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Langmuir 1998, 14, 796-799
Effect of the Hydrophobicity of Chain on Ca2+ Binding to Ionic Gels Shigeo Sasaki,* Kumi Yataki, and Hiroshi Maeda Department of Chemistry, Faculty of Science, Kyushu University, 33 Hakozaki, Higashiku, Fukuoka 812, Japan Received July 30, 1997. In Final Form: November 20, 1997 Binding isotherms of Ca2+ to copolymer gels of acrylamide and acrylate (AA), N-isopropylacrylamide and acrylate (NA), and n-butylacrylate and acrylate (BA) were investigated and were compared with each other for examining the effect of the hydrophobicity of chain on the Ca2+ binding. The highest binding constant and the largest shrinkage in the volume were observed for the BA gel. The counterion condensation theory developed by Manning could not explain the observed binding isotherms. The analysis using the theory for the cooperative binding developed by McGhee and Hippel indicates that the binding to BA gel is more cooperative than those to the others. The present experimental result indicates that the hydrophobic circumstance promotes the Ca2+ binding to carboxylate.
1. Introduction It is well-known that many functions in the biological systems are activated or deactivated by the Ca2+ binding to proteins,1 the binding sites of which are COO- groups. The binding constants, which determine the critical concentration of Ca2+ to activate or deactivate the functions, are widely varied from 10-8 to 10-3 mol-1 dm3. The physicochemical regulation mechanism of such a wide variation of the binding constant has not been fully clarified yet. From the fact that the binding sites are often situated under the hydrophobic circumstances, the hydrophobic effect on the binding is considered to be key for understanding the mechanism. However, our understanding about the effect of the hydrophobic entity on the Ca2+ binding to COO- groups has been poor, although a role of the electrostatic interaction to play in the mechanism has been well clarified with the aid of counterioncondensation theories.2 -4 The present investigation aims at clarifying the effect of the hydrophobic entity on the binding behavior. Many investigations5 ,6 on the divalent counterion binding to polyelectrolytes have been conducted by the counterion-condensation theories.2-4 The coupling effect of the binding with the conformational change has been scarcely paid much attention, although polyelectrolytes bound by divalent counterions are known to take the compact conformation7 and form the precipitate in some cases,8 which are induced by the poor affinity of the chain segment to water. The dehydration of chain accompanied by the counterion binding makes the affinity poor. The hydrophobic attractive interaction between the chain segments makes the chain compact or precipitate. Our recent investigation9 on the volume phase transition of the hydrated gels has demonstrated that the binding (1) Calcium Binding Proteins; Drabikowski, W., Strzelecka-Golaszewska, H., Carafoli, E., Eds.; (Elsevier Publisher Co.: Paris, 1974; Proc. International Symposium, Jablonna, July 1973. (2) Fuoss, R. M.; Katchalsky, A.; Lifson, S. Proc. Natl. Acad. Sci. U.S.A. 1951, 37, 579. (3) Oosawa, F. J. Polym. Sci. 1957, 13, 43. (4) Manning, G. S. Q. Rev. Biophys. 1978, 11, 179. (5) Mattai, J.; Kwak, J. C. J. Phys. Chem. 1982, 86, 1026. (6) Kowblansky, M.; Zema, P. Macromolecules 1981, 14, 1448. (7) Huber, K. J. Phys. Chem. 1993, 97, 9825. (8) Wall, F. T.; Drenan, J. W. J. Polym. Sci. 1951, 7, 83. (9) Sasaki, S.; Maeda, H. Phys. Rev. E 1996, 54, 2761. (10) Flory, P. J. Principles of Polymer Chemistry; Cornel University Press: Ithaca, NY, 1953; Chapter 13.
