Reversal of Hofmeister Ordering for Pairing of NH4+ vs Alkylated

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Reversal of Hofmeister Ordering for Pairing of NH4+ vs Alkylated Ammonium Cations with Halide Anions in Water Jan Heyda,† Mikael Lund,*,‡ Milan Oncˇa´k,§ Petr Slavı´cˇek,§ and Pavel Jungwirth*,† Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, and Center for Biomolecules and Complex Molecular Systems, FlemingoVo na´m. 2, 16610 Prague 6, Czech Republic, Department of Theoretical Chemistry, Lund UniVersity, P.O. Box 124, SE-22100 Lund, Sweden, and Department of Physical Chemistry, Institute of Chemical Technology, Technicka´ 5, Prague 6, Czech Republic ReceiVed: February 15, 2010; ReVised Manuscript ReceiVed: June 22, 2010

Pairing of halide anions with ammonium, as well as with trialkylated and tetraalkylated ammonium cations in water, is investigated by molecular dynamics simulations, which are verified by ab initio calculations and experimental excess chemical potentials. We find that ammonium prefers to pair with smaller halides over the larger ones, while the order is reversed for tetraalkylated ammonium cations. Trialkylated ammonium cations exhibit an intermediate behavior, with the acidic hydrogen preferring smaller anions and alkyl chains interacting attractively with larger halides. This Hofmeister reversal of anionic ordering upon tetraalkylation of the ammonium cation is robustly predicted by both nonpolarizable and polarizable force fields and supported by experimental evidence. Introduction Specific interactions of ions with charged, polar, and nonpolar groups at a protein surface, together with pairing with other ions in solution, are decisive for their ordering into the lyotropic (Hofmeister) series.1,2 This series, originally derived from salting out experiments,3,4 has been also invoked in other processes involving proteins, including changes in stability and enzymatic activity.5-10 Since the systems involved are rather complex, it is worth trying to separate the interactions of ions in aqueous solutions of biomolecules into more “elementary” contributions, such as those mentioned in the beginning of this paragraph. Such a reductionists approach has its limitations, since the overall effect does not necessarily have to be a sum of the individual separate interactions. Nevertheless, it is the logical initial step and in many cases also a reasonable first approximation.11 Significant attention has been paid recently to calculations of affinities of ions for hydrophobic aqueous interfaces, which can serve as a starting model for interactions with nonpolar surface patches of proteins. A strongly ion specific behavior has been observed, with larger and softer (more polarizable) ions exhibiting stronger affinity for such interfaces.12,13 This translates into interactions with hydrophobic regions of protein surfaces, with issues connected with the sizes and shapes of such regions also coming into play.14 Ion pairing and, to a lesser extent, interactions of ions with charged amino acid side chains in peptides and proteins have also been under intense computational scrutiny.15-20 Such pairing can be a strong effect as exemplified by appreciable peaks on radial distribution functions for many cation-anion pairs. The empirical law of matching water affinities, stating that ions of comparable strengths of hydration tend to pair in water, can serve as a rough guide to * To whom correspondence should be addressed. E-mail: mikael.lund@ teokem.lu.se (M.L.), [email protected] (P.J.). † Academy of Sciences of the Czech Republic and Center for Biomolecules and Complex Molecular Systems. ‡ Lund University. § Institute of Chemical Technology.

ion specificity.21 Recently, we have provided a semiquantitative rationalization of this behavior in terms of an unfavorable dielectric screening of hydration in pairs of unevenly sized ions.22 The ammonium group is one of the biologically most relevant positively charged moieties. It forms the positive end of zwitterionic aqueous amino acids (the reminder of which are the amide groups at the protein backbone), and it terminates the side chain of lysine. Additionally, it can be present freely in the solution as the ammonium cation or its alkylated analogues, which are also used as phase transfer catalysts.23 In our previous study, we investigated interactions of halide anions with the amide group of N-methylacetamide, finding these interactions to be very weak.24 In addition, pairing of tetraalkylated ammonium cations with counteranions has been investigated using capillary zone electrophoresis25 and simulations with a united-atom force field.26 Here, we scrutinize the strength and specificity of pairing of halides with ammonim and alkylated ammonium cations in water using molecular dynamics (MD) simulations, verified by ab initio calculations and earlier measurements of excess chemical potentials and ion pairing constants. We find that the strength of pairing of halide anions with NH4+ follows the Hofmeister series, while the anionic order is reversed for tetraalkylated ammonium cations. Trialkylated ammonium cations represent interesting intermediate cases, with different pairing patterns at the acidic hydrogen vs the alkyl groups. Methods MD simulations were performed to study ion pairing in aqueous solutions of ammonium and alkylated ammonium halide salts. The investigated cations were ammonium (NH4+) and its tetraalkylated derivatives (TAAs), namely, tetramethylammonium (TMA), tetraethylammonium (TEA), and tetrapropylammonium (TPA). In addition, we also studied trialkylated derivatives (TriAAs) of the ammonium cationstrimethylammonium (TriMA) and tripropylammonium (TriPA). As counteranions we considered the halide series, i.e., fluoride, chloride,

