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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

Radial distribution function  (Eq. 44) of water oxygen atoms around the sodium ion 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 to 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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Fig6: Radial distribution function (Eq. 44) of water oxygen atoms around the sodium ion 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 to 1.4 (A), 1.0–1.9 (B), 1.1–1.9 (C) or 1.2–1.9 nm (D) around the ion

Mentions: The impact of cutoff-truncated electrostatic interaction functions on the solvent density, orientational correlation and polarization around ionic solutes has been discussed in detail before [63, 65]. Here, only artifacts transpiring in the immediate vicinity of the cutoff distance shall be pointed out again. The radial solvent polarization exhibits an artificial dip at with the BM and BA schemes. By virtue of atom-based rather than molecule-based cutoff truncation, this dip is less pronounced with the BA scheme (Fig. 5). However, interestingly, artifacts in are more pronounced with the BA scheme than with the BM scheme (Fig. 6). Obviously, omission of a reaction-field correction has severe effects on the solvent polarization. For the CM scheme, shows strong overpolarization immediately before and underpolarization immediately after . Application of a polarization restraint successfully removes these artifacts (Fig. 5). If the range of action of the polarization restraint is extended beyond the immediate neighborhood of , further polarization artifacts can be rectified. This is evident for the CM scheme, where the spurious overpolarization in was addressed by e.g., applying the restraint in the shell between 1.0 and 1.4 nm from the ion. Since the polarization restraint was implemented such that also water molecules outside the cutoff sphere of the ion can be involved, the underpolarization normally occurring outside the cutoff sphere of the ion can also be corrected, e.g., as done here, up to a distance of 1.9 nm from the ion (Fig. 5). For the system investigated in this study, another advantage of the polarization restraint is that it achieves a long-range polarization closer to the Born polarization than obtained from a simulation with a lattice-sum electrostatic interaction function in a computational box of the same edge length (4.04 nm). This finding is depicted and discussed (along with thermodynamic considerations) in Figure S1 in Supplementary Material.Fig. 5


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)

Radial distribution function  (Eq. 44) of water oxygen atoms around the sodium ion 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 to 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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Fig6: Radial distribution function (Eq. 44) of water oxygen atoms around the sodium ion 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 to 1.4 (A), 1.0–1.9 (B), 1.1–1.9 (C) or 1.2–1.9 nm (D) around the ion
Mentions: The impact of cutoff-truncated electrostatic interaction functions on the solvent density, orientational correlation and polarization around ionic solutes has been discussed in detail before [63, 65]. Here, only artifacts transpiring in the immediate vicinity of the cutoff distance shall be pointed out again. The radial solvent polarization exhibits an artificial dip at with the BM and BA schemes. By virtue of atom-based rather than molecule-based cutoff truncation, this dip is less pronounced with the BA scheme (Fig. 5). However, interestingly, artifacts in are more pronounced with the BA scheme than with the BM scheme (Fig. 6). Obviously, omission of a reaction-field correction has severe effects on the solvent polarization. For the CM scheme, shows strong overpolarization immediately before and underpolarization immediately after . Application of a polarization restraint successfully removes these artifacts (Fig. 5). If the range of action of the polarization restraint is extended beyond the immediate neighborhood of , further polarization artifacts can be rectified. This is evident for the CM scheme, where the spurious overpolarization in was addressed by e.g., applying the restraint in the shell between 1.0 and 1.4 nm from the ion. Since the polarization restraint was implemented such that also water molecules outside the cutoff sphere of the ion can be involved, the underpolarization normally occurring outside the cutoff sphere of the ion can also be corrected, e.g., as done here, up to a distance of 1.9 nm from the ion (Fig. 5). For the system investigated in this study, another advantage of the polarization restraint is that it achieves a long-range polarization closer to the Born polarization than obtained from a simulation with a lattice-sum electrostatic interaction function in a computational box of the same edge length (4.04 nm). This finding is depicted and discussed (along with thermodynamic considerations) in Figure S1 in Supplementary Material.Fig. 5

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