Article pubs.acs.org/JPCB
“Hydration Shells” of CH2 Groups of ω‑Amino Acids as Studied by Deuteron NMR Relaxation Sevastyan O. Rabdano,†,‡ Alexey V. Donets,‡ Mikhail A. Vovk,§ Dieter Michel,∥ and Vladimir I. Chizhik*,‡ †
Laboratory of Biomolecular NMR, St. Petersburg State University, St. Petersburg 199034, Russia Department of Physics, St. Petersburg State University, St. Petersburg 198504, Russia § Center for Magnetic Resonance, St. Petersburg State University, St. Petersburg 198504, Russia ∥ Institute of Experimental Physics II, University of Leipzig, Linnéstr. 5, D-04103 Leipzig, Germany ‡
ABSTRACT: Hydration phenomena play a very important role in various processes, in particular in biological systems. Water molecules in aqueous solutions of organic compounds can be distributed among the following substructures: (i) hydration shells of hydrophilic functional groups of molecules, (ii) water in the environment of nonpolar moieties, and (iii) bulk water. Up to now, the values of hydration parameters suggested for the description of various solutions of organic compounds were not thoroughly analyzed in the aspect of the consideration of the total molecular composition. The temperature and concentration dependences of relaxation rates of water deuterons were studied in a wide range of concentration and temperature in aqueous (D2O) solutions of a set of ω-amino acids. Assuming the coordination number of the CH2 group equal to 7, which was determined from quantum-chemical calculations, it was found that the rotational correlation times of water molecules near the methylene group is 1.5−2 times greater than one for pure water. The average rotational mobility of water molecules in the hydration shells of hydrophilic groups of ω-amino acids is a bit slower than that in pure solvent at temperatures higher that 60 °C, but at lower temperatures, it is 0.8−1.0 of values of correlation times for bulk water. The technique suggested provides the basis for the characterization of different hydrophobic and hydrophilic species in the convenient terms of the rotational correlation times for the nearest water molecules.
1. THE PROBLEM OF HYDRATION OF AMPHIPHILIC MOLECULES Hydration phenomena play a very important role in various processes, in particular in biological systems. Organic molecules can be composed of both hydrophilic and hydrophobic molecular groups. In solutions, water molecules form hydrogen bonds with the polar hydrophilic groups such as carboxylic or amine groups. Water molecules near the nonpolar hydrophobic groups like methylene CH2 and methyl CH3 behave differently in comparison with the bulk water because of the so-called “hydrophobic effect”. Water molecules, located near the hydrophobic part of solute molecules in a solution, cannot be involved in strong interactions with those fragments, but they form a distorted hydrogen bond network, that leads to the perturbed molecular dynamics. Hence, water molecules in aqueous solutions of organic compounds can be distributed among the following substructures: (i) hydration shells of hydrophilic functional groups of molecules, (ii) water in the environment of nonpolar moieties, and (iii) bulk water. Translational and rotational mobility, and geometry of the hydrogen bond network are different for water molecules in different substructures. Many researchers have shown that it is necessary to consider at least two substructures of water in solutions of organic compounds.1−14 The presence of some functional groups, for example, halogen atoms, can induce significant peculiarities in water structure and dynamics.15 © XXXX American Chemical Society
Therefore, a certain number of substructures is required for the adequate description of these systems. A natural way to determine the number of possible substructures is to take into account the number of different molecular groups in a solute molecule plus the substructure of the bulk water. Nevertheless, up to now, the values of hydration parameters, which were suggested for the description of various solutions of organic compounds, are not thoroughly analyzed in the aspect of the consideration of the total molecular composition. Only general qualitative conclusions have been made about the character of molecular motion in solutions due to the presence of the hydrophobic and hydrophilic parts of organic molecules.4,6−10,16−19 For a long time, the method of the nuclear magnetic relaxation has been successfully used for the investigation of the reorientational mobility in the liquid state.20−23 The magnetic relaxation processes are determined by the intensity of fluctuating electromagnetic fields in matter. Thus, the investigation of these processes is in close interweaving with the study of the nature and velocity of thermal molecular motion, which produces those fluctuating fields. Modern NMR spectrometers provide the possibility to investigate the Received: July 9, 2015 Revised: August 15, 2015