10.1021/jp101393k  2010 American Chemical Society Published on Web 08/02/2010

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TABLE 1: Partial Charges on All Atoms of the Investigated Cations residue name NH4 TriMA

TMA TEA

TriPA

TPA

atom name

partial charge

N H N C H(C) H(N) N C H N C1 C2 H(C1) H(C2) N C1 C2 C3 H(C1) H(C2) H(C3) H(N) N C1 C2 C3 H(C1) H(C2) H(C3)

-0.7075 0.4269 0.0136 -0.3269 0.1811 0.3368 0.0965 -0.1654 0.1304 0.0266 0.0250 -0.0690 0.0684 0.0502 -0.0449 -0.1034 0.0365 -0.0812 0.1079 0.0272 0.0449 0.2747 0.0026 -0.0064 0.0228 -0.1130 0.0687 0.0316 0.0484

bromide, and iodide. Each of the cation-anion combinations of these ions were investigated in separate simulations at varying concentrations. The unit cell always contained eight cations and eight anions. These ions were dissolved in an appropriate number of water molecules to provide 0.25, 0.5, and 1 M solutions of ammonium and TAA salts. For TriAA salts only one concentration was simulated, 0.5 M for TriMA and 0.2 M for TriPA. Most of the simulations were performed using a nonpolarizable force field; however, the effect of polarization was also investigated for ammonium and alkylated ammonium halides at selected concentrations. For water, we employed either the nonpolarizable SPC/E27 or the polarizable POL328 model. For halide anions and TAA cations we used the same force field parameters (without or with polarizability) as in our previous studies.29-31 For TriAA cations Lennard-Jones parameters were adopted from NH4+ and the corresponding TAAs, with partial charges evaluated using the ab initio RESP procedure as recommended for the Amber force field.32 The partial charges for all investigated cations are presented in Table 1. The reliability of the obtained parameters was also verified by comparing potential energy surfaces of alkylated ammonium cations against accurate quantum chemical calculations. The sizes of the unit cells ranged from 25 × 25 × 25 Å for 1 M solutions to 37 × 37 × 37 Å for 0.25 M solutions. 3D periodic boundary conditions were applied with long-range electrostatic interactions beyond the nonbonded cutoff (from 9 Å for 1 M solutions to 12 Å for 0.25 M systems) accounted for using the particle mesh Ewald (PME) method.33 To check for the effect of system size, unit cells of twice the size were simulated for selected systems, giving quantitatively comparable results. The Berendsen temperature (300 K) and pressure (1 atm) couplings were employed,34 and all bonds containing hydrogens were constrained using the SHAKE algorithm.35 The total

