Bioelectromagnetics 36:377^385 (2015)
Water Response to Intense Electric Fields: A Molecular Dynamics Study Paolo Marracino, Micaela Liberti, Guglielmo d’Inzeo, and Francesca Apollonio* Department of Information Engineering, Electronics and Telecommunications (DIET), Italian Inter-University Center of Electromagnetic Fields and Biosystems (ICEmB), La Sapienza University of Rome, Italy This paper investigated polarization properties of water molecules in close proximity to an ionic charge in the presence of external electric fields by using an approach based on simulations at the atomic level. We chose sodium and chloride ions in water as examples of dilute ionic solutions and used molecular dynamics simulations to systematically investigate the influence of an external static electric field on structural, dipolar, and polarization properties of water near charged ions. Results showed that a threshold electric field higher than 108 V/m is needed to affect water polarization and increase mean dipole moment of water molecules close to the ion. A similar threshold holds for water permittivity profiles, although a field 10 higher is needed to ensure that water permittivity is almost constant independently of the position close to the ion. Electric fields of such intensities can greatly enhance polarizability of water in hydration shells around ions. Bioelectromagnetics. 36:377–385, 2015. © 2015 Wiley Periodicals, Inc. Key words: water solutions; permittivity; electrostatics; molecular simulations; hydration shell
INTRODUCTION Water is essential for life with specific properties not found in other materials. For example, water is a polar molecule, has high permittivity, small molecule size, and is an excellent solvent for ionic compounds and salts. The properties of the hydration layer of water surrounding biomolecules have unique features and are clearly different from the bulk water extensively studied both experimentally and computationally [Ball, 2008; Battacharjee and Biswas, 2011]. Such unique hydration properties determine three-dimensional structures of proteins, nucleic acids and other biomolecules, and control their functions [Heugen et al., 2006; Wood et al., 2007]. Water is the most studied liquid in the last 60 years [Hasted et al., 1948; Buchner et al., 1999], either alone or as an electrolyte solution [Leberman and Soper, 1995]. In bioelectromagnetics research, ionic aqueous solutions have been investigated since the 1980s, both experimentally looking at frequency profiles for dielectric permittivity [Gabriel et al., 1996] and theoretically for behavior of electric dipoles in presence of very intense, non-uniform electric fields [Chiabrera et al., 1989]. For such theoretical investigations, molecular simulations provide the only tool to obtain insight into behaviors at an atomic level, 2015 Wiley Periodicals, Inc.
unravelling microscopic information on structure and dynamics of hydration shells of different cations and anions in diverse environments. In the past, significant effort was put into designing models of water molecules to predict values from computer simulations [van der Spoel et al., 1998; van Maaren and van der Spoel, 2001; D’Alessandro et al., 2008]. Simulations of ionic aqueous solutions have mostly found good agreement with experiments on: (i) principal thermodynamics properties of water [Hyun and Ichiye, 1997; D’Alessandro et al., 2002]; (ii) water structure, indicating a first, and second shell from the central water molecule [Liu and Ichiye, 1999; van Maaren and van der Spoel, 2001; D’Alessandro et al., 2008]; (iii) dielectric properties of ionic aqueous solutions and behavior of pure water Conflict of interest: None. *Correspondence to: Francesca Apollonio, University of Rome, Department of Information Engineering, Electronics and Telecommunications, Via Eudossiana 18 00184 Rome, Italy. E-mail: [email protected] Received for review 9 March 2014; Accepted 11 March 2015 DOI: 10.1002/BEM.21916 Published online 14 April 2015 in Wiley Online Library (wileyonlinelibrary.com).
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in electric fields [Jung et al., 1999; Suresh et al., 2006; Reale et al., 2013; Reale et al., 2014]; and (iv) dielectric saturation effects [Alper and Levy, 1990], which are important in solvent regions close to ions where electric field strengths are very large. Nevertheless, investigating intense electric field effects on water molecules polarization in narrow shells around charged ions is still a challenging issue, and no definitive conclusions have been reached. This is even more interesting given the present increase in significant applications involving intense electric fields above 107 V/m [Beebe and Schoenbach, 2005; Mulero et al., 2010; Merla et al., 2012; Tokman et al., 2013; Ho et al., 2013]. This paper investigated structural, dipolar, and polarization properties of water in close proximity to sodium and chloride ions in the presence of external electric fields. The methodology applied, based on a simple atomic model of the charged ion and water solution, made use of molecular dynamic (MD) simulations. Electric fields of different intensities are used to determine the extent an external electric perturbation can affect the endogenous environment around ions or near charged interfaces, as reported in DanielewiczFerchmin et al. [2003]. This technique is also used to evaluate both electric field dependent water permittivity profile and threshold for the applied field to modify water polarization and dipolar orientation. Our approach provided outcomes at mesoscopic and microscopic levels, and may help understand polarization response subjected to an external applied field. MATERIALS AND METHODS Our target was a monovalent ion solvated by thousands of water molecules (about 2,200), modelling an extremely diluted solution. This means there is no significant difference in the hydrogenhydrogen bond distribution and pair correlation function within the first hydration shell, between water alone, and the solution [Leberman and Soper, 1995; Omta et al., 2003]. Our approach to characterize water polarization properties is presented in Figure 1. It is well known from linear response theory (LRT) that the macroscopic dielectric permittivity of water can be defined considering volume Vbox [van der Spoel et al., 1998] (out of the dashed box, Fig. 1) that is sufficiently large compared to microscopic scale so as not to see granularity of individual atoms, but small enough compared to macroscopic level to see heterogeneity of the material. This is the basis of the permittivity calculation from MD simulations, predicting macroscopic frequency-dependent dielectric Bioelectromagnetics
Fig. 1. Schematic representation of physical properties of water at different spatial scales. Region V box corresponds to the whole simulation box, where water permittivity eðv; EÞ is usually evaluated, as a function of angular frequency, and electric field applied. Regions (Vsphere ) correspond to mesoscopic subdomains defined in this paper; in such regions the difference (De), between e of hydrated ion and the one of water, has been evaluated as a function of position r and E field. Finally, ðvshell Þ and (vcyl ) regions correspond to microscopic domains where mean dipole moment mðr; EÞ and water density distribution have been evaluated.