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DOI: 10.1021/acs.jpcb.5b06584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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aqueous solutions of organic compounds. Results of such studies revealed the big difference in the hydration of hydrophilic and hydrophobic functional groups. For instance, Yogeswari et al. carried out the quantum chemical calculations of the aqueous complexes of glycine and diglycine by gradually increasing the number of water molecules.34,35 Water molecules primarily form hydrogen bonds with the hydrophilic parts of a solute molecule. The aqueous environment around hydrophobic fragments starts when the hydration shells of hydrophilic functional groups are filled. It was estimated that the structures near hydrophobic fragments are energetically more favorable than the structures with hydrogen bonds between water molecules and hydrophilic groups. Monte Carlo simulations36−40 and classical41−44 and quantum45,46 molecular dynamics provide the radial distribution functions (RDFs) between atoms of water and solute molecules. RDFs for hydrophilic functional groups have sharp first maxima at the distance of a typical hydrogen bond. For hydrophobic functional groups, a broad maxima is located at 1−2 Å farther. Alagona et al. obtained the distributions of the angle formed by one of the O−H bonds of a water molecule with the X−O axis, where X is an atom of the functional group considered.36−38 As might be expected, the hydrophobic fragments do not orient water molecules: the distribution is broad, and all orientations are present. Water molecules in hydration shells of hydrophilic functional groups are forced to be oriented in accordance with the rule of hydrogen bonds: the defined above angle has relatively sharp maxima at about tetrahedral angle (109.5°). Monte Carlo simulations show that the interaction energy between the water molecules increases near hydrophobic moieties of propionic acid.39 Campo et al. obtained the lifetimes of water molecules in the environments of functional groups of the glycine zwitterion by the molecular dynamics method.44 Their results predict no significant difference in lifetimes of water molecules near hydrophobic and hydrophilic moieties and in the bulk phase. Using molecular dynamics, Beck et al. obtained the residence times for water molecules in hydration shells of molecular groups of various L-amino acids.43 For hydrophobic moieties of amino acids, they predict the higher mobility of water molecules as compared with bulk water and the lower one near hydrophilic functional groups. These results do not coincide with experimental observations reviewed above. This short overview of the results obtained with different methods shows that the understanding of the microstructure of solutions of organic substances is still far from the desirable level. Here we present the approach in which the hydration shell of a solute molecule is considered as the superposition of hydration shells of molecular groups. We prove that in the first approximation the hydration shells of individual functional groups can be characterized by independent structure and dynamics of water molecules. This model was applied to aqueous solutions (D2O) of ω-amino acids: glycine (GLY), βalanine (bALA), γ-aminobutyric acid (GABA), and ε-aminocaproic acid (6ACA). The relaxation rates of deuterons of water molecules near methylene CH2, carboxylic COO−, and amine NH3+ (ND3+) groups were obtained and analyzed to obtain rotational correlation times.
relaxation processes of practically all nuclei in both solvent and solute molecules. Thus, NMR relaxation is characterized by the high selectivity of information about the local molecular mobility in contrast, for example, to viscosity, which reflects the integrated translational mobility in a system. This work focuses on the relaxation processes of water deuterons. Deuteron NMR relaxation is connected to important dynamic and structural parameters: rotational correlation time of molecule τc and electric field gradient (EFG) at a nucleus position.20,23 Deuterons have low natural abundance, and therefore, at first glance, it is more reasonable to use the proton resonance. However, proton magnetic relaxation is greatly influenced by the interaction with spins of paramagnetic species, like molecular oxygen (see the Materials and Methods section). Moreover, the analysis of 1H and 2H NMR relaxation in water and aqueous solutions did not lead to significant differences in the estimations of the mobility of water molecules.10,24−26 Thus, in our investigation, the water enriched