behavior of water molecules to the chains (the hydration behavior of the chain) is strongly correlated to the conformation of chain. Generally, the binding that decreases the conformational free energy of chain is promoted and the binding that increases the energy is suppressed. The shrinkage in the chain dimension decreases the conformational free energy due to an increase in conformational entropy. The hydrophobic chain favors the compact conformation.10 Therefore the higher binding constants are theoretically expected for the more hydrophobic chains. For examining the prediction, the gel system is considered to be a suitable object for the investigation since the conformation can be easily evaluated by measuring the gel volume, which is proportional to cubic of the end-to-end distance of the chain.10 The present investigation was carried out using a polymer gel of acrylate (A-gel), and the copolymer gels of acrylamide and acrylate (AA-gel), N-isopropylacrylamide and acrylate (NA-gel), and, n-butylacrylate and acrylate (BA-gel) which have different hydrophobic alkyl groups on the chains. Our interest is the correlation between the Ca2+ binding isotherms and the chain dimensions for the copolymer gels. The chain dimension in the solution was evaluated from the gel volume. The degree of Ca2+ binding to the gel chain equilibrating with a solution of a given Ca2+ concentration can be estimated from the stoichiometry of the Ca2+. From the relation between the binding isotherms and the volume change with binding, we found that the more Ca2+ bound to the more hydrophobic gel and that the counterion condensation theory3 for the mixture of univalent and divalent counterions was not applicable to the Ca2+ binding to the present gels. The high cooperativity of the Ca2+ binding was observed for the BA-gel at a degree of binding higher than 0.5, while the binding to the AA-gel was found to be anti-cooperative. 2. Experiments Gels were prepared by radical copolymerization in the solution of acrylate (1M), N,N′-methylenebis(acrylamide) (10 mM), and comonomers (1 M), which were acrylamide for the AA-gel, N-isopropylacrylamide for the NA-gel, and n-butylacrylate for the BA-gel. The A-gel was also prepared by radical copolymerization in the solution of acrylate (2 M) and N,N′-methylenebis(acrylamide) (10 mM). The solvents used were water for the Aand AA-gels and dimethyl sulfoxide (DMSO) for the BA- and NA-gels. The polymerization was initiated by ammonium peroxydisulfate in the aqueous solution or R,R′-azobis(isobuty-
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Figure 2. Gel volume V normalized by V at β ) 0 as functions of the degree of Ca2+ binding, β.
Figure 1. Binding isotherm of Ca2+. ronitrile) in the DMSO solution and was carried out at 60 °C. Gels, synthesized in a plate form of 1 mm thickness, were rinsed thoroughly with the methanol-water mixture several times and cut into small pieces. The gels were dried under vacuum and were stocked. Mole ratios of acrylate to the total monomeric units of AA-, NA-, and BA-gels were 0.50, 0.49, and 0.49, respectively, which were determined by the potentiometric titration method. The ratios were very close to the composition of acrylate (0.5) in the polymerizing solution, which suggests the random distributions of the comonomers along the chains11 ,12). In the titration curve corrected for the blank titration, a pH jump from 7 to higher than 9 at the end point was clearly observed. All chemicals used were reagent grade. Experiments were carried out at 25.0 ( 0.5 °C. A small piece of dry gel was suspended in a volume of NaCl solution of a given concentration. Neutralization of the gel was carried out using the NaOH solution, followed by the addition of a given amount of CaCl2. In the present experiment, the added amount of NaCl and CaCl2 was adjusted to [NaCl] + 2[CaCl2] ) Cs and 2[CaCl2]/ [NaCl] < 0.1, where [S] represents the concentration of S. The gels were equilibrated with the solution phase for more than 2 weeks. The gel volume per 1 mol of the acrylate, V, was determined by the relation V ) (Wg/Wd)(Ma/F), where Wg, Wd, Ma, and F, respectively, denote the weight of gel, the weight of the dry gel, the weight of the gel containing 1 mol of acrylate group, and the density of the gel. It was assumed that F is identical to the density of solution outside the gel. Here the volume of gel chain is assumed to be negligibly small compared with the total gel volume. The degree of Ca2+ binding to the acrylate group of the gel, β, was obtained from the stoichiometric relation, β(Wd/ Ma) + 2CoutV0 ) 2mCa, where mCa, V0, and Cout, respectively, are the total mole amount of Ca2+, the total volume of the system (the gel + the solution outside it), and the concentration of Ca2+ in the solution outside the gel. In the definition, β ) 1 indicates that whole acrylate groups are bound by Ca2+. Cout was obtained from the absorption of atomic spectrum measured by using a Hitachi atomic absorption spectrophotometer, Model 180-50.