permittivity ðeÞ for water, or dilute aqueous solution [Boresch et al., 2004], and is in good agreement with experimental data. Nevertheless, a more detailed dielectric picture at the nanometer and/or molecular scale requires a new approach, which considers subdomains of the total volume Vbox . Here a multi-scale decomposition was proposed. We defined an equivalent dielectric permittivity based on water dipole fluctuations over spherical volumes ðVsphere Þ of increasing radius covering up to a few nanometer; such volumes give rise to mesoscopic scale illustrated in Figure 1. Conversely, microscopic domain was defined over smaller volumes of different shape, either spherical shells, or cylinders ðvshell; vcyl Þ, covering up to fractions of a nanometer, allowing an evaluation of the water density properties, and local dipole moment (Fig. 1). Figure 2 shows our approach. Figure 2a is a schematic of the spherical volumes of increasing radius Vsphere around the charge used for mesoscopic outcomes. Figure 2b and c indicate spherical ðvshell Þ and cylindrical ðvcyl Þ microscopic volumes used to evaluate results for water dipole moment and density. Simulations at the atomic scale reproduce the effective structure of water and provide the permittivity profile, mean dipole moment, and density distribution of water surrounding the ion charge when the external electric field is applied. Simulation Details Simulations on three different systems were performed using an MD package (GROningen MAchine for Chemical Simulations developed by the
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Fig. 2. Mesoscopic and microscopic domains (a) Spherical regions ofincreasingradius ðVsphere Þ, centered on a fixedion position; (b) microscopic shell domains (vshell ) formed by subtracting volumes of two concentric spheres, differing in radius by 0.2 nm, foreach radial distance from the ion, givingrise to spherical shells of increasing volumes but with constant thickness; (c) microscopic cylindrical regions (vcyl ), of fixed height (0.3 nm) and diameter (0.6 nm), containing few water molecules (around 3), spanning from one side of the simulation box to the other, in the same directionas applied external E field (x-axis).
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GROMACS development team at Uppsala University [Uppsala, Sweden]; Stockholm University [Stockholm, Sweden]; and the Royal Institute of Technology [Stockholm, Sweden]) [van der Spoel et al., 2005]. Our reference system to assess bulk water properties was a cubic box (4 nm side) with 2,178 single point charge (SPC) water molecules [Berendsen et al., 1981]. This results in an experimental density of 1,000 kg/m3. To evaluate behavior of water near ions, two extremely dilute solutions were simulated, each consisting of a single ion placed in the center of the box (i.e., sodium or chloride ion) surrounded by the same number of water molecules used in the reference system. Since we were not interested in ion translational motions, but rather in fast relaxation associated with the collective motion of water near the ion [Kubota et al., 2012], the solute molecule was constrained using the normal freezing option in GROMACS [D’Abramo et al., 2004]. This procedure, which speeds up solvent relaxation around the solute, provides correct statistical mechanics, and thermodynamics of the system (SPC plus a rigid solute), as demonstrated by D’Alessandro et al. [2002] and D’Abramo et al. [2004]. Following energy minimization and subsequent solvent relaxation, the system was gradually heated from 50 K to 300 K using short (typically 10 ps) MD simulations. Several MD simulations of the three systems were performed, both in unexposed (no external E-field) and exposed conditions, using a wide range of field intensities (107 V/m up to 5 109 V/m). For fields below 107 V/m it has already been shown that effect on molecular targets is not significant [Apollonio et al., 2008], while 5 109 V/m is the highest intensity available in literature for molecular simulations. We considered the external electric field as acting on each atom in the simulation domain without depolarization terms, i.e., under tinfoil boundary conditions [Yeh and Berkowitz, 1999; Apol et al., 2002]. Dissipation of heating from the field was taken into account by using a thermal coupling available in GROMACS, i.e., the Berendsen T-coupling [Berendsen et al., 1984], suitably arranged to reproduce an isothermal temperature coupling [Evans and Morriss, 2008], and being fully consistent with statistical mechanics [Brown and Clarke, 1984]. This was obtained by setting the Berendsen T-coupling time constant with the same time-step used for integration algorithm (i.e., 2 fs). All bond lengths were constrained using the LINear Constrain Solver (LINCS) algorithm [Hess et al., 1997]. Long-range electrostatic interactions were computed by the Particle Mesh Ewald method [Darden et al., 1993] with 34 wave vectors in each Bioelectromagnetics
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dimension and a 4th order cubic interpolation. Finally, since it is well known that in a periodic system the net charge must be zero, in non-neutral periodic systems it is necessary to include a compensating background charge, the Ewald potential. Here, we followed the most standard way to satisfy the neutrality requirement by adding a homogeneous background charge density that exactly cancelled the unit charge [Heyes, 1981; Figueirido et al., 1995; Bogusz et al., 1998]. The GROMOS force field parameters were adopted [van Gunsteren et al., 1996]. Trajectories were propagated up to 20 ns in an NVT canonical ensemble (number of particles [N], volume [V], and temperature [T] are kept constant) using an integration step of 2 fs. Mesoscopic and Microscopic Polarization Properties To represent mesoscopic length scale we introduced a quantity called “apparent” dielectric permittivity, ea ðr; vÞ, as a function of position r and angular frequency v; this quantity can be interpreted as dielectric permittivity of specific spherical volumes ðVsphere Þ, rather than of whole simulation box ðVbox Þ. This approach has been used by other authors [Hyun et al., 1995; Nymeyer and Zhou, 2008]. It is obtained [Nymeyer and Zhou, 2008] by a matching continuum calculations (Poisson Equation) and free energy calculations (molecular dynamics simulations) to produce a position-dependent dielectric profile in aqueous solutions and in non-homogeneous systems such as biological membranes. Apparent dielectric permittivity ðea Þ was determined (regions Vsphere , in Fig. 2a) by taking into account the time correlation function FVsphere ðtÞ of the water dipole moment MVsphere in volumes Vsphere FVsphere ðtÞ ¼ hMVsphere ðtÞ MVsphere ð0Þi
ð1Þ
where total dipole moment MVsphere is calculated for each frame of the MD simulation and describes species polarization, and brackets represent an ensemble average. Then ea was calculated via the LRT using the equation: ea ðr; vÞ 1 ¼