with deuterons was chosen as a solvent. A study of solvent molecular dynamics on the basis of quantitative analysis of the deuteron magnetic relaxation in various molecular substructures was carried out in the present work. An important problem is the influence of chemical exchange, affecting both protons and deuterons, on the measured relaxation rates. The influence of exchange processes on the relaxation functions can be taken into account analytically on the basis of the Bloch−McConnell equations.27,28 In many cases, the situation is simplified, since the chemical exchange is fast in the NMR relaxation time scale,29,30 that gives rise to weighted average values of relaxation rates. In order to follow the goal of the paper, we have to consider the already available knowledge on hydration phenomena in aqueous solutions of organic molecules. Most frequently, the two‑phase model is used for the description of solvent microstructure in a solution. NMR and dielectric relaxation,1−14 infrared and microwave absorption,31,32 viscosity,33 and other various physical processes are usually described via the superposition of contributions from the bulk water and the hydration shell of a solute molecule. However, in some studies, water molecules in aqueous solutions of organic compounds, which contain charged or halogenated groups, are divided into the bulk water, hydration shells of those groups, and hydration shell of the rest of the solute molecule.15,33 Changing the molecular composition, it was possible to reveal and explain some peculiarities of hydration shells of specific fragments of a solute molecule. For example, the rather good correlation between the rotational retardation factor (ratio of rotational correlation times of water molecules in the hydration shell and in bulk water) and number of sp3 hybridized carbon atoms in a solute molecule was found for many compounds.17 Water molecules in the environment of hydrophobic methylene and methyl groups slow down their rotational motion in comparison with the bulk phase. The question on the mobility near hydrophilic species, which can form hydrogen bonds with water molecules, is rather open, but the authors of refs 12 and 15 supposed that the mobility of water molecules near small hydrophilic functional groups was higher than that in the bulk phase. These qualitative conclusions are the starting point for the more quantitative analysis of mobility of water molecules in various substructures in solutions. The investigation of water structure in solutions of organic molecules is also possible with various computational methods, which provide insight into the complex microstructure of
2. MATERIALS AND METHODS 2.1. Samples. The samples of glycine (+H3N−CH2− COO−), β-alanine (+H3N−(CH2)2−COO−), γ-aminobutyric acid (+H3N−(CH2) 3−COO−), and ε-aminocaproic acid B
DOI: 10.1021/acs.jpcb.5b06584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B (+H3N−(CH2)5−COO−) were prepared using compounds of high purity (better than 99%) and D2O with 99.9% deuteration. Solutions of amino acids have a pH* value (pH value without isotope correction) almost equal to the isoelectric point of the corresponding amino acid (6.0 for GLY, 6.9 for bALA, 7.3 for GABA, and 7.6 for 6ACA). pH was monitored by a Mettler Toledo FEP20 pH-meter. Under these conditions, all amino acids were in the zwitterionic form. Concentrations of samples are given in units of aquamolality m, i.e., the number of moles of a solute per 55.5 mol of D2O. Concentrations were in the range from 0 m to almost the limit of solubility (3.1 m for GLY, 8.1 m for bALA, 7 m for GABA, and 7 m for 6ACA). 2.2. NMR Experiment. The 2H NMR spectra (at 76.8 MHz) and the 2H spin−lattice relaxation times (T1) in aqueous solutions of organic molecules were measured using a Bruker AVANCE III 500 MHz spectrometer equipped with a broadband inverse (BBI) probe. In the relaxation measurements, the deuteron resonance was used in order to avoid the time-consuming procedure of degassing of samples to remove dissolved from air paramagnetic oxygen. The temperature was varied in the range from 2 to 75 °C using a heated or cooled airflow. The temperature stability was ±0.2 °C. For the T1 measurement, the standard “inversion-recovery” pulse sequence was used. The spectra were processed using Bruker TopSpin 3.2, and the relaxation curves were fitted with the Bruker Dynamics Center 2.1.8 software. For all systems, singleexponential relaxation functions were observed. The deuteron relaxation rate R10 = 1/T10 for pure D2O was determined with an accuracy of 0.7% (results are in agreement with data for deuteron relaxation of pure D2O published in refs 25 and 47). The accuracy of the deuteron relaxation rates R1 = 1/T1 in D2O solutions of organic compounds was better than 0.8%.
