Bridging Machine Learning and Thermodynamics for Accurate p K a Prediction

Abstract

Integrating scientific principles into machine learning models to enhance their predictive performance and generalizability is a central challenge in the development of AI for Science. Herein, we introduce Uni-pK _a, a novel framework that successfully incorporates thermodynamic principles into machine learning modeling, achieving high-precision predictions of acid dissociation constants (pK _a), a crucial task in the rational design of drugs and catalysts, as well as a modeling challenge in computational physical chemistry for small organic molecules. Uni-pK _a utilizes a comprehensive free energy model to represent molecular protonation equilibria accurately. It features a structure enumerator that reconstructs molecular configurations from pK _a data, coupled with a neural network that functions as a free energy predictor, ensuring high-throughput, data-driven prediction while preserving thermodynamic consistency. Employing a pretraining-finetuning strategy with both predicted and experimental pK _a data, Uni-pK _a not only achieves state-of-the-art accuracy in chemoinformatics but also shows comparable precision to quantum mechanics-based methods.

Scheme 1. Schematic Overview of Uni-pK_a Framework

(A) Data preparation workflow. We implement a microstate enumerator to systematically build the protonation ensemble from a single structure. (B) Pretraining workflow. Our pretraining strategy combines 1 weakly supervised task, pK_a-prediction, and 3 self-supervised pretraining tasks, masked atom prediction, masked charge prediction, and 3D position recovery, to make the most use of the chemical information in 3 million microstate structures. In the pK_a-prediction task, we introduce a free energy-to-pK_a (FE2pK_a) module to establish the relationship between the model-predicted free energy and pK_a. This module also enables us to predict pK_a from free energies. (C) Finetuning workflow. In this phase, we also employ the FE2pK_a module, training the model using experimental pK_a to enhance its capability for predicting pK_a with high accuracy. (D) Inference workflow. After pretraining and finetuning, the well-trained Uni-pK_a framework is equipped to handle three inference tasks, including macro-pK_a prediction, micro-pK_a prediction, and distribution fraction prediction.

Scheme 2. Inference Stage of Uni-pK_a

(A) Structures of microstates in the protonation ensemble of one reference molecule are reconstructed by the microstate generator. (B) The atom types, atomic charges, and geometry information of the microstates are fed into the Uni-Mol backbone, and the free energies are predicted for each microstate. (C) If the acid and base macrostates are specified by the user input, the macro-pK_a-free-energy formula is used to transform the free energy prediction to macro-pK_a prediction. If the microstates are further specified, the micro-pK_a-free-energy formula is used as a special case of the macro-pK_a prediction where there is only one microstate in both macrostates. (D) If pH is given by the user input, the distribution-free-energy formula is used to calculate the fraction of all the microstates in the protonation ensemble.

Figure 1

Uni-pK_a’s concern for detailed acid–base equilibria. (A) Example of 2-hydroxybenzoic acid, where one of the dissociation is dominant. (B) Example of 2-((dimethylamino)methyl)phenol, where both reactions are dominant. (C) Uni-pK_a results on SAMPL6 micro-pK_a data sets involving tautomerism. (D) Thermodynamic cycle of the glycine. pK_i is the dissociation equilibrium constant. The green and orange arrows indicate different protonation routes.