Ion-Specific Effects in Carboxylate Binding Sites - The Journal of

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Ion Specific Effects in Carboxylate Binding Sites Mark J. Stevens, and Susan Rempe J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b10641 • Publication Date (Web): 16 Nov 2016 Downloaded from http://pubs.acs.org on November 22, 2016

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The Journal of Physical Chemistry

Ion Specific Effects in Carboxylate Binding Sites Mark J. Stevens∗,† and Susan L. B. Rempe∗,‡ †Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM, 87185 ‡Biological and Engineering Sciences, Sandia National Laboratories, Albuquerque, NM, 87185 E-mail: [email protected]; [email protected]

Abstract −

Specific ion binding by carboxylates (-COO ) is a broadly important topic because -COO− is one of the most common of functional groups coordinated to metal ions in metallo-proteins and in synthetic polymers. We apply quantum chemical methods and the quasi-chemical free energy theory to investigate how variations in the number of -COO− ligands in a binding site determines ion binding preferences. We study a series of monovalent (Li+ , Na+ , K+ , Cs+ ) and divalent (Zn2+ , Ca2+ ) ions relevant to experimental work on ion channels and ionomers. Of two competing hypotheses, our results support the ligand field strength hypothesis and follow the reverse Hofmeister series for ion solvation, and for ion transfer from aqueous solution to binding sites with the preferred number of ligands. New insight arises from the finding that ion binding sequences can be manipulated and even reversed just by constraining the number of carboxylate ligands in the binding sites. Our results help clarify the discrepancy between ion association by molecular ligands in aqueous solutions and ionomers compared with their chemical analogues in ion channel binding sites.

Introduction

participate, the associations are special. In metallo-proteins, -COO− is a prevalent functional group coordinated to metal ions. 8 In biological ion channels 11 and synthetic ionomers, 12 carboxylates may form binding sites that solvate simple metal ions and lower free energy barriers to ion conduction. An important and current question is which properties of carboxylates determine ion solvation, especially preferential solvation of specific metal ions. 3 We focus on acetate (CH3 COO− ), the simplest carboxylate, to study specific ion binding to carboxylate groups. The two hypotheses predict different sequences of binding association. In the ‘ligand field strength’ hypothesis, binding free energies for alkali metals should follow the sequence ordered by ion size, with the most favored binding associated with the smallest ion: Li+ < Na+ < K+ < Rb+ < Cs+ . The idea also applies to divalent ions. 5 Similarly, a cation should favor interactions with carboxylates over water, and binding site complexes with multiple ligands over a single ligand due to the higher electronegativity. In contrast, the ‘equal affinities’ hypothesis asserts that ion binding preferences should follow the sequence of cation hydration free energies 13 ordered by similarity with ligand (acetate) hydration, not cation size. Thus, acetate should preferentially associate with Na+ , followed by K+ < Rb+ < Li+ < Cs+ , which differs from the above sequence predicted by the ligand field strength hypothesis. In addition to addressing the two hypotheses for ligands in isolation, we also investigate them in the context of ion transfer between aqueous solution and carboxylate binding sites. Ion transfer better represents experiments carried out in aqueous solutions. In particular, we examine the effect of structural constraints on the binding site. Structural constraints occur in many molecules, including ion channels, but neither theoretical hypothesis explicitly takes them into account. Constraints may change the binding site significantly. An example is a constraint that fixes the number of ligands that interact directly with the ions. How do constraints on

The binding of ions to ligands is a fundamental phenomenon in chemistry that has broad application to many systems. In particular, the properties of a ligand that determine ion solvation, especially preferential solvation of specific metal ions, has been the focus of abundant research. 1–3 Two distinct hypotheses emerged in the chemistry and biophysics fields from that research, but the efforts have been mostly unaware of each other. Early studies of monovalent cations interacting with anionic binding sites on glass electrodes in aqueous solution supported the idea that ligand chemistry plays the key role in selective ion binding. 4 Those studies correlated electronegativity of the ligating anion with preferential cation solvation, ordered by cation size. According to this ‘ligand field strength’ hypothesis, higher anionic field strength of a binding site should favor smaller over larger cations. 5 An alternative hypothesis, developed to explain the Hofmeister sequences of preferential interactions observed between ions and proteins, 2,6 invokes hydration as a key factor in determining specific ion binding trends. The Hofmeister series orders ions as a monotonic function of their surface charge density, thus their water affinity. According to the ‘equal affinities’ hypothesis, 7 entities with matching hydration free energies tend to associate. Here, we present a new computational study of cation binding to carboxylates that provides decisive insight into the merits of each hypothesis. The carboxylate functional group (-COO− ) is ubiquitous in biological 8 and synthetic molecules. 9,10 Every protein contains at least one carboxylic acid (-COOH), and the side chains of two common amino acid residues are terminated by this chemical group (aspartic and glutamic acid). Carboxylates also decorate the backbones of many synthetic polymers. As a charged moiety, -COO− favors solvation by water and direct association, or ligation, with positivelycharged ions through strong electrostatic interactions. Because either one (mono-) or two oxygens (bi-dentate) may

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ligand number alter ion binding sequences compared with sequences that arise when ions interact with their preferred, optimal number of ligands? In the cases studied here, we find that constraints on ligand number switch ion binding from a sequence predicted by the ligand field strength hypothesis, to one that resembles the equal affinities hypothesis, to another that is inverted from the ligand field strength series. Overall, our results give new insight into the design of an ionic channel for transport, whether in a protein or a synthetic material.