are characterized by different rotational correlation times τc and quadrupole coupling constants χ. Quantum chemical calculations have however shown that the difference between the χ for bulk water and hydration shells of solute molecules is about 5−10%.6,48,49 For example, Pavlova and Chizhik carried out accounting this difference for the precise calculation of rotational correlation times in the hydration shells of ions in electrolyte solutions.48 For hydration shells of organic molecules, there is some evidence that the change of τc is considerably greater than 5−10% in comparison to τc of bulk water.1,3−5,7−9,12,16−18,50 Eventually, the variations in NMR relaxation rate R1 are mainly caused by changes in rotational correlation times. Hence, in the following, the EFGs and asymmetry parameters for all solvent substructures are considered to be the same. Owing to some difficulties in the calculations of the absolute magnitude of χ in eq 1, it is appropriate to introduce the relative reorientation times λi =
2 η2 ⎞⎛ eQVzz ⎞ 3⎛ ⎜ ⎟ + τc 1 ⎟ ⎜ 8⎝ 3 ⎠⎝ ℏ ⎠
(2)
where R10 and τc0 are the deuteron relaxation rate and rotational correlation time in the structure of pure water, respectively. Equation 2 also allows the convenient comparison of results obtained from data of different resonances. Let us consider the reaction of the deuteron exchange between several sites characterized by different τc in aqueous solutions of organic molecules (see Scheme 1). Scheme 1. Transfer of Deuterons between Water Molecules
3. THEORETICAL BACKGROUND As is well-known for deuterons (spin I = 1), the dominating relaxation mechanism is due to the interaction of nuclear quadrupole moments with fluctuating electric field gradients.20,23 In this case, the relaxation is described by a single-exponential function. In our case, for all investigated solutions, the extreme narrowing limit is realized that was confirmed by the control measurements at the resonance frequency of 13.8 MHz (spin−lattice relaxation rates are independent of the resonance frequency). Then, for I = 1, the spin−lattice relaxation rate R1 is given by the formula20,23 R1 =
R1i τ = ci R10 τc0
The fast exchange of water molecules between various sites in Scheme 1 is realized (k ≫ R1), and hence, the averaging of the observable R1 is to be taken into account29 N
R1 =
i ∑ pR i 1
(3)
i=1
Ri1
where N is the number of substructures, is the relaxation rate in the ith substructure, and pi is the relative concentration of site i, with ∑pi = 1. The relative concentration for water molecules in a particular site is given by the ratio of the number of water molecules in the site and the total number of water molecules per one solute molecule Ntotal ni mni pi = = Ntotal 55.5 (4)
(1)
Here η = (Vxx − Vyy)/Vzz is the asymmetry parameter of the electric field gradient (EFG), Vxixj denotes the second derivative of the electric potential V with respect to xi and xj coordinates, e is the electron charge, eQ is the nuclear quadrupole moment, ℏ is the reduced Plank constant, and τc is the rotational correlation time. It is worth noting that, in solutions which do not contain small multiply charged ions, the reorientation times for both rotational and translational movement are nearly equal.26 The value χ = eQVzz/ℏ is called the quadrupole coupling constant. Thus, R1 is connected to the important dynamic and structural hydration parameters: the rotational correlation times of a molecule and electric field gradient induced at the nuclei position. Water molecules in aqueous solutions of organic molecules are distributed among various substructures of a solvent, which
where m is the aquamolality of a solution and ni is the number of water molecules in the ith site. The relative concentration for the bulk water is given by (1 − ∑N−1 i=1 pi) (bulk water is the Nth solvent substructure). The formulas 3 and 4 are valid in the concentration range from 0 to m = 55.5/∑ni. The analysis of relaxation rates as functions of the concentration of a solution with known composition can yield the reorientational mobility of water molecules in all distinguishable solvent substructures. Despite the relatively narrow considered temperature range, it is possible to estimate the activation energies for the reorientation of water molecules in hydration shells of functional groups of amino acids from the C
DOI: 10.1021/acs.jpcb.5b06584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B temperature dependences of deuteron R1 using Arrhenius fit of relaxation data: ⎛ E ⎞ R1 ∝ τc = τ0 exp⎜ − a ⎟ ⎝ RT ⎠
where R10 is the relaxation rate in the pure water and B is the well-known B-coefficient for the relaxation rate (see, for example, refs 3 and 6). The B-coefficient describes the slope of the concentration dependence. Similar values are often used for the description of different characteristics of electrolyte and nonelectrolyte solutions.6,26 The positive slope says that the motion of water molecules averaged over all molecules in the hydration shell of a solute molecule slows down with respect to the bulk water, whereas the negative one says that the mobility of these water molecules is higher than that in the bulk water. All experimental concentration dependences were fitted with eq 6 to obtain B-coefficients. The concentration dependences of deuteron relaxation rates for the solutions of all amino acids considered here have positive slope. Thus, it can be concluded that the total influence of methylene, carboxylic, and amino groups of amino acids on the mobility of water molecules is such that the average mobility of D2O in the whole hydration shell of a solute molecule is less than that in the bulk water. It is clearly seen from Figure 2 that B-coefficients almost linearly depend on the number of methylene groups in amino acids at different temperatures. The similar behavior of Bcoefficients was spotted for many compounds. For example, the linear correlation between dynamic hydration number ξ and number of sp3 carbon atoms in a solute was discussed by Qvist
(5)
4. RESULTS AND DISCUSSION 4.1. Concentration Dependences of Deuteron Relaxation in Aqueous Solutions of Amino Acids. The spin− lattice deuteron NMR relaxation rates R1 in aqueous solutions (D2O) of GLY, bALA, GABA, and 6ACA were measured as functions of concentration. The results for temperatures 2, 25, and 55 °C are presented in parts a, b, and c of Figure 1, respectively.
