12336
J. Phys. Chem. B 2002, 106, 12336-12343
Enthalpy and Entropy Decomposition of Free-Energy Changes for Side-Chain Conformations of Aspartic Acid and Asparagine in Acidic, Neutral, and Basic Aqueous Solutions Tomohiro Kimura,† Nobuyuki Matubayasi,† Hirofumi Sato,‡ Fumio Hirata,‡ and Masaru Nakahara*,† Institute for Chemical Research, Kyoto UniVersity, Uji, Kyoto 611-0011, Japan, and Department of Theoretical Study, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan ReceiVed: May 21, 2002; In Final Form: September 12, 2002
Trans and gauche conformational equilibria in the side chains of aspartic acid (Asp) and asparagine (Asn) were investigated by measuring the vicinal spin-spin coupling constants of 1H NMR in acidic, neutral, and basic aqueous solutions over a wide range of temperature (5-90 °C). The standard free-energy changes ∆G0 were obtained for the trans to gauche conformational variations on the CR-Cβ bond with respect to the R-carboxyl group and the β-carboxyl group in Asp (β-amide in Asn) and were decomposed into enthalpic ∆H0 and entropic -T∆S0 components. The hydration of ionic and polar groups in Asp competes against the large intramolecular electrostatic repulsion energy and stabilizes the gauche more than the trans conformer in correspondence to a larger degree of separation of positive and negative partial charges. In the neutral solutions, where both the carboxyl groups are negatively ionized, the hydration part even overwhelms the intramolecular repulsion and leads to a negative ∆H0. The fact that the hydration almost cancels the intramolecular electrostatic repulsion contradicts the widely accepted view that the trans preference in the conformational equilibrium is due to the intramolecular repulsion between R-CO2- and β-CO2- (or β-CONH2).
1. Introduction Understanding the conformational equilibrium in water is a very important issue in biochemistry and biophysics. Conceivable controlling factors for conformational equilibrium are electrostatic interactions, van der Waals interactions, hydrogen bonds, and hydrophobic effects.1 Among these, intramolecular electrostatic interaction between ionized groups has been believed to control the ionized side-chain conformer distributions of amino acids and peptides in aqueous solution.2-5 This is indeed the case in the gas phase. In aqueous solution, however, the simple interpretation must be scrutinized because of the presence of the hydration effect on the ionic and polar functional groups. Our purpose here is to gain insight into the role of hydration. The hydration effect is studied for aspartic acid (Asp) and asparagine (Asn), whose side-chain conformational equilibria at different ionization states can be inspected in detail by varying the pH (see the Asp and Asn structures in Figure 1a). Comprehensive measurements of the vicinal coupling constants in 1H NMR at dilute conditions will be performed by applying the three-staggered-state model shown in Figure 1b.6 For an understanding of the role of hydration of ionizable groups in the conformer free energies, it is of interest to carry out ab initio calculations for the molecule of interest in the gas phase. A determination of the energy change in the gas phase (∆E0gas) accompanying the conformational variation leads to the estimation of the hydration part of the free-energy change * To whom correspondence should be addressed. E-mail: nakahara@ scl.kyoto-u.ac.jp. Phone: +81-774-38-3070. Fax: +81-774-38-3076. † Kyoto University. ‡ Institute for Molecular Science.
Figure 1. (a) Molecular structures of Asp and Asn with their ionization states in aqueous solution at neutral pH. The arrows represent the dihedral angles analyzed. (b) Staggered side-chain conformers of Asp or Asn with respect to the dihedral angles analyzed. C represents the β-carboxyl carbon for Asp or the β-amide carbon for Asn. N represents the R-amino nitrogen, and C represents the R-carboxyl carbon.
