
([L] - [L]T)/a + [M]T K[M] ) 1 + K[M] nP × [P]T
(13)
where n
M + L T ML, with KL1 ) ML + L T ML2, with KL2 )
[ML] [M][L] [ML2] [ML][L]
a) (5)
(6)
Θ K × (1 - Θ)
[M] ) [MLj] [MLj-1][L]
(7)
.....
[MLn] [MLn-1][L]
MLj + P T PM + jL, 0 e j e n
Θ K × (1 - Θ)
(9)
Establishing these equilibria will largely determine the measured heat released or absorbed. It can be deduced that the percentage of chelated metal species MLj (defined as Fj) of all the metal species, except that bound with macromolecule ([M]T - [PM]), is
+ nP × [P]T × Θ + ([M]T - nP × n
(8)
When this metal-chelator solution is injected into the cell, the macromolecule competes with the weak chelator to bind to the metal cations:
(15)
By substituting eqs 13, 14, and 15 into eq 12, we obtain the following function f([L]), with [L] being the only unknown or unassigned variable:
f([L]) ) MLn-1 + L T MLn, with KLn )
(14)
On the basis of eq 13, the concentration of free [M] can be represented as
.....
MLj-1 + L T MLj, with KLj )
j × Fj ∑ j)1
[P]T × Θ) ×
Fj - [M]T ) 0 ∑ j)1
The numerical method (Secant method) is used to find the root of the above equation with calculated values for [P]T, [M]T, and [L]T and assigned values for K and np, which gives the concentration of free ligand, [L]. With resolved [L], the concentration of each species [M], [ML], ..., [MLj], ..., [MLn], [PM], and [P] can be calculated using eqs 10, 13, and 15. The heat upon each injection can be presented as
(
∆Q ) V0 H∆[PM] +
n
∑ j)1
(
j
∆[MLj] ×
(∑
HLt ∑ t)1
))
n
j
[L] Fj )
n
1+
∑ r)1
j
(
KLt ∏ t)1
[L]r
r
Vinj
j)1
)
KLt ∏ t)1
,1ejen
(16)
j
([MLj]S ×
HLt ∑ t)1
)
(17)
(10) in which V0 is the volume of the ITC reaction cell, H is the heat of metal ion binding to macromolecules, HLt is the heat of metal binding to the tth weak ligand L, Vinj is the volume of
606 J. Phys. Chem. B, Vol. 112, No. 2, 2008
Hong et al.
the injections, and [MLj]S is the concentration of MLj in the syringe, which can be determined as follows: In the syringe, where there is no macromolecule competing for metal ions, the total amount of ligand, [L]ST, is n
[L]ST ) [L]S +
j × [MLj]S ) ∑ j)1
(∑ ) n
[L]S + [M]ST ×
j × FjS (18)
j)1
where [M]ST is the total concentration of metal species in the injecting syringe, and FjS is the percentage of [MLj]S of all the metal-containing species in the syringe and is calculated as defined in eq 10, using the concentration of free ligand in the syringe [L]S. Thus, only one variable [L]S is presented in eq 18, and we use the Secant method to solve for [L]S and further obtain the concentrations of [MLj]S. To obtain a precise determination of the concentrations of each species and the heat change in the ITC reaction cell, the dilution of samples caused by the displacement of solution in the reaction cell upon each injection must be considered. Sigurskjold models the dilution factor (Di) for the ith injection to be Di ) exp(-Vinj(i)/V0), where Vinj(i) is the injecting volume of the ith injection.3 Using this model and taking Di into account, eq 17 can be rewritten as
( ) ( ( )) n
∆Qi ) V0(H([PM]i - [PM]i-1Di) +
j
HLt ∑ ∑ j)1 t)1
×
([MLj]i - [MLj]i-1 × Di)) - (1 - Di) × n
∑ j)1
j
([MLj]S ×
HLt ∑ t)1
(19)
Thus, we obtain nP, H, and K for the binding of metal (M) to macromolecule (P) by fitting the ITC experimental curve with eq 19. Finally, we consider how to correct for the heat of dilution. This heat of dilution is generally corrected by performing an ITC titration with ligand injected into buffer only under the same experimental parameters used to examine binding to the macromolecule.34 This “control” isotherm is then subtracted from the ligand-macromolecule data.34 However, when the injectant is a metal-ligand complex, the control isotherms contain contributions from both the heat of dilution and the heat of dissociation of the