Figure 1. Concentration dependences of deuteron R1 in aqueous solutions of GLY (1, black), bALA (2, blue), GABA (3, red), and 6ACA (4, green) at 2 °C (a), 25 °C (b), and 55 °C (c).
All dependences reveal the monotonic increase in R1 with concentration. The relaxation rates are linear functions of m at low concentrations, and R1 demonstrates this behavior to concentrations corresponding to the disappearance of bulk solvent (when all water molecules are settled in the total hydration shell of a solute molecule). The dependence on concentration m in those limits can be described with the formula R1(m) = R10(1 + Bm)
Figure 2. Dependence of the B-coefficients (eq 6) of deuteron NMR relaxation on the number of methylene groups in a molecule at temperatures of 2 °C (a), 25 °C (b), and 55 °C (c).
(6) D
DOI: 10.1021/acs.jpcb.5b06584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry B et al.,17 who derived dynamic hydration numbers from Bcoefficients as ξ=
solutions of amino acids, which comprise different numbers of CH2 groups, contains information about the deuteron relaxation rate R1CH2 in the hydration shell of CH2: mnCH2 R1′ − R1″ = ΔNCH2 (R1CH2 − R10) (7) 55.5
55.5B +1 nR10
Here n is the coordination number of a solute molecule. The observed additivity of the slope of concentration dependences for amino acids with different numbers of CH2 groups suggests that the contributions into the total relaxation rate can be analyzed, taking into account the detailed composition of a solute molecule. Thus, it seems very promising to consider the hydration shell of a solute molecule as superposition of hydration shells of separate molecular groups. To the best of our knowledge, the similar (but simplified) approach was used only for halogenated alcohols and acetamides by Mizuno et al.15 They considered the hydration shell of a solute molecule as the sum of water molecules near the halogen group and near the rest of the solute. Unfortunately, they obtained only qualitative conclusions about the hydration of a halogen group. According to their data, the water mobility around molecular groups of a solute molecule except the halogen group remains almost unchanged from that before halogenation. The halogen group increases the mobility of water in its vicinity. The y-intercept of the linear fit of B-coefficients dependence on the number of CH2 groups tends to have a small value (see Figure 2). The y-intercept of this dependence corresponds to the B-coefficient for a “molecule” comprised from molecular groups except methylene ones; i.e., for the considered amino acids, these are only carboxylic and amino groups. It follows that they produce a small summary effect on the mobility of water molecules in their hydration shells. Therefore, the linear increase of relaxation rate with the increase of concentration can exclusively be attributed to the influence of methylene groups on the mobility of water molecules near them. The slope of the B dependence on NCH2 is positive (see Figure 2); thus, the reorientational mobility of water molecules near CH2 is less than that in the bulk water. The existence of a coordination sphere around the methylene CH2 group requires special consideration, since this group does not coordinate water molecules by direct bonds. Nevertheless, the water molecules, which are close to this functional group, should be picked out to separate class. In support of this statement, one can mention the pronounceable slowdown of the reorientational mobility of water near hydrophobic parts of organic molecules in comparison with the bulk water.7 Under the “hydration shell” of CH2, we will below imply the molecules of water near this functional group that have a mobility which differs from the mobility of water in other solvent substructures. 4.2. “Hydration Shell” of the CH2 Group. The relaxation rate of D2O deuterons averages between R1 of all sites, where D2O can be located, accordingly to the populations of these sites (see eq 3). We suggest to consider the four following sites: the bulk water and the hydration shells of methylene, carboxylic, and amine groups. Exchangeable hydrogen atoms in the amine group also should be picked out into the separate class, but their exchange with water is fast and they demonstrate a similar relaxation rate as in the bulk water (see discussion in section 4.3). Thus, these atoms could be “included” in the bulk water site. Let us start from eq 3 for GLY, bALA, GABA, and 6ACA. It was found that the difference of D2O relaxation rates in
Here R″1 and R′1 are the deuteron relaxation rates in solutions of two different amino acids and ΔNCH2 is the difference in the number of methylene groups for the pair of amino acids. Thus, R1CH2 can be calculated using the coordination number nCH2 for the CH2 group and B-coefficients for amino acids which comprise different numbers of CH2 groups. Combining eqs 6 and 7, one can obtain R1CH2 = R10 +
55.5 (B ′ − B ″ ) ΔNCH2nCH2
(8)
