NMR Chemical Shift References for Binding Constant Determination

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J. Phys. Chem. B 2001, 105, 7361-7365

7361

NMR Chemical Shift References for Binding Constant Determination in Aqueous Solutions Noriaki Funasaki,* Masao Nomura, Seiji Ishikawa, and Saburo Neya Kyoto Pharmaceutical UniVersity, Misasagi, Yamashina-ku, Kyoto 607-8414, Japan ReceiVed: February 28, 2001; In Final Form: May 10, 2001

For deuterium oxide solutions of various compounds including cyclic and acyclic saccharides, oligoglycines, and sodium chloride, the proton chemical shifts of these solutes and the tetramethylammonium ion (TMA), referred to an external standard, change linearly with the molarity of solute. This slope is almost independent of the kind of protons of solute and TMA and is proportional to the product of the molar volume of the solute and the difference in volume magnetic susceptibility between deuterium oxide and the solute. The equilibrium formation constant and structure of ion-pair of TMA and the benzenesulfonate ion (BS) are evaluated from chemical shifts referred to an internal standard. At least some of the four methyl groups of TMA in the ion-pair complex are located above the benzene ring of BS. This structure indicates that TMA and BS form their ion pair by hydrophobic and electrostatic attraction. These results serve not only for choosing appropriate internal references and internal or external standard methods for chemical shift measurements in aqueous solutions but also for correcting the chemical shift referred to the external standard.

Introduction NMR chemical shifts have become by far the most important method of determining the equilibrium constant of binding between two molecules in solutions. This method utilizes the difference between the chemical shifts of a molecular species in the free and bound states.1,2 The chemical shift is measured using an external or internal standard.3-5 A convenient reference signal is one that is sharp and well separated from other signals in the NMR spectrum. The use of an internal reference signal has the advantage that no bulk-susceptibility corrections are necessary. These procedures are satisfactory only when specific solvent and solution effects are unimportant. Sodium 3-(trimethylsilyl)2,2,3,3-tetradeuteriopropionate and sodium 4,4-dimethyl-4-silapentane-1sulfonate (DSS) have been often used for such primary internal references in aqueous solution systems. These compounds, however, form complexes with cyclodextrins (CD). For aqueous CD solutions, therefore, the tetramethylammonium ion (TMA), and methanol (MeOH) were recommended as secondary internal references, because they are practically unbound with CDs.6 Apart from inclusion complexes, TMA forms the ion-pair complex with benzenesulfonate ion (BS), an anion, by electrostatic attraction, though their ion-pair formation has not well been understood. For such anionic compounds, sodium methanesulfonate and sodium methyl sulfate were recommended as secondary internal standards.7 On the other hand, Matsui and Tokunaga found that the chemical shift of TMA referred to external DSS decreases linearly with increasing CD concentration, and this negative slope increases with increasing number of glucose units. They suggested that this upfield shift is ascribed to a change in water structure with the addition of CD.6 We observed the same upfield shift of CD protons and corrected these changes to determine the binding constant, and the values of the binding constants of acetonitrile and R-CD were the same whether an * To whom correspondence should be addressed. Fax: +81-75-5954762. E-mail: [email protected].