ligand-metal complex, MLj (1 e j e n). The concentrations of total M and L in the injection syringe are larger than those in the cell, and so the concentrations of L, M, and MLj (1 e j e n) in the cell will differ from that in the injection syringe and, moreover, will change with each injection. The extent of the dissociation not only varies with the total concentrations of M and L in the reaction cell, but also with the amount of macromolecule present. Thus the ITC curve created by injecting an M-L complex solution into buffer cannot be used as the background titration for the corresponding experiment with the biological macromolecule present. The direct subtraction of such a background curve from the titration of an M-L complex to macromolecules would yield inaccurate thermodynamic constants. To address this issue, we use an alternative method. Specifically, the constant heat observed following saturation of the
macromolecules present is subtracted from all data points of the titration.11 This constant is not explicitly considered in our theory. Thus it is essential to make sure an isotherm of a competitive binding without heat of dilution returns to zero at the end of the titration (ending heat) in order to correctly account for the experimental heat of dilution. It is clear that, with different binding affinities of metal to the weak ligand and different concentrations of reactants, the experimental time required for the baseline to go back to zero will differ. Care must be taken in choosing the experimental conditions to make sure the ending heat (not including the heat of dilution) is essentially zero. We will shortly examine simulations of competitive binding experiments in order to understand this effect on the titration and to guide in determining the range of experimental parameters for obtaining accurate thermodynamic values. Materials and Experiments Materials. CaCl2‚2H2O and anhydrous MgSO4 were purchased from Fisher Scientific. CuCl2‚2H2O, glycine, N-(2hydroxyethyl) piperazine-N′(2-ethanesulfonic acid) (HEPES) and ethylenediaminetetraacetic acid (EDTA) were purchased from Sigma-Aldrich. All reagents were g99% pure. The peptide amyloid β(1-16) (Aβ(1-16)) was purchased as a custom synthetic peptide, >95% purity, from Biosynthesis, Inc. (Lewisville, TX). All solutions were made with nanopure water (>18 MΩ, resistance). Simulation of Binding Isotherms. The binding isotherms of macromolecules titrated with an M-L complex are simulated for varying conditions using eq 19. The curves were generated using Igor Pro (Wavemetrics, Inc., Lake Oswego, OR) and are shown in Figures 1-3. Isothermal Titration Calorimetry. ITC measurements were carried out on a VP-ITC ultrasensitive microcalorimeter (MicroCal, Northampton, MA). All the solutions were degassed before titrations were performed. The data, specifically the heat normalized per mole of injectant, were obtained using ITC data analysis software and were subsequently analyzed with our thermodynamic model using Igor Pro (Wavemetrics, Inc.). Titration of CaCl2 by EDTA-Mg. This procedure was performed as follows: EDTA-Mg (0.67 mM, molar ratio 1:1) and CaCl2 (0.061 mM) were prepared in the same HEPES buffer (20 mM, 150 mM NaCl, pH 7.4 at 25 °C). During the titration, 7 µL of EDTA-Mg solution was injected in 5 min intervals into the CaCl2 solution in the reaction cell. The cell was stirred at 307 rpm to maintain homogeneous mixing. The titration was conducted at 25°C. Titration of Aβ(1-16) by Cu(Gly)2. This procedure was carried out as follows: Cu(Gly)2 solution (0.7 mM Cu(II) with 2.8 mM glycine) and Aβ(1-16) (∼75 µM) solution were prepared in HEPES buffer (20 mM, 150 mM NaCl, pH 7.2, at 37 °C). During the titration, 8 µL of the Cu(Gly)2 solution was injected in 5 min intervals into the peptide