Another way to calculate R1CH2 from experimental data is to fit the dependence of B-coefficients on the number of methylene groups in a solute molecule (see, for example, Figure 2a) with the following formula derived from eqs 3, 4, and 6: nCH2 n B= (R1CH2 − R10)NCH2 + rest (R1rest − R10) (9) 55.5 55.5 Here nrest is the coordination number for the rest of a solute molecule without methylene groups and R1rest is the relaxation rate of molecules in hydration shells of that part. R1CH2 is calculated from the slope of the linear fit. The averaged relaxation rate for water near hydrophilic carboxylic and amino groups R1rest is calculated from the y-intercept of the dependence of B-coefficients on the number of methylene groups in a solute molecule. It is clear that the knowledge of values of coordination numbers for both individual functional groups and a whole solute molecule is important for the calculations of R1CH2. The coordination number of a whole solute molecule is equal to the sum of coordination numbers of all of its molecular groups. Considered amino acids comprise the amine group (NH3+), carboxylic group (COO−), and methylene groups (CH2). Hydrophilic groups coordinate water molecules via hydrogen bonds. Thus, coordination numbers for them are governed by the number of possible hydrogen bonds that they can form with water molecules.26,51 Therefore, for the amine group, the coordination number nNH3 is equal to 3 (one hydrogen bond for each of three hydrogens), and for the carboxylic one, nCOO is equal to 4 (two hydrogen bonds via lone electron pairs for each of two oxygens). The value for the coordination number for CH2 depends on the way in which it is defined. It is important that the sign of the effect (increase/decrease in mobility of water molecules in hydration shells) is independent of the coordination number value. The coordination number only scales the magnitude of the effect, this can be seen from eq 8. The higher the value of nCH2, the lower the calculated mobility of water molecules will be obtained. Therefore, nCH2 should be accurately determined. The quantum chemical calculations were performed for clusters comprised of a molecule of an amino acid and different numbers of water molecules. The hydration environment of a solute molecule was formed by gradual addition of water molecules to a cluster followed by geometry optimization. The E
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tion times of water molecules in hydration shells of different ions.26 We used coordination numbers obtained in the way described and were able to calculate relative rotation correlation times of water molecules in hydration shells of the whole solute molecule (λ), methylene group (λCH2), and the rest of a solute molecule comprised of carboxylic and amine groups (λrest). The results of calculations are presented in Table 1. Earlier, the relative reorientation times for water in the hydration shells of the methylene group were not estimated. Therefore, we cannot compare them with published data, but relative reorientation times for water in hydration shells of a solute molecule could also be calculated from the 17O relaxation data in aqueous solutions of amino acids presented by Ishimura and Uedaira.4 They measured R1 of oxygen-17 in water molecules as a function of amino acid concentration for GLY, bALA, and GABA at 25 °C. Reported B-coefficients for 17O relaxation correspond to λ equal to 1.13, 1.20, and 1.19 for GLY, bALA, and GABA, accordingly. Within 5%, these results are in agreement with λ obtained here from deuteron relaxation. The additivity of contributions of hydration shells of methylene groups into an observable relaxation rate could be considered as rather the general rule. Using initial data of refs 4, 6, 8, and 10, one can also reveal a linear dependence of Bcoefficients on the number of methylene groups in a solute molecule for D2O solutions of alcohols, tetraalkylammonium bromides, and some other compounds. Some deviations from linearity may occur, which are caused by a molecular size effect (this effect was also observed by Uedaira et al. for oligosaccharides with different numbers of OH groups),5 although nevertheless, the general tendency for relatively small molecules is clear: (i) each additional methylene group changes the mobility of water molecules in a solution on approximately constant value, and (ii) methylene groups slow down the reorientational motion of water molecules in their hydration shells. These facts make feasible the application of the described above approach for studies of hydration phenomena for other molecular groups. The temperature features of molecular motion in hydration shells of CH2, COO−, and NH3+ are discussed below. The deuteron relaxation rates R1 in 1 m D2O solutions of GLY, bALA, GABA, and 6ACA were measured as functions of temperature. For each amino acid at all temperatures, the Bcoefficient was calculated using R 10 and R 1 at 1 m concentration. Then, for each temperature, the dependence of B-coefficients on the number of methylene groups in a solute molecule (NCH2) was fitted using eq 9 to obtain deuteron relaxation rates in the hydration shell of the methylene group (R1CH2) and in the hydration shells of carboxylic and amine groups (R1rest). The results are presented in Figure 3. The coefficient of determination for all fits was above 0.98. The relaxation rates for deuterons in the hydration shell of the methylene group of amino acids is 1.5−2 times greater than the relaxation rate for pure D2O in the considered temperature range. As a first approximation, the single Arrhenius exponential term can be used for the description of the temperature dependences of R10, R1CH2, and R1rest. From the fits of experimental data by eq 5, the activation energies for molecular reorientations were estimated as 20, 23, and 18 kJ/ mol for R10, R1CH2, and R1rest, respectively. On the basis of the
