A First‐Principles Molecular Dynamics Study of Calcium in Water

Abstract

Herein, we report on Car-Parrinello [1] simulations of the divalent calcium ion in water, aimed at understanding the structure of the hydration shell and at comparing theoretical results with a series of recent experiments. We show some of the progress in the investigation of aqueous solutions brought about by the advent of ab initio molecular dynamics and highlight the importance of accessing subtle details of ion-water interactions from first principles.Calcium plays a vital role in many biological systems, including signal transduction, blood clotting, and cell division. In particular, calcium ions are known to interact strongly with proteins as they tend to bind well to both negatively charged (e.g. in aspartate and glutamate) and uncharged oxygens (e.g. in main-chain carbonyls). [2,3] The ability of calcium to coordinate multiple ligands (from six to eight oxygen atoms) with an asymmetric coordination shell enables it to cross-link different segments of a protein and induce large conformational changes. The great biochemical importance of the calcium ion has led to a number of studies to determine its hydration shell and its preferred coordination number in water.Experimental studies have used a variety of techniques, including X-ray diffraction (XRD), [4][5][6] extended X-ray absorption fine structure (EXAFS) spectroscopy, [7,8] and neutron diffraction [9,10] to elucidate the coordination of Ca 2 + ions in water. The range of coordination numbers (n C ) inferred by X-ray diffraction studies varies from six to eight, and is consistent with that reported in EXAFS experiments (8 [7] and 7.2 [8] ). A wider range of values (6 to 10) was found in early neutron diffraction studies, [9] depending on concentration, while a more recent measurement by Badyal et al. reports a value close to seven. [10] In addition to experimental measurements, many theoretical studies have been carried out to investigate the solvation of Ca 2 + ions in water and have also reported a wide range of coordination numbers. Most of the classical molecular dynamics (MD) [4,7,11] and quantum molecular (QM)/MM simulations [12,13] report n C values in the range of eight to ten; in general, n C appears to be highly sensitive to the choice of the ion-water potential used in the calculations.[11] Even ab initio MD simulations have so far obtained conflicting values for n C . For the structure of the first solvation shell Naor et al. found n C = 7 to 8 and a Ca 2 + -oxygen average distance (r Ca-O ) of 2.64 , [14] while Bakó et al. found n C = 6 and r Ca-O = 2.45 . [15] In view of the existing controversies, we have carried out extensive Car-Parrinello [1,16] simulations of Ca 2 + solvation in water, using both a rigid and a flexible water model, up to time scales of 40 ps. Our simulations show variations of coordination numbers from 6, 7 and 8 occurring over intervals of % 0.3 to 0.4 exchanges per picosecond, and yielding average coordination numbers of 6.2 and 7 for flexible and rigid water models, respectively. These results are consistent with ...

Local Effects in the X-ray Absorption Spectrum of Salt Water

“…In contrast, Ca 2+ has a somewhat flexible first solvation shell with coordination numbers varying between 6 and 8, which is also in agreement with existing results. 11 The dominant configuration for calcium, or 75.5% in our molecular dynamics simulation, is a 7-fold distorted octahedral arrangement. In contrast to the divalent cations, Na + is coordinated by fewer water molecules (between 4 and 6; see Figure 2) but exhibits the floppiest first solvation shell.…”

“…We observe a clear double-peaked character to the Mg 2+ simulation results, in agreement with previous simulations that also showed that bulk water would have a broad featureless distribution. 11 From Mg 2+ to Ca 2+ , we observe a narrowing in the separation of the two peaks, originally at 0.30 and 0.34 Å, to 0.30 and 0.32 Å. The sodium simulation exhibits a broad peak centered around 0.32 Å, but it lacks significant separation between the two peaks observed in the Mg 2+ and Figure 6.…”

“…[10][11][12] Inclusion of the chloride anion was motivated by the need to compare directly to experimental X-ray absorption spectra. It is not universally agreed upon whether the Cl -ion itself imparts any specific changes to the features of the XAS of different solutions.…”

“…22 The rigid water model has been shown to have only a minor effect on the first solvation shell around calcium. 11 The elimination of high-frequency ionic motion provides a number of benefits, the most notable of which is allowing for a longer time step of 0.97 fs, while the flexible NaCl simulations were carried out with a 0.48 fs time step. The production runs for the CaCl 2 and MgCl 2 cases were both about 28 ps in length, and they were collected in the NVE ensemble following an initial equilibration at 340 K using velocity rescaling for about 3 ps.…”

“…Both XRD 4 and EXAFS results 9 suggest a coordination number between six and eight for Ca 2+ , while Mg 2+ has been shown by XRD to be coordinated octahedrally with six water molecules, 3 and XRD experiments indicate Na + is coordinated by four to six water molecules. 5 Importantly, first-principles molecular dynamics calculations were shown to be necessary in order to recover experimentally observed coordination numbers for Mg 2+ , 10 Ca 2+ , 11 and Na + . 12 Classical molecular dynamics simulations with simple force fields tend to overestimate the structure and coordination number for the solvation shell of these ions.…”