3. Results Figure 1 shows the binding isotherms of the AA-, BA-, NA-, and A-gels. The chemical equilibrium of Ca2+ + 2COO- T Ca(COO)2 is described by the thermodynamic relation -T ln Cout ) {2µA(β) - µA2Ca(β)+} + µCa0, where µA(β), µA2Ca(β), and µCa0, respectively, are the chemical potentials of the binding sites in the biding free state, in (11) Vollmert, B. Angew. Makromol. Chem. 1968, 3, 1. (12) Flory, P. J. Principles of Polymer Chemistry; Cornel University Press: Ithaca, NY, 1953; Chapter 5.
the binding state at a given β, and the chemical potential of the free Ca2+ in the solution at Cout ) unit concentration (1 M). Here T is the Landau or Boltzmann temperature. Figure 1 demonstrates that the Cout value at a given β increases with Cs for both of the AA- and BA-gels. This is due to the shielding effect of salt on the electrostatic interaction between the ionized groups. The electrostatic free energy, which contributes to the increase in µA(β), decreases with the increase in Cs, and so does the free energy difference, 2µA(β) - µA2Ca(β), since the electrostatic free energy does not contribute to µA2Ca(β) so much. Figure 1 also shows that the Cout value at a given β for the A-gel is smaller than those for the AA-gel. This is due to the chemical structure of higher charge density along the chain of the A-gel than that of AA-gel at a given β, since the electrostatic free energy of the ionized site and the µA(β) increases with the charge density. It is interesting to find out that the binding isotherms of AA- and NA-gels at Cs ) 0.01 M are almost same within the experimental error (5% of Cout and β at most) and that the Cout value at a given β for the AA-gel is greater than that for the BA-gel at the Cs investigated. This indicates that 2µA(β) µA2Ca(β) for the AA-gel is smaller than that for the BA-gel and is almost same as that for NA gel. Figure 2 shows the β dependence of the volume relative to that at β ) 0. The V values observed at β ) 0 were 12 ( 2 dm3 mol-1 at Cs ) 0.1 M and 4.0 ( 0.4 dm3 mol-1 at Cs ) 0.01 M for the AA-, BA-, and NA-gels. The fact that the similar volumes were observed for these gels at β ) 0 suggests that the hydrophobic attractive interaction between the hydrophobic groups in the BA- and NA-gels is negligibly small compared with the electrostatic repulsive interaction between the ionized carboxyl groups in the solution at Cs less than 0.1 M. Differences in the behavior of the volume change with β among the gels are observed in Figure 2. The shrinkage in the volume is partly due to the reduction of the swelling osmotic pressure with the binding, which causes a decrease in the concentration of free counterion. The poor affinity of the polymer segments in binding state to water can make the chain conformation compact and can reduce the volume. The poor affinity of the Ca2+ bound carboxylate is inferred from the fact that the volume of the A-gel (V ) 2.2 dm3 mol-1) at β ) 0.5 in the solution of Cs ) 0.1 M is smaller than that of the half neutralized A-gel (V ) 3.5 dm3 mol-1) at β ) 0 in the solution of Cs ) 0.1 M. The Ca2+ bound carboxylate might be partly dehydrated. The hydrophobic interaction becomes effective to reduce the gel volume with increase in β. Higher hydrophobicity of the nbutylacrylate of BA-gel than that of the acrylamide of
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Figure 3. Comparison between the counterion condensation theory and the experiment. The experimental data for the AAgel are shown by the open squares (Cs ) 0.1 M) and open circles (Cs ) 0.01 M). The solid (Cs ) 0.01 M) and broken (Cs ) 0.1 M) lines, respectively, are the calculated curves obtained by using eqs 1 and 2.