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avoids blocking ion conduction due to high free energy barriers. 5,32,33 A common view relevant to cations is that increased negative charge in a binding site enhances ion conduction, 28 and hence provides the right amount of ion solvation. Thus, studying ion binding is generally important for understanding ion conduction in nanoscale pathways. Binding between ions and carboxylates relevant to ion conduction occurs in both synthetic ionomers 34,35 and in biological ion channels. 14,36–39 Ionomers are polymers with a small fraction of charged groups (e.g., -COO− ). Recently, ionomers have been identified as possible battery electrolytes. Ion channels are transmembrane proteins that catalyze ion conduction across cellular membranes. 11 Crystal structures show pores lined with polar and charged functional groups (e.g.,-C=O, -COO− ) in the narrowest regions of the ion permeation pathways in some of the best-known channels. 17,40–44 Channels play a critical role in health. The relevant environment for ion channels is aqueous solution. In contrast, dry ionomers function with no solvent. 34,35,45–47 For those reasons, we treat ion binding to carboxylates in a low dielectric environment and following transfer from aqueous solution. Because the free ions in dry ionomers exist in a relatively low dielectric polymer medium, their strong ionic attraction to the charged groups in the polymer typically leads to ionic aggregation. This aggregration results in a peak in X-ray scattering known as the ionomer peak. 48–50 A molecularlevel understanding of ionic aggregation in ionomers is fundamental to their material properties. Moreover, the aggregate structure influences ionic conductivity. 51 Thus, a better understanding of the nature of the ion-ligand binding would help to design ionomers with better conductivity. Recent molecular dynamics simulations have revealed a new picture of ionic aggregation in ionomers in which the aggregate structure is stringy instead of spherical and depends on the specific metal ion with respect to cluster size and percolation. 34,35,45–47 Here, we show that the binding geometry between the carboxylate ligand and the ion plays a key role in the different ionic aggregate structures.

Previous Work Much effort has gone into testing the ligand field strength and equal affinities hypotheses. On the one hand, computational studies carried out in gas phase confirmed that a single ligand, 14 or a group of ligands, 15 with higher field strength than water preferentially associates with a smaller cation (Na+ ) compared to a larger one (K+ ), in support of the ligand field strength proposal. Yet functional studies of cation binding 16 and crystallographic observations of cation association with the dehydrated K+ binding sites of potassium ion channels documented the opposite trend in binding free energies (K+ < Na+ ). 17 On the other hand, the hydration free energy of N -methylacetamide, a molecular analogue of potassium channel binding sites, is only a fraction of the value for sodium or potassium. 18 Thus, the latter observations contradict both theories. Experimental and computational studies of acetate association with simple metal ions in aqueous solution have also produced apparently mixed results. Spectroscopic measurements reported preferential ion association ordered by ion size for CH3 COO− ligands 19 and carboxylate side chains in polypeptides, 20 in support of the ligand field strength hypothesis. In comparisons of sodium and potassium ions interacting with carboxylates, most researchers reported higher binding affinities and lower binding free energies for sodium (Na+ < K+ ) independent of salt concentrations. 21–25 Although that trend is typically cited in support of the equal affinities hypothesis, it also supports the ligand field strength hypothesis equally well, and thus does not distinguish between the theories. A notable observation concerns ligand number. In the example above where solvation by potassium ion channels favors the larger ion (K+ < Na+ ), eight polar functional groups (-C=O) from the protein backbone ligate the ions in the crystal structure. 26 In aqueous solution where ions interact with their preferred numbers of ligands, hydration favors the smaller ion (Na+ < K+ ) and fewer ligands on average coordinate K+ . 27 That observation encourages a quantitative study of the two hypotheses while varying the number of ligands, as reported here. Few calculations have studied the carboxylate-ion structure and binding free energies in a low dielectric medium. 28–30 Most studies have treated only the interaction between a single ligand (n=1) and an ion, with only a recent exception. 31 While those works provide data for comparison, as described below, there is a clear need for calculations for a range of ligand number and ions.

Varying Ion Type and Ligand Number In this study, we present results of electronic structure calculation of the absolute binding free energies of carboxylate ligands to a selection of mono- and di-valent cations. Because of the strong interactions between charged carboxylates and metal ions that involve polarizable electronic charge distributions, electronic structure methods are required. 52,53 Ordered by size (smallest to largest), the ions studied are monovalents Li+ , Na+ , K+ , Cs+ , and divalents Zn2+ and Ca2+ . Although different in charge, Li+ and Zn2+ are the same size, as are Na+ and Ca2+ . Li+ is the primary candidate for use in battery electrolytes. 54–58 Several other cases have been part of X-ray scattering studies to understand the nature of the ionic aggregates in ionomers. Na+ , Zn2+ , and Ca2+ ions are important to cell signaling mediated by ion channels with binding rings composed of carboxylates. 59 In assessing ion-specific effects in carboxylate binding sites, one of the key questions is what number of ligands (n) optimally binds to a specific ion. The optimal number of carboxylates that directly interact with an ion, and their arrangement, represent the most probable ligand composition (¯ n) within the first solvation shell of a specific ion. Does a given ion favor binding with a single carboxylate or multiple carboxylates, as predicted by the ligand field strength

Ion Channels and Ionomers While the focus of this work is on ion binding, the results have implications for ion conduction. For fast conduction, binding sites should solvate the preferred ion by an amount that avoids ion traps due to deep free energy wells, and also