1 3Vsphere k B T
h i _ V ðt Þ ; F F sphere
ð2Þ
where Vsphere is volume of mesoscopic subdomain (Fig. 2a), kB is Boltzmann’s constant and T is (constant) temperature of the system. The F operation represents the Fourier transform of the time derivative of the correlation function FVsphere ðtÞ. Bioelectromagnetics
To obtain the profile of ea ; 15 spherical volumes ðVsphere Þ, centered on the ion position with increasing radius from r ¼ 0.1 to 2 nm (boundary of the simulation box), were considered. Over each of these volumes total dipole moment MVsphere was calculated and static ea obtained via Equation 2 considering v ¼ 0: FVsphere ð0Þ ¼ hMVsphere ð0Þ MVsphere ð0Þi ¼ hMVsphere ð0Þ2 i hMVsphere ð0Þi2
ð3Þ
The term hMVsphere ð0Þi represents the combined average value of the water total dipole moment while hMVsphere ð0Þ2 i represents the combined average of its second order moment. The ea profile gives a spatially dependent permittivity function of water and is able to describe local behavior of water molecules near the ion, both under unexposed and exposed conditions. To give a detailed picture of water characteristics on smaller volumes up to a fraction of nanometer (Fig. 2), the microscopic scale was introduced. Spherical shell regions ðvshell Þ with thickness of 0.2 nm, increasing from the center to the box boundaries (Fig. 2b), were initially taken into account. Moreover, a small cylindrical volume ðvcyl Þ of fixed height 0.3 nm and diameter 0.6 nm, containing few water molecules (about 3), was considered. Such volume was translated along the x-axis of a Cartesian reference frame in steps of 0.1 Å , in the direction of the external electric field (Fig. 2c). This approach may be representative, for example, of water dielectric properties in a direction perpendicular to the charged surface (e.g., a planar membrane, proteinwater interfaces, etc). In both cases, microscopic quantities as mean dipole moment and water density distribution were evaluated under the influence of external electric fields. RESULTS Application of LRT to the regions Vsphere of increasing radii gave the profile of ea as a function of distance from both sodium and chloride ions, where the action of the ionic radial electrostatic field becomes progressively weaker (Fig. 2a). The ea profiles exhibited two major peaks close to the ion and a generally increasing trend towards the static macroscopic permittivity (Fig. 3). Two major fluctuation peaks, at about 0.3 and 0.5 nm from both chloride and sodium ions (Fig. 3a, b), confirmed the presence of water hydration shells. Such profiles are due to the Coulombic electric field generated by the ion (Fig. 3a, b, solid lines).
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Fig. 3. Apparent dielectric permittivity ea of water as a function of distance from fixed chloride (a) and sodium (b) ions, fordifferent exposure conditions: no field (black line),108 V/m (dark gray dashed line) and 109 V/m (light gray dotted line). Difference of the ea curve of bulk water with respect to ionic solutions: chloride solution (c), sodium solution (d), withandwithout externalelectric fields.
The application of an electric field of 108 V/m, although not modifying the profile of the hydration shells, slightly changed the ea curves, starting from 0.5 nm (Fig. 3a, b, dashed lines). This behavior is even clearer if comparing the ion in solution with the situation of water alone as shown in Figures 3c, d, where the ea difference (D) between hydrated ion and water is reported as a function of distance from the center of the box where the ion is located (i.e., Vsphere radius). Exposure to 109 V/m was still not able to overcome peculiarities of the hydration shells as shown in
Figures 3a, b (dotted lines). Close to the ion the ea profile still showed an oscillating trend where two peaks relative to the first and second shells were visible, although with low strength. As shown in Figures 3c, d, for a radius just greater than 0.6 nm, value of D for 109 V/m electric field tends to zero, suggesting that application of such an external field can order water molecules regardless of presence of the ion [Amadei et al., 2002] and can make water permittivity profile almost independent of the position close to the ion. Figure 4a gives water dipole moment averaged over spherical shell ðvshell Þ (Fig. 2b) and a clear Bioelectromagnetics
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electric field effect is demonstrated for values higher than 108 V/m. This result indicates a strong effect on the water mean dipole moment for both 108 V/m and 109 V/m fields corresponding to 0.3 nm and 0.5 nm (for the sodium solution, peaks were slightly translated closest to the ion, data not shown); such distances were identified as boundaries of the first and second hydration shells for the chloride ion. This represents the effectiveness of the external electric field in perturbing the intrinsic symmetry of water dipoles around ions, which in the absence of external perturbations, gives rise to a zero mean dipole
moment (solid line of Fig. 4), due to the spherical symmetry of the volumes in which dipole moments are calculated. Field intensities less than 108 V/m have been tested but no effect was shown on mean dipole moment. Figure 4b shows results obtained for cylindrical regions ðvcyl Þ (Fig. 2c); they are totally consistent with ones obtained for a spherical symmetry (Fig. 4a). In the case of no field applied, mean dipole moment is not zero since dipoles are mainly oriented by the Coulombic electric field due to chloride ion; however, as in the case of spherical shells, external electric fields starting from 108 V/m can overcome such local fields. A similar behavior was observed for the sodium solution (data not shown). The effect of the applied field on dipole moment was not related to changes in water density in spherical shell volumes around the ion. In fact, for intensities up to 109 V/m there was no statistically significant difference from the no-exposure condition (Fig. 5), while for intensities of 5 109 V/m the effect was confined to small percentage variations (around 5%). This result also applies to sodium ion (data not shown). DISCUSSION LRT application to total volume of simulation domain ðVbox Þ has been evaluated and preliminary
Fig. 4. Mean dipole moment of water within microscopic shells as a function of distance from fixed chloride ion, for different intensities of external electric field: (a) microscopic spherical shells (vshell ) and (b) microscopic cylindrical regions (vcyl ). Bioelectromagnetics
Fig. 5. Water density profile, calculated in microscopic spherical shells (vshell ), as a function of distance from fixed chloride ion and for different intensities of external electric field. Error bars were evaluated by calculating standard error between five subparts of total equilibrium trajectories.