solution in the reaction cell. The cell was stirred at 307 rpm. The titration was conducted at 37 °C. The peptide concentrations were estimated by the BCA Assay (Pierce Biotechnology). Since we observed only one single set of binding in ITC and considering the length of Aβ(1-16), we suggest that the peptide-to-Cu ratio is 1:1, which has been suggested in previous works.35,36 Thus we set the stoichiometry as 1.0 when fitting the ITC isotherms using eq 19. Results and Discussions Simulation of Binding Isotherms. For all the simulations, we only consider the heat change resulting from the complex-
Thermodynamics of Macromolecule-Metal Chelate Binding
J. Phys. Chem. B, Vol. 112, No. 2, 2008 607
Figure 1. Simulated binding isotherms with varying KL (left) and HL (right). The simulated titration conditions are np ) 1, [P]T ) 0.06 mM, [L]T ) [M]T ) 0.7 mM, K ) 1.0 × 107 M-1, and H ) -5000 cal/mol. In the left plot, HL ) 3000 cal/mol, and, from left to right, KL is set equal to 1 × 102, 3 × 102, 1 × 103, 3 × 103, 1 × 104, 3 × 104, 1 × 105, 3 × 105, 1 × 106, 3 × 106, 1 × 107, and 3 × 107 M-1. In the right plot, KL ) 1 × 105 M-1, and, from left to right, HL is set equal to -10000, -8000, -5000, -3000, 0, and 3000 cal/mol. When K is small compared to KL, large heat outputs are observed for the initial injection points because the macromolecule concentration is large compared to that of the ligand, and can therefore extract metal ions from the ligand.
Figure 2. Simulated binding isotherms with varying K (1eft) and H (right). The simulated titration conditions are np ) 1, [P]T ) 0.06 mM, [L]T ) [M]T ) 0.7 mM, KL ) 1.0 × 105 M-1, and HL ) 3000 cal/mol. In the left plot, H ) 5000 cal/mol, and, from left to right, K is set equal to 1 × 104, 3 × 104, 1 × 105, 3 × 105, 1 × 106, 3 × 106, 1 × 107, 3 × 107, 1 × 108, 3 × 108, 1 × 109, 3 × 109, 1 × 1010, and 3 × 1010 M-1. In the right plot, K ) 1 × 107 M-1, and, from left to right, H is set equal to -11000, -8000, -5000, -2000, 1000, and 4000 cal/mol.
Figure 3. Simulated binding isotherms with varying KL’s (left) and K (right). The simulated titration conditions are np ) 1, [P]T ) 0.06 mM, [M]T ) 0.7 mM, [L]T ) 2.8 mM, K ) 1 × 109 M-1, KL1 ) 9 × 105 M-1, KL2 ) 4 × 104 M-1, H ) -8000 cal/mol, HL1 ) -300 cal/mol and HL2 ) -1500 cal/mol, unless varied as described below. In the left plot, K ) 1 × 109 M-1, and, from left to right, KL1 is set equal to 9 × 102, 2.7 × 103, 9 × 103, 2.7 × 104, 9 × 104, 2.7 × 105, 9 × 105, 2.7 × 106, 9 × 106, 2.7 × 107, and 9 × 107 M-1, with KL2 varying accordingly to keep the ratio of KL1/KL2 constant as 22.5. In the right plot, KL2 ) 4 × 104 M-1, and, from let to right, K is set equal to 1 × 106, 3 × 106, 1 × 107, 3 × 107, 1 × 108, 3 × 108, 1 × 109, 3 × 109, 1 × 1010, 3 × 1010, 1 × 1011, 3 × 1011, and 1 × 1012 M-1. The jink observed in the first two curves of the left plot arises because of the competition between ligand and macromolecule binding to the metal. During the initial part of titration, the metal is predominantly bound by the macromolecule. As the concentration of ligand increases, ligand binding competes with that of the macromolecule. The shift in equilibrium from macromolecule-bound to ligand-bound releases heat, while the binding of metal by macromolecules absorbs heat. The two processes have opposite signs in terms of the heat, and the competing equilibria and their dependences on concentrations cause the jink.
ation of metal to macromolecules and from the dissociation of metal-ligand complexes. The heat of dilution is not simulated. We focus on (1) whether the curve shape is sensitive enough
for adequate fitting to obtain a binding constant, and (2) whether the curve goes back to zero at the end of the titration (ending heat) to ensure the right correction for the heat of dilution.
