Developing and Assessing Nonbonded Dummy Models of Magnesium Ion with Different Hydration Free Energy References

Abstract

A large diversity in the targeted hydration free energies (HFEs) during model parameterization of metal ions was reported in the literature with a difference by dozens of kcal/mol. Here, we developed a series of nonbonded dummy models of the Mg 2+ ion targeting different HFE references in TIP3P water, followed by assessments of the designed models in the simulations of MgCl 2 solution and biological systems. Together with the comparison of existing models, we conclude that the difference in the targeted HFEs has a limited influence on the model performance, while the usability of these models differs from case to case. The feasibility of reproducing more properties of Mg 2+ such as diffusion constants and water exchange rates using a nonbonded dummy model is demonstrated. Underestimated activity derivative and osmotic coefficient of MgCl 2 solutions in high concentration reveal a necessity for further optimization of ion-pair interactions. The developed dummy models are applicable to metal coordination with Asp, Glu, and His residues in metalloenzymes, and the performance in predicting monodentate or bidentate binding modes of Asp/Glu residues depends on the complexity of metal centers and the choice of protein force fields. When both the binding modes coexist, the nonbonded dummy models outperform point charge models, probably in need of considering polarization of metal-binding residues by, for instance, charge calibration in classical force fields. This work is valuable for the use and further development of magnesium ion models for simulations of metalcontaining systems with good accuracy.

Rational Design of Nonbonded Point Charge Models for Divalent Metal Cations with Lennard-Jones 12-6 Potential

“… a Standard deviations for diffusion constants at the infinite dilution solution ( D 0 , eq ) amount to ca. 0.08 × 10 –5 ; the free energy of activation (Δ G † ) and water exchange rate ( k ) are obtained from PMF calculations (eq ); IOD min is the IOD at which the interaction energy (IE) between Mg 2+ and one water molecule reaches its minimum. b Taken from ref . c Taken from ref and corrected using eq . d From ref . e From ref . f From ref . g From ref . h From ref . i From ref . …”

“…Following our previous work, , two-stage thermodynamic integration (TI) was performed to calculate the HFEs of the metal ions with different LJ combinations. An alchemical reaction coordinate of λ = 0, 0.02, 0.04, 0.07, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.93, 0.96, 0.98, and 1 (25 in total) was used for decoupling Coulombic interactions .…”

Rational Design of Nonbonded Point Charge Models for Monovalent Ions with Lennard-Jones 12–6 Potential

“…74 The calculated Ø G , ε 0 , η, and D 0 were collected from previous reports. 39,67,75 For the halide anions, R ranged from 1.5 to 3 Å with a step of 0.1 Å, and −log(ε) ranged from −2 to 4 kcal/mol with a step of 0.5, resulting in 16 × 13 = 208 R−ε combinations. For the anion model in the a99SB-disp water model, the scanned R and −log(ε) were extended to 5 Å and 8 kcal/mol, respectively.…”

“…The LJ parameter scanning above generated discrete points of HFE and IOD, from which we constructed the surface of both properties using a two-dimensional (2D) cubic spline interpolation. 39,40,56,67 The contour lines corresponding to experimental HFE and IOD properties of the ions were then generated and plotted in a 2D graph of −log(ε) versus R. We utilized an in-house Python script to execute the interpolation and plotting. The intersection point of both contours (if any) gave an R−ε combination that was able to reproduce the HFE and IOD simultaneously.…”

“…Following previous work, ,, the HFEs of monovalent ions were computed by thermodynamic integration (TI) with a stepwise decoupling of the interaction between the ions and water molecules. The 25 λ values for the TI calculations were 0, 0.02, 0.04, 0.07, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.93, 0.96, 0.98, and 1 for Coulomb decoupling.…”