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The Journal of Physical Chemistry Table 1: Free energies for formation of clusters with one ion and n waters in gas phase at T =298 K and 1 atmosphere. Energies are in kcal/mol.

proposal? To assess the two hypotheses of ion specificity in carboxylate binding, we calculate preferences in ion solvation for each binding composition (n) of one to four acetates, noting whether that preference relates to ion size or matching affinity with acetate solvation. We compare the results of monovalent with divalent ions to determine the influence of charge. Additional questions addressed include how a specific ion influences geometrical and electrostatic properties of its ligands, especially a ligand’s induced dipole moment. Finally, we investigate how binding site composition affects the specificity in ion transfer from water, paying attention to the role of ligand number and whether the solvation environment favors ion conduction. Our results highlight the important role of binding site composition (n) in solvation of specific ions.

ion Li+

Na+

K+

Cs+

Methods and Validation The local clustering of acetate ligands about an ion corresponds to the following reaction, Xm+ + nCH3 COO− ⇄ Xm+ (CH3 COO− )n , Xm+

Ca2+

(1)

na 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 5→6

∆G(calc)b -27.2 -49.0 -62.6 -67.4 -17.1 -30.9 -39.2 -45.7 -11.2 -18.9 -26.3 -30.9 -5.7 -10.4 -14.2 -16.2 -14.7

∆G(exp)c -27.1 -46.1 -59.4 -66.9 -18.8 -31.9 -40.9 -46.9 -11.8 -20.7 -27.0 -31.4 -7.9 -13.8 -18.0 -21.0 -16.1

a

All clusters formed from an isolated ion interacting with n waters except for Ca2+ , which forms a cluster with n=6 waters by adding a water to the cluster with n=5 waters. b Calculated values denoted ‘calc.’ Additional calculated values for Ca2+ and Zn2+ with n=6 waters appear in Table 2. c Experimental values denoted ‘exp.’ and are taken from Ref. 66 for Li+ , Na+ , and K+ , Ref. 67 for Cs+ , and Ref. 68 for Ca2+ .

m+

where indicates an ion with charge binding with n=1 to 4 charged acetate ligands (CH3 COO− ) to form an ion-acetate complex, Xm+ (CH3 COO− )n . We assume the clustering equilibria take place in an idealized environment that does not influence the reaction through long-ranged dispersive and electrostatic interactions or structural constraints on the clusters. Our treatment is thus equivalent to an uncoupled quasi-chemical analysis carried out in a low dielectric environment (ǫ=1). 60,61 As a first approximation, this treatment is appropriate for an ionomer system because polymers can have significant flexibility and they occupy a low dielectric environment. Ion channels and ionophore binding sites may also be surrounded by an environment equivalent to a low dielectric medium. 14,37 Ionophores are small molecules that may bind a specific ion selectively. Structural constraints on the binding sites due to interactions with the surrounding environment or covalent bonds within the binding site may be more likely for ion channels and ionophores than ionomers. 37,38 As an example, the binding site cavity size may be fixed. 36,62 Alternatively, the number of ligands (n) interacting with the ion may be fixed. Here, we assess the role of constraints on ligand number (n) and defer the more complicated analysis of other environmental effects for future work, which will be facilitated by recent theoretical advances for analyzing structural constraints. 61,63 The treatment performed here will provide a reference to future constrained calculations. The structure and stability of Li+ and Na+ binding to single carboxylate molecules has been studied previously using density functional theory (DFT) with the hybrid exchange-correlation functional B3LYP and a triple-zeta basis set (6-311+G(d,p)). 64 Tafipolsky and Schmid performed DFT calculations for a variety of different exchange-correlation functionals and determined that the B3LYP functional coupled with a correlation-consistent all-electron triple-ζ basis set augmented with diffuse functions (aug-cc-pVTZ) reproduces coupled cluster calculations well. Further, Tafipolsky and Schmid found that the smaller, and computationally less expensive, double-zeta (aug-cc-pVDZ) basis delivers reliable results for acetate ions, in agreement with Oomens and Steill. 65 Recently, Mehandzhiyski, et al. studied Ca2+ and Na+ in carboxylic acids using B3LYP with triple-ζ basis sets with one diffuse function and one set of d polarization functions for the heavy atoms (6-311+G(d)). 31 In conjunction with mass spectrometry experiments, energies and some bond lengths have been calculated using DFT with B3LYP/6-31+G for carboxylates interacting with many ions, including Li+ , Na+ and Cs+ . 69 The carbonyl interaction with Li+

