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

Abstract

Exploring a metal-involved biochemical process at a molecular level often requires a reliable description of metal properties in aqueous solution by classical nonbonded models. An additional C 4 term for considering ion-induced dipole interactions was previously proposed to supplement the widely used Lennard-Jones 12-6 potential (known as the 12-6-4 LJ-type model) with good accuracy. Here, we demonstrate an alternative to modeling divalent metal cations (M 2+ ) with the traditional 12-6 LJ potential by developing nonbonded point charge models for use with 11 water models: TIP3P, SPC/E, SPC/E b , TIP4P-Ew, TIP4P-D, and TIP4P/2005 and the more recent OPC3, TIP3P-FB, OPC, TIP4P-FB, and a99SB-disp. Our designed models simultaneously reproduce the experimental hydration free energy, ion−oxygen distance, and coordination number in the first hydration shell accurately for most of the metal cations, an accuracy equivalent to that of the complex 12-6-4 LJ-type and double exponential potential models. A systematic comparison with the existing M 2+ models is presented as well in terms of effective ion radii, diffusion constants, water exchange rates, and ion−water interactions. Molecular dynamics simulations of metal substitution in Escherichia coli glyoxalase I variants show the great potential of our new models for metalloproteins.

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

“…Following the model generation, model validation and comparison were presented in terms of HFE, IOD, CN, ionic radii, vdW radii, diffusion constants, ion-water/ion–ion interactions, activity derivatives, osmotic coefficients of alkali chloride solutions, and properties of alkali halides in gas and crystal states. This, together with our previous work on di-, tri-, and tetravalent metal cations, , demonstrates the feasibility and application of the 12–6 LJ potential in ion modeling and is valuable for exploring the strength and weakness of classical force fields.…”

“…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.…”

“…The 12−6 LJ R parameters of our point charge models for di-, tri-, and tetravalent metal cations were found to be smaller than Shannon's revised effective ionic radii 57 by 0.10, 0.15, and 0.24 Å on average, respectively. 39,40 This appears unphysical because the R parameter is known as the vdW radius and the vdW radii of ions should be, in principle, larger than the ionic radii (Table 1). 30 The R values of our monovalent ions are, however, larger than Shannon's ionic radii by about 0.15 and 0.62 Å for the +1 and −1 ions, respectively, as indicated by the MSEs in Table S5.…”

“…38 By enlarging the LJ parameter space, a full charge plus a 12− 6 LJ potential were able to accurately reproduce the HFE and IOD values of di-, tri-, and tetravalent metal cations simultaneously, as verified in our previous work. 39,40 In this work, we will show the feasibility of the simple 12−6 LJ potential in monovalent ions. Experimental HFE and IOD properties were chosen as target references, and 11 water models, including five three-site models of OPC3, 41 SPC/E, 28 SPC/E b , 42 TIP3P, 27 and TIP3P-FB 43 and six four-site models of a99SB-disp, 44 OPC, 45 TIP4P/2005, 46 TIP4P-D, 47 TIP4P-Ew, 29 andTIP4P-FB 43 were considered for the design of 14 monovalent ion models.…”