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results obtained for both frequency-dependent water permittivity ðeÞ and non-linear behavior of water permittivity in the presence of intense electric fields (data not shown). These outcomes are in agreement with previous experimental data and consistent with theoretical and numerical results [Booth, 1951; Amadei et al., 2002]. Our approach provided outcomes both at the mesoscopic and microscopic levels. As for the mesoscopic level, apparent permittivity ea was introduced and spatially dependent profiles of local permittivity extrapolated. These profiles provided information on water order, on shielding properties close to the ion, and on strength of electrostatic forces that water molecules experience in the vicinity of the ion. The results are in agreement with Teschke et al. [2001], who measured a decrease in water permittivity close to a solid-liquid interface. Our data provided a space-dependent permittivity profile that shows decreasing values approaching the position of the ion. Moreover, Figure 3 shows that an external field of 109 V/m is needed to overcome the Coulombic electric field generated by the ion. The application of this field produces a profile converging to a value around 20 (obtained by applying the LRT to the whole box with a 109 V/m electric field). This is almost constant with respect to the other profiles, indicating that water dipole moments are ordered by external field much more than by the ion. All profiles in Figure 3 show welldefined regions where local radial field produced by the ion still affects water behavior. Therefore, the need to investigate a lower spatial scale (down to few water molecules), i.e., microscopic one, is needed. Microscopic regions vshell; vcyl (Fig. 2b, c) are identified to evaluate directly mean dipole moment hMvshell ð0Þi or hMvcyl ð0Þi of water. The effect of the external electric field on hydration shells, both around sodium, and chloride ions (about 0.3 nm for the chloride ion and 0.2 nm for sodium ion) provide data in accordance with the literature [Liu and Ichiye 1999; van Maaren and van de Spoel 2001]. The application of the external field does not modify shell configurations around the ion, while intensity of 109 V/m greatly affects mean dipole moment hMvshell ð0Þi in all hydration shells (Fig. 4). The effect is still observed at intensities of 108 V/m. If planar vcyl instead of spherical symmetry is used, outcomes remain consistent. On the whole our results confirm that locally (i.e., over microscopic volumes), mean dipole moment is affected by fields with a threshold around 108 V/m, although clearer, and marked effects are obtained for 109 V/m fields. This lower threshold is consistent with the one at 109 V/m of Figure 3, if one considers that
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mean dipole moment is the statistical first order moment while ea is based on a second-order one where a more pronounced masking effect is plausible. CONCLUSIONS In this paper, polarization properties of dilute ionic solutions in presence of intense electric fields were assessed. Our approach rigorously takes into account water structure and can evaluate both mesoscopic quantities and microscopic data related to water polarization. When an external electric field is applied, the threshold for affecting both apparent permittivity and dipole moment profile is about 108 V/m, showing that these or higher intensities can interact with water molecules polarized around a simple charged ion. Such field intensities overcome local Coulombic field due to ionic charge and can greatly enforce the polarizability of water in hydration shells around the ion. Reorganization of such shells due to the field has important implications in terms of ion mobility and aqueous chemical reaction mechanisms; as an example, the ionic aqueous hydration layer surrounding biological molecules has been considered as one possible environment able to sense electromagnetic field and trigger biological effects [Apollonio et al., 2013]. A similar methodology can be extended to more complex molecular systems such as proteins, enzymes, and membrane bilayers and may provide important insights into behavior of water at the interface with charged surfaces, where fundamental biochemical processes take place. ACKNOWLEDGMENTS We want to thank Andrea Amadei for his guidance in approaching molecular computations and for his support in theoretically interpreting the outcomes from molecular dynamics, and Michael Repacholi for assistance in editing the final text. This project was performed within the framework of the Joint IIT-Sapienza LAB on Life-NanoScience Project (81/13 16-04-2013). REFERENCES Alper HE,Levy RM. 1990. Field strength dependence of dielectric saturation in liquid water. J Phys Chem 94:8401–8403. Amadei A, Apol ME, Brancato G, Di Nola A. 2002. Theoretical equations of state for temperature and electromagnetic field dependence of fluid systems, based on the quasi-gaussian entropy theory. J Chem Phys 116:4437. Bioelectromagnetics
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use with a reaction field. J Chem Phys 108: 10220–10230. van Gunsteren WF, Billeter SR, Eising AA, Hunemberger PH, Kruger P, Mark AE, Scott VRP, Tironi IG. 1996. Biomolecular Simulation: The GROMOS96 Manual and User Guide. Z€urich, Switzerland: vdf Hochschulverlag, ETH. pp. 1–1042. van Maaren PJ, van der Spoel D. 2001. Molecular dynamics simulations of water with novel shell-model potentials. J Phys Chem B 105:2618–2626. Wood K, Plazanet M, Gabel F, Kessler B, Oesterhelt D, Tobias DJ, Zaccai G, Weik M. 2007. Coupling of protein and hydration-water dynamics in biological membranes. PNAS 104:18049–18054. Yeh IC, Berkowitz ML. 1999. Dielectric constant of water at high electric field: Molecular dynamics study. J Chem Phys 110:7935–7942.