in a polymer has been studied by Eilmes. 29 Dudev and Lim studied metal-carboxylate interactions for a range of metals relevant for metalloproteins using the S-VWN exchange-correlation functional and the 6-31+G(p) basis set for the ions of interest in this article. In particular, they studied the factors governing the maximum number of metal-bound carboxylates. We calculated the free energy change (∆G) for the reactions in Eq. 1 using the Gaussian 09 quantum chemistry package. 70 For most systems, the geometry optimizations were carried out in the gas phase using the density functional theory approach with the hybrid B3LYP approximation to the exchange-correlation energy 71 and Dunning’s correlation-consistent polarized doublezeta basis sets augmented with diffuse functions (aug-cc-pvDz). 72 The B3LYP functional is the most widely used approximation in chemistry due to its balance between computational efficiency and ability to describe strongly interacting systems. 73 Correlationconsistent basis sets were developed to describe core-core and core-valence electron correlation effects in molecules and previously have been shown to be accurate for a single carboxylate. 30 For Cs+ , we used the LANL2DZ effective core potential and valence electron basis set for computational efficiency. 74 As the correlation consistent basis sets are not available for K+ and Ca2+ , we used the 6-311+G(2df,2pd) basis set, which is similar to that used earlier for a variety of ions with water as a ligand. 37,75–82 We calculated the basis set superposition error (BSSE) correction of the interaction energy by the counterpoise method. 83 To obtain free energies, we performed a normal mode frequency analysis 84 using the same level of theory as for optimization. We also performed some calculations using the post-Hartree-Fock Moller-Plesset perturbation theory (MP2) to test that approximation of electron correlation and dispersion interactions on the results. 85 Stable structures for which the forces are zero and frequencies positive confirmed true minima on the potential energy surfaces. The thermodynamic analysis yielded zero point energies and thermal corrections to the electronic energy due to translational, electronic, and vibrational motions calculated at a tem-



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perature of 298 K and pressure of 1 atm. To calculate the free energy change for the reactions in Eq. 1, we took the difference in free energy between the product (p) and the sum of the reactants (r) in stoichiometric proportions (nr ): ∆G = Gp − Σnr Gr .

(2)

The enthalpic component of the reaction free energy (∆H) is computed with an analogous equation. We further validated the exchange-correlation functional and basis set choice through a set of comparisons with experimental data. The dipole moment of acetic acid (gas phase) is 1.70 ±0.03 D. 86 Our calculation using the B3LYP exchange-correlation functional with the aug-cc-pvDz basis gives a dipole moment of 1.71 D, in good agreement with experiment. An MP2 calculation with the same basis yields a dipole moment for acetic acid that is too high (1.95 D). We also calculated ligand dipole moments and ion charge in the ion-acetate clusters, as described in the Supplementary Information (Figs. S1 and S2). Cluster-ion formation free energies in water measured experimentally have been compiled by Tissandier and colleagues, 66 and additional data reported by Kebarle and colleagues. 67,68 In Table 1, we compare our calculated ∆G for formation of ion-water clusters with those experimentally-determined values. All calculated results agree reasonably well with the experimental data. Other works also studied these ion-water clusters using density functional theory, 87–90 but only a few reported ∆G. 37,53 Agreement for Na+ is better with the present basis set than in earlier calculations. 37 No experimental data is available for comparisons with our calculated free energies for formation of ion-carboxylate clusters.

Figure 1: The change in free energy (∆G) for formation of ioncarboxylate complexes as a function of the number (n) of acetate ligands in a low dielectric environment (ǫ = 1). A dashed line separates monovalent and divalent ions. All binding site compositions favor the smallest ion of the same charge (Li+ < Na+ < K+ < Cs+ ; and Zn2+ < Ca2+ ), with divalents more stable than monovalents. Numerical values for ∆G and ∆H given in Tables S1-S3.

Further, the three acetates in the lowest energy complex coordinate the X2+ ions in a triple bidentate, six-fold coordinated structure. For all X+ and X2+ ions except Ca2+ , the closest state to the minimum free energy state has one less ligand and the energy difference is in the range 30-40 kcal/mol, which represents a large free energy barrier. For Ca2+ , the n=4 ion-acetate complex is the next closest state to the minimum and the free energy difference is 10 kcal/mol. Due to their large favorable formation free energies, all clusters should form stable complexes in a low dielectric environment. Cs+ complexation with n=4 acetates results in a free energy change that is closest to zero (∆G ∼ -12 kcal/mol), which would promote conduction except this value is too large. 5

Results Preferred ligand compositions To determine the sequences of ion binding and test the hypotheses, we obtained the optimized structures for each ion and for varying numbers of ligands. We computed the change in free energy (∆G, Eqs. 1 and 2) for formation of carboxylate complexes centered on the different ions as a function of the number (n) of acetate ligands (Fig. 1). For monovalent ions, the minimum occurs at n = 2 acetates. At the minimum composition as well as all other compositions, the free energy is lowest and most favorable for the smallest cation, Li+ , and increases with ion size, which agrees with the ligand field hypothesis. In the lowest energy complex, the two acetates coordinate the X+ ions in a bidentate mode. Thus, the most probable solvation complex for all monovalent ions studied here consists of a double bidentate, four-fold coordinated structure. Four-fold coordination is defined with respect to the oxygen (O) atoms in the carboxylate groups (-COO− ). This preferred X+ (CH3 COO− )2 binding site composition (¯ n = 2) has a net charge of -1. For the divalent ions, much lower free energy values result for ion binding to acetate ligands compared with the monovalent ions, as expected for the doubled charge. Similarly, the minimum in free energy occurs for complexes formed with a higher n = 3 number of acetate ligands compared with the monovalents. Prior work also reported three carboxylates around Ca2+ as the complex with the lowest interaction energy. 31 As with the monovalent ions, the preferred ion-carboxylate cluster for the divalent ions, X2+ (CH3 COO− )3 (¯ n = 3), has a net charge of -1. Also analogous to the monovalent cases, the free energy is more favorable for the smaller divalent ion for all binding site compositions, in support of the ligand field strength hypothesis.