Heyda et al. sampling time for each system was 10 ns after 1 ns of equilibration. The employed time step was 1 fs. Coordinates were saved every 1 ps, yielding 10 000 frames for further analysis. By performing several very long (up to 100 ns) trajectories, we checked that the simulation length was adequate for providing converged results. The simulated trajectories were analyzed primarily in terms of cation-anion radial distribution functions (RDFs) and their integrals, which provide the total number of counterions within a given distance from the investigated ion. For ammonium and alkylated ammonium ions the nitrogen atom was considered as the center for evaluating RDFs. The anisotropic cation-anion pairing for the trialkylated ammonium ions was further analyzed in terms of spatial distribution functions of the given halide around the TriAA cation. All MD simulations were performed using the Amber 10 program.36 Additionally, quantum chemical calculations were used to verify the empirical force field employed in this study, in particular that of TriPA. Points on the potential energy surface, including local minima and transition states, were calculated at the MP2 level of theory with the 6-31+g* basis set. Energies of stationary points were corrected for zero-point energy (ZPE). These ab initio calculations were performed using the Gaussian 03 program package.37 To evaluate activity coefficients of ammonium and TAA salt solutions, which could be directly compared to experiment, Metropolis Monte Carlo (MC) simulations were performed in the canonical ensemble using a cubic, periodic box and the minimum image convention. Salt particles were randomly translated (106 configurations per particle for production runs), and the corresponding trial energy, ∆U, determined if the move was accepted. If ∆U < 0, the move was accepted, and if ∆U > 0, the move was accepted with the probability exp(-β∆U), where β ) 1/kBT represents the inverse thermal energy at 300 K. The system energy was evaluated as the sum of all pair interactions, described using effective pair potentials obtained from the above MD simulations. After equilibration, excess chemical potentials, µex, were sampled using the Widom particle insertion technique.38 The energy of inserting a non-perturbing 1:1 salt pair, at random locations, was used to collect the following ensemble average

βµex ) -ln〈exp[-β∆U]〉 related to the mean activity coefficient by γ( ) exp(βµex/2). The MC simulations contained 100 salt pairs, and we sampled the above Widom average every 10th configuration. The described method has proven accurate for determining activity coefficients for a large range of salt solutions.39,40 All MC simulations were performed using the Faunus framework.41 An additional experimentally available parameter, albeit poorly defined, is the association constant, KA, describing direct ion pairing. This property can be approximately obtained from the pair-correlation function, w(r) ) -ln g(r) as

KA )

∞ (e-w(r)/kT - 1)4πr2 dr ∫contact

However, in a statistical mechanical framework, equilibrium constants are ill defined since we have to choose what defines a bound and unbound state. The same is actually true for different experimental setups.

Reversal of Hofmeister Ordering

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Figure 1. Cation-anion radial distribution functions and integrals thereof of 0.25, 0.5, and 1 M ammonium halide solutions.

Figure 2. Cation-anion radial distribution functions and integrals thereof of 0.25, 0.5, and 1 M tetramethylammonium halide solutions.

The above approach to association constants is cumbersome also computationally, due to the fact that it requires a very smooth radial distribution function obtained, ideally, from infinitely diluted system. For this reason we opted for another approach. Namely, the stoichiometric association constant, KA*, for two species, A and B, can be estimated from MD simulations by averaging the N number of free ions and pairs as

KA* )

〈V〉〈NAB〉 [AB] ) [A][B] 〈NA〉〈NB〉

Within a statistical mechanical framework, where the spatial distribution of weakly interacting particles is continuous, the definition of an “ion pair” is, of course, operational. We here define a pair as two particles within a cutoff distance, rp, set to the distance of the first minimum after the first peak in the radial distribution function. The adopted rp distances for halide anion-TAA cation pairs were as follows: F- (NH4+, 3.5 Å;

TMA, 5.5 Å; TEA, 6.5 Å; TPA, 7 Å), Cl- (4.0, 6.0, 7.0, 7.5 Å), Br- (4.2, 6.2, 7.2, 7.7 Å), I- (4.5, 6.5, 7.5, 8.0 Å). Results The most straightforward way to quantify the degree of ion pairing is via the cation-anion RDFs. Figures 1-4 show RDFs and integrals thereof for the following cation-anion pairs in 0.25, 0.5, and 1 M aqueous solutions. The investigated cations were ammonium, TMA, TEA, and TPA, while the anions spanned the halide series fluoride, chloride, bromide, and iodide. It directly follows from Figure 1, which depicts the results for ammonium halide RDFs, that the strength of pairing follows the Hofmeister series F- > Cl- > Br- > I-. Relatively strong contact and solvent-separated ion pairs are formed between NH4+ and F-, as exemplified by the large height of the first peak of the RDF at about 2.8 Å and an appreciable second peak around 4.5 Å. Moving down the periodic table, pairing of NH4+ with halide ions becomes gradually weaker (Figure 1). There is also a small but systematic decrease of the strength of ion

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Figure 3. Cation-anion radial distribution functions and integrals thereof of 0.25, 0.5, and 1 M tetraethylammonium halide solutions.