(∆G0hyd) given by
∆G0hyd ) ∆G0 - ∆E0gas
(1)
where ∆G0 is the experimentally obtainable overall free-energy change in solution. ∆G0hyd describes the effect of water on the conformational equilibrium and is the major target of the present study. To elucidate the role of hydration, it is crucial to investigate separately the enthalpic (∆H0) and entropic (-T∆S0) compo-
10.1021/jp021246o CCC: $22.00 © 2002 American Chemical Society Published on Web 11/05/2002
Conformations of Aspartic Acid and Asparagine
J. Phys. Chem. B, Vol. 106, No. 47, 2002 12337
nents of ∆G0 in aqueous solution. To the best of our knowledge, however, no attempt has ever been made to separate ∆H0 and -T∆S0 for the side chains of amino acids and peptides in aqueous solution. Although the temperature effect on the conformer distributions was examined by NMR in a few papers,3,7-9 the separation into ∆H0 and -T∆S0 can be achieved only by studying the fine temperature effect. Only in the case of water-containing methanol solutions were ∆H0 and -T∆S0 separated for the side chains of tryptophan (Trp) and histidine (His), and the compensation of ∆H0 and -T∆S0 was referred to.10,11 To examine the reliability and limitations of the intramolecular electrostatic view for aqueous solution, we extract ∆H0 from ∆G0 because ∆H0 more directly reflects the electrostatic interaction energy, whereas other effects such as the excluded volume, in general, are also important in ∆G0. The experimentally observed ∆H0 value consists of the intramolecular term ∆E0gas and the hydration term ∆H0hyd:
∆H0 ) ∆E0gas + ∆H0hyd
(2)
Thus, by combining the experimental results and theoretical calculations, the conformational energetics of the hydration and intramolecular effects can be separately discussed. Similarly, by separating -T∆S0, we can discuss the hydration entropy T∆S0hyd since -T∆S0 can be assumed here to be dominated by the hydration effect. The organization of this paper is as follows. We introduce the basis for conformational analysis in section 2. In section 3, we describe the procedures for the NMR measurements and theoretical calculations. We present the ionization state and temperature dependence of the observed Jvic in section 4.1 and the conformer distributions and ∆G0 in section 4.2. In section 4.3, we characterize the trends of the obtained values of ∆H0 and -T∆S0 and discuss the role of hydration in determining the thermodynamic quantities. Concluding remarks will be given in section 5.
name the conformers according to the method used above to focus on the dihedral angle for the R-carboxyl and β-carboxyl carbons in Asp (β-amide in Asn); T represents trans, whereas G+ and G-, gauche. The conformer distribution of the side chain can be evaluated by solving eqs 3a-3c. We also mention that the NMR signals from the two β-protons were assigned to β1 and β2 on the basis of the deuterium labeling experiment.4 To determine the probabilities in the rapid-exchange mechanism from the observed JRβ1 and JRβ2, we need a set of parameters Jt and Jg. It is known that the parameters depend on the electronegativity of the substituent.15 An appropriate set including the substituent effect for amino acids was developed by Pachler14 and has been used widely.6 In this work, the sidechain conformer probabilities of Asp and Asn amino acids were estimated by using Pachler’s parameter set. It was reported that the substituent effect on Jvic depends on the relative configuration of the substituent with regard to the coupling nuclei,16 and Feeney’s parameter set takes account of this effect in parameters Jt and Jg.17 In this paper, we report the results from Pachler’s parameter set because it was confirmed that the examination with the two parameter sets of Pachler and Feeney provides identical conclusions on the distribution trend. 2.2. Standard Thermodynamic Quantities. The equilibrium constant (Kx/T) between conformers T and x is represented by
Kx/T )
ln Kx/T ) -
JRβ1 ) P(T)Jt + P(G+)Jg + P(G-)Jg
(3a)
JRβ2 ) P(T)Jg + P(G+)Jt + P(G-)Jg
(3b)
P(T) + P(G+) + P(G-) ) 1
(3c)
where P(T), P(G+), and P(G-) are the probabilities for conformers T, G+, and G- defined in Figure 1b and Jt and Jg are the Jvic values between the R- and β-protons in the trans and gauche conformers, respectively. In Figure 1b, the β1-proton takes the trans conformation to the R-proton in conformer T and the gauche conformation in conformers G+ and G-. We
(4)