Ligand geometrical properties specific to Li+ We show the optimized structures of Li+ in Figure 2 for n = 1 to 4 acetate ligands. Numerical values for the geometry are given in Supplementary Table S4. Those values are averages over all possible values for the given geometry. In the table, we include distances (and angles) that are not associated with bonds to describe the structures fully. The structure of the single carboxylate bound to Li+ agrees with previous calculations. 64,91 In general, the Li+ ion is symmetrically located among the oxygen (O) atoms on the carboxylate. For a single carboxylate, the Li+ atom is on the bisector of the carboxylate OCO angle. The 1.513 ˚ A carbon-carbon (C-C) bond has shrunk relative to the value of 1.560 ˚ A calculated for the isolated acetate ion (CH3 COO− ). For two carboxylates, the same bidentate geometry holds for each carboxylate individually. In addition, to reduce the repulsion of the O atoms on separate carboxylates, the ligands are rotated so that the planes made by the OCO groups are perpendicular. The Li-O separation increases with the addition of the second ligand. This n=2 structure,


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Ligand geometry specific to X+ vs. X2+

(a) n = 1, Q = 0, ℓ = 2

The average distances between the coordinating oxygen atoms and all X+ and X2+ metal ions are given in Figure 3. Interesting trends can be discerned regarding the ordering by ion size and discontinuities in ion-ligand separation distances. In particular, separation distances at each coordination (n) are ordered by ion size, recalling the ligand field strength hypothesis, with the ligands closer to the smaller ions of the same charge. As with Li+ , the separation distances expand with increasing number of acetate ligands up to the preferred coordination (¯ n=2 for monovalents, n ¯ =3 for divalents), then drop to smaller values that mark a shift from bidentate to monodentate binding modes. Cs+ follows a different trend from the smaller monovalent ions. Details are given below. The structures with Na+ and K+ cations have the same geometric layout as for Li+ (Fig. 2), but with different spacings (see Fig. 3 and Tables S5 and S6). Since the trends for K+ are similar for Na+ , we will only discuss the Na+ data.

(b) n = 2, Q = −1, ℓ = 4

(d) n = 4, Q = −3, ℓ = 4 (c) n = 3, Q = −2, ℓ = 3 Figure 2: Lowest energy structures for Li+ with acetate ligands. The color scheme is Li+ (pink), C (cyan), O (red) and H (white). In each complex, n gives the number of acetates, Q the total charge, and ℓ the number of O atoms that coordinate Li+ . Acetates preferentially coordinate Li+ in a bidentate mode when n=1 (a) and n=2 (b). Analogous structures result for the other ions studied here, except that Cs+ , Zn2+ , and Ca2+ differ in complexes with n=3 acetates (see Fig. 4). All X+ ions preferentially form n=2 complexes (see Fig. 1).

in which the ion is four-fold coordinated by the O atoms, has the lowest free energy of all the cases. The geometry of acetate oxygens surrounding Li+ in the preferred coordination of n=2 acetates resembles that of water about Li+ , which also prefers a four-fold coordination in a liquid water environment. 75,92,93 While we do not expect our calculated Li-O separations to match those of hydrated Li, the numbers should be close and the comparisons are also interesting. The Li-O separations at the different n bracket recently measured values of the Li-O separation for hydrated systems, which vary from 1.96-1.98 ˚ A. 92–94 DFT 95 61,81 ˚ ˚ calculations give 1.96 A or 1.95 A for the Li-O separation in liquid water. For the preferred Li+ coordination of n ¯ =2 acetates, the Li-O separation is 2.03 ˚ A. With only one acetate ligand, the Li-O separation is slightly closer at 1.85 ˚ A. When a third ligand is added, the geometry changes significantly relative to n=2 (Fig. 2c). Only one of the O atoms on the carboxylate is positioned close to the Li; the other is far away from the Li+ . That ligand configuration is monodentate. The separation distance of 1.90 ˚ A between the close O atoms and Li+ is shorter than for the n = 2 case, but longer than the single ligand case. In addition, the C-O bond length for the O atoms close to the Li+ is longer than for the O atoms far from the Li+ . The set of all O atoms and Li+ are co-planar for n=3. For four ligands (n=4), one of the O atoms is again close to the Li+ at 2.10 ˚ A separation distance, with the other positioned far from the Li+ . The four O atoms close to the Li+ have a tetrahedral mono-dentate arrangement (Fig. 2d) that resembles Li+ hydration structure except that the carboxylate ligands are positioned further from the ion due to crowding and repulsive interactions between the ligands.

Figure 3: Average distance (rOX ) between metal ion and coordinating oxygens as a function of the number of acetate ligands, n, in the lowest energy ion-acetate complexes. Numerical values are given in Supplementary Tables S4-S9.

Na+ is a larger atom than Li+ , thus the Na-O spacing increases by about 0.3 ˚ A for all n. The most recent measured hydrated Na-O separation distances are 2.34 ˚ A 94 and 2.43 ˚ A, 92 which match well with the n = 2 value of 2.35 ˚ A (Fig. 3, Table S5). The same trends as a function of n are seen for Na+ as were seen for Li+ . For example, the O-Na+ distance increases between n = 1 and 2, but decreases between n = 2 and 3. As in the Li+ system, the n = 3 and 4 structures have one carboxylate O closer to the Na+ than the other. In the n = 3 case, the C-O bond of the close O atom is longer than that with the far O atom. Similarly, the C-C-O angle differs between the close and far O atoms. For n = 1 and 2, the structures of the Cs+ systems have the same geometric layout as Li+ , Na+ , and K+ . Since Cs+ is larger, the distance between Cs+ and the nearest O atoms is much larger than for the other monovalent ions. Recent experimental Cs-O distances in aqueous systems are 3.15 ˚ A 96 and 3.07 ˚ A, 92 which match well with the 3.16 ˚ A value for n = 2 acetates. The four-fold coordinated state with n=2 ligands is the lowest energy state for Cs+ , as it is for Li+ , Na+ and K+ . In contrast to the smaller monovalent ion systems, the Cs+ structure differs fundamentally at n = 3. The change in geometry is clearly seen in the value of the O-Cs-O angle (Table S7), which is small (38.7◦ ) compared to the 120◦ for Li+ , Na+ , and K+ . Both O atoms on each carboxylate are