Figure 4. Cation-anion radial distribution functions and integrals thereof of 0.25, 0.5, and 1 M tetrapropylammonium halide solutions.

pairing with increasing salt concentration. This decrease is most pronounced for F-, and it all but disappears for I-, showing that lighter halides tend to salt in their ammonium salts for submolar concentrations. For tetraalkylated ammonium ions the tendency for pairing with halide anions reverses, following now the inverse Hofmeister series I- > Br- > Cl- > F- (Figures 2-4). This is in accord with the empirical rule stating that large cations tend to pair with large anions.21 As a matter of fact, fluoride exhibits virtually no tendency to pair with TAA cations, the ion pairing becoming more appreciable for heavier halides. Upon moving from TMA to TEA and TPA, the cation-heavier halide peak at the RDF becomes lower and broader and the distinction between first and second peaks washes out. This is a consequence of the presence of the four alkyl chains of increasing length, which leads to smearing of the RDF peaks. Figure 5 shows the distributions of water oxygen and hydrogen atoms around ammonium, TMA, TEA, and TPA, averaged over the production runs. It clearly demonstrates the change of the interaction site for water oxygen from being highly directional next to positively charged hydrogens in ammonia

to more diffuse interstitial structures for TAAs. While TMA behaves as a “hard” core, water molecules do penetrate into the more soft structures of TEA and TPA.42 Still, the increasing chain length of the cations provides further sterical constraints to the water spatial distribution, resulting in a lower number of water molecules within equivalent distances upon increasing the size of the TAAs. The strength of ion pairing in water can sensitively depend on the employed force field. As in our previous study on counterion pairing with positively charged amino acid side chains,20 we have also performed simulations with a polarizable potential. The results for pairing of halides with ammonium and tetramethylammonium ions are depicted in Figures 6 and 7. Inclusion of polarization interactions does not change the ordering of the ions in terms of their affinities for ammonium or TMA. Quantitatively, polarization leads to a sizable decrease of ion pairing of NH4+ with F- (which, however, still remains the strongest among the halides), while all the other ion pairs are affected only slightly. Let us now move to the behavior of cations which possess both acidic hydrogens and alkyl chains on a single ion, i.e., the



Figure 5. Density distributions of water oxygen (red) and water hydrogen (gray) around ammonium, TMA, TEA, and TPA. For TEA and TPA note a deeper water penetration than expected for rigid molecules.

Figure 6. Cation-anion radial distribution functions and integrals thereof of 1 M ammonium halide solutions from simulations with a polarizable force field.

TriAAs. An interesting pattern of cation-halide anion pairing occurs for these species, as depicted in Figures 8 (TriMA) and 9 (TriPA). We can see from the RDFs that the acidic hydrogen of TriAAs prefers pairing with F- over that with heavier halides, as does NH4+ (normal Hofmeister series). In contrast, the three alkyl chains exhibit pairing with heavier rather than with lighter halides, as TAAs do (inverse Hofmeister series). These separate zones of affinity for lighter and heavier halides are best depicted in Figures 10 and 11, which show density distributions of F-, Cl-, Br-, and I- around aqueous TriMA and TriPA, extracted

from the same simulations as the RDFs. Around both cations, fluoride is found only at the acidic hydrogen, while the heavier halide densities are more evenly spread, and moving down the periodic table, the anionic affinity progressively shifts toward the alkyl chains. Additionally, we have investigated the torsional potential of the alkyl chains of TriPA. Instead of favoring geometries near the symmetric (C3V) conformation, the propyl groups tend to twist and to partially bury the acidic hydrogen. This phenomenon, which has been previously denoted as sterically hindered

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Figure 7. Cation-anion radial distribution functions and integrals thereof of 1 M tetramethylammonium halide solutions from simulations with a polarizable force field.

Figure 8. Cation-anion radial distribution functions and integrals thereof of 0.5 M trimethylammonium halide solutions. The total distribution is broken into contributions from the acidic hydrogen and the methyl groups.

Figure 9. Cation-anion radial distribution functions and integrals thereof of 0.2 M tripropylammonium halide solutions. The total distribution is broken into contributions from the acidic hydrogen, the three carbon atoms, and the propyl groups.



