Tractable and Thermodynamically Consistent pKa Prediction via First-Dissociation Aggregation

Predicting the aqueous pKa of a molecule is a complex task, as the ionization of molecules governs their behavior. Current methods either struggle with the computational burden of enumerating all possible protonation states or fail to maintain thermodynamic consistency in their predictions. In this study, researchers have derived an exact thermodynamic identity that directly links the macroscopic first-dissociation constant to the populations of protonated microstates and the unique events of the first deprotonation.

This eliminates the need for complex algebraic manipulations involving the deprotonated ensemble, reducing the computational complexity to O(n+E) operations, where n represents the number of atoms and E the number of edges in the molecular graph.

The researchers implemented this identity in a novel dual-head graph neural network called DTi-pKa. This innovative model comprises two interconnected heads: one responsible for predicting the free energy, and the other tasked with determining the dissociation constant. These heads are linked through thermodynamic constraints, ensuring that the model outputs are both accurate and thermodynamically consistent.

The performance of DTi-pKa was evaluated on four external datasets containing 355 molecules. The model achieved a mean absolute error (MAE) of 0.5665 pKa units across all datasets, and 0.6285 on a subset of 169 records that did not have overlapping training data. Moreover, DTi-pKa provides valuable insights into the molecular structure by delivering site-resolved micro-pKa values and the corresponding protonation-state populations.

The researchers conducted controlled ablations to understand the impact of their design choices. They found that placing the thermodynamic constraints at the level of the reported macroscopic equilibrium had a more significant impact on the model's performance than achieving precise microscopic label accuracy. This finding suggests that the approach can be adapted to other domains of physics-informed machine learning, not just chemistry.

To ensure the robustness of their results, the researchers performed closure diagnostics, which exposed numerical self-consistency as an open frontier in the field. They reported their findings transparently to facilitate further research in this area. By replacing a computationally intensive process with a fundamental physical identity, DTi-pKa successfully combines macroscopic accuracy with microscopic interpretability within a unified framework.