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Water Response to Intense Electric Fields: A Molecular Dynamics Study Paolo Marracino, Micaela Liberti, Guglielmo d’Inzeo, and Francesca Apollonio* Department of Information Engineering, Electronics and Telecommunications (DIET), Italian Inter-University Center of Electromagnetic Fields and Biosystems (ICEmB), La Sapienza University of Rome, Italy This paper investigated polarization properties of water molecules in close proximity to an ionic charge in the presence of external electric fields by using an approach based on simulations at the atomic level. We chose sodium and chloride ions in water as examples of dilute ionic solutions and used molecular dynamics simulations to systematically investigate the influence of an external static electric field on structural, dipolar, and polarization properties of water near charged ions. Results showed that a threshold electric field higher than 108 V/m is needed to affect water polarization and increase mean dipole moment of water molecules close to the ion. A similar threshold holds for water permittivity profiles, although a field 10 higher is needed to ensure that water permittivity is almost constant independently of the position close to the ion. Electric fields of such intensities can greatly enhance polarizability of water in hydration shells around ions. Bioelectromagnetics. 36:377–385, 2015. © 2015 Wiley Periodicals, Inc. Key words: water solutions; permittivity; electrostatics; molecular simulations; hydration shell
INTRODUCTION Water is essential for life with specific properties not found in other materials. For example, water is a polar molecule, has high permittivity, small molecule size, and is an excellent solvent for ionic compounds and salts. The properties of the hydration layer of water surrounding biomolecules have unique features and are clearly different from the bulk water extensively studied both experimentally and computationally [Ball, 2008; Battacharjee and Biswas, 2011]. Such unique hydration properties determine three-dimensional structures of proteins, nucleic acids and other biomolecules, and control their functions [Heugen et al., 2006; Wood et al., 2007]. Water is the most studied liquid in the last 60 years [Hasted et al., 1948; Buchner et al., 1999], either alone or as an electrolyte solution [Leberman and Soper, 1995]. In bioelectromagnetics research, ionic aqueous solutions have been investigated since the 1980s, both experimentally looking at frequency profiles for dielectric permittivity [Gabriel et al., 1996] and theoretically for behavior of electric dipoles in presence of very intense, non-uniform electric fields [Chiabrera et al., 1989]. For such theoretical investigations, molecular simulations provide the only tool to obtain insight into behaviors at an atomic level, 2015 Wiley Periodicals, Inc.
unravelling microscopic information on structure and dynamics of hydration shells of different cations and anions in diverse environments. In the past, significant effort was put into designing models of water molecules to predict values from computer simulations [van der Spoel et al., 1998; van Maaren and van der Spoel, 2001; D’Alessandro et al., 2008]. Simulations of ionic aqueous solutions have mostly found good agreement with experiments on: (i) principal thermodynamics properties of water [Hyun and Ichiye, 1997; D’Alessandro et al., 2002]; (ii) water structure, indicating a first, and second shell from the central water molecule [Liu and Ichiye, 1999; van Maaren and van der Spoel, 2001; D’Alessandro et al., 2008]; (iii) dielectric properties of ionic aqueous solutions and behavior of pure water Conflict of interest: None. *Correspondence to: Francesca Apollonio, University of Rome, Department of Information Engineering, Electronics and Telecommunications, Via Eudossiana 18 00184 Rome, Italy. E-mail: [email protected] Received for review 9 March 2014; Accepted 11 March 2015 DOI: 10.1002/BEM.21916 Published online 14 April 2015 in Wiley Online Library (wileyonlinelibrary.com).
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in electric fields [Jung et al., 1999; Suresh et al., 2006; Reale et al., 2013; Reale et al., 2014]; and (iv) dielectric saturation effects [Alper and Levy, 1990], which are important in solvent regions close to ions where electric field strengths are very large. Nevertheless, investigating intense electric field effects on water molecules polarization in narrow shells around charged ions is still a challenging issue, and no definitive conclusions have been reached. This is even more interesting given the present increase in significant applications involving intense electric fields above 107 V/m [Beebe and Schoenbach, 2005; Mulero et al., 2010; Merla et al., 2012; Tokman et al., 2013; Ho et al., 2013]. This paper investigated structural, dipolar, and polarization properties of water in close proximity to sodium and chloride ions in the presence of external electric fields. The methodology applied, based on a simple atomic model of the charged ion and water solution, made use of molecular dynamic (MD) simulations. Electric fields of different intensities are used to determine the extent an external electric perturbation can affect the endogenous environment around ions or near charged interfaces, as reported in DanielewiczFerchmin et al. [2003]. This technique is also used to evaluate both electric field dependent water permittivity profile and threshold for the applied field to modify water polarization and dipolar orientation. Our approach provided outcomes at mesoscopic and microscopic levels, and may help understand polarization response subjected to an external applied field. MATERIALS AND METHODS Our target was a monovalent ion solvated by thousands of water molecules (about 2,200), modelling an extremely diluted solution. This means there is no significant difference in the hydrogenhydrogen bond distribution and pair correlation function within the first hydration shell, between water alone, and the solution [Leberman and Soper, 1995; Omta et al., 2003]. Our approach to characterize water polarization properties is presented in Figure 1. It is well known from linear response theory (LRT) that the macroscopic dielectric permittivity of water can be defined considering volume Vbox [van der Spoel et al., 1998] (out of the dashed box, Fig. 1) that is sufficiently large compared to microscopic scale so as not to see granularity of individual atoms, but small enough compared to macroscopic level to see heterogeneity of the material. This is the basis of the permittivity calculation from MD simulations, predicting macroscopic frequency-dependent dielectric Bioelectromagnetics
Fig. 1. Schematic representation of physical properties of water at different spatial scales. Region V box corresponds to the whole simulation box, where water permittivity eðv; EÞ is usually evaluated, as a function of angular frequency, and electric field applied. Regions (Vsphere ) correspond to mesoscopic subdomains defined in this paper; in such regions the difference (De), between e of hydrated ion and the one of water, has been evaluated as a function of position r and E field. Finally, ðvshell Þ and (vcyl ) regions correspond to microscopic domains where mean dipole moment mðr; EÞ and water density distribution have been evaluated.