AA-gel can explain the result that the volume decrease of BA-gel with binding is more than that of the AA-gel. It is interesting to find out that both of the volume change behavior with binding and the binding isotherms for the AA-gel are very similar to those observed for NA-gel as shown in Figures 1 and 2. The hydrophobicity of the Ca2+ bound acrylate combined with N-isopropylacrylamide seems almost the same as that with acrylamide although the hydrophobicity of the former amide is greater than that of the latter. 4. Discussions If the Ca2+ binding is territorial and regulated by the electrostatic interaction only, the counterion condensation theory can well predict the binding isotherm. According to the Manning’s “two-variable theory for the divalent counterion binding in the univalent salt solution”,4 the binding isotherms can be described by the following equations
1 + ln
θ ) -2ξ(1 - C1 - β) ln(1 - e-κb) C1VP ln
θ β ) 2 ln +1 2CoutVP C1VP
(1) (2)
where
VP ) 2.718(1 - ξ-1)
(κb)2 C1
2
ξ)
e0 DTb
κ ) x8πξbC1 Here θ, b, C1, e0, and D, respectively, are a degree of univalent counterion binding, an average distance between the neighboring ionized groups on the chain, a concentration of univalent salt, an elementary charge, and a dielectric constant of the medium. It is very interesting to examine whether the theory can describe the observed binding isotherms. A comparison between the theory and the experimental result of the AA-gel was made and is
Figure 4. Apparent binding constant Kapp as functions of β. The Kapp values are evaluated by using eq 3.
shown in Figure 3. It was assumed that b ) 0.5 nm, C1 ) Cs and D ) 80 in the calculation for finding out the set of θ and β values which satisfies eqs 1 and 2 for each Cout value. Figure 3 demonstrates that the theory cannot explain the experiment. The Cout values of the experiment at a given β are about 1/100 times the theoretically predicted values as shown in Figure 3. This indicates that the energy about 4T adding to the electrostatic energy contributes to 2µA(β) - µA2Ca(β). The free energy being necessary to form the ion complex of dehydrated Ca2+ with neighboring two COO- groups on the polymer chain is considered to be responsible for the additional free energy. The present result indicates that the site binding occurs rather than the territorial binding in the Ca2+ binding to carboxylate. If Ca2+ binds randomly to the successive two binding sites, then the apparent binding constant Kapp is given by13
log Kapp ) log
β(2 - β) 4(1 - β)2
- log Cout
(3)
Figure 4 shows the relations between log Kapp and β for the AA- and BA-gels at Cs ) 0.1 and 0.01 M. It is observed that the Kapp of the AA-gel tends to decrease slightly with β and that the Kapp of the BA-gel increases with β at the high β. The binding isotherms can be also analyzed by using the theory which takes the cooperative binding into account.14 The theory gives the following equation.
{
}
(2u - 1)(1 - β) - R + β/2 β ) K(1 - β) × 2Cout 2(u - 1)(1 - β) 1 + R - 3β/2 2(1 - β)
{
}
2
(4)
where
R ) x(1 - 3β/2)2 + 2uβ(1 - β) Here, K and u, respectively, are a binding constant for the binding to the isolated successive two binding sites having the neighboring sites in the binding free state and a cooperativity parameter. If u is more than 1, the contiguous binding is favorable, otherwise unfavorable. (13) Hill, T. L. J. Polym. Sci. 1957, 23, 549. (14) McGhee, J. D.; von Hippel, P. H. J. Mol. Biol. 1974, 86, 469.
