Deep Neural Network Model to Predict the Electrostatic Parameters in the Polarizable Classical Drude Oscillator Force Field

Abstract

The Drude polarizable force field (FF) captures electronic polarization effects via auxiliary Drude particles that are attached to non-hydrogen atoms, distinguishing it from commonly used additive FFs that rely on fixed charges. The Drude FF currently includes parameters for biomolecules such as proteins, nucleic acids, lipids, and carbohydrates and small-molecule representative of those classes of molecules as well as a range of atomic ions. Extension of the Drude FF to novel small druglike molecules is challenging as it requires the assignment of partial charges, atomic polarizabilities, and Thole scaling factors. In the present article, deep neural network (DNN) models are trained on quantum mechanical (QM)-based partial charges and atomic polarizabilities along with Thole scale factors trained to target QM molecular dipole moments and polarizabilities. Training of the DNN model used a collection of 39 421 molecules with molecular weights up to 200 Da and containing H, C, N, O, P, S, F, Cl, Br, or I atoms. The DNN model utilizes bond connectivity, including 1,2, 1,3, 1,4, and 1,5 terms and distances of Drude FF atom types as the feature vector to build the model, allowing it to capture both local and nonlocal effects in the molecules. Novel methods have been developed to determine restrained electrostatic potential (RESP) charges on atoms and external points representing lone pairs and to determine Thole scale factors, which have no QM analogue. A penalty scheme is devised as a performance predictor of the trained model. Validation studies show that these DNN models can precisely predict molecular dipole and polarizabilities of Food and Drug Administration (FDA)-approved drugs compared to reference MP2 calculations. The availability of the DNN model allowing for the rapid estimation of the Drude electrostatic parameters will facilitate its applicability to a wider range of molecular species.

Harnessing Deep Learning for Optimization of Lennard-Jones Parameters for the Polarizable Classical Drude Oscillator Force Field

“…Thole scale factors screen the atomic dipole–dipole interactions between 1-2 and 1-3 covalently linked atom pairs, thereby optimizing the molecular polarizability . The partial atomic charges on the atoms and lone pair sites of the molecule were derived as recently described . The method used an in-house adaptation of the restrained electrostatic surface potential (RESP) model available in Psi4 package at MP2/Sadlej model chemistry.…”

“…75 The partial atomic charges on the atoms and lone pair sites of the molecule were derived as recently described. 76 The method used an in-house adaptation of the restrained electrostatic surface potential (RESP) 77 model available in Psi4 package 71 at MP2/Sadlej model chemistry. The α values were obtained using a parallel implementation of the GDMA code by Stone and Misquitta 78,79 available in Psi4 combined with the method of Heid et al 80 for charged species.…”

PyRESP: A Program for Electrostatic Parameterizations of Additive and Induced Dipole Polarizable Force Fields

“…The importance of modeling polarization effects is well known. For example, during the protein folding process, amino acids forming a hydrophobic core must move from the hydrated environment to the more hydrophobic interior, experiencing considerably different dielectric environments. , Additive force fields are also considered to be unable to capture the important cation−π interactions between aromatic rings and charged amino acids, leading to unrealistic receptor–ligand interaction simulations. , Therefore, a great deal of effort has been directed to developing polarizable models, including the fluctuating charge models, , the Drude oscillator models, − and models incorporating induced dipoles , or continuum dielectric. , …”

Flexible Polarizable Water Model Parameterized via Gaussian Process Regression

“…Fitting methods for finding parameters for force fields with Drude oscillators have been developed in recent years. These methods are based on a more traditional parameter fitting process 32 or deep learning models 33 that adjust the force fields with Drude oscillators to reproduce the reference quantum results.…”