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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

Effect of applying finite-size and approximate-electrostatics corrections [63, 64] to the charging free energies of cationic and anionic molecules, illustrated for the case of sodium and chloride ions with effective radii of [65]  and 0.246 nm, respectively, and with Lennard-Jones parameters according to the GROMOS 54A8 force field [65, 66] in combination with the SPC water model [159]. a The charging free energies of the infinitely dilute ions in a macroscopic nonperiodic system with Coulombic electrostatic interactions are given by . For the spurious simulated situation of the BM scheme under periodic boundary conditions in a cubic computational box with  nm,  and  nm, the charging free energies evaluate to . The correction terms, evaluated according to Ref. [64] are , , ,  and  for the sodium ion and , , ,  and  for the chloride ion, where the fitted functions described in Ref. [64] were used for  and . b The magnitude of the overall correction term is reduced by  and  if an electrostatic potential restraint involving these two corrections is used. For the example of sodium ion hydration, these two quantities evaluate to [63, 64]  or  and  or  for the schemes with reaction-field correction (BM, BA) or the CM scheme, respectively. The correction term  for the BM scheme thus amounts to . Its contributions (, , ) are reported in (a). For the CM scheme,  has contributions from  and  ( and , respectively) and for the BA scheme, it has contributions from ,  and  (,  and  respectively)
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Fig1: Effect of applying finite-size and approximate-electrostatics corrections [63, 64] to the charging free energies of cationic and anionic molecules, illustrated for the case of sodium and chloride ions with effective radii of [65] and 0.246 nm, respectively, and with Lennard-Jones parameters according to the GROMOS 54A8 force field [65, 66] in combination with the SPC water model [159]. a The charging free energies of the infinitely dilute ions in a macroscopic nonperiodic system with Coulombic electrostatic interactions are given by . For the spurious simulated situation of the BM scheme under periodic boundary conditions in a cubic computational box with  nm, and  nm, the charging free energies evaluate to . The correction terms, evaluated according to Ref. [64] are , , , and for the sodium ion and , , , and for the chloride ion, where the fitted functions described in Ref. [64] were used for and . b The magnitude of the overall correction term is reduced by and if an electrostatic potential restraint involving these two corrections is used. For the example of sodium ion hydration, these two quantities evaluate to [63, 64] or and or for the schemes with reaction-field correction (BM, BA) or the CM scheme, respectively. The correction term for the BM scheme thus amounts to . Its contributions (, , ) are reported in (a). For the CM scheme, has contributions from and ( and , respectively) and for the BA scheme, it has contributions from , and (, and respectively)

Mentions: In principle, generalization to the case of multiple solutes is possible. Future work will explore the application of the two restraints to the calculation of an ion–ion potential of mean force. It has been suggested before [65, 66] that ion–ion potentials of mean force in water, i.e., the free energy describing the reversible association–dissociation equilibrium of two hydrated ions, calculated with an approximate-electrostatic interaction function, are afflicted by errors due to the underhydration of cations when their ion–water Lennard-Jones parameters were calibrated against methodology-independent hydration free energies. This is because for cations, the correction terms converting a methodology-dependent hydration free energy to the corresponding methodology-independent value are negative and of large magnitude. Consider, for instance, the hydration of a sodium ion in Fig. 1a. The ion was parameterized such that the methodologically independent solvation contribution due to the free energy of charging the ion matches the target value of . This value is exempt of contributions for air–water interface crossing, cavity formation and standard-state conversion (i.e., this value refers to identical ion concentrations in air and in water) [58]. If all three of the latter contributions were added, one could compare the resulting number to an experimental real hydration free energy and if only the last two were added, one could compare the resulting number to an experimental intrinsic hydration free energy (based on a standard intrinsic proton hydration free energy of ) [58]. In theoretical work, e.g., using a cubic box with edge length 4.04 nm, molecule-based cutoff truncation at a distance of 1.4 nm for electrostatic interactions, as well as a reaction-field correction for omitted electrostatic interactions, the calculated value () is obtained from two components: a “raw” charging free energy of that is deduced from a computer simulation and another from the indicated corrections that are added manually in post-simulation work. However, this means that the underlying sampling during the simulation (and hence the forces) corresponds to an ion with a charging free energy of . Hence, a large part of the actual hydrophilicity of the cation is not accounted for in simulations that are performed in the “usual” way, i.e., in microscopic or periodic systems and with electrostatic interactions that are not strictly Coulombic. As a consequence, the interaction of cations with species other than water might be too favorable. On the contrary, for anions, the magnitude of the correction terms is not that large, because a considerable contribution due to the spurious summation of the electrostatic potential () is positive. This is because it is proportional to the ionic charge rather than to its square. Therefore, this contribution decreases the magnitude of the overall (negative) correction term (Fig. 1a). Note that these considerations only hold for the specific case of solvent molecules with a positive molecular quadrupole moment trace (e.g., the SPC water model) and for simulations carried out with an effective electrostatic interaction function involving this particular summation artifact [68].Fig. 1


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)