internal or an external reference was used.7,8 However, it is not certain what substances cause such shifts and why such shifts occur. These uncertainties will attract the interest of researchers who use chemical shift data to determine binding constants. In this work, we investigate the chemical shifts of various compounds including cyclic and acyclic saccharides, oligoglycines, and sodium chloride using an external reference and analyze these data in terms of volume magnetic susceptibilities and molar volumes of these compounds. The equilibrium formation constant and structure of ion-pair of TMA and BS are estimated from chemical shifts referred to an internal standard. It will be shown that this ion-pair formation is driven by electrostatic and hydrophobic interactions. Experimental Section Materials. Commercial samples of TMA (Nacalai Tesque Co.), 99.9 at. % D deuterium oxide, sodium 3-(trimethylsilyl)2,2,3,3-tetradeuteriopropionate, sodium 4,4-dimethyl-4-silapentane-1-sulfonate (DSS, Aldrich), glycylglycine, glycylglycylglycine, (Tokyo Kasei Organic Chemicals Co.), sodium chloride, acetonitrile, MeOH, ethanol, glycine, D-glucose, sucrose, N-methylurea, (Wako Pure Chemicals Co.), maltopentaose (Seikagaku Kougyou Co.), and R-CD (Ensuiko Seitou Co.) were used as received. These chemicals are of reagent grade. Reagent grade BS (Tokyo Kasei Organic Chemicals Co.) was recrystallized from a 50%-50% mixture of water and ethanol. NMR Measurements. All 300 MHz proton NMR spectra were recorded with a Varian XL-300 NMR spectrometer at 294.2 ( 0.5 K. These spectra were deconvoluted with a Nuts NMR data processing software (Acorn NMR Inc.). Deuterium oxide was used as solvent for all solutions. These solutions were prepared in volumetric flasks, so that the molarity scale was used as concentration unit. The NMR spectra for the external reference were recorded using a Wilmad WGS-5BL cylindrical coaxial tube. A 100 mmol dm-3 (mM) DSS deuterium oxide solution was placed in the inner tube and a sample solution was in the outer tube. The chemical shift, δ, was measured as a function of solute

10.1021/jp010774h CCC: $20.00 © 2001 American Chemical Society Published on Web 06/28/2001

7362 J. Phys. Chem. B, Vol. 105, No. 30, 2001

Funasaki et al. reference and sample molecules is exactly the same. However, the compounds used as references must be inert with respect to the sample as regards intermolecular effects. External referencing avoids the difficulty of dealing with solute-solvent reference interactions, but the problem of differential shielding now arises. Owing to polarization near the surface, the field experienced by the reference and sample, Beff, depends on the shape of the container:

Beff ) B0(1 - Sfχ)

(2)

Here B0 and Sf stand for the magnetic field and the shape factor of the container.3-5 For long and perfectly cylindrical coaxial tubes placed in a superconducting solenoid, we can write the intrinsic δ value as3-5

δint ) δobsd + 4π(χref - χsample)/3 Figure 1. Chemical shift variation of TMA, referred to external DSS, plotted against the molarity of acetonitrile (O), N-methylurea (b), sodium chloride (0), and sucrose (9). The solid lines are calculated using eq 9 with volume magnetic susceptibility and molar volume data shown in Table 1.

If there are no specific interactions between water and additive (component 2), the magnetic susceptibility, χsample, of their mixture may be written as

χsample ) φwχw + φ2χ2 concentration for many kinds of solutes. The upper concentration of N-methylurea was 2 M, though those of the other solutes were smaller than 500 mM. Using the internal standard of 1 mM MeOH, the proton chemical shifts of 1 mM TMA were measured as a function of concentration of BS up to 250 mM. The chemical shift of 1 mM MeOH was 3.358 ppm, referred to internal sodium 3-(trimethylsilyl)2,2,3,3-tetradeuteriopropionate. Results Concentration Dependence of Chemical Shifts Referred to External Reference. The proton chemical shifts, δ, referred to external DSS, of TMA and additive were determined as a function of additive concentration. These chemical shifts changed linearly with the concentration, C2, of additive (component 2):

∆δ ) δ - δ0 ) aC2

(1)

Here, δ0 stands for the chemical shift in the absence of additive. In Figure 1, chemical shift variations, ∆δ, of TMA are shown for acetonitrile, N-methylurea, sodium chloride, and sucrose. Such slopes (termed molar shifts) for protons of TMA and additives are summarized in Table 1. The molar shift for the water proton is close to those for TMA and additives. Such data are not shown in Table 1, because the chemical shift of the water proton was less accurate. The molar shifts are dependent on the kind of additive and almost independent of TMA or additive. The molar shift of N-methylurea is very close to zero, those of acetonitrile, MeOH, and ethanol are positive, and those of the other solutes in Table 1 are negative. To analyze these data, we compiled the bulk (volume) magnetic susceptibilities, χ, of the compounds investigated. The volume magnetic susceptibility, χw, of deuterium oxide is -0.705 × 10-6. The sign of the molar shift is determined by relative magnitude of χ values to this value. Therefore, we suggest that the volume magnetic susceptibility of an aqueous solution changes from that of water to that of additive, as the additive concentration is increased. The advantage of an internal reference lies in the fact that the effective magnetic field, experienced by the nuclei of both