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binding constant for the BA-gel increases with β at the large β as shown in Figure 4. As a result the binding becomes cooperative as shown by the case of BA-gel in Figure 5 and Table 1. The fact that the binding to the A-gel is anti-cooperative as shown in Figure 1 indicates that the hydrophobicity of Ca2+ bound carboxylate groups is not enough to make the binding cooperative. The binding constant of Ca2+ to the carboxylate groups on the polymer chain or the binding sensitivity to the Ca2+ concentration increases with the hydrophobicity of the chain. The differences between the binding free energy at Cs ) 0.01 and 0.1 M, [ln{K(Cs ) 0.01 M)} - ln{K(Cs ) 0.1 M)}]T, are evaluated to be 3.8 T for the AA-gel, 4.2 T for the BA-gel at the low β, and 3.9 T for the BA-gel at the high β from the data of Table 1. The Cs dependence of the binding constant seems not much affected by the strength of hydrophobicity of side groups of the chain. If the Cs dependence of the binding constant is explained by the Cs dependence of the electrostatic free energy of the charged site, the difference, [ln{K(Cs ) 0.01 M)} ln{K(Cs ) 0.1 M)}]T, can be approximately given by16 Figure 5. Binding isotherms of Ca2+. The symbols are same as those in Figure 1. The solid lines are the calculated curves obtained by using eq 4 with the K and u values tabulated in Table 1. Table 1. Binding Constant K and Cooperativity Parameter u Giving the Best Fitting Curves to the Experiment Shown in Figure 5 gel
Cs/mol dm-3
K/mol-1 dm3
u
no. in Figure 5
AA AA BA(low β) BA(high β) BA(low β) BA(high β)
0.01 0.1 0.01 0.01 0.1 0.1
16000 350 70000 6290 1000 122
0.6 0.6 0.4 6 0.6 10
2 1 6 5 4 3
Generally u is less than 1 for the counterion binding to polyelectrolyte as demonstrated by the pH titration curve.15 The K and u values giving the best fitting to the experiment shown in Figure 5 are tabulated in Table 1. The u values for the BA-gel at the high β are much larger than 1, while those for BA-gel at the low β and the AA-gel at any β are less than 1. The large u values observed for the binding to BA-gel is considered to be related to the formation of compact conformation of chain at the high β as shown in Figure 2. The hydrophobic butylacrylate of the BA-gel makes the chain conformation more compact than the acrylamide of the AA-gel when the charge density along the chain decreases with Ca2+ binding. The compact conformation makes the circumstances around ionized carboxyl groups more hydrophobic and makes the dielectric constant there decrease because of the low dielectric constant of the hydrophobic residue. The electrostatic free energy of ionized group increases with decrease in the dielectric constant and so does µA(β). The compact conformation reduces the area of the hydrophobic residue contacting with the water molecules, which results in decreasing the free energy. The free energy of the hydrophobic sites bound by Ca2+, µA2Ca(β), on the chain in the compact conformation is smaller than that in the extended conformation. Therefore the free energy difference, 2µA(β) - µA2Ca(β), of the hydrophobic gel increases with decrease in the gel volume. Thus the apparent (15) Nagasawa, M.; Murase, T.; Kondo, K. J. Phys. Chem. 1965, 77, 4005. (16) Hill, T. L. Arch. Biochem. Biophys. 1995, 57, 229.
[
2e02 K0(κ(Cs ) 0.01 M)r) Db κ(Cs ) 0.01 M)rK1(κ(Cs ) 0.01 M)r) K0(κ(Cs ) 0.1 M)r)
]
κ(Cs ) 0.1 M)rK1(κ(Cs ) 0.1 M)r)
with assuming that the chain is a cylindrical rod with the radius r. Here K0(x) and K1(x) are the modified Bessel functions of the second kind. The value is evaluated to be 2.5 T with assuming r ) b. This is a little bit smaller than the observed values. If less r, b, and/or D values than those used in the present calculation (r ) 0.5 nm and D ) 80) are used, the evaluated value is more close to the observed [ln{K(Cs ) 0.01 M)} - ln{K(Cs ) 0.1 M)}]T value. Here it should be mentioned that b of the shrunken gel might be smaller than that of the expanded gel and that the D value in the hydrophobic circumstances might be smaller than that of water. We can say that the Cs dependence of the K can be substantially explained by the Cs dependence of electrostatic free energy. 5. Conclusion The fact that the counterion condensation theory3 for the mixture of univalent and divalent counterions cannot be applicable to the Ca2+ binding to the hydrophilic AAgel reveals that the site binding occurs rather than the territorial binding to the carboxylate. The strong correlation between the Ca2+ binding isotherms and the volume change with the binding reveals the coupling of Ca2+ binding and conformational change of chain. The binding constant to the site surrounded by the hydrophobic residue, which makes the chain conformation compact, is high as observed for that of the BA-gel. The binding promoted by the compact conformation formed with the binding is cooperative as observed in the binding isotherm of the hydrophobic BA-gel, while the binding to the gels being less hydrophobic is anti-cooperative. These findings suggest that the transition-like change of the volume and the degree of binding can occur in the highly hydrophobic ionic gel system. Acknowledgment. This work was partially supported by Grant-in Aids for Scientific Research (B) (No.08454184) and (C) (No. 08640742) from the Ministry of Education, Science, Sports and Culture of Japan. LA970845X