where P(T) and P(x) are the probabilities of conformers T and x, respectively (x denotes either conformer G+ or G-). Conformer T is chosen as the reference since the large probability of this conformer is of particular interest in view of the role of intramolecular electrostatic interaction between R-CO2- and β-CO2- in Asp (β-CONH2 in Asn). The Kx/T value is then related to the standard free-energy change ∆G0(T f x) from T to x through the thermodynamic relation
2. Basis for Conformational Analysis 2.1. Conformer Probabilities. A vicinal spin-spin coupling constant (Jvic) exhibits dihedral-angle dependence,12 which allows us to examine the conformations of amino acids, peptides, and proteins for both the backbone and side chains.6 For amino acid residues of ABX-type spin systems in 1H NMR, where the two β-protons couple strongly only with one R-proton, Jvic between the R- and β-protons (JRβ1 and JRβ2) can be explicitly calculated by employing the reported procedure.13 The experimentally observed JRβ1 and JRβ2 in solution are probabilityweighted averages due to fast exchanges on the NMR time scale for the component conformers on the CR-Cβ bond shown in Figure 1b.14 According to the three-staggered-state model, we express the observed JRβ1 and JRβ2 as
P(x) P(T)
∆G0(T f x) RT
(5)
where the T is the absolute temperature (K) and R is the gas constant (kJ mol-1 K-1). The standard enthalpy change ∆H0(T f x) is obtained from the van’t Hoff equation, and the standard entropy change -T∆S0(T f x) is simply given by ∆G0(T f x) - ∆H0(T f x). 3. Methods 3.1. Materials. L-Aspartic acid (Asp) monopotassium salt (GR grade) was purchased from Nakalai, and L-asparagine (Asn) was from Sigma. Both of these materials were used without further purification. Deuterium oxide solvent (D2O; 99.90% D) was purchased from Euriso-top. D2O solutions of DCl (18 wt %) and NaOD (40 wt %) used to control the solution pD were from Aldrich. Aqueous solutions of Asp and Asn were prepared at 20 mM. At this concentration, we can neglect the effect of intermolecular interactions among the solute molecules on the conformer distributions. To vary the solute ionization state, the aqueous solutions were prepared at three different pD conditions (see the pD values in Table 1). The pD values were obtained by adding 0.4 unit to the pH meter (HORIBA D-21) readings.18 3.2. 1H NMR Measurements. 1H NMR measurements of aqueous solutions of Asp and Asn were carried out on a 270MHz spectrometer (JEOL JNM-EX270) equipped with probes
12338 J. Phys. Chem. B, Vol. 106, No. 47, 2002
Kimura et al.
TABLE 1: Observed Spin-Spin Coupling Constants (Hz) among the r- and β-Protons of Asp and Asn Amino Acids in Acidic, Neutral, and Basic Aqueous Solutions at Various Temperatures amino acid Asp
Asn
a
solution condition acidic (pD ) 0.9)
J
JRβ1 JRβ2 Jβ1β2 neutral JRβ1 (pD ) 7.3) JRβ2 Jβ1β2 basic JRβ1 (pD ) 13.8) JRβ2 Jβ1β2 acidic JRβ1 (pD ) 1.2) JRβ2 Jβ1β2 neutral JRβ1 (pD ) 7.7) JRβ2 Jβ1β2 basic JRβ1 (pD ) 12.6) JRβ2 Jβ1β2
10
20
30
6.28 ( 0.01 4.18 ( 0.01 18.37 ( 0.00 9.07 ( 0.03 3.49 ( 0.03 17.52 ( 0.04 10.17 ( 0.01 3.59 ( 0.00 15.37 ( 0.00 6.23 ( 0.02 4.43 ( 0.03 17.37 ( 0.01 7.93 ( 0.01 4.05 ( 0.02 16.92 ( 0.01 9.18 ( 0.02 4.63 ( 0.02 14.72 ( 0.00
6.33 ( 0.00 4.27 ( 0.01 18.36 ( 0.01 9.08 ( 0.02 3.54 ( 0.01 17.50 ( 0.01 10.12 ( 0.01 3.63 ( 0.01 15.33 ( 0.01 6.36 ( 0.03 4.44 ( 0.03 17.45 ( 0.01 7.95 ( 0.01 4.08 ( 0.00 16.90 ( 0.00 9.11 ( 0.01 4.68 ( 0.01 14.76 ( 0.01
6.37 ( 0.05 4.32 ( 0.05 18.36 ( 0.01 9.10 ( 0.01 3.58 ( 0.02 17.47 ( 0.01 10.08 ( 0.00 3.64 ( 0.01 15.30 ( 0.00 6.55 ( 0.02 4.31 ( 0.03 17.44 ( 0.01 7.96 ( 0.01 4.12 ( 0.02 16.89 ( 0.00 9.05 ( 0.01 4.71 ( 0.01 14.77 ( 0.00
40
temperature/°C 50
60
70
80
90
a a a a a 6.45 ( 0.01 a a a a a 4.34 ( 0.02 a a a a a 18.33 ( 0.01 9.13 ( 0.00 9.17 ( 0.01 9.21 ( 0.00 9.25 ( 0.01 9.28 ( 0.01 9.31 ( 0.01 3.62 ( 0.01 3.64 ( 0.01 3.64 ( 0.00 3.67 ( 0.01 3.68 ( 0.01 3.68 ( 0.02 17.42 ( 0.01 17.39 ( 0.01 17.34 ( 0.01 17.30 ( 0.01 17.27 ( 0.01 17.21 ( 0.03 10.02 ( 0.01 9.97 ( 0.00 9.95 ( 0.01 9.88 ( 0.02 9.84 ( 0.00 9.81 ( 0.01 3.70 ( 0.01 3.72 ( 0.00 3.74 ( 0.00 3.78 ( 0.00 3.79 ( 0.00 3.80 ( 0.01 15.27 ( 0.00 15.24 ( 0.00 15.21 ( 0.00 15.18 ( 0.00 15.16 ( 0.00 15.13 ( 0.00 a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
7.98 ( 0.01 8.00 ( 0.01 8.03 ( 0.01 8.03 ( 0.01 8.06 ( 0.01 8.07 ( 0.01 4.13 ( 0.01 4.14 ( 0.02 4.16 ( 0.01 4.18 ( 0.01 4.18 ( 0.02 4.19 ( 0.03 16.88 ( 0.01 16.86 ( 0.01 16.85 ( 0.01 16.83 ( 0.01 16.82 ( 0.02 16.84 ( 0.01 8.98 ( 0.01 8.90 ( 0.00 8.83 ( 0.00 8.78 ( 0.01 8.71 ( 0.00 8.65 ( 0.01 4.74 ( 0.01 4.76 ( 0.00 4.79 ( 0.01 4.80 ( 0.00 4.83 ( 0.01 4.84 ( 0.02 14.79 ( 0.00 14.81 ( 0.00 14.83 ( 0.00 14.84 ( 0.01 14.86 ( 0.01 14.88 ( 0.01
Values could not be obtained because of signal overlap.