(3)

(4)

Here, φw and φ2 denote the volume fractions of water and the additive. When these volume fractions are expressed using the partial molar volumes, Vw and V2, of water and the additive, eq 4 is written as

χsample ) (xwVwχw + x2V2χ2)/(xwVw + x2V2)

(5)

In eq 5, xw and x2 denote the mole fractions of water and the additive. The partial molar volume is equal to the molar volume in the liquid state for thermodynamically ideal solutions. For nonideal solutions, however, it differs from that in the liquid state and depends on the solute mole fraction, x2. For dilute aqueous solutions, eq 5 is approximately reduced to

χsample ) {(1000 - C2V2)χw + C2V2χ2}/1000

(6)

Here, V2 stands for the partial molar volume of the additive in infinite dilution. From eqs 3 and 6, the observed chemical shift, δ0, in the absence of additive (C2 ) 0) can be written as

δint ) δ0 + 4π(χref - χw)/3

(7)

From eqs 3, 6, and 7, the observed chemical shift, δ, at C2 mol dm-3 can be written as

δ ) δ0 + 4π(χ2 - χw)V2C2/3000

(8)

Thus, we can obtain a theoretical a value from comparison between eqs 1 and 8

a ) 4π(χ2 - χw)V2/3000

(9)

To use eq 9, we need the molar volume and volume magnetic susceptibility of additive in the liquid state. The molar volumes and volume magnetic susceptibilities of additives at the liquid and solid states and at infinite dilution in aqueous solutions are compiled in Table 1. Generally, the molar volumes and volume magnetic susceptibilities are not much dependent on these states. Molar volumes of some additives are estimated by assuming the additivity rule for group molar volumes.9 Because the volume magnetic susceptibilities of saccharides are about -0.88 × 10-6, we employed this value for cyclic and acyclic

NMR Chemical Shift References

J. Phys. Chem. B, Vol. 105, No. 30, 2001 7363

TABLE 1: Volume Magnetic Susceptibilities and Molar Volumes of Additives and Theoretical and Observed Molar Shifts (ppm M-1) of Eq 1 for Protons of TMA and Additives additive

-χ × 106

V mL mol-1

acetonitrile methanol ethanol H2O D2O N-methylurea glycine glycylglycine glycylglycylglycine D-glucose sucrose methylglucopyranoside maltopentaose R-CD β-CD glucosyl-R-CD γ-CD 6-O-R-D-glucosyl-β-CD 6-O-R-maltosyl-β-CD sodium chloride

0.534(l)a,b

52.8(l)a,c

0.530(l)b 0.594(l)d 0.721(l)c 0.705(l)b 0.725(s)b 0.846(s)b 0.846(s)f 0.846(s)f 0.869(s)b 0.877(s)b 0.880(s)f 0.880(s)f 0.880(s)f 0.880(s)f 0.880(s)f 0.880(s)f 0.880(s)f 0.880(s)f 1.151(s)b

40.7(l)c 58.7(l)c 18.0(l) 18.1(l)d 63.2(s)f 64.7(s)g 111.4(s)f 158.1(s) f 115.3(s)b 215.7(s)g 133.0(s)f 506.5(s)f 611.4(aq)j 703.8(aq)j 711.8(aq)f 801.2(aq)j 804.2(aq)f 904.6(aq)f 26.9(s)g

atheory

aobsd TMA

additive

0.038 0.030 0.027

0.035 0.026 0.027

0.036 0.020 0.027e

0.000 -0.0053 -0.038 -0.066 -0.093 -0.079 -0.155 -0.097 -0.371 -0.448 -0.516 -0.522 -0.587 -0.590 -0.663 -0.050

-0.0063 -0.038 -0.061 -0.088 -0.093 -0.175 -0.068 -0.413 -0.421k -0.467k -0.487 -0.598k -0.559 -0.612 -0.045

-0.0079 -0.027 -0.059h -0.087h -0.095i -0.171i -0.433g -0.420l -0.511l -0.601l

a Abbreviations in parentheses indicate the following states; l ) liquid, s ) solid, and aq ) aqueous solution at infinite dilution. b CRC Handbook of Chemistry and Physics, 59th ed.; CRC Press: West Palm Beach, FL, 1978-1979; Chapters C and E-127. c Taken from ref 4. d International Critical Tables; McGraw-Hill: New York, 1929; Vol. 6. e Methyl proton. f Estimated from volume magnetic susceptibilities and molar volumes of similar compounds. g Merck Index, 7th ed.; Merck: Rahway, NJ, 1960. h Protons of CH2COO-. i H1 proton of saccharide. j Szejtli, J. Cyclodextrin Technology; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1988; p 12. k Taken from ref 6. l Average over all kinds of CD protons, taken from ref 7.