Figure 10. Density distributions of halide anions around the trimethylammonium cation. Note the different behavior of the acidic hydrogen vs the methyl groups.

Figure 11. Density distributions of halide anions around the tripropylammonium cation. Note the different behavior of the acidic hydrogen vs the propyl groups.

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Figure 12. Classical force field and ab initio gas-phase 2D potential energy surfaces of the tripropylammonium cation in terms of the H(N)-N-C1-C2 dihedral angle and the H(N)-C3 distance: empirical force field, upper left panel; ab initio calculations, upper right panel; empirical force field in water, lower left panel; schematic description of individual minima, lower right panel. Energy in kcal/mol.

TABLE 2: Relative Energy of Local Minima on the Gas-Phase Potential Energy Surface of TriPA Computed ab Initio and with the Amber Force Fielda Amber

ab initio

structure

dihedral angle

bond length

∆E

dihedral angle

bond length

∆E

LM1 LM2 LM3 LM4 LM5

5 5 45 45 180

2.7 3.9 2.6 4 4.6

2.2 1.4 0.57 0.0 0.48

17.6 36.1 48.7 50.5 177.1

2.86 4.01 2.63 4.04 4.54

1.3 0.0 0.81 0.98 0.87

a Dihedral angles in degrees, bond lengths in angstroms, and relative energies in kilocalories per mole.

bonds,43 follows already from a close inspection of the gasphase torsional potential energy surface (Figure 12). We found five relevant local minima characterized by different distances between the acidic hydrogen and the most distant propyl carbon (H(N)-C3) and by different H(N)-N-C1-C2 dihedral angles. The basin of the first four minima corresponds to geometries with the N-H bond sterically hindered by the propyl group, while the last minimum represents a symmetric structure with stretched out propyl groups. This behavior is interesting per se, as it suggests a decreased acidity of the N-H moiety in TriPA. To check the reliability of the described PES calculated with an empirical force field, the geometries obtained at this level were compared to those from the MP2/6-31+g* method (Figure 12). This approach, which should be superior to the commonly employed density functional theory (DFT) methods, correctly reproduces the experimentally observed twisted minimum.43 The respective local minima were also reoptimized (Table 2). In the gas phase, all classical and ab initio minima are very close to each other in geometry and energy (within 2 kcal/mol), and quantitative agreement between the two methods is obtained for the whole potential energy surface.

Figure 13. Experimental and simulated excess chemical potential connected with replacing iodide for chloride in solutions of ammonium and tetraalkylammonium halides. Note the sign reversal upon moving from ammonium to tetramethylammonium.

Discussion To establish a direct connection with experiment, it is important to determine how the calculated NH4+-halide and TAA-halide pair interactions influence measurable properties, such as mean activity coefficients.44,45 For this purpose we extrapolate the finite concentration MD RDFs to zero concentration and use these as input for subsequent MC simulations. To arrive at infinite dilution, we subtract a generic Debye-Hu¨ckel potential and are thus left with a concentration-independent ionspecific “fingerprint” of the ion pair. To this result, a watermediated Coulomb potential is added so that the final MC potential of mean force reads

βw(r) ) -ln g(r) + [1 - exp(-κr)]lBz1z2/r where lB ) 7 Å is the Bjerrum length for water at 300 K and κ is the inverse Debye screening length, dictated by the salt concentration at which the RDF, g(r), is obtained. In accord



Figure 14. Halide anion-TAA cation association constant obtained from MD simulations of 0.25 M tetraalkylammonium halide salts. Experimental data obtained from ref 48.

