Implicit-solvent models can allow interstitial high dielectrics (e.g., water), but they give incorrect PMFs between nonbonded atoms. Other approaches have been applied to improving implicit-solvent models. To correct for the energy errors in implicit modeling, radii can be adjusted empirically, but this can sacrifice transferability. However, implicit-solvent models do not capture the subtle features of PMFs, which require some representation of particulate water (29, 30) (see Figure 1). (19-26) Implicit-solvent models have the advantage of computational speed: a PMF costs around 100 h of MD simulation time in explicit water but only minutes on a personal computer for PB PMF or fractions of a second for GB. (13, 15) An alternative is to use implicit-solvent models (such as Poisson–Boltzmann (PB) or generalized Born (GB)), (16-19) in which the solvent is approximated as a dielectric continuum. For simple salt solutions, integral-equation theories often predict qualitatively correct trends (11-15) but not quantitative details. On the other hand, treating water explicitly in analytical theories is challenging, because of the need to properly account for the orientation (angular) effects of water. Various sampling techniques have been introduced to mitigate the computational expense: (3, 4) constraints, (5-8) umbrella sampling, (9) and weighted histogram methods, (10) for example. Even in the case of simple spherical solutes, extensive sampling is required to get converged results. However, these simulations are often computationally too expensive for many of the calculations that would be of practical interest. We also find that our data is consistent with Collins’ “law of matching affinities” of ion solubilities: small–small or large–large ion pairs are poorly soluble in water, whereas small–large are highly soluble.Ĭurrently, the gold standard for computing the PMFs between large molecules-such as are typical in biology-is to use explicit-solvent simulations with semiempirical force fields. This process may be useful for rapid and accurate calculation of the strengths of salt bridges and the effects of bridging waters in biomolecular simulations. Whereas it can take 100 h to simulate each PMF by MD, we can compute an equivalently accurate i-PMF in seconds. The advantage of the interpolation process is computational cost. We develop an interpolation scheme, called i-PMF, that is capable of capturing the full set of PMFs for arbitrary combinations of ion sizes ranging from 2 to 5.5 Å. We extract their potentials of mean force (PMFs). We perform extensive molecular dynamics (MD) simulations between pairs of ions of various diameters (2–5.5 Å in increments of 0.5 Å) and charge (+1 or −1) interacting in explicit water (TIP3P) under ambient conditions.
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