Molecular dynamics simulations depend on carefully developed force-fields to give results that reproduce experimental data. Force-fields for lipids and ions are typically constructed separately to work in water. Mutual interactions between lipids and ions are estimated using approximate mixing rules for their Lennard-Jones (LJ) components. Herein, we assess the use of the Lorentz-Berthelot (LB) mixing rules, which are typically used for computing the LJ components of ion-ligand interactions, including ion-lipid interactions. We use 1-palmitoyl-2-oleoyl-sn-glycero-phosphosholine (POPC) as our model lipid and Na+ as our model cation. Benchmarked quantum mechanical calculations show that the LB rules yield large errors in POPC-Na+ interactions. Specifically, we report that methyl-acetate and diethyl-phosphate, which are small molecule representatives of the POPC head-group, under-bind Na+ (relative to water) by more than 75 kJ/mol. Using a high-dimensional simultaneous search for all cross-terms of Na+ with methyl-acetate and diethyl-phosphate — performed with our ParOpt software — we present a new set of cross-terms that reduces average interaction errors to 7 kJ/mol, with only minor effects on minimum-energy geometries. The use of these new cross-terms results in the binding of a larger number of Na+ to POPC bilayers compared to those obtained from using the LB rules. Surprisingly, the predicted POPC bilayer structure is more similar to a system without ions than a system simulated with erroneous LB rules. This result is closer to what is observed in small angle X-ray and neutron scattering experiments. These findings demonstrate that improvements in local energetics and geometries do improve predictions of macroscopic properties. Furthermore, our proposed approach is generic and can be applied to any system of interacting molecules using mixed force fields.

Determining explicit ion-lipid cross terms for MD simulation using high dimensional parameter search

ACS Spring 2022

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