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etate clusters, ∆∆G. The transfer free energy is the difference in free energies for ion solvation in an n-fold acetate cluster (denoted as COO− n ) and ion hydration in aqueous solution (aq), ∆∆Gaq→COO− = ∆GCOO− − ∆Gaq . n n

(3)

Transfer free energies reveal whether a specific ion prefers solvation by liquid water or a binding site composed of ligands with higher electronegativity than water. If ∆∆G > 0, then the ion favors hydration in water. If ∆∆G < 0, then the ion favors solvation in the acetate binding site with n ligands. If ∆∆G = 0, then the ion has no preference for either solvation environment, which is a condition that promotes ion conduction. The ion transfer free energies (Eq. 3) can be computed readily using the results presented above (Fig. 1) for ion solvation free energies in acetate binding sites (∆GCOO− ≡ n ∆G(n)), and performing a similar analysis adapted for ion hydration free energy (∆Gaq ). Specifically, the uncoupled quasi-chemical analysis used to predict free energies for the ion-carboxylate clustering reactions (Eq. 1) can be modified for ion binding to water (H2 O) ligands and coupled to an aqueous solvation environment, 60,61

Figure 4: Structure of the lowest energy Zn2+ complex with n=3 acetate ligands, which interact with the ion in a bidentate mode (n = 3, Q = −1, ℓ = 6). The largest monovalent ion considered here, Cs+ , and the divalent ion, Ca2+ , form similar six-coordinate structures with n=3 acetates. Both X2+ ions preferentially form n=3 complexes (see Fig. 1).

coordinated to the Cs+ , yielding a 6-fold coordination of Cs+ . The geometric layout is the same as Zn2+ (Fig. 4). For Cs+ , however, this 6-fold coordination is not the lowest energy state. The optimized geometries for Zn2+ have the same ligand orientations as for Li+ for n = 1 and n = 2 (Table S8). The Zn-O separations of 1.97 (n=1 acetate) and 2.03 ˚ A (n=2 acetates) fall between the Li+ and Na+ values (Fig. 3). The more recently measured Zn-O separation in hydrated systems is 2.05 ˚ A, which matches the n = 2 value, but is smaller than the n = 3 value of 2.18 ˚ A. 94 In contrast to the mono2+ valent ions, the divalent Zn has its minimum free energy structure at n = 3 and the coordination number jumps to 6 as all O atoms are near neighbors to Zn2+ . This geometry is shown in Fig. 4. Increasing the number of ligands to n=4 results in an optimized structure for Zn2+ that is similar to the n=4 structure for Li+ (Fig. 2). The Zn2+ is then a 4-fold tetrahedrally coordinated ion, with one O of carboxylate near the Zn2+ and one far away. The Zn2+ ion has the strongest effect on the C-C bond length, shrinking it from the 1.560 ˚ A value in the isolated acetate ion to 1.496 ˚ A in the n=1 cluster. The C-O bond expands more than for the monovalent ions. The structure of the ligands about Ca2+ (Table S9) follows the same geometric layout as Zn2+ for n = 1, 2 and 3. As with Zn2+ , the minimum free energy structure has n=3. For n = 4, the positions of the carbonyl groups are similar to the Zn2+ complex, but the methyl groups are rotated in some cases. This ion-size sequence in acetate binding matches the dipole moment behavior (Fig. S1) in which the divalents polarize the acetate ligands more than the monovalents, and the smaller monovalents (e.g., Li+ ) polarize the acetate ligands more than the larger monovalent ions (e.g., Cs+ ). The sequence mostly holds in the ionic partial charges although similar amounts of charge transfer from the acetates to Li+ , Na+ , and K+ . The charge most weakly deviates from the valence (Fig. S2) in Cs+ . The smaller amount of charge transfer observed in Cs+ is consistent with the larger separation observed between Cs+ and the carboxylate ligands (Fig. 3). In summary, the trends show consistency with the ligand field strength proposal for selective ion binding.

Xm+ (g) + nH2 O(aq) ⇄ Xm+ (H2 O)n (aq).

(4)

The quasi-chemical free energy analysis proceeds with the same computation of free energy change for the reaction Eq. 4 as done before (Eq. 2), but now applied to n=4 water ligands for the monovalent ions and n=6 waters for the divalents. Those ligand numbers correspond to stable, innershell complexes observed in ab initio molecular dynamics simulations of monovalent and divalent ions in aqueous solution. 27,75–77,82,97 The ion-acetate complexes shown in Figures 2 and 4 illustrate inner-shell complexes, distinguished from other possible solvation complexes by direct interaction between ligands and ion. 53,82 In the case of water ligands, the n=4 and n=6 inner-shell complexes screen the ions, and thus provide favorable conditions for including interactions of the ion-water complexes with the surrounding aqueous environment using a polarizable continuum model. More details on the approach can be found in prior publications and the Supplementary Information. 82,97 Table 2: Free energies for ion hydration (∆Gaq ) based on quasi-chemical analysis of the defined cluster formed from one cation and n water molecules in a low dielectric medium (ǫ = 1). The first three columns refer to calculated and experimental changes in enthalpy (∆H) and free energy (∆G) for the reactions in a low dielectric, while the last two columns refer to aqueous phase. Energies are in kcal/mol.