water molecules were added manually in the randomly chosen position. This approach introduces only small perturbations of the initial geometry of a cluster: the changes mainly concern the water molecules, that were added, and their neighbors. In the way described, the clusters [GLY + 1−60 H2O] and [bALA + 1−70 H2O] were grown. The optimization of geometry in a growing cluster was made with the ROHF level of theory with the basis 6-31G. The geometry of the clusters with the largest number of water molecules was optimized using density functional theory with the hybrid functional B3LYP and basis 631++G(d,p). All calculations were performed in the program Firefly 7.1G.52 The calculations gave a coordination number for the methylene group of nCH2 = 7. This coordination number is significantly higher than the number obtained by Monte Carlo and molecular dynamics simulations, because these approaches take into account only van der Waals interaction between water molecules and the CH2 group. The coordination number nCH2 = 7 for CH2 leads to reasonable values of R1CH2 (Table 1). Table 1. Relative Reorientation Times of Water in the Total Hydration Shell of the Solute Molecule (λ), in the Hydration Shell of CH2 (λCH2, Calculated from R1CH2 in eq 8 Using Data for Pairs of Different Amino Acids), and in the Hydration Shells of COO− and NH3+ (λrest, Calculated from R1rest (see eq 9) Using Data for All Compounds) 2 °C
25 °C
55 °C
λ GLY bALA GABA 6ACA
1.04 1.07 1.12 1.16 λCH2
1.15 1.21 1.26 1.30
1.25 1.30 1.40 1.41
GLY, bALA GLY, GABA GLY, 6ACA bALA, GABA bALA, 6ACA GABA, 6ACA
1.6 1.9 2.0 2.2 2.1 2.1
1.7 1.8 1.8 1.9 1.9 1.8
1.5 1.7 1.6 1.9 1.6 1.5
all compounds
2.0
1.8
1.6
0.9
1.0
λCH2 λrest all compounds
0.8
Moreover, the total hydration number for GLY is 14 (3 from NH3+ + 4 from COO− + 7 from CH2), that for bALA is 21 (as for GLY plus 7 from CH2), that for GABA is 28 (as for bALA plus 7 from CH2), and that for 6ACA is 35 (as for GABA plus 14 from two CH2). These coordination numbers give concentration values of 4.0, 2.6, 2.0, and 1.3 m, accordingly, that correspond to the situation when all water molecules in a solution belong to the hydration shell of a solute molecule. Parts a and c of Figure 1 provide the illustration of the deviation of the concentration dependences from linearity just at the calculated concentrations (except GLY, since it is not soluble at 4 m). This fact supports the proposed values of the coordination numbers for CH2, COO−, and NH3+. In other words, from concentrations at which one observes deviation from linearity, it is possible to calculate the coordination numbers for solute molecules. Such an approach was very fruitful for electrolyte solutions. One of the authors successfully determined the coordination numbers and relative reorientaF
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that corresponds to the averaged resonance line from the OD group of water and the ND3+ group of the amino acid. At temperatures below 30 °C, the spectra contain two resonance lines: from D2O and ND3+. Thus, the typical pattern of intermediate and slow exchange of deuterons between the amine group and water was observed. The influence of chemical exchange was observed also for proton spectra, and this was confirmed by observing the positive exchange peaks in proton NOESY spectra (data not shown). The coalescence point for deuteron spectra locates at ∼35 °C, at which Δωτex ∼ 1
where Δω is the difference between resonance frequencies for exchanging sites and τex is the time constant for the chemical exchange. From the deuteron data, τex was estimated as ca. 0.7 ms at the coalescence point. It follows from obtained data that, although below 30 °C the hydrogen exchange between the amine group and water is slow in the chemical shift time scale, this process is fast in the time scale of the spin−lattice relaxation times: τex is much less than the smallest relaxation time measured (25 ms). Therefore, eq 3 can be applied in the whole range of investigated temperatures. In order to estimate the contributions of different terms in eq 3, the deuteron relaxation rates for ND3+ and D2O lines were measured (see Figure 4b). The temperature dependence of spin−lattice relaxation for ND3+ and D2O lines was registered in GLY D2O solutions with low pH, which was induced by the addition of 1.4 mol of HCl for slowing down the chemical exchange process. Even at 2 °C, when the exchange rate has the smallest value in our experiment, the difference in R1 for deuterons of D2O and amino group is less than 20%. The multiplication of this difference by the relative population of amine deuterons (2.7% at 1 m concentration) gives the effect beyond the R1 measurement accuracy. Therefore, the effect of the chemical exchange of amine deuterons with the solvent can be neglected in the calculations of relaxation rates. Moreover, due to this circumstance, it is not necessary to estimate the value of the quadrupole coupling constant (see eq 1) of deuterons in the ND3+ group, which must differ from the one in water molecules.