with similar methodologies,40,46 this extrapolation procedure is reasonable for distribution functions obtained for salt concentrations in the submolar range. Finally, ions of the same charge interact via a repulsive water-mediated Coulomb potential only. In Figure 13 we present excess chemical potential differences between chloride and iodide ammonium and TAA salts, i.e., the estimated free energy change connected with replacing chloride with iodide. An excellent agreement is found between experiment44,45 and theory, which hints that the MD simulations capture the essential physical driving forces of the system. In particular, both experiment and calculations clearly show that, as the alkyl chain length of TAA becomes gradually longer, interaction with iodide is increasingly preferred over that with chloride, with the opposite anionic preference being observed for the ammonium cation (Figure 13). Note that the present results are also in accord with the experimentally observed increase of the association constant of TMA with the counteranion upon moving from chloride to bromide.47 It should be stressed that integration of microscopic information, such as distribution functions, into thermodynamic properties is a very sensitive procedure. Seemingly small changes in the RDF quantitatively change the calculated activity coefficients, and the invoked MC simulation procedure, therefore, represents a stringent test against experimental data. Minor changes in the water dielectric constant or the choice of initial MD concentration resulted in excess chemical potential differences of (0.2 kBT (at 0.8 M). The qualitative trends, however, remain unchanged and in accord with experiment. In Figure 14 we present calculated association constants, KA*, for the most dilute (0.25 M) tetraalkylammonium halide solutions. Consistently with excess chemical potential calculations, lighter halides pair more strongly with ammonia than heavier ones, with the situation reversing for TMA and, even more so, for TEA and TPA. The corresponding experimental results are sparse and rather spread out; nevertheless, bromide data from dielectric spectroscopy42 are in very good quantitative agreement with the present calculations. Conclusions Using MD simulations, we investigated trends in ion pairing between the series of halide anions and bare, trialkylated, and tetraalkyllated ammonium in water. The strength of pairing with

ammonium cation follows the Hofmeister series, i.e., F- > Cl> Br- > I-. Upon tetraalkylation the series, however, reverses, while trialkylated ammonium is an intermediate case, with the acidic hydrogen preferring small halides and the alkyl chains the large ones. In addition, the interaction of the acidic hydrogen of TriPA with small halides is to a certain extent obscured by bending alkyl chains, as revealed by both classical and ab initio calculations. The Hofmeister reversal upon tetraalkylation is in perfect agreement with the experimental reversal of excess chemical potentials when replacing chloride for iodide in ammonium vs tetraalkylammonium halide solutions. The present results have direct implications for ion-specific effects in biological systems, where the ammonium group and its derivatives are among the most abundant positively charged species. Acknowledgment. Support from the Czech Science Foundation (Grant 203/08/0114) and the Czech Ministry of Education (Grant LC512) is gratefully acknowledged. J.H. and M.O. thank the International Max-Planck Research School and M.L. thanks the Linneaus Center “Organizing Molecular Matter” in Lund, Sweden, for support. Part of the work in Prague was supported via Project Z40550506. References and Notes (1) Pegram, L. M.; Record, M. T. J. Phys. Chem. B 2008, 112, 9428. (2) Mason, P. E.; Dempsey, C. E.; Vrbka, L.; Heyda, J.; Brady, J. W.; Jungwirth, P. J. Phys. Chem. B 2009, 113, 3227. (3) Hofmeister, F. Arch. Exp. Pathol. Pharmakol. 1888, 24, 247. (4) Kunz, W.; Henle, J.; Ninham, B. W. Curr. Opin. Colloid Interface Sci. 2004, 9, 19. (5) Pinna, M. C.; Bauduin, P.; Touraud, D.; Monduzzi, M.; Ninham, B. W.; Kunz, W. J. Phys. Chem. B 2005, 109, 16511. (6) Sedlak, E.; Stagg, L.; Wittung-Stafshede, P. Arch. Biochem. Biophys. 2008, 479, 69. (7) Cacace, M. G.; Landau, E. M.; Ramsden, J. J. Q. ReV. Biophys. 1997, 30, 241. (8) Baldwin, R. L. Biophys. J. 1996, 71, 2056. (9) Bauduin, P.; Nohmie, F.; Touraud, D.; Neueder, R.; Kunz, W.; Ninham, B. W. J. Mol. Liq. 2006, 123, 14. (10) Heyda, J.; Pokorna, J.; Vrbka, L.; Vacha, R.; Jagoda-Cwiklik, B.; Konvalinka, J.; Jungwirth, P.; Vondrasek, J. Phys. Chem. Chem. Phys. 2009, 11, 7599. (11) Jungwirth, P.; Winter, B. Annu. ReV. Phys. Chem. 2008, 59, 343. (12) Jungwirth, P.; Tobias, D. J. Chem. ReV. 2006, 106, 1259. (13) Chang, T. M.; Dang, L. X. Chem. ReV. 2006, 106, 1305. (14) Chandler, D. Nature 2005, 437, 640. (15) Chialvo, A. A.; Simonson, J. M. J. Mol. Liq. 2007, 134, 15.

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