cluster Li(H2 O)+ 4 Na(H2 O)+ 4 K(H2 O)+ 4 Cs(H2 O)+ 4 Zn(H2 O)2+ 6 Ca(H2 O)2+ 6

∆H -98.8 -72.4 -53.4 -35.5 -335.2 -234.4

∆G -67.4 -45.7 -30.9 -16.2 -281.5 -184.6

∆Gexp -66.9 -46.9 -31.4 -21.0

∆Gaq -123.4 -98.1 -75.4 -59.0 -486.5 -379.5

a ∆Gexp aq -117.1 -90.8 -74.0 -63.3 -470.7 -363.2

Experimental data, 98 denoted as ‘exp,’ has been adjusted to correspond to ion transfer from 1 M (ideal) gas to 1 M (ideally diluted) solution as used also in the calculations.

a

Calculation and validation of ion transfer Given the experimental relevance of ion partitioning from aqueous solution into the binding sites of ion channels, we calculated ion transfer free energies between water and ac-

A comparison of our predicted values (∆Gaq ) with exper-


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imental values tabulated by Marcus 98 (∆Gexp aq ) shows that the computational methods are sufficiently accurate to capture the correct trends (Table 2). As expected for strongly charged systems, the enthalpic (∆H) terms make larger contributions to the cluster formation free energies (∆G) than the entropic terms. An observation relevant to the hypotheses on specific ion binding is that the same trends appear in ion hydration free energies as observed above for ion solvation by water (Tables 1 and 2) and acetate ligands (Fig. 1) in a low dielectric environment (∆G). In particular, the free energy for monovalent ion hydration is lowest and most favorable for the smallest cation, Li+ , and increases with ion size. The same trend appears for divalent ion hydration, with the smaller Zn2+ more favorably hydrated than Ca2+ . The divalent ions are several times more favorably hydrated than the monovalent ions due to the doubled charge. A recent study of Na+ hydration concluded that a variety of density functionals can predict ∆Gaq values that fall within experimental error, with or without corrections for electron correlation and delocalization. 53 Local interactions incorporated in ∆G account for one-third to two-thirds of ion hydration free energies in Table 2, meaning interactions with the distant solvation environment account for the remainder and are equally important to the ∆Gaq predictions. That analysis indicates why prior works reported good agreement between tabulated and predicted ion hydration free energies using quasi-chemical theory despite differences in functionals and basis sets. 37,78,82,97 While the predicted hydration free energies (Table 2) may be improved by better methods, the added expense does not provide added benefits. Considering that our focus is on the trends rather than detailed numerical values, the methods used are sufficiently accurate. Since the trends in the transfer free energies sought here (Eq. 3) remain the same whether the predicted or experimental ∆Gaq values are used, we apply the tabulated experimental ion hydration values to calculate ion transfer free energies (∆∆G).

Figure 5: The change in free energy (∆∆G) for ion transfer from liquid water to carboxylate complexes (aq → COO− ) in a low dielectric environment (ǫ = 1) as a function of the number (n) of acetate ligands. Blue regions indicate transfer free energies that favor ion solvation in aqueous solution (∆∆G > 0), while white regions indicate favored ion solvation in n-coordinate acetate complexes (∆∆G < 0). Numerical values are given in Supplementary Tables S10-S11.

types, X+ and X2+ . At n=1 for the divalents and n=4 for the monovalents, for example, the ions follow an inverse size order: Cs+ ∼ K+ < Na+ < Li+ ; and Ca2+ < Zn2+ . For n=3, the monovalent ion binding preferences resemble the ordering predicted by the ‘equal affinities’ hypothesis due to the preference for Na+ binding over K+ and Cs+ . But the trend is disrupted by Li+ , which binds more favorably to the n = 3 acetate cluster than K+ and produces the following trend: Na+ < Li+ < K+ < Cs+ . To gain more insight into the change in ion ordering of ∆∆G with number of acetate ligands (Fig. 5), we decomposed the ion transfer free energies for Li+ and Cs+ into their free energy components (Eq. 3): ∆Gaq and ∆GCOO− . n Those components (see Fig. 6) re-emphasize that the smaller Li+ ion is thermodynamically more stable than Cs+ in aqueous solution. Further, the smaller Li+ is also more stable than Cs+ in each n-coordinated ion-acetate complex, as determined above (Fig. 1). The switch in ∆∆G ordering from favored smaller ions to favored larger ions occurs because binding site composition (n) affects specific ions differently. Whereas both Li+ and Cs+ ions are stabilized by n=1-3 acetates, the smaller Li+ gains 20 kcal/mol more stability than Cs+ on transfer from water to the preferred number (¯ n=2) of acetate ligands. In contrast, the smaller Li+ loses 15 kcal/mol more stability than Cs+ on transfer to the destabilizing n=4 acetate cluster. Interestingly, four (4) oxygen atoms coordinate the ions in both n ¯ =2 and n=4 configurations (Fig. 2). The increased loss of stability by the smaller ion relative to the larger one in the crowded n=4 binding site relates to repulsion between ligand dipoles, as discussed earlier for water ligands 53 and for carboxylate ligands. 31 As a consequence, ion transfer free energies, ∆∆G, shift from favoring the smaller ion, Li+ < Cs+ for n =1-3 acetates, to favoring the larger ion, Cs+ < Li+ for n =4 (Fig. 5).