Figure 2. The observed molar shift a defined by eq 1 as a function of molar volumes of all saccharides (O) and oligoglycines (2) listed in Table 1. The solid and dashed lines show the theoretical slopes calculated using eq 9 with volume magnetic susceptibilities of -0.880 × 10-6 (oligosaccharides) and -0.846 × 10-6 (oligoglycines) and their molar volume data shown in Table 1.

oligosaccharides. For glycylglycine and glycylglyclglycine, the volume magnetic susceptibility of glycine was employed. As shown in Table 1 and Figure 1, the theoretical a values calculated from eq 9 are close to the observed ones. For the oligoglycines and cyclic and acyclic oligosaccharides listed in Table 1, the observed a values are plotted against the molar volumes in Figure 2. The dashed and solid lines for these oligoglycines and oligosaccharides, calculated from eq 9 with the molar volumes and magnetic susceptibilities shown in Table 1, are very close to the observed data. Ion-Pair Formation of TMA and BS. A convenient reference signal is one that is sharp and well separated from other signals in the NMR spectrum. The use of an internal reference signal has the advantage that no bulk-susceptibility corrections

Figure 3. Chemical shift of TMA, referred to internal 1 mM methanol, plotted against the BS concentration. The solid line is calculated using eq 11 with best fit values of ∆δTMA‚BS ) -0.1654 ppm and K1 ) 2.43 M-1.

are necessary. These procedures are satisfactory only when specific solvent and solution effects are unimportant.3-5 Sodium 3-(trimethylsilyl)2,2,3,3-tetradeuteriopropionate and DSS have been often used for such primary internal references in aqueous solution systems. However, these compounds can form complexes with many solutes, such as CDs and cationic compounds. For aqueous CD solutions, therefore, TMA, the methyl sulfate ion, the methanesulfonate ion, and MeOH were recommended as internal references, because they are practically inert.6,7 The signals of these secondary internal references may overlap with other signals in the NMR spectrum. Apart from inclusion complexes, TMA forms the ion-pair complex with BS by electrostatic attraction.7 To investigate the interactions between TMA and BS in more detail, we determined the chemical shift of TMA, referred to internal MeOH, as a function of BS concentration. As shown

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Funasaki et al.

in Figure 3, the chemical shift of the methyl protons of TMA decreases with increasing BS concentration, CBS. This change results from the 1:1 ion-pair formation:

TMA+ + BS- ) TMA‚BS

(10)