608 J. Phys. Chem. B, Vol. 112, No. 2, 2008 Herein, we simulate the isotherms of macromolecules titrated by an M-L complex with stoichiometric ratios of n ) 1 (ML) and n ) 2 (ML2). The number of data points (injections) for each curve was set to 40 with 7 µL per injection. Simulated Isotherms of the Titration of Macromolecules by ML. In this section, we examine simulated binding isotherms of macromolecules (binding to metal as 1:1) titrated with ML (1:1 stoichiometry) for varying conditions as modeled by eq 19 with n ) 1. Because we will verify this model using an ITC titration of Ca(II) by EDTA originally chelated with Mg(II), we chose parameters similar to those of the EDTA, Ca(II), and Mg(II) system. Figure 1 shows the effects of KL (left) and HL (right) on the binding isotherms. It can be clearly seen that HL has a negligible effect on the shape of the curve and the ending value of the heat. Thus, HL is not a critical parameter, as long as the heat change after each injection is large enough so that it can be measured accurately. KL, on the other hand, greatly affects the shape of the binding isotherm and the value of the ending heat. For KL in the range of 102-104 M-1, the ending heat does not return to zero when the molar ratio of injectant to macromolecule reaches 2.4. This occurs because, for this range of KL, the dissociation of ML still occurs after the macromolecule saturation, causing a considerable amount of heat change in the reaction cell. But when KL is increased to ∼3 × 104 M-1, the ending heat nearly goes back to zero at the end of the titration. This result is due to the fact that, with a large KL, there should be a lesser degree of dissociation of the ML complex after its injection into the reaction cell. As for the shape of the curve, with increasing KL, the slope of the isotherm becomes less steep, and the sigmoidal shape changes to an exponential shape when KL (g3 × 106 M-1) is comparable to K. The synthesized curves, under our conditions for simulation, suggest that the isotherms are reasonably sensitive for fitting to obtain K when KL is in the range of 102-106 M-1. Considering how the heat of dilution is corrected in ITC, that is, the ending heat should be ∼0, then a KL value within 3 × 104 to 106 M-1 is a good working range. It must be pointed out that this range can be varied by other parameters, for example, the concentration of macromolecules, the binding constant K, and the resulting heat of interaction. Figure 2 shows the effects of K (left) and H (right) on the binding isotherms. Similar to previous observations, varying the H has little effect on the shape of the isotherms and the ending heat. However, different from KL, variations in the value of K only change the shape of binding isotherms, not the ending heat. We attribute this observation to the fact that the value of KL we set in the simulation is pretty high as 105 M-1, and is in the range where the isotherms return to zero once the molar ratio reaches 2.4, as discussed in the previous sections. The shapes of the isotherms change from sigmoidal to exponential when K decreases to 106 M-1. The plots suggest that, for the simulated conditions, the isotherms are reasonably sensitive to obtain the binding constant K when it is in the range from 106 to 109 M-1. Again, this range can be varied by other parameters, for example, the concentration of macromolecules, the binding constant of metal to ligand KL, and the resulting heat of interaction. Simulated Isotherms of the Titration of Macromolecules by ML2 (1:2 Stoichiometry). In this section, we examine the simulated binding isotherms of macromolecules (binding to metal as 1:1) titrated with ML2 (1:2 stoichiometry) for varying conditions as modeled by eq 19 with n ) 2. Previous analysis
