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Toward the correction of effective electrostatic forces in explicit-solvent molecular dynamics simulations: restraints on solvent-generated electrostatic potential and solvent polarization.

Reif MM, Oostenbrink C - Theor Chem Acc (2015)

Bottom Line: The restraints are applied to the explicit-water simulation of a hydrated sodium ion, and the effect of the restraints on the structural and energetic properties of the solvent is illustrated.It is discussed how the restraints can be generalized to situations involving several solute particles.Although the present study considers a very simple system only, it is an important step toward the on-the-fly elimination of finite-size and approximate-electrostatic artifacts during atomistic molecular dynamics simulations.

View Article: PubMed Central - PubMed

Affiliation: Institute for Molecular Modeling and Simulation, University of Natural Resources and Life Sciences, Vienna, Muthgasse 18, 1190 Vienna, Austria.

ABSTRACT

Despite considerable advances in computing power, atomistic simulations under nonperiodic boundary conditions, with Coulombic electrostatic interactions and in systems large enough to reduce finite-size associated errors in thermodynamic quantities to within the thermal energy, are still not affordable. As a result, periodic boundary conditions, systems of microscopic size and effective electrostatic interaction functions are frequently resorted to. Ensuing artifacts in thermodynamic quantities are nowadays routinely corrected a posteriori, but the underlying configurational sampling still descends from spurious forces. The present study addresses this problem through the introduction of on-the-fly corrections to the physical forces during an atomistic molecular dynamics simulation. Two different approaches are suggested, where the force corrections are derived from special potential energy terms. In the first approach, the solvent-generated electrostatic potential sampled at a given atom site is restrained to a target value involving corrections for electrostatic artifacts. In the second approach, the long-range regime of the solvent polarization around a given atom site is restrained to the Born polarization, i.e., the solvent polarization corresponding to the ideal situation of a macroscopic system under nonperiodic boundary conditions and governed by Coulombic electrostatic interactions. The restraints are applied to the explicit-water simulation of a hydrated sodium ion, and the effect of the restraints on the structural and energetic properties of the solvent is illustrated. Furthermore, by means of the calculation of the charging free energy of a hydrated sodium ion, it is shown how the electrostatic potential restraint translates into the on-the-fly consideration of the corresponding free-energy correction terms. It is discussed how the restraints can be generalized to situations involving several solute particles. Although the present study considers a very simple system only, it is an important step toward the on-the-fly elimination of finite-size and approximate-electrostatic artifacts during atomistic molecular dynamics simulations.

No MeSH data available.


Related in: MedlinePlus

Orientational correlation function  (Eq. 44) of water dipole moment vectors and the vectors connecting corresponding oxygen atoms and the sodium ion site for simulations in the absence (“unres.”) or presence (“res.”) of an electrostatic potential restraint (Eq. 11) and involving the BM, CM or BA scheme for the treatment of electrostatic interactions (Sect. 3.1)
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Fig3: Orientational correlation function (Eq. 44) of water dipole moment vectors and the vectors connecting corresponding oxygen atoms and the sodium ion site for simulations in the absence (“unres.”) or presence (“res.”) of an electrostatic potential restraint (Eq. 11) and involving the BM, CM or BA scheme for the treatment of electrostatic interactions (Sect. 3.1)

Mentions: It can be seen from Eq. 17 that the electrostatic potential restraint forces relate to the “normal” electrostatic forces through a scalar factor. The concomitant effect on water density can be seen in Fig. 2. With the BM and BA schemes, the ion is underhydrated in the unrestrained simulations in comparison with the target electrostatic potential (Table 1). This underhydration is remedied by the restraint through an increased water density around the ion, as evidenced by increased heights of the first peak of the ion–water radial distribution (Fig. 2). In contrast, with the CM scheme, the ion is overhydrated in the unrestrained simulations in comparison with the target electrostatic potential (Table 1). This overhydration is remedied by the restraint through a reduced water density around the ion, as evidenced by a reduced height of the first peak of the ion–water radial distribution (Fig. 2). Note that the height of the first peak in from restrained simulations differs between the BM (8.31), CM (6.95) and BA (8.45) simulations. In particular, it is markedly lower for the CM scheme, which is probably due to the strong overpolarization shortly before the cutoff distance caused by the absence of a reaction field. This is illustrated here by the bump in at distances of 1.25–1.38 nm from the ion (Fig. 3). Besides the ion–water radial distribution function, the electrostatic potential restraint also appears to slightly affect the ion–water dipole orientational correlation function (Fig. 3). Although this is at first glance not expected based on the functional form of the restraint forces, it might be a consequence of the altered water density.Fig. 2


Toward the correction of effective electrostatic forces in explicit-solvent molecular dynamics simulations: restraints on solvent-generated electrostatic potential and solvent polarization.