Therefore, δ can be written as

δ ) {[TMA]δTMA + [TMA‚BS]δTMA‚BS}/CTMA ) {[TMA]δTMA + K1[TMA][BS]δTMA‚BS}/CTMA (11) Here δTMA and δTMA‚BS denote the chemical shifts of TMA and the complex and K1 is the equilibrium constant of ion-pair formation. Once δTMA‚BS and K1 are given, δ at CTMA ) 1 mM can be calculated as a function of CBS from eq 11. Thus, we determined best fit values of ∆δTMA‚BS ) -0.1654 ppm and K1 ) 2.43 M-1 by nonlinear least-squares method. The chemical shift of a proton near the benzene molecule increases or decreases by the ring-current effect, depending on the position of the TMA ion relative to the benzene ring. The proton held in a position directly above the benzene ring resonates in higher field.10,11 Therefore, a negative value of ∆δTMA‚BS ) -0.1654 ppm indicates that at least some of the tetramethyl protons are located above the benzene ring (strongly shielded location) of BS. This is due to the hydrophobic interaction between these methyl groups of TMA and the phenyl group of BS. The positive nitrogen ion of TMA will be strongly attracted to the negative sulfonate moiety. Therefore, TMA, a positively charged and weakly hydrophobic compound, is not suitable as the internal reference for BS, a negatively charged and weakly hydrophobic compound, in aqueous systems. Generally, two amphiphilic ions opposite in sign tend to form an ion-pair by hydrophobic and electrostatic interactions. Keeping this fact in mind, we must choose an appropriate internal standard. Discussion Volume Magnetic Susceptibility Effect. Chemical shifts of a nucleus in binary liquid mixtures are determined as a function of composition and are analyzed in terms of the difference in volume magnetic susceptibility between solute and solvent and intermolecular interactions (hydrogen bond, self-association, complex formation, and other reactions) between solute and solvent or two solutes.2,3,5,14-16 For instance, the equilibrium formation constants of charge-transfer complexes have been determined by chemical shift measurements.15,16 The effect of a considerable number of diamagnetic salts on the chemical shift of water (uncorrected for volume magnetic susceptibility) was examined and separated into the contributions of anion and cation by Shoolery and Alder.17 For instance, their molar shift value of sodium chloride is -0.058 ppm M-1. This value is close to our observed and theoretical molar shifts of sodium chloride (Table 1). This agreement suggests that most of the molar shift for each ion, estimated by them, results from the change of the volume magnetic susceptibility of the aqueous solution with addition of salt. However, the important uncertainty in application of eq 9 to electrolytes is concerned with the molar volumes of electrolytes. No electrolyte forms a thermodynamically ideal solution with water, though eq 9 is based on this assumption. The partial molar volume of an electrolyte in infinite dilution usually differs from its molar volume in the solid state.12 For instance, the partial molar volume of sodium chloride in infinite dilution at 298.2 K is 16.6 cm3 mol-1,13 but this value differs far from the molar

volume of sodium chloride in the solid state (Table 1). Therefore, the applicability of eq 9 to electrolytes should be investigated further. Recently, many artificial host molecules have been synthesized and chemical shift measurements have been used to determine their binding constants of various guest compounds in water and organic solvents.1,2 Natural host molecules, CDs, can include hydrophobic molecules, such as DSS and drugs, into their cavities. Acyclic saccharides as well as CDs can change the chemical shift of TMA referred to external DSS, and the molar shifts of acyclic saccharides and CDs are roughly proportional to the number of glucose units. The reason for these results was ascribed to the changes in the magnetic susceptibility of water due to hydrogen bonding with the glucose units.6,7 The correct reason, however, is that the volume magnetic susceptibility of an aqueous solution changes from that of the pure solvent toward the value for that of the solute. Though this is the main reason, other small effects must be taken into consideration. For instance, the observed molar shift of the methanol proton is significantly different from the theoretical value in Table 1. This difference may be due to the hydrogen bond of methanol and water. Chemical Shift Method for Binding Constant Determination. From chemical shifts using internal and external standards, binding constants have been determined for various host-guest systems.1,2,6-8,11 The external standard method has the advantage of inertness to the system to be measured but the disadvantage of having to apply volume susceptibility corrections. Uncorrected chemical shift data are often used for binding constant determination. Corrected data gave the same binding constants as those determined from chemical shifts referred to internal standards.7,15 However, such corrections are tedious and are not easy, particularly for multicomponent systems. Appropriate internal standards for binding constant determination should be as inert as possible to the system under investigation and should exhibit negligible changes in chemical shift with any molecular interactions. Such standards in aqueous systems include MeOH, TMA, sodium methyl sulfate, sodium methanesulfonate, and HDO. Because MeOH is an uncharged molecule and has small binding constants (0.9 and 0.3 M-1 for R-CD and β-CD), it is an excellent internal standard.6 Though the binding constants of TMA with CDs have not been determined, they would be smaller than those of MeOH. TMA is also an excellent internal standard for neutral and cationic compounds. For systems of neutral and cationic guests with R-CD, chemical shift data referred to internal TMA or MeOH signal gave accurate binding constants.6,18 For anionic compounds, sodium methyl sulfate and sodium methanesulfonate have been suggested to be good internal standards.7 The logarithms of binding constants of R-CD and sodium alkanesulfonates change linearly with the number, nC of carbon atoms of alkanesulfonates (nC ) 4 to 6).19 From this linearity, the binding constant of sodium methanesulfonate is extrapolated to be 1.3 M-1. This small binding constant indicates that sodium methanesulfonate is a good internal standard for R-CD systems. The 1:1 binding constants of R-CD with sodium methanesulfonate, sodium methyl sulfate, and MeOH will be larger than those of β-CD and γ-CD. Because β-CD and γ-CD have cavities large enough to include a guest and a small thin molecule simultaneously, they can form ternary complexes.20 For β-CD and γ-CD, therefore, we cannot completely exclude the possibility of ternary complexation of these internal standards. For instance, β-CD forms a ternary complex with pyrene and