Figure 3. Temperature dependences of the deuteron relaxation rate of water in pure D2O (solid black line), in hydration shells of the methylene group (1, blue), and in hydration shells of the carboxylic and amine groups (2, red).
data obtained, it can be concluded that the reorientation of water molecules is more hampered in the hydration shells of methylene groups in comparison to the bulk water, but the reorientation of water molecules is slightly speeded up in the averaged hydration shells of hydrophilic carboxylic and amine groups. These conclusions correlate well with some experimental and computational literature data.39,53−55 4.3. The Special Case of Hydrogen Exchange between the Amine Group of Glycine and Water. The deuteron NMR spectra of GLY solutions in D2O are presented in Figure 4a. At temperatures above 30 °C, the spectra contain one peak
5. CONCLUSION The temperature and concentration dependences of relaxation rates of water deuterons were studied in wide ranges of concentration and temperature in aqueous (D2O) solutions of a set of ω-amino acids. At low concentrations, the observed relaxation rates of solvent nuclei were found to depend almost linearly on the number of methylene groups in a solute molecule. Thus, the approximate additivity of their contributions into the observable average relaxation rate was proved and on this basis the model of the environment of molecules of the investigated ω-amino acids was suggested. Assuming a coordination number of the CH2 group equal to 7, which was predicted from quantum-chemical calculations and confirmed in the experiment, it was found that the rotational correlation times of water molecules near the methylene group is 1.5−2 times greater than the one for pure water. The average rotational mobility of water molecules in the hydration shells of hydrophilic groups of ω-amino acids is a bit slower than that in pure solvent at temperatures higher that 60 °C, but at lower temperatures, it is 0.8−1.0 of values of correlation times for bulk water. Despite the slowdown of amine deuteron exchange in glycine solutions, the formalism of fast exchange between all
Figure 4. (a) Deuteron NMR spectra of 1 m GLY solution in D2O at different temperatures. (b) The temperature dependence of deuteron relaxation rate: solid black line, pure D2O; blue circles, D2O; red circles, ND3+ group of GLY in the 1 m GLY−D2O solution with the addition of 1.4 mol of HCl. G
DOI: 10.1021/acs.jpcb.5b06584 J. Phys. Chem. B XXXX, XXX, XXX−XXX
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substructures can be applied for description of the deuteron relaxation, since this exchange process does not affect significantly the observed relaxation rate. The approach presented here allowed the quantitative characterization of the dynamics of solvation water in hydration shells of molecular groups. The main attention was paid to the CH2 group. The technique suggested provides the basis for the characterization of different hydrophobic and hydrophilic species in the convenient terms of the rotational correlation times for the nearest water molecules. The approach can be applied to solutions of other organic compounds (for example, solutions of short-chain surfactants and ionic liquids) for the quantitative description of hydration shells of individual fragments of molecules and, probably, can turn out useful for the analysis of water−protein interactions.
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AUTHOR INFORMATION
Corresponding Author
*Phone: +7 (812) 428-75-59. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The work is supported by the grant of Russian Foundation for Basic Research (13-03-01073). NMR measurements were performed at the Center for Magnetic Resonance of Research park of St. Petersburg State University. pH measurements were performed in Resource Center for diagnosis of functional materials for medicine, pharmacology and nanoelectronics, St. Petersburg State University. Research was carried out using computational resources provided by Resource Center “Computer Center of St. Petersburg State University”.
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