Octa-Coordination and the Aqueous Ba2+ Ion - American Chemical

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Octa-coordination and the Aqueous Ba Ion Mangesh I. Chaudhari, Marielle Soniat, and Susan B. Rempe J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b03050 • Publication Date (Web): 18 Jun 2015 Downloaded from http://pubs.acs.org on June 21, 2015

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The Journal of Physical Chemistry

Octa-coordination and the Aqueous Ba2+ Ion Mangesh I. Chaudhari,∗,† Marielle Soniat,∗,‡ and Susan B. Rempe∗,† Center for Biological and Material Sciences, Sandia National Laboratories, Albuquerque, NM, 87185, and Department of Chemistry, University of New Orleans, New Orleans, LA, 70148 E-mail: [email protected]; [email protected]; [email protected]

Abstract The hydration structure of Ba2+ ion is important for understanding blocking mechanisms in potassium ion channels. Here, we combine statistical mechanical theory, ab initio molecular dynamics simulations, and electronic structure methods to calculate the hydration free energy and local hydration structure of Ba2+ (aq). The predicted hydration free energy (- 304±1 kcal/mol) agrees with the experimental value (-303 kcal/mol) when a maximally occupied, unimodal inner solvation shell is treated. In the local environment defined by the first shell of hydrating waters, Ba2+ is directly and stably coordinated by eight (8) waters. Octacoordination resembles the crystal structure of Ba2+ and K+ bound in potassium ion channels, but differs from the local hydration structure of K+ (aq) determined earlier.

Introduction

ter and ionic solutions, Bernal and Fowler proposed an unusual octa-coordinated Ba2+ hydration structure as an exception to the anticipated hexa-coordination of smaller divalent ions. 24 Structural data to test that proposition directly is sparse. One reason is that Ba2+ extensively absorbs X-rays, leading to unfavorable conditions for structural studies. 25 Consequently, only a few experimental groups have targeted Ba2+ ion, producing discrepant results. X-ray diffraction studies reported a hydration number greater than eight (9.5), 26 while extended X-ray absorption fine structure (EXAFS) spectroscopy experiments reported hydration numbers of eight (8.1 and 7.8). 27,28 Similarly, theoretical analysis of Ba2+ hydration using ab initio methods has been limited, partly due to the large number of electrons involved. 29 No purely ab initio studies of hydration structure in aqueous solution have been reported. One study combined an ab initio quantum mechanical approach with classical molecular mechanics simulations (QM/MM) and re-

Barium (Ba2+ ) ion is about the same size as potassium (K+ ) based on crystal ionic radii that fall within 0.03 ˚ A. 1 Both ions partition between water and octa-coordinated binding sites in potassium ion channels. 2–6 Thus, Ba2+ can act as an analogue of K+ . Octa-ligation by oxygens along the protein backbone of K channels is widely believed to facilitate K+ permeation by mimicking that ion’s local hydration structure. 5,7,8 While K+ permeates rapidly, Ba2+ instead sticks and blocks permeation of other ions. That inhibitory behavior has been used since the 1970’s to probe the mechanism of K channel function. 3,8–20 Yet, recent works still debate the blocking mechanism and structure of the blocking sites in various K channels. 21–23 To help clarify the debate, we analyze here the physical chemical properties of Ba2+ in aqueous solution, the reference environment for ion channel block. In a 1933 landmark theoretical paper on wa-

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ported a hydration number of nine (9.3). 29 That structural result was not substantiated by a prediction of hydration free energy. Classical simulations have produced values ranging from eight 30,31 to nine. 28 Those simulations are typically not designed to provide sole determination of such properties, but they may shed light on issues determining the hydration number of ions. A statistical mechanical theory developed earlier permits computation of solvation free energy based on local structural results determined for systems treated with ab initio models. 32–36 The coupling of structure with thermodynamic predictions provides an advantage for validating the results compared to more standard studies of structure alone. Also, structural data obtained by molecular simulation contains information about the spatial distributions of each neighboring solvent molecule. Although a neighborship analysis is typically unresolvable for experimental data and seldom applied to simulation data, the results can help clarify how many solvent molecules define the local hydration structure around an ion. The free energy theory has been coupled with structural studies to obtain new insights about K+ 37–39 and its monovalent analogue, rubidium (Rb+ ). 40 Here, we apply this approach for the first time to Ba2+ (aq) to resolve fundamental questions about that ion’s interactions in bulk liquid water. We base the structural analysis on the first purely ab initio studies of Ba2+ (aq). At the same time, we also investigate how choices in the theoretical analysis affect the free energy predictions. Our studies suggest that the best hydration free energy predictions result from analysis of a maximally occupied, unimodal inner solvation shell, as determined by a neighborship analysis. Those restrictions on inner-shell occupation and boundary arise because of the dielectric continuum approximation used here to treat water outside the inner shell. Contributions from water within and outside the inner shell are both important for predicting the total hydration free energy. Barium ion directly coordinates with n=8 waters in aqueous solution, in contrast to lower hydration numbers