Hong et al. showed that the binding heats H and HL generally have little effect on the shape of isotherms and the ending heats. We then focus on examining the effects of the metal-to-macromolecule binding constant, K, and the binding constants of metal to ligand, KL1 and KL2, on the isotherms. Because we will apply this model to analyze the ITC titration of Aβ by Cu(II) originally chelated with glycine (Gly), we chose parameters similar to those of that system. The left panel in Figure 3 shows the effects of KL’s on the binding isotherms. KL’s have effects on both the shape of the isotherms and the ending heat, in the same manner as KL in the previous simulation of the titration of a macromolecule by ML(1:1). Considering the fitting accuracy, the correction for the heat of dilution, and the stabilization of metal ions in solution, we suggest that KL1 values within 105-107 M-1 is a good range to work. The right panel shows the effect of K on the isotherms. Since KL1 is in the range where the ending heat goes back to zero, we observed that, when K is high enough (>108 M-1), the ending heat is ∼0. The isotherms indicate that, with our current method under the simulated conditions, we can resolve a binding constant K from 108-1011 M-1. These simulations demonstrate that, when competitive binding reactions are taking place, the experimental conditions for obtaining adequate fitting data are not easily determined. The binding constant of the metal to the macromolecule, the binding constant(s) of the metal to the weak ligand, the concentration of macromolecule (concentration of injectants accordingly), and the associated heats all factor into the experimental design. The Interaction of EDTA-Mg and Ca(II). To verify our theory, we studied the complexation of Ca(II) to EDTA which is originally associated with Mg(II). For this displacement reaction, the binding stoichiometry, binding heat, and binding constants of EDTA to both Mg(II) and Ca(II) are well-known. A titration of an EDTA-Mg complex into a buffered solution of CaCl2 was performed. Since Ca(II) competes with Mg(II) for binding to EDTA, Ca(II) is considered to be the macromolecule, EDTA is the “metal species”, and Mg(II) is the weak ligand in the theory. These unusual assignments are made in order to mimic the binding of macromolecules to metals chelated with weak ligand, where both the macromolecule and the weak ligand bind to metal cations, much like the competition between Mg(II) and Ca(II) for binding to EDTA. The individual heat contributions that might be involved in the titration include (a) the binding heat of Ca(II) to EDTA; (b) the binding heat of Mg(II) to EDTA; (c) the heat of protonation of EDTA (at pH 7.4, EDTA free of metal should contain one proton among its four carboxylic acid residues); and (d) the heat of ionization of HEPES buffer. We calculated the concentration of each species after each injection. The alteration of the concentration of EDTA free of any metal (both Ca(II) and Mg(II)) in the reaction cell is less than 0.1% of the total amount of EDTA and less than 1% of the alteration of Ca-EDTA or Mg-EDTA concentration. Therefore the heat contributions due to both the protonation of EDTA and the ionization of HEPES are negligible. The heats involved in the procedure then become only the dissociation of EDTA-Mg and the association of EDTA-Ca. Literature values are used to set the initialization parameters for EDTA-Mg in the fit (n ) 1, KL ) 6.3 × 105 M-1 and HL) 3.4 kcal/mol).37 The isotherm of the titration is shown in Figure 4. The fit of the above thermodynamic model to the data is given by the solid line in the bottom plot. The binding parameters determined for EDTA-Ca are np ) 1.00 ( 0.002, K ) (4.6 ( 0.1) × 107 M-1 and H ) -7.1 ( 0.1 kcal/mol
Thermodynamics of Macromolecule-Metal Chelate Binding
Figure 4. ITC data for the titration of Ca(II) (0.061 mM) with a 0.67 mM EDTA-Mg complex in 20 mM HEPES buffer, 150 mM NaCl, pH 7.4, at 25 °C. The thermodynamic fit (solid line in the bottom plot) to the experimental data gives binding parameters for EDTACa of np ) 1.00 ( 0.002, K ) (4.6 ( 0.1) × 107 M-1, and H ) -7.1 ( 0.1 kcal/mol, which are in excellent agreement with published literature values (np) 1, K ) (5.0-8.0) × 107 M-1, and H ) -6.3 ( 0.2 kcal/mol).