permittivity ðeÞ for water, or dilute aqueous solution [Boresch et al., 2004], and is in good agreement with experimental data. Nevertheless, a more detailed dielectric picture at the nanometer and/or molecular scale requires a new approach, which considers subdomains of the total volume Vbox . Here a multi-scale decomposition was proposed. We defined an equivalent dielectric permittivity based on water dipole fluctuations over spherical volumes ðVsphere Þ of increasing radius covering up to a few nanometer; such volumes give rise to mesoscopic scale illustrated in Figure 1. Conversely, microscopic domain was defined over smaller volumes of different shape, either spherical shells, or cylinders ðvshell; vcyl Þ, covering up to fractions of a nanometer, allowing an evaluation of the water density properties, and local dipole moment (Fig. 1). Figure 2 shows our approach. Figure 2a is a schematic of the spherical volumes of increasing radius Vsphere around the charge used for mesoscopic outcomes. Figure 2b and c indicate spherical ðvshell Þ and cylindrical ðvcyl Þ microscopic volumes used to evaluate results for water dipole moment and density. Simulations at the atomic scale reproduce the effective structure of water and provide the permittivity profile, mean dipole moment, and density distribution of water surrounding the ion charge when the external electric field is applied. Simulation Details Simulations on three different systems were performed using an MD package (GROningen MAchine for Chemical Simulations developed by the
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Fig. 2. Mesoscopic and microscopic domains (a) Spherical regions ofincreasingradius ðVsphere Þ, centered on a fixedion position; (b) microscopic shell domains (vshell ) formed by subtracting volumes of two concentric spheres, differing in radius by 0.2 nm, foreach radial distance from the ion, givingrise to spherical shells of increasing volumes but with constant thickness; (c) microscopic cylindrical regions (vcyl ), of fixed height (0.3 nm) and diameter (0.6 nm), containing few water molecules (around 3), spanning from one side of the simulation box to the other, in the same directionas applied external E field (x-axis).
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GROMACS development team at Uppsala University [Uppsala, Sweden]; Stockholm University [Stockholm, Sweden]; and the Royal Institute of Technology [Stockholm, Sweden]) [van der Spoel et al., 2005]. Our reference system to assess bulk water properties was a cubic box (4 nm side) with 2,178 single point charge (SPC) water molecules [Berendsen et al., 1981]. This results in an experimental density of 1,000 kg/m3. To evaluate behavior of water near ions, two extremely dilute solutions were simulated, each consisting of a single ion placed in the center of the box (i.e., sodium or chloride ion) surrounded by the same number of water molecules used in the reference system. Since we were not interested in ion translational motions, but rather in fast relaxation associated with the collective motion of water near the ion [Kubota et al., 2012], the solute molecule was constrained using the normal freezing option in GROMACS [D’Abramo et al., 2004]. This procedure, which speeds up solvent relaxation around the solute, provides correct statistical mechanics, and thermodynamics of the system (SPC plus a rigid solute), as demonstrated by D’Alessandro et al. [2002] and D’Abramo et al. [2004]. Following energy minimization and subsequent solvent relaxation, the system was gradually heated from 50 K to 300 K using short (typically 10 ps) MD simulations. Several MD simulations of the three systems were performed, both in unexposed (no external E-field) and exposed conditions, using a wide range of field intensities (107 V/m up to 5 109 V/m). For fields below 107 V/m it has already been shown that effect on molecular targets is not significant [Apollonio et al., 2008], while 5 109 V/m is the highest intensity available in literature for molecular simulations. We considered the external electric field as acting on each atom in the simulation domain without depolarization terms, i.e., under tinfoil boundary conditions [Yeh and Berkowitz, 1999; Apol et al., 2002]. Dissipation of heating from the field was taken into account by using a thermal coupling available in GROMACS, i.e., the Berendsen T-coupling [Berendsen et al., 1984], suitably arranged to reproduce an isothermal temperature coupling [Evans and Morriss, 2008], and being fully consistent with statistical mechanics [Brown and Clarke, 1984]. This was obtained by setting the Berendsen T-coupling time constant with the same time-step used for integration algorithm (i.e., 2 fs). All bond lengths were constrained using the LINear Constrain Solver (LINCS) algorithm [Hess et al., 1997]. Long-range electrostatic interactions were computed by the Particle Mesh Ewald method [Darden et al., 1993] with 34 wave vectors in each Bioelectromagnetics
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dimension and a 4th order cubic interpolation. Finally, since it is well known that in a periodic system the net charge must be zero, in non-neutral periodic systems it is necessary to include a compensating background charge, the Ewald potential. Here, we followed the most standard way to satisfy the neutrality requirement by adding a homogeneous background charge density that exactly cancelled the unit charge [Heyes, 1981; Figueirido et al., 1995; Bogusz et al., 1998]. The GROMOS force field parameters were adopted [van Gunsteren et al., 1996]. Trajectories were propagated up to 20 ns in an NVT canonical ensemble (number of particles [N], volume [V], and temperature [T] are kept constant) using an integration step of 2 fs. Mesoscopic and Microscopic Polarization Properties To represent mesoscopic length scale we introduced a quantity called “apparent” dielectric permittivity, ea ðr; vÞ, as a function of position r and angular frequency v; this quantity can be interpreted as dielectric permittivity of specific spherical volumes ðVsphere Þ, rather than of whole simulation box ðVbox Þ. This approach has been used by other authors [Hyun et al., 1995; Nymeyer and Zhou, 2008]. It is obtained [Nymeyer and Zhou, 2008] by a matching continuum calculations (Poisson Equation) and free energy calculations (molecular dynamics simulations) to produce a position-dependent dielectric profile in aqueous solutions and in non-homogeneous systems such as biological membranes. Apparent dielectric permittivity ðea Þ was determined (regions Vsphere , in Fig. 2a) by taking into account the time correlation function FVsphere ðtÞ of the water dipole moment MVsphere in volumes Vsphere FVsphere ðtÞ ¼ hMVsphere ðtÞ MVsphere ð0Þi
ð1Þ
where total dipole moment MVsphere is calculated for each frame of the MD simulation and describes species polarization, and brackets represent an ensemble average. Then ea was calculated via the LRT using the equation: ea ðr; vÞ 1 ¼