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reported earlier in experimental and theoretical studies of K+ 37–39,41–44 and its analogue, Rb+ . 40,45–47 An interesting observation is that octa-coordinated ion binding sites in K channels appear to mimic the local hydration structure of Ba2+ , a blocking ion, not the permeant ions, K+ and Rb+ .

Theory Quasi-chemical theory (QCT) 32–36,39 divides the excess chemical potential of Ba2+ hydra(ex) tion, µBa2+ , into three contributions, (ex)

µBa2+ = −kT lnKn(0) ρnH2 O + kT lnpBa2+ (n) (ex)

+ (µBa(H

(ex)

2+ 2 O)n

− nµH2 O ). (1)

The first term represents an equilibrium ratio (0) Kn for Ba2+ -water association reactions (Eq. 2) treated as in an ideal gas phase, hence the superscript (0): Ba2+ + nH2 O ⇋ Ba(H2 O)2+ n .

(2)

The association reactions occur within a chosen observation volume. While any shape may be selected, 35,36 we choose a sphere of radius r = λ centered around the ion for convenience. Other works have also chosen a spherical boundary. 37–39,44,48–55 Solvent molecules within λ, measured here by the location of water oxygen atoms, are local to the ion and constitute inner-shell solvent. Accordingly, the reactions form inner-shell solvation complexes, Ba(H2 O)2+ n . The density of water in solution, ρH2 O , accounts for the availability of (0) water ligands. Both Kn and ρH2 O are made dimensionless by scaling with the density of water equivalent to an ideal gas at ambient pressure, p=1 atm. In the second term, pBa2+ (n) is the probability of observing n waters around Ba2+ within the inner solvation shell of radius λ. This term accounts for fluctuations in the inner-shell solvent population in aqueous solution. The population fluctuation term will contribute zero if the inner shell is strictly occupied by a single


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Computational Methods

coordination number, n, so that p(n)=1. The probability is readily evaluated from ab initio molecular dynamics (AIMD) simulations. The third term represents solvation of a Ba2+ water inner-shell complex by the outer solvation environment, and removal of the water ligands from the same environment. Note that the environment accounts for the compositions of bulk solutions studied experimentally. That combi(ex) (ex) nation, µX(H O)2+ − nµH2 O , balances the free en2 n ergy for the association reaction when the solute, X, is only weakly solvated. Gas molecules provide example cases. 36,56–59 A balance is not anticipated here because Ba2+ hydration free (ex) energy, µBa2+ , is large. The Boltzmann factor, k, and absolute temperature, T , set the energy scale. (ex) The overall hydration free energy, µBa2+ , is independent of the choices made for λ and n in QCT (Eq. 1). In fact, Eq. 1 applies to any single n that occurs within the chosen innershell boundary, λ. Nevertheless, specific n or λ may be more effective than others in practical applications that evaluate the free energy contributions approximately. One goal pursued here is to determine how different choices for the radius (λ) and occupancy (n) of the inner solvation shell affect QCT predictions when the terms (Eq. 1) are evaluated by electronic structure, AIMD, and dielectric continuum models. To achieve that goal, we analyze AIMD simulation data to inform the selection of the inner shell boundary and occupancy. In place of the single λ value considered previously, our study compares hydration free energies computed with seven λ values (2.9-3.5 in increments of 0.1 ˚ A). Those values define inner-shell regions that include specific structural features found in the simulated Ba2+ -oxygen radial distribution function, g(r). We also consider n that span the full range of possible occupancy distributed exclusively within the first hydration shell of Ba2+ (aq). Those occupancies are identified by a neighborship analysis of g(r).

