Short report by Luisa Kärmer: Electron Density Prediction by Equivariant Neural Networks with Applications in Computer Aided Drug Design (March-May)
Earlier this year, I had the incredible opportunity to experience the Nashville side of the Meiler Lab at Vanderbilt University with the help of a fellowship from the Max Kade Foundation. From May through March, I extended my master’s project on electron density in computer-aided drug design at this prestigious institution. The unique charm of the city, coupled with the stimulating environment at Vandy, truly enriched my experience.
My master’s project centered on the importance of electron density in understanding how small molecules interact with target proteins. Existing computer-aided drug design tools typically use atom positions as a proxy for electron density, which limits their ability to accurately describe directional interactions.
Directly using electron density is rare because it depends on quantum mechanical calculations, which usually require iterative adjustments of basis function coefficients to approximate wavefunctions and minimize system energy. This makes Density Functional Theory calculations, yielding electron densities, particularly time-consuming. To address these challenges, we explored the use of equivariant neural networks trained on ab initio data from small molecular fragments to predict electron densities for larger molecular systems. Our Electron Density Neural Network (ElektroNN) model demonstrated unbelievably good generalization abilities, predicting electron densities of drug molecules and peptides with a mean deviation of under 1% per atom across various levels of molecular complexity. To utilize this rich molecular representation, one can use existing density-derived descriptors such as Fukui functions from conceptual density functional theory, or focus gradients and Laplacians of electron density from the quantum theory of atoms in molecules (QTAIM), or design new descriptors — possibly in “basis function space” instead of “grid space”. Explicit equations relating the electron density of a protein-ligand complex to a Hellmann-Feynman interaction energy require the solution of rather complex integrals. I focused on using the density predictions of ElektroNN as input for additional models to predict DFT-SAPT interaction energies that correlate well with experimental enthalpies and can be generated as “synthetic data”.
I am very grateful for this opportunity and the new connections I made with like-minded scientists at Vanderbilt, who focus on method development for computer-aided drug design. Nashville’s vibrant culture and the stimulating academic environment provided an enjoyable backdrop for both academic and personal growth. Exploring Nashville’s lively nightlife and witnessing my first total eclipse were particularly memorable experiences. I will definitely visit again given the chance.x