1 3Vsphere k B T
h i _ V ðt Þ ; F F sphere
ð2Þ
where Vsphere is volume of mesoscopic subdomain (Fig. 2a), kB is Boltzmann’s constant and T is (constant) temperature of the system. The F operation represents the Fourier transform of the time derivative of the correlation function FVsphere ðtÞ. Bioelectromagnetics
To obtain the profile of ea ; 15 spherical volumes ðVsphere Þ, centered on the ion position with increasing radius from r ¼ 0.1 to 2 nm (boundary of the simulation box), were considered. Over each of these volumes total dipole moment MVsphere was calculated and static ea obtained via Equation 2 considering v ¼ 0: FVsphere ð0Þ ¼ hMVsphere ð0Þ MVsphere ð0Þi ¼ hMVsphere ð0Þ2 i hMVsphere ð0Þi2
ð3Þ
The term hMVsphere ð0Þi represents the combined average value of the water total dipole moment while hMVsphere ð0Þ2 i represents the combined average of its second order moment. The ea profile gives a spatially dependent permittivity function of water and is able to describe local behavior of water molecules near the ion, both under unexposed and exposed conditions. To give a detailed picture of water characteristics on smaller volumes up to a fraction of nanometer (Fig. 2), the microscopic scale was introduced. Spherical shell regions ðvshell Þ with thickness of 0.2 nm, increasing from the center to the box boundaries (Fig. 2b), were initially taken into account. Moreover, a small cylindrical volume ðvcyl Þ of fixed height 0.3 nm and diameter 0.6 nm, containing few water molecules (about 3), was considered. Such volume was translated along the x-axis of a Cartesian reference frame in steps of 0.1 Å , in the direction of the external electric field (Fig. 2c). This approach may be representative, for example, of water dielectric properties in a direction perpendicular to the charged surface (e.g., a planar membrane, proteinwater interfaces, etc). In both cases, microscopic quantities as mean dipole moment and water density distribution were evaluated under the influence of external electric fields. RESULTS Application of LRT to the regions Vsphere of increasing radii gave the profile of ea as a function of distance from both sodium and chloride ions, where the action of the ionic radial electrostatic field becomes progressively weaker (Fig. 2a). The ea profiles exhibited two major peaks close to the ion and a generally increasing trend towards the static macroscopic permittivity (Fig. 3). Two major fluctuation peaks, at about 0.3 and 0.5 nm from both chloride and sodium ions (Fig. 3a, b), confirmed the presence of water hydration shells. Such profiles are due to the Coulombic electric field generated by the ion (Fig. 3a, b, solid lines).
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Fig. 3. Apparent dielectric permittivity ea of water as a function of distance from fixed chloride (a) and sodium (b) ions, fordifferent exposure conditions: no field (black line),108 V/m (dark gray dashed line) and 109 V/m (light gray dotted line). Difference of the ea curve of bulk water with respect to ionic solutions: chloride solution (c), sodium solution (d), withandwithout externalelectric fields.
The application of an electric field of 108 V/m, although not modifying the profile of the hydration shells, slightly changed the ea curves, starting from 0.5 nm (Fig. 3a, b, dashed lines). This behavior is even clearer if comparing the ion in solution with the situation of water alone as shown in Figures 3c, d, where the ea difference (D) between hydrated ion and water is reported as a function of distance from the center of the box where the ion is located (i.e., Vsphere radius). Exposure to 109 V/m was still not able to overcome peculiarities of the hydration shells as shown in
Figures 3a, b (dotted lines). Close to the ion the ea profile still showed an oscillating trend where two peaks relative to the first and second shells were visible, although with low strength. As shown in Figures 3c, d, for a radius just greater than 0.6 nm, value of D for 109 V/m electric field tends to zero, suggesting that application of such an external field can order water molecules regardless of presence of the ion [Amadei et al., 2002] and can make water permittivity profile almost independent of the position close to the ion. Figure 4a gives water dipole moment averaged over spherical shell ðvshell Þ (Fig. 2b) and a clear Bioelectromagnetics
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electric field effect is demonstrated for values higher than 108 V/m. This result indicates a strong effect on the water mean dipole moment for both 108 V/m and 109 V/m fields corresponding to 0.3 nm and 0.5 nm (for the sodium solution, peaks were slightly translated closest to the ion, data not shown); such distances were identified as boundaries of the first and second hydration shells for the chloride ion. This represents the effectiveness of the external electric field in perturbing the intrinsic symmetry of water dipoles around ions, which in the absence of external perturbations, gives rise to a zero mean dipole
moment (solid line of Fig. 4), due to the spherical symmetry of the volumes in which dipole moments are calculated. Field intensities less than 108 V/m have been tested but no effect was shown on mean dipole moment. Figure 4b shows results obtained for cylindrical regions ðvcyl Þ (Fig. 2c); they are totally consistent with ones obtained for a spherical symmetry (Fig. 4a). In the case of no field applied, mean dipole moment is not zero since dipoles are mainly oriented by the Coulombic electric field due to chloride ion; however, as in the case of spherical shells, external electric fields starting from 108 V/m can overcome such local fields. A similar behavior was observed for the sodium solution (data not shown). The effect of the applied field on dipole moment was not related to changes in water density in spherical shell volumes around the ion. In fact, for intensities up to 109 V/m there was no statistically significant difference from the no-exposure condition (Fig. 5), while for intensities of 5 109 V/m the effect was confined to small percentage variations (around 5%). This result also applies to sodium ion (data not shown). DISCUSSION LRT application to total volume of simulation domain ðVbox Þ has been evaluated and preliminary
Fig. 4. Mean dipole moment of water within microscopic shells as a function of distance from fixed chloride ion, for different intensities of external electric field: (a) microscopic spherical shells (vshell ) and (b) microscopic cylindrical regions (vcyl ). Bioelectromagnetics
Fig. 5. Water density profile, calculated in microscopic spherical shells (vshell ), as a function of distance from fixed chloride ion and for different intensities of external electric field. Error bars were evaluated by calculating standard error between five subparts of total equilibrium trajectories.