The main challenge in predicting local hydration structure and hydration free energy for ions is to represent the broad range of molecular interactions involved in ion complexation reactions. Previous studies suggest that treatment of multi-body interactions is important for those predictions. 60–62 Accordingly, we chose to model Ba2+ and near water neighbors using density functional theory (DFT) since that approach naturally accounts for interactions between pairs and larger groups of atoms. Ab initio molecular dynamics (AIMD) simulations on a single Ba2+ solvated by 64 waters were performed using the VASP AIMD simulation package 63 to investigate local hydration structure. Simulations were carried out for a total time of 41 ps. A system with 64 waters extends well beyond the first hydration shell of Ba2+ , which is the region of interest in this study. The ion/water ratio was chosen to match a 0.8 M ion concentration studied experimentally. 27 The simulated AIMD system was defined by a cubic box of 12.417 ˚ A with periodic boundary conditions to mimic bulk liquid conditions. In that box volume, the water density matches the experimental density of liquid water at standard conditions of room temperature and pressure used in experimental structural studies. 27,28 The boundaries contain a background charge to neutralize the overall charge of the system. We utilized the PW91 generalized gradient approximation (GGA) to the electron density 64 to facilitate comparisons with earlier work on K+ 43,44 and Rb+ 40 hydration. As a pure GGA functional, PW91 enables a significant computational savings over more specialized functionals such as the hybrid GGA, B3LYP, and metaGGA, TPSS. We described the core-valence interactions using the projector augmented-wave (PAW) method, 65 expanded the valence electronic orbitals in plane waves with a high kinetic energy cut-off of 36.75 Ry (500 eV), and used 10−6 eV as the convergence criteria for the electronic structure self-consistent iterations. We also used a time step of 0.5 fs to resolve water vibrational motions. Prior to the pro-


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fied to match the chosen λ value. Additionally, default parameters from the PCM model were used for hydrogen and oxygen radii in the clusters and for individual waters. The radii define cavities for the PCM solvation model based on a set of overlapping spheres. The dielectric constant of the outer-shell environment was set to mimic water at room temperature (78). The ion-water complexes were re-optimized in the presence of the environment. Hydration free energies were calculated at standard conditions of T =298 K and p=1 atm by adding the individual contributions of Eq. 1. The density in the first term was subsequently adjusted to account for the actual concentration of water ligands in liquid water, ρH2 O =1 g cm−3 , to match experimental conditions. If this density is tracked as an adjustment to the ideal gas pressure, then it corresponds to a pressure factor of 1354 atm. 32,89 Predicted values are compared with the absolute hydration free energy compiled by Marcus. 85 Due to a sign error, the compiled value was adjusted by 2 × −1.9 kcal/mol to convert to the standard state pertaining to hydration (1M Ba2+ in gas phase and aqueous solution). 32

determined gas phase free energies for sequential addition of waters to Ba2+ under standard conditions of room temperature and ambient pressure provided data 74 for selecting the exchange-correlation functional and basis sets (FIG. 1). A comparison of density functionals led to selection of the TPSS exchange-correlation density functional with the aug-cc-pvtz (oxygen) and cc-pvtz (hydrogen) basis sets 83 and the MWB46 84 (Ba) effective core potential and corresponding basis set. The slightly smaller basis on hydrogen atoms results in negligible changes to structure and electronic energy, but represents as much as a five-fold savings in computational time compared with the aug-cc-pvtz basis set. As anticipated, the exchange-correlation functionals produced nearly identical lowestenergy structures. Note also that differences in binding free energies among functionals are small relative to total ion hydration free energy (≈ -300 kcal/mol 85 ), particularly between TPSS, PW91, and PBE (FIG. 1). That agreement means that the final results from combining terms in Eq. 1 will not depend sensitively on the level of electronic structure theory. Cluster conformations were exhaustively sampled from the ab initio simulation trajectories and then submitted to the G09 software to obtain optimized geometries and electronic energies. Tight convergence criteria on the optimization (10−5 a.u.) and energy (10−8 a.u.), along with an ultra-fine integration grid, facilitated the optimization procedure. Vibrational frequency analysis based on the normal modes 86,87 were performed to obtain thermal corrections to the electronic energy under the same standard conditions studied experimentally. All vibrational frequencies were positive, confirming that optimized cluster configurations represent minimum-energy geometries. To evaluate the outer-shell solvation term of Eq. 1, the outer environment was treated implicitly as a reaction field with a polarizable continuum model (PCM). 88 The PCM model includes contributions to the outer-shell solvation free energy from electrostatic, packing, and dispersion terms. 88 The radius of the barium atom within each Ba(H2 O)2+ n cluster was modi-

