Phosphates and Phosphorylated Amino Acids for the AMOEBA-HFC Polarizable Force Field

Protein phosphorylation plays a crucial role in regulating protein activity, localization, and signaling in many biological processes. While nonpolarizable models for molecular dynamics (MD) simulations include parameters for phosphorylated amino acids, their counterparts for polarizable models are lacking. This limits the ability to understand environment-dependent effects associated with phosphorylation processes such as electric-field-induced polarization and nonadditive many-body energetic contributions. Such effects are expected to contribute substantially due to phosphate's high negative charge and strong electrostatic field. To address this, we extend the AMOEBA-HFC polarizable force field to include phosphates and phosphorylated forms of amino acids in their monoanionic (-1 e) and dianionic (-2 e) states. Atomic multipoles are assigned using a standard AMOEBA protocol using Stone's Generalized Distributed Multipole Analysis (GDMA) approach. Polarization and van der Waals parameters are derived using our AMOEBA-HFC protocol that accounts for high electric field effects and improves the relative energetic contributions arising from local and distant interactions. Dihedral parameters are optimized to reproduce both the one-dimensional (1D) and two-dimensional (2D) potential energies. Reference data for local interactions are determined from benchmarked quantum mechanics (QM), and reference data in the condensed phase are taken from experiments. The resulting model exhibits high accuracy in describing molecular dipole moments (R² = 0.99), electric field responses (mean absolute error (MAE) < 0.2 D), and electrostatic surface potentials (MAE < 1 kcal/mol/e). Excellent agreement is also achieved in reproducing local interactions of phosphates with waters, ions, and protein side chains. The model also reproduces all experimentally derived condensed-phase properties, including hydration-free energies of phosphates and NMR J-coupling values of the phosphorylated dipeptides. Finally, we demonstrate that the dipeptide parameters transfer well to full proteins, as they capture phosphorylation-induced changes in the structure and dynamics of ubiquitin characterized by NMR spectroscopy.