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results obtained for both frequency-dependent water permittivity ðeÞ and non-linear behavior of water permittivity in the presence of intense electric fields (data not shown). These outcomes are in agreement with previous experimental data and consistent with theoretical and numerical results [Booth, 1951; Amadei et al., 2002]. Our approach provided outcomes both at the mesoscopic and microscopic levels. As for the mesoscopic level, apparent permittivity ea was introduced and spatially dependent profiles of local permittivity extrapolated. These profiles provided information on water order, on shielding properties close to the ion, and on strength of electrostatic forces that water molecules experience in the vicinity of the ion. The results are in agreement with Teschke et al. [2001], who measured a decrease in water permittivity close to a solid-liquid interface. Our data provided a space-dependent permittivity profile that shows decreasing values approaching the position of the ion. Moreover, Figure 3 shows that an external field of 109 V/m is needed to overcome the Coulombic electric field generated by the ion. The application of this field produces a profile converging to a value around 20 (obtained by applying the LRT to the whole box with a 109 V/m electric field). This is almost constant with respect to the other profiles, indicating that water dipole moments are ordered by external field much more than by the ion. All profiles in Figure 3 show welldefined regions where local radial field produced by the ion still affects water behavior. Therefore, the need to investigate a lower spatial scale (down to few water molecules), i.e., microscopic one, is needed. Microscopic regions vshell; vcyl (Fig. 2b, c) are identified to evaluate directly mean dipole moment hMvshell ð0Þi or hMvcyl ð0Þi of water. The effect of the external electric field on hydration shells, both around sodium, and chloride ions (about 0.3 nm for the chloride ion and 0.2 nm for sodium ion) provide data in accordance with the literature [Liu and Ichiye 1999; van Maaren and van de Spoel 2001]. The application of the external field does not modify shell configurations around the ion, while intensity of 109 V/m greatly affects mean dipole moment hMvshell ð0Þi in all hydration shells (Fig. 4). The effect is still observed at intensities of 108 V/m. If planar vcyl instead of spherical symmetry is used, outcomes remain consistent. On the whole our results confirm that locally (i.e., over microscopic volumes), mean dipole moment is affected by fields with a threshold around 108 V/m, although clearer, and marked effects are obtained for 109 V/m fields. This lower threshold is consistent with the one at 109 V/m of Figure 3, if one considers that
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mean dipole moment is the statistical first order moment while ea is based on a second-order one where a more pronounced masking effect is plausible. CONCLUSIONS In this paper, polarization properties of dilute ionic solutions in presence of intense electric fields were assessed. Our approach rigorously takes into account water structure and can evaluate both mesoscopic quantities and microscopic data related to water polarization. When an external electric field is applied, the threshold for affecting both apparent permittivity and dipole moment profile is about 108 V/m, showing that these or higher intensities can interact with water molecules polarized around a simple charged ion. Such field intensities overcome local Coulombic field due to ionic charge and can greatly enforce the polarizability of water in hydration shells around the ion. Reorganization of such shells due to the field has important implications in terms of ion mobility and aqueous chemical reaction mechanisms; as an example, the ionic aqueous hydration layer surrounding biological molecules has been considered as one possible environment able to sense electromagnetic field and trigger biological effects [Apollonio et al., 2013]. A similar methodology can be extended to more complex molecular systems such as proteins, enzymes, and membrane bilayers and may provide important insights into behavior of water at the interface with charged surfaces, where fundamental biochemical processes take place. ACKNOWLEDGMENTS We want to thank Andrea Amadei for his guidance in approaching molecular computations and for his support in theoretically interpreting the outcomes from molecular dynamics, and Michael Repacholi for assistance in editing the final text. This project was performed within the framework of the Joint IIT-Sapienza LAB on Life-NanoScience Project (81/13 16-04-2013). REFERENCES Alper HE,Levy RM. 1990. Field strength dependence of dielectric saturation in liquid water. J Phys Chem 94:8401–8403. Amadei A, Apol ME, Brancato G, Di Nola A. 2002. Theoretical equations of state for temperature and electromagnetic field dependence of fluid systems, based on the quasi-gaussian entropy theory. J Chem Phys 116:4437. Bioelectromagnetics
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use with a reaction field. J Chem Phys 108: 10220–10230. van Gunsteren WF, Billeter SR, Eising AA, Hunemberger PH, Kruger P, Mark AE, Scott VRP, Tironi IG. 1996. Biomolecular Simulation: The GROMOS96 Manual and User Guide. Z€urich, Switzerland: vdf Hochschulverlag, ETH. pp. 1–1042. van Maaren PJ, van der Spoel D. 2001. Molecular dynamics simulations of water with novel shell-model potentials. J Phys Chem B 105:2618–2626. Wood K, Plazanet M, Gabel F, Kessler B, Oesterhelt D, Tobias DJ, Zaccai G, Weik M. 2007. Coupling of protein and hydration-water dynamics in biological membranes. PNAS 104:18049–18054. Yeh IC, Berkowitz ML. 1999. Dielectric constant of water at high electric field: Molecular dynamics study. J Chem Phys 110:7935–7942.
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