Reif MM, Oostenbrink C - Theor Chem Acc (2015)

Orientational correlation function  (Eq. 44) of water dipole moment vectors and the vectors connecting corresponding oxygen atoms and the sodium ion site for simulations in the absence (“unres.”) or presence (“res.”) of an electrostatic potential restraint (Eq. 11) and involving the BM, CM or BA scheme for the treatment of electrostatic interactions (Sect. 3.1)
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4470580&req=5

Fig3: Orientational correlation function (Eq. 44) of water dipole moment vectors and the vectors connecting corresponding oxygen atoms and the sodium ion site for simulations in the absence (“unres.”) or presence (“res.”) of an electrostatic potential restraint (Eq. 11) and involving the BM, CM or BA scheme for the treatment of electrostatic interactions (Sect. 3.1)
Mentions: It can be seen from Eq. 17 that the electrostatic potential restraint forces relate to the “normal” electrostatic forces through a scalar factor. The concomitant effect on water density can be seen in Fig. 2. With the BM and BA schemes, the ion is underhydrated in the unrestrained simulations in comparison with the target electrostatic potential (Table 1). This underhydration is remedied by the restraint through an increased water density around the ion, as evidenced by increased heights of the first peak of the ion–water radial distribution (Fig. 2). In contrast, with the CM scheme, the ion is overhydrated in the unrestrained simulations in comparison with the target electrostatic potential (Table 1). This overhydration is remedied by the restraint through a reduced water density around the ion, as evidenced by a reduced height of the first peak of the ion–water radial distribution (Fig. 2). Note that the height of the first peak in from restrained simulations differs between the BM (8.31), CM (6.95) and BA (8.45) simulations. In particular, it is markedly lower for the CM scheme, which is probably due to the strong overpolarization shortly before the cutoff distance caused by the absence of a reaction field. This is illustrated here by the bump in at distances of 1.25–1.38 nm from the ion (Fig. 3). Besides the ion–water radial distribution function, the electrostatic potential restraint also appears to slightly affect the ion–water dipole orientational correlation function (Fig. 3). Although this is at first glance not expected based on the functional form of the restraint forces, it might be a consequence of the altered water density.Fig. 2

Bottom Line: The restraints are applied to the explicit-water simulation of a hydrated sodium ion, and the effect of the restraints on the structural and energetic properties of the solvent is illustrated.It is discussed how the restraints can be generalized to situations involving several solute particles.Although the present study considers a very simple system only, it is an important step toward the on-the-fly elimination of finite-size and approximate-electrostatic artifacts during atomistic molecular dynamics simulations.

View Article: PubMed Central - PubMed

Affiliation: Institute for Molecular Modeling and Simulation, University of Natural Resources and Life Sciences, Vienna, Muthgasse 18, 1190 Vienna, Austria.

ABSTRACT

Despite considerable advances in computing power, atomistic simulations under nonperiodic boundary conditions, with Coulombic electrostatic interactions and in systems large enough to reduce finite-size associated errors in thermodynamic quantities to within the thermal energy, are still not affordable. As a result, periodic boundary conditions, systems of microscopic size and effective electrostatic interaction functions are frequently resorted to. Ensuing artifacts in thermodynamic quantities are nowadays routinely corrected a posteriori, but the underlying configurational sampling still descends from spurious forces. The present study addresses this problem through the introduction of on-the-fly corrections to the physical forces during an atomistic molecular dynamics simulation. Two different approaches are suggested, where the force corrections are derived from special potential energy terms. In the first approach, the solvent-generated electrostatic potential sampled at a given atom site is restrained to a target value involving corrections for electrostatic artifacts. In the second approach, the long-range regime of the solvent polarization around a given atom site is restrained to the Born polarization, i.e., the solvent polarization corresponding to the ideal situation of a macroscopic system under nonperiodic boundary conditions and governed by Coulombic electrostatic interactions. The restraints are applied to the explicit-water simulation of a hydrated sodium ion, and the effect of the restraints on the structural and energetic properties of the solvent is illustrated. Furthermore, by means of the calculation of the charging free energy of a hydrated sodium ion, it is shown how the electrostatic potential restraint translates into the on-the-fly consideration of the corresponding free-energy correction terms. It is discussed how the restraints can be generalized to situations involving several solute particles. Although the present study considers a very simple system only, it is an important step toward the on-the-fly elimination of finite-size and approximate-electrostatic artifacts during atomistic molecular dynamics simulations.

No MeSH data available.


Related in: MedlinePlus