NMR Chemical Shift References MeOH.21 Therefore, MeOH will not be a very good internal standard for binding constant determination of the β-CD-pyrene system. The HDO signal may be used as a good internal standard.11 Because temperature affects this signal sensitively, temperature must be kept as constant as possible. Acknowledgment. Thanks are due to Ms. Noriko Nagai for her precise NMR measurements. We also thank reviewers for their valuable suggestions. The work was supported by Grantsin-Aids from the Scientific Research Program (No. 116721153) and the Frontier Research Program of the Ministry of Education, Science, Sports, and Culture of Japan. References and Notes (1) Schneider, H.-J.; Yatsimirsky, A. K. Principles and Methods in Supramolecular Chemistry; John Wiley and Sons: New York, 2000; Chapter E4. (2) Fielding, L. Tetrahedron 2000, 56, 6151. (3) Pople, J. A.; Schneider, W. G.; Bernstein, H. J. High-Resolution Nuclear Magnetic Resonance; McGraw-Hill: New York, 1959; Chapters 4, 15, 16, and 18 and Appendix C. (4) Martin, M. L.; Martin, G. J.; Delpuech, J.-J. Practical NMR Spectroscopy; Heyden: London, 1980; Chapter 5. (5) Emsley, J. W.; Feeney, J.; Sutcliffe, L. H. High-Resolution Nuclear Magnetic Resonance Spectroscopy; Pergamon: Oxford, 1965; Chapters 7 and 10.

J. Phys. Chem. B, Vol. 105, No. 30, 2001 7365 (6) Matsui, Y.; Tokunaga, S. Bull. Chem. Soc. Jpn. 1996, 69, 2477. (7) Funasaki, N.; Nomura, M.; Yamaguchi, H.; Ishikawa, S.; Neya, S. Bull. Chem. Soc. Jpn. 2000, 73, 2727. (8) Ishikawa, S.; Neya, S.; Funasaki, N. J. Phys. Chem. B 1998, 102, 2502. (9) Funasaki, N.; Hada, S.; Neya, S. J. Phys. Chem. 1984, 88, 1243. (10) Bovey, F. A. Nuclear Magnetic Resonance Spectroscopy; Academic Press: New York and London, 1969; Chapter 3 and Appendix C. (11) Hada, S.; Ishikawa, S.; Neya, S.; Funasaki, N. J. Phys. Chem. B 1999, 103, 2579. (12) Millero, F. S. Chem. ReV. 1971, 71, 147. (13) Millero, F. S. J. Phys. Chem. 1970, 74, 356. (14) Kuntz, I. D., Jr.; Johnston, M. D., Jr. J. Am. Chem. Soc. 1967, 89, 6008, and references therein. (15) Chudek, J. A.; Foster, R.; Livingston, D. J. J. Chem. Soc., Faraday Trans. I 1979, 1222. (16) Ja¨ckel, H.; Stamm, H. J. Phys. Chem. 1990, 94, 3495, and references therein. (17) Shoolery, J. N.; Alder, B. J. Chem. Phys. 1955, 23, 805. (18) Funasaki, N.; Yamaguchi, H.; Ishikawa, S.; Neya, S. J. Phys. Chem. B 2001, 106, 760. (19) Tee, O. S.; Bozzi, M.; Hoeven, J. J.; Gadosy, T. A. J. Am. Chem. Soc. 1993, 115, 8990. (20) Szejtli, J. Cyclodextrin Technology; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1988; Chapter 2. (21) Hamai, S. J. Phys. Chem. 1989, 93, 2074.