(average values of two experiments), which are in excellent agreement with the published literature values (np ) 1, K ) (5.0-8.0) × 107 M-1 and H ) -6.3 ( 0.2 kcal/mol).37 This agreement between the literature values and the parameters derived from the experiment using the thermodynamic model developed above serve as a control, establishing the validity of using eq 19 to model such reactions. It is important to note that the fit obtained by the one-setof-sites binding model built into the ITC data analysis software in Origin gave a binding constant (Kapp) of 1.3 × 106 M-1, which is 1 order of magnitude lower than the literature value. This result indicates that a correction of Kapp obtained from the onesite binding model cannot be performed by simply multiplying Kapp by the metal-ligand binding constant (6.3 × 105 M-1 for EDTA-Mg, pH 7.4), as suggested in previous publications.10,17 Application in Examining the Interaction of Cu(Gly)2 and Aβ(1-16). Aβ(1-16) is a 16-residue peptide of the N terminus of amyloid β (Aβ), a peptide ranging from 39 to 42 residues in length and the main component of amyloid plaques in the brains of individuals with Alzheimer’s disease. Elevated copper contents have been found in amyloid plaques, and physiological concentrations of Cu(II) can induce the aggregation of Aβ, which is believed to prelude the formation of amyloid plaques.38,39 To understand the basics of this process, the interaction of Cu(II) with Aβ has been extensively studied.13,38,40-47 Various methods have given a wide range of binding constants from 105 to 1010 M-1. Herein we will use ITC to examine Cu(II) binding to Aβ(1-16) and to analyze the data within the described theoretical model. We then reconcile our results with a previously reported binding constant by taking into account (as we have done for ITC) how the presence of the weak ligand
J. Phys. Chem. B, Vol. 112, No. 2, 2008 609
Figure 5. ITC data for the titration of Cu(Gly)2 into ∼75 µM Aβ(1-16) in 20 mM HEPES buffer, 150 mM NaCl, pH 7.2, at 37 °C. The thermodynamic fit to the data is given by the solid line; the binding parameters determined for the 1:1 Cu(II)/Aβ(1-16) complex are K ) 1.5 × 109 M-1 and H ) -8.1 kcal/mol.
and its binding to Cu(II) affects measured binding constants in which this interaction is not modeled. We first consider the details of modeling the titration of Aβ(1-16) peptide with Cu(Gly)2 using ITC. In the injecting syringe, Cu(II) cations are stabilized by complexation with glycine, a weak Cu(II) ligand with 1:2 (Cu(II)/Gly) binding stoichiometry. The titration isotherm curve is shown in Figure 5. The binding of Cu(II) to glycine (37 °C and pH 7.2) can be written as
Cu + Gly T Cu(Gly)
(20)
with K1 ) [Cu(Gly)]/[Cu][Gly] ) 8.7 × 105 M-1 and H1 ) -5.6 kcal/mol,37 and
Cu(Gly) + Gly T Cu(Gly)2
(21)
with K2 ) [Cu(Gly)2]/[Cu(Gly)][Gly] ) 4.5 × 104 M-1 and H2 ) -6.9 kcal/mol.37 However, in this specific example using Cu(Gly)2, different from the displacement of Mg(II) from EDTA by Ca(II), both the protonation of glycine and the ionization of HEPES buffer play important roles. The binding of Cu(II) to peptide results in the release of glycine, which becomes protonated in HEPES buffer at pH 7.2. It can be calculated that, at pH7.2, ∼99.1% of the metal-free glycine molecules are protonated. It can therefore be expected that, when 100 Cu-Gly bonds dissociate, about 99 glycine molecules will bind protons, which are ionized from the buffer. These analyses mean that the HL’s used for the analysis of Cu(II) to Aβ(1-16) should be a net combination of the binding heat of Cu-Gly (HL1 ) -5.6 cal/mol and HL2) -6.9 kcal/mol), the deprotonation heat of glycine (10.4 kcal/
