Global Optimization of the Lennard-Jones Parameters for the Drude Polarizable Force Field

Abstract

Molecular dynamics (MD) simulations based on atomic models play an important role in the drug-discovery process to screen molecules, estimate binding free energies, and optimize lead compounds in chemical space. Accurate computations of thermodynamic and kinetic properties using MD simulations are highly dependent on the accuracy of the underlying atomic force field. In this context, going beyond nonpolarizable fixed-charge model by accounting explicitly for induced polarization is highly desirable. The CHARMM polarizable force field based on classical Drude oscillators, in which an auxiliary charged particle is attached via a harmonic spring to its parent nucleus, offers both a computationally convenient and rigorous framework to model explicitly induced electronic polarization in MD simulations. For any molecule of interest, electrostatic partial charges, atomic polarizabilities and Thole shielding factors, as well as bonded parameters can either be determined from ab initio calculations or ascribed from the knowledge-based library of the CHARMM Generalized force field (CGenFF). While this approach is fairly reliable in general, it is well understood that the overall accuracy of the models with respect to thermodynamic properties such as bulk density, enthalpies, and solvation free energies is particularly sensitive to the nonbonded Lennard-Jones (LJ) parameters. In the present study we systematically refined the set of LJ parameters for the atom types available in the Drude force field to best match the experimental thermodynamic properties for 416 small drug-like organic molecules. To further test the transferability of the optimized parameters, the hydration free energy of 372 molecules was computed. The calculations resulted in a small average error of 0.46 kcal/mol and a Pearson R of 0.9, representing a significant improvement over the additive GAFF force field in our previous study, where an average error of ~2 kcal/mol was obtained.SUPPLEMENTARY MATERIAL Refer to https://github.com/chetanrrk/LJOptimization/tree/main/SI for all supplementary information. The README.md contains details about the content. The indicated SI folder in the link includes the following materials: 1.feh.xlsx: Contains free energy of hydration (FEH) of molecules including their scientific name, experimental FEH, FEH computed with optimized LJ and standard combination rule, and FEH computed with optimized LJ and NBFIX based scaled combination rule. 2.init_final_params.xlsx: Contains optimized atom types with initial and optimized Emin and Rmin. 3.training.xlsx: Contains molecules used in training along with their names, molecular volumes (experimental and computed), and heat of vaporization (experimental and computed). 4.testing.xlsx: Contains molecules used in testing along with their names, molecular volumes (experimental and computed), and heat of vaporization (experimental and computed).

Quantitative molecular simulations

“…169 Following a similar optimization protocol for the polarizable Drude model the errors on the pure liquid density and heats of vaporization were 2% and 6%, respectively, whereas for the hydration free energies the error decreased to 0.5 kcal mol −1 together with the SWM4-NDP water model. 172,173…”

“…pure liquid density and vaporization energy) – even for a class or library of compounds – but not yield satisfactory results for other observables (hydration free energy). 172 Such transferability has been explicitly considered for cyanide in water. 98,174,175 Using one single parametrization based on fluctuating multipolar electrostatics 21 it was possible to obtain quantitative results for vibrational energy relaxation, the 1d- and 2d-IR spectroscopy, and the hydration free energy.…”

“…169 Following a similar optimization protocol for the polarizable Drude model the errors on the pure liquid density and heats of vaporization were 2% and 6%, respectively, whereas for the hydration free energies the error decreased to 0.5 kcal mol À1 together with the SWM4-NDP water model. 172,173 One recurring theme in assessing the quality of (empirical) energy functions is that a particular parametrization may yield favourable comparison for only one or a few experimentally determined properties (e.g. pure liquid density and vaporization energy) -even for a class or library of compounds -but not yield satisfactory results for other observables (hydration free energy).…”

Quantitative Molecular Simulations

“…142 Following a similar opti-mization protocol for the polarizable Drude model the errors on the pure liquid density and heats of vaporization were 2 % and 6 %, respectively, whereas for the hydration free energies the error decreased to 0.5 kcal/mol together with the SWM4 water model. 145,146 One recurring theme in assessing the quality of (empirical) energy functions is that a particular parametrization may yield favourable comparison for only one or a few experimentally determined properties (e.g. pure liquid density and vaporization energy) -even for a class or library of compounds -but not yield satisfactory results for other observables (hydration free energy).…”

“…pure liquid density and vaporization energy) -even for a class or library of compounds -but not yield satisfactory results for other observables (hydration free energy). 145 Such transferability has been explicitly considered for cyanide in water. 90,147,148 Using one single parametrization based on fluctuating multipolar electrostatics 13 it was possible to obtain quantitative results for vibrational energy relaxation, the 1d-and 2d-IR spectroscopy, and the hydration free energy.…”