Effect of applying finite-size and approximate-electrostatics corrections [63, 64] to the charging free energies of cationic and anionic molecules, illustrated for the case of sodium and chloride ions with effective radii of [65]  and 0.246 nm, respectively, and with Lennard-Jones parameters according to the GROMOS 54A8 force field [65, 66] in combination with the SPC water model [159]. a The charging free energies of the infinitely dilute ions in a macroscopic nonperiodic system with Coulombic electrostatic interactions are given by . For the spurious simulated situation of the BM scheme under periodic boundary conditions in a cubic computational box with  nm,  and  nm, the charging free energies evaluate to . The correction terms, evaluated according to Ref. [64] are , , ,  and  for the sodium ion and , , ,  and  for the chloride ion, where the fitted functions described in Ref. [64] were used for  and . b The magnitude of the overall correction term is reduced by  and  if an electrostatic potential restraint involving these two corrections is used. For the example of sodium ion hydration, these two quantities evaluate to [63, 64]  or  and  or  for the schemes with reaction-field correction (BM, BA) or the CM scheme, respectively. The correction term  for the BM scheme thus amounts to . Its contributions (, , ) are reported in (a). For the CM scheme,  has contributions from  and  ( and , respectively) and for the BA scheme, it has contributions from ,  and  (,  and  respectively)
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4470580&req=5

Fig1: Effect of applying finite-size and approximate-electrostatics corrections [63, 64] to the charging free energies of cationic and anionic molecules, illustrated for the case of sodium and chloride ions with effective radii of [65] and 0.246 nm, respectively, and with Lennard-Jones parameters according to the GROMOS 54A8 force field [65, 66] in combination with the SPC water model [159]. a The charging free energies of the infinitely dilute ions in a macroscopic nonperiodic system with Coulombic electrostatic interactions are given by . For the spurious simulated situation of the BM scheme under periodic boundary conditions in a cubic computational box with  nm, and  nm, the charging free energies evaluate to . The correction terms, evaluated according to Ref. [64] are , , , and for the sodium ion and , , , and for the chloride ion, where the fitted functions described in Ref. [64] were used for and . b The magnitude of the overall correction term is reduced by and if an electrostatic potential restraint involving these two corrections is used. For the example of sodium ion hydration, these two quantities evaluate to [63, 64] or and or for the schemes with reaction-field correction (BM, BA) or the CM scheme, respectively. The correction term for the BM scheme thus amounts to . Its contributions (, , ) are reported in (a). For the CM scheme, has contributions from and ( and , respectively) and for the BA scheme, it has contributions from , and (, and respectively)
Mentions: In principle, generalization to the case of multiple solutes is possible. Future work will explore the application of the two restraints to the calculation of an ion–ion potential of mean force. It has been suggested before [65, 66] that ion–ion potentials of mean force in water, i.e., the free energy describing the reversible association–dissociation equilibrium of two hydrated ions, calculated with an approximate-electrostatic interaction function, are afflicted by errors due to the underhydration of cations when their ion–water Lennard-Jones parameters were calibrated against methodology-independent hydration free energies. This is because for cations, the correction terms converting a methodology-dependent hydration free energy to the corresponding methodology-independent value are negative and of large magnitude. Consider, for instance, the hydration of a sodium ion in Fig. 1a. The ion was parameterized such that the methodologically independent solvation contribution due to the free energy of charging the ion matches the target value of . This value is exempt of contributions for air–water interface crossing, cavity formation and standard-state conversion (i.e., this value refers to identical ion concentrations in air and in water) [58]. If all three of the latter contributions were added, one could compare the resulting number to an experimental real hydration free energy and if only the last two were added, one could compare the resulting number to an experimental intrinsic hydration free energy (based on a standard intrinsic proton hydration free energy of ) [58]. In theoretical work, e.g., using a cubic box with edge length 4.04 nm, molecule-based cutoff truncation at a distance of 1.4 nm for electrostatic interactions, as well as a reaction-field correction for omitted electrostatic interactions, the calculated value () is obtained from two components: a “raw” charging free energy of that is deduced from a computer simulation and another from the indicated corrections that are added manually in post-simulation work. However, this means that the underlying sampling during the simulation (and hence the forces) corresponds to an ion with a charging free energy of . Hence, a large part of the actual hydrophilicity of the cation is not accounted for in simulations that are performed in the “usual” way, i.e., in microscopic or periodic systems and with electrostatic interactions that are not strictly Coulombic. As a consequence, the interaction of cations with species other than water might be too favorable. On the contrary, for anions, the magnitude of the correction terms is not that large, because a considerable contribution due to the spurious summation of the electrostatic potential () is positive. This is because it is proportional to the ionic charge rather than to its square. Therefore, this contribution decreases the magnitude of the overall (negative) correction term (Fig. 1a). Note that these considerations only hold for the specific case of solvent molecules with a positive molecular quadrupole moment trace (e.g., the SPC water model) and for simulations carried out with an effective electrostatic interaction function involving this particular summation artifact [68].Fig. 1

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