Results and Discussion The hydration structure determined by the Ba2+ -oxygen radial distribution function, g(r), shows a distinct division between water neighbors occupying the first and second hydration shells (FIG. 2). Analysis of the near neighbor distributions reveals that n=1-6 waters fill in the principal maximum at rmax ≈ 2.8 ˚ A. That position agrees with experimental results of rmax =2.81 ˚ A 27 and 2.78 ˚ A. 28 Those waters, and the n=7th and n=8th near neighbors, directly coordinate the ion and contribute to the first peak in a unimodal way. An inflection point on the running coordination number hn(r)i at the first minimum in g(r), rmin ≈ 3.5 ˚ A, defines the first hydration shell and confirms h¯ ni = 8 as the average and most probable hydration number, in agreement with the average hydration structure from EXAFS data of hni=8.1 27 and 7.8. 28 The radial distri-


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permeant K+ , but not the smaller impermeant sodium ion (Na+ ). 39,44,96 An interesting observation is that ion binding sites in K channels appear to mimic the local hydration structure of a blocking ion (Ba2+ ), not the permeant ion (K+ ). This result establishes a foundation for future molecular studies of the blocking mechanism and blocking sites of K channels.

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and barium binding in NaK2K. J. Gen. Phys. 2014, 144, 181–192. (6) Koepfer, D.; Song, C.; Gruene, T.; Sheldrick, G.; Zachariae, U.; de Groot, B. L. Ion permeation in K+ channels occurs by direct Coulomb knock-on. Science 2014, 346, 352 – 355. (7) Zhou, Y.; Morais-Cabral, J.; Kaufman, A.; MacKinnon, R. Chemistry of ion coordination and hydration revealed by a K+ channel-Fab complex at 2.0 ˚ A resolution. Nature 2001, 414, 43–48.

Acknowledgements We thank Lawrence R. Pratt, Sameer Varma, and Dubravko Sabo for helpful discussions. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under Contract DE-AC0494AL8500. This work was supported by Sandia’s LDRD program (M. I. C. and S. B. R.) and the State of Louisiana Board of Regents (M. S.).

(8) Piasta, K. N.; Theobald, D. L.; Miller, C. Potassium-selective block of barium permeation through single KcsA channels. J. Gen. Phys. 2011, 138, 421–436. (9) Hagiwara, S.; Miyazaki, S.; Moody, W.; Patlak, J. Blocking effects of barium and hydrogen ions on the potassium current during anomalous rectification in the starfish egg. J. Physiol. 1978, 279, 167– 185.

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Page 16 of 24

Page 17The of 24 Journal of Physical Chemistry

−kT lnK(n−1)→n (kcal/mol)

−5

(0)

1 2 3 4 −10 B3LYP 5 M06 6 7 PW91 8 PBE0 9 −15 10 CAM − B3LYP 11 TPSS 12 Experiment ACS Paragon Plus Environment 13 −20 14 5 6 7 8 15

n

gBa2+ O (r)

1 2 3 4 5 6 7 8 9 10 11 12 13

10

The Journal of Physical Chemistry Page 18 of 24

8

8

6

6 1-6

4

4 1 23 45

2

2

67

9

8

0


2.5

3.0 r (˚ A)

3.5

0 4.0

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10

Page 19 of 24





Page 20 of 24

kT lnpBa2+ (nλ = n)

Page6 21 of 24The Journal 2.9 ˚ A of Physical Chemistry

3.0 3.1 3.2

4

1 2 2 3 4 5 0 6 7 −2 8 9 −4 10 11 12−6 0 13

˚ A ˚ A ˚ A


2

4

n

6

8

10

−200

The Journal of Physical ChemistryPage 22 of 24

λ = 3.5 ˚ A −225

(ex)

µBa2+ (kcal/mol)

1 2 3 4 −250 5 6 7 −275 8 9 10 −300 11 12 1 13

λ = 2.9 ˚ A ACS Paragon Plus Environment

2

3

4

n

5

6

7

8

0

Page 23 of 24The Journal of Physicalassociation Chemistry free energy

kcal/mol

1 2 3 −100 4 5 6 7 8 9 −200 10 11 12 13 14 15−300 16 1 17

with ligand density outer − shell hydration free energy


2

3

4

n

5

6

7

8

−200

The Journal of Physical ChemistryPage 24 of 24

λ = 3.5 ˚ A −225

(ex)

µBa2+ (kcal/mol)

1 2 3 4 −250 5 6 7 −275 8 9 10 −300 11 12 1 13

λ = 2.9 ˚ A ACS Paragon Plus Environment

2

3

4

n

5

6

7

8

Octa-Coordination and the Aqueous Ba2+ Ion - American Chemical

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