for 5- or 10-mm o.d. sample tubes. Free-induction decay (FID) signals were accumulated 8 to 64 times. The digital frequency resolution was set to 0.01 Hz. The temperature effect was examined at an interval of 10 °C from 10 to 90 °C except at the acidic pD, where the examination was done at an interval of 5 °C from 5 to 40 °C for Asp and from 5 to 30 °C for Asn. At the acidic pD, we restricted the temperature range because of the signal overlap at the higher temperatures. The temperature uncertainties were (0.1 °C. The FID signals were obtained more than 30 min after a temperature change. At each temperature, the measurement was repeated two or three times. 3.3. Calculations of Conformer Energies and Effective Polarities. Calculations of the electronic structure and effective charges qj on the constituent atoms j of the side-chain conformers of Asp in the gas phase were carried out at the ab initio Hartree-Fock level of approximation. The Gaussian basis set, (9s, 5p)/[3s, 2p], for the double-ζ qualities of Slater-type orbitals was used with the single d-polarization functions (exponents 0.75 for carbon, 0.80 for nitrogen, and 0.85 for oxygen).19 The consideration of electron correlation by the second-order perturbative Møller-Plesset (MP2) formalism or the use of a larger basis set of 6-311G(d,p) affected the conformational energy change by less than ∼4 kJ mol-1. The effective charges in the solute molecule were determined by the electrostatic potential (ESP) fitting procedure. The geometry optimizations were carried out with the dihedral angles constrained to those shown in Figure 1b. The ionization states calculated correspond to those at the experimental pD conditions. In the optimization, the orientation of the neutral R-carboxyl group (or β-carboxyl group) was chosen so that the carbonyl oxygen was closer than the hydroxyl oxygen to the R-ammonium group (or R-carbon). The orientation of hydroxyl part of the carboxyl group was also chosen so that the hydroxyl hydrogen was closer to the carbonyl group. It was confirmed that the alternative orientations lead to an increase in the conformational energy. The conformation of the neutral amino group was optimized to ensure the energy minimum. All of the computations were performed with the program package GAMESS.20 According to thorough ab initio investigations of the gasphase potential energy surface of glycine, there is general agreement that R-amino acids in the gas phase are energetically
more favorable in the neutral form than in the zwitterionic form.21,22 However, for our present purpose of discussing the hydration effect on the charged species, it is useful to determine the ab initio gas-phase energy of the zwitterionic form, which often appears as a local minimum for certain basis sets including ours.23 To see the effect of the hydration part of the free energy change ∆G0hyd given by eq 1, it is of interest to seek the correlation of the ∆G0hyd value with some index for the solutesolvent interactions. Since the molecules of interest in the present study carry both positive and negative charges, we introduce the effective polarity µ† as an empirical index with which to characterize the strength of the solute-solvent interaction. µ† is defined as the dipole moment with its coordinate origin positioned at the charge center b re ) ∑j|qj|r bj/∑j|qj|:
µ† ) )
∑j qj(br j - br e) 2Q+Ql Q + + Q-
(6)
where b rj represents the position of a partial charge qj, 2Q+Q-/ + (Q + Q-) is the harmonic mean of the sum of the positive charges Q+ ) ∑ qj and the sum of the negative charges Q- ) qj>0
∑ |qj|, and l is the distance between the centers of positive
qj