610 J. Phys. Chem. B, Vol. 112, No. 2, 2008 mol, ∼37 °C,37), and the protonation heat of HEPES buffer (-5.02 kcal/mol48), thus HL1 ) -0.3 kcal/mol and HL2 ) -1.6 kcal/mol. With KL1, KL2, HL1, and HL2 set as 8.7 × 105 M-1, 4.5 × 104 M-1, -0.3 kcal/mol, and -1.6 kcal/mol, respectively, the isotherm of the association of peptide with Cu(II) was then fit with eq 19 with n ) 2. The thermodynamic fit to the data is given by the solid line in Figure 5; the binding parameters determined for the 1:1 Cu(II)/Aβ(1-16) complex are K ) 1.5 × 109 M-1 and H ) -8.1 kcal/mol. We would like to point out that this reported heat H could include an additional contribution from the ionization of binding sites in Aβ, and consequent protonation of buffer. We are currently exploring that possibility. For our purposes, we focus herein on the binding constant. We also point out that it has been suggested that the binding site is likely to involve one or more peptide backbone N atoms, and, upon Cu(II) binding, one or more proton should then be released.49 Thus, the binding constant is pH dependent. The binding constant determined herein, 1.5 × 109 M-1 at pH 7.2, is higher than values published in the literature.36,38,43,46 We consider the results of Ma et al., who approached the measurement of the binding constant of Cu(II) to Aβ(1-16) by noting that the binding of Cu(II) quenched the fluorescence of model Aβ peptides at pH 7.8.43 Thus, they explored the ability of added Gly and histidine (His) to restore the peptide fluorescence that was initially quenched by Cu(II). From their analyses, a binding constant of ∼107-108 M-1 was determined.43 Ma et al. found that Gly concentrations ∼40 times that of Aβ(1-16) restore the fluorescence signal of the tyrosine moiety in Aβ(1-16) to half of its maximum value, which was quenched by the addition of Cu(II) ions. His has a higher binding affinity to Cu(II) than Gly and, as expected, can restore the fluorescence signal to half of the maximum with less than 2 mol equiv of Aβ(1-16). The authors suggested that the binding of Cu(II) to this peptide is much higher than that of Cu(II) to Gly (with K1 ) 1.8 × 106 M-1) and lower than that of histidine (6.7 × 108 M-1). However, the analysis used neglects the fact that the binding of either Gly or His to Cu(II) occurs in a stoichiometric ratio of 2:1, and therefore both equilibria K1 (formation of Cu(II)L) and K2 (formation of Cu(II)L2) must be taken into account. We now show that, by explicitly taking into account both K1 and K2, these data result in a higher binding constant for Cu(II) to the Aβ peptide of ∼1010 M-1, which can be reconciled with our ITC data. First, consider the result that, when the total glycine concentration is 40 times that of peptide, then the tyrosine fluorescence signal is about half of the maximum value, suggesting that the fraction of occupied sites of the macromolecules is Θ ) 1/2.43 Under these conditions, the binding constant (eq 2) is given by K ) 1/[Cu], where [Cu] is the concentration of free Cu(II) that is bound neither to the peptide nor to glycine. This value can be calculated directly from the following equation, which takes into account both equilibria by which Cu(II) binds to glycine:
[Cu] )
1 ([Cu]T - [CuP]) (22) 1 + K1[Gly] + K1K2[Gly]2
In the above expression, K1 ) 1.86 × 106 M-1 (pH 7.8), K2 ) 1.86 × 105 M-1 (pH 7.8),50 [CuP] is ∼0.025 or ∼0.05 mM (depending on stoichiometry and, in their work, taken to be ∼0.05 mM), [Cu]T is ∼0.1 mM, and [Gly] ∼1.9 mM. With these values, the fluorescence data reveal a binding constant of Cu(II) to Aβ(1-16) of ∼2 × 1010 M-1. This work was