Ion transfer from water to acetate clusters Free energy changes (∆∆Gaq→COO− ) computed for ion n transfer from water into complexes with different numbers of acetate ligands appear in Figure 5. The monovalent ions favor complexation with acetates for n=1-3, but favor hydration over n=4 acetates. Binding to acetates is strongly favored, as evident from ion transfer free energies that range from -20 (Cs+ (CH3 COO− )3 ) to -85 kcal/mol (Li+ (CH3 COO− )2 and Na+ (CH3 COO− )2 ). Ion (X + ) hydration is favored over complexation with n = 4 acetates by more than 60 kcal/mol. In contrast, the divalent ions favor hydration for n=1 (by 50-60 kcal/mol), but complexation with acetates for n=2-4 (by over 100 kcal/mol). No ion transfer free energy comes closer to zero than 20 kcal/mol (Cs+ (aq) → Cs+ (CH3 COO− )3 ), meaning that conditions that favor ion conduction (∆∆G ∼ 5 kcal/mol) are not met. 5 In the preferred binding site composition for monovalent ions (¯ n=2 acetates), the ions are ordered mainly by size: Li+ ∼ Na+ < K+ < Cs+ . Similarly, the divalent ions are ordered by size for the preferred (¯ n=3) composition: Zn2+ < 2+ Ca . Thus the ligand field strength applies for the lowest free energy compositions. The ion ordering changes and no longer supports the ligand field strength hypothesis as binding site composition (n) deviates from the preferred composition (¯ n) for both ion



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that the optimal structure for multiple ions differs for Cs+ compared with Li+ and Na+ , as found in the MD simulations. Finally, the ionomer structure with Zn2+ differs from the monovalent cases. The aggregates in the Zn2+ systems tend to form more isolated, compact clusters. This finding is consistent with the DFT results of much stronger binding with the optimal single Zn2+ structure at n ¯ = 3 (Fig. 1), in which the ion is surrounded by carboxylates (Fig. 4), and thus does not as readily allow the formation of larger clusters by stacking.

at the Center for Integrated Nanotechnologies, a U.S. DOE Office of BES user facility at Los Alamos National Lab (Contract DE-AC52-06NA25396) and Sandia National Labs (Contract DE-AC04-94AL85000). Funding was provided by Sandia’s LDRD program and the DTRA-Joint Science and Technology Office for Chemical & Biological Defense (IAA number DTRA10027IA-3167)(S.B.R.). Sandia National Labs is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE’s NNSA under contract DE-AC04-94AL85000

Conclusions

References

To test two competing hypotheses of ion binding, we found the minimum energy structures and solvation free energies (∆G) for n=1 to 4 acetate molecules bound to a set of mono- and di-valent ions in a low dielectric medium. Our calculations of ∆G for acetate molecules bound to an ion followed the same size-based (small to large) selectivity sequences for divalent (Zn2+ < Ca2+ ) and monovalent (Li+ < Na+ < K+ < Cs+ ) ions as hydration free energies and reverse Hofmeister series. The size-based ion binding sequence supports the ligand field strength hypothesis, but not the equal affinities hypothesis. Additional support for the ligand field strength hypothesis appeared in the ∆G results: each ion favored binding sites with higher field strength acetate ligands over lower field strength waters; and each ion favored complexation with more than a single ligand. All monovalent ions preferred n ¯ =2 acetates interacting in bidentate mode. Divalent ions preferred larger clusters with n ¯ =3 acetates, also in bidentate mode. Also, a binding site with maximum negative charge (n=4 acetates) destabilized Cs+ solvation toward ∆G ∼ 0, providing support for the idea that increased negative charge in a binding site can promote ion conduction. For ion transfer between aqueous solution and carboxylate binding sites (∆∆G), the size-based ion-binding sequences could be modified by constraining the binding site to a nonpreferred composition (n 6= n ¯ ). Even though the same ligand chemistries are involved in non-preferred binding site compositions, the ligand field strength hypothesis fails to account for the results because it does not account for constraints on a binding site. The ∆∆G results help clarify differences in ion solvation preferences by molecular ligands in aqueous solutions compared with their chemical analogues in more restrictive environments like ion channels. Our results show that a sizebased sequence in ion binding occurs when ligands have adequate freedom to adopt the preferred binding site composition (¯ n), as they do in recent experimental studies on acetate molecules and polypeptides with carboxylate side chains in aqueous solutions. Decomposition of ∆∆G revealed that ion ordering shifts because binding site composition (n) affects each monovalent ion uniquely, destabilizing specific ions by different amounts relative to the preferred composition. As a result, the binding site composition (n) can be used to alter ion solvation preferences, from one ordered by ion size to one that resembles the equal affinities hypothesis, even to one that follows an inverse size sequence. Supporting Information Calculation and figures of the atomic charges and induced ligand dipole moments; tables of ∆G and ∆H for all cases; tables giving the optimized geometries; tables of ∆∆G for transfer from aqueous to acetate environment. Acknowledgements This work was performed, in part,

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carboxylate ionomer

PLGIC channel

ACS Paragon Plus Environment

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Ion-Specific Effects in Carboxylate Binding Sites - The Journal of

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