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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: 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.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.

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 (A-D) of a polarization restraint (Eq. 26) and involving the BM, CM or BA scheme for the treatment of electrostatic interactions (Sect. 3.1). The dashed vertical lines are a guide for the eye and indicate distances of 1.0, 1.1, 1.2, 1.4 and 1.9 nm from the ion. The polarization restraint was applied in spherical shells extending from 1.0–1.4 (A), 1.0–1.9 (B), 1.1–1.9 (C) or 1.2–1.9 nm (D) around the ion
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Fig7: 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 (A-D) of a polarization restraint (Eq. 26) and involving the BM, CM or BA scheme for the treatment of electrostatic interactions (Sect. 3.1). The dashed vertical lines are a guide for the eye and indicate distances of 1.0, 1.1, 1.2, 1.4 and 1.9 nm from the ion. The polarization restraint was applied in spherical shells extending from 1.0–1.4 (A), 1.0–1.9 (B), 1.1–1.9 (C) or 1.2–1.9 nm (D) around the ion

Mentions: Within the region where it was applied, the polarization restraint was not found to affect the ion–water radial distribution function (Fig. 6), while the ion-dipole orientational correlation function reflects the changes already observed in (Fig. 7). The changes in water molecular orientation are effected by the term in square brackets in the first sum of Eq. 35. This term is the partial derivative of the component of the water molecular dipole moment along the ion-oxygen connecting vector with respect to the position of the ion.Fig. 6


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 (A-D) of a polarization restraint (Eq. 26) and involving the BM, CM or BA scheme for the treatment of electrostatic interactions (Sect. 3.1). The dashed vertical lines are a guide for the eye and indicate distances of 1.0, 1.1, 1.2, 1.4 and 1.9 nm from the ion. The polarization restraint was applied in spherical shells extending from 1.0–1.4 (A), 1.0–1.9 (B), 1.1–1.9 (C) or 1.2–1.9 nm (D) around the ion
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4470580&req=5

Fig7: 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 (A-D) of a polarization restraint (Eq. 26) and involving the BM, CM or BA scheme for the treatment of electrostatic interactions (Sect. 3.1). The dashed vertical lines are a guide for the eye and indicate distances of 1.0, 1.1, 1.2, 1.4 and 1.9 nm from the ion. The polarization restraint was applied in spherical shells extending from 1.0–1.4 (A), 1.0–1.9 (B), 1.1–1.9 (C) or 1.2–1.9 nm (D) around the ion
Mentions: Within the region where it was applied, the polarization restraint was not found to affect the ion–water radial distribution function (Fig. 6), while the ion-dipole orientational correlation function reflects the changes already observed in (Fig. 7). The changes in water molecular orientation are effected by the term in square brackets in the first sum of Eq. 35. This term is the partial derivative of the component of the water molecular dipole moment along the ion-oxygen connecting vector with respect to the position of the ion.Fig. 6

Bottom Line: 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.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.

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