Hong et al. conducted at pH 7.8, different from our ITC titration (pH 7.2). Miura et al. suggested that binding of Cu(II) to Aβ results in releasing one or more protons from the backbone of the peptide.49 The binding constant at pH 7.8 will be higher than that at pH 7.2 by a proportionality factor of ∼2 × 10(7.8-7.2) ) 8. Thus, the data from the work of Ma et al.’s work is in excellent agreement with our value of 1.5 × 109 M-1. We are currently examining the binding of Cu(II) to the full Aβ(140) peptide, and these results will be reported elsewhere. Conclusions ITC has been extensively applied in studying the interaction of metals with macromolecules. In many cases these metal ions are chelated with a weak ligand. Herein, we have developed an accurate ITC data analysis method for use in analyzing the binding of macromolecules specifically to metal cations stabilized in aqueous solution by association with a weak ligand. The agreement between literature values and those derived from our analysis of the ITC isotherms for the displacement of Mg(II) from EDTA by Ca(II) validates the developed thermodynamic model. We then applied this analysis to determined that the binding constant of Cu(II) to Aβ(1-16) is 1.5 × 109 M-1 at pH 7.2. Although previous reports indicated a binding constant of ∼107 M-1 or less, we find that, with proper accounting of the competitive binding equilibria between Cu(II) and the weak ligands, these data reveal a higher binding constant on the order of ∼1010 M-1 at pH 7.8, consistent with our work. Our analysis has now provided both an accurate measure of the binding constant and the underlying reason for the disparity in the published literature. Acknowledgment. This work was supported by the Air Force Office of Scientific Research through the MFEL program. References and Notes (1) Wiseman, T.; Williston, S.; Brandts, J. F.; Lin, L. N. Anal. Biochem. 1989, 179, 131. (2) Bolles, T. F.; Drago, R. S. J. Am. Chem. Soc. 1965, 87, 5015. (3) Sigurskjold, B. W. Anal. Biochem. 2000, 277, 260. (4) Saboury, A. A. J. Iran. Chem. Soc. 2006, 3, 1. (5) ITC Data Analysis in Origin, Tutorial Guide, version 7.0; MicroCal: Northampton, MA, 2004. (6) Privalov, P. L.; Dragan, A. I. Biophys. Chem. 2007, 126, 16. (7) Homans, S. W. Top. Curr. Chem. 2007, 272, 51. (8) Behbehani, G. R.; Saboury, A. A. Thermochim. Acta 2007, 452, 76. (9) Ababou, A.; Ladbury, J. E. J. Mol. Recognit. 2007, 20, 4. (10) Zerovnik, E.; Skerget, K.; Tusek-Znidaric, M.; Loeschner, C.; Brazier, M. W.; Brown, D. R. FEBS J. 2006, 273, 4250. (11) Velazquez-Campoy, A.; Freire, E. Nat. Protoc. 2006, 1, 186. (12) Sivaraja, V.; Kumar, T. K. S.; Rajalingam, D.; Graziani, I.; Prudovsky, I.; Yu, C. Biophys. J. 2006, 91, 1832. (13) Guilloreau, L.; Damian, L.; Coppel, Y.; Mazarguil, H.; Winterhalter, M.; Faller, P. JBIC, J. Biol. Inorg. Chem. 2006, 11, 1024. (14) Frasca, V. Am. Biotechnol. Lab. 2006, 24, 8. (15) Ababou, A.; Ladbury, J. E. J. Mol. Recognit. 2006, 19, 79. (16) Tinoco, A. D.; Valentine, A. M. J. Am. Chem. Soc. 2005, 127, 11218. (17) Thompsett, A. R.; Abdelraheim, S. R.; Daniels, M.; Brown, D. R. J. Biol. Chem. 2005, 280, 42750. (18) Creagh, A. L.; Tiong, J. W. C.; Tian, M. M.; Haynes, C. A.; Jefferies, W. A. J. Biol. Chem. 2005, 280, 15735. (19) Ladbury, J. E. BioTechniques 2004, 37, 885. (20) Kim, H.-S. J. Ind. Eng. Chem. (Seoul, Repub. Korea) 2004, 10, 273. (21) Clugston, S. L.; Yajima, R.; Honek, J. F. Biochem. J. 2004, 377, 309. (22) Bekker, E. G.; Creagh, A. L.; Sanaie, N.; Yumoto, F.; Lau, G. H. Y.; Tanokura, M.; Haynes, C. A.; Murphy, M. E. P. Biochem. 2004, 43, 9195. (23) Abajian, C.; Yatsunyk, L. A.; Ramirez, B. E.; Rosenzweig, A. C. J. Biol. Chem. 2004, 279, 53584.
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