Predicting quantum-accurate electron densities for DNA with equivariant neural networks

Abstract

One of the fundamental limitations of accurately modeling biomolecules like DNA is the inability to perform quantum chemistry calculations on large molecular structures. We present a machine learning model based on an equivariant Euclidean Neural Network framework to obtain quantum-accurate electron densities for arbitrary DNA structures that are much too large for conventional quantum methods. The model is trained on representative B-DNA base pair steps that capture both base pairing and base stacking interactions. The model produces accurate electron densities for arbitrary B-DNA structures with typical errors of less than 1%. Crucially, the error does not increase with system size, which suggests that the model can extrapolate to large DNA structures with negligible loss of accuracy. The model also generalizes well to other DNA structural motifs such as the A- and Z-DNA forms, despite being trained on only B-DNA configurations. We show that this machine learning electron density model can be used to calculate electrostatic potentials of DNA with quantum accuracy. These electrostatic potentials produce more accurate results compared to classical force fields and do not show the usual deficiencies at short range. Lastly, the model is used to calculate electron densities of several large-scale DNA structures, and we show that the computational scaling for this model is linear.

Building an ab initio solvated DNA model using Euclidean neural networks

“…In this study, we successfully extended a machine learning density model previously developed for gas-phase DNA [21,30] to model solvated DNA with solvent interactions included explicitly. This was achieved by fragmenting the original DNA training structures based on an entire base-pair step into molecular fragments encompassing the key local interactions (i.e.…”

“…The procedure for training the DNA-solvent machine learning model is similar to that used in the previous gas-phase DNA model [21,30]. We provide an abbreviated description of the procedure here, focusing on the modifications that were performed to adapt the training procedure to the current model.…”

“…We note that the training structures used in this study do not represent the only possible way to construct fragments for a DNA model. As a guiding principle, we aimed for fragment sizes of 30 to 60 atoms, which is two to four times smaller than the previous model's training structures with the entire base-pair step [21,30]. Further, we constructed the fragments such that the key local interactions (covalent and non-covalent) for a double-stranded DNA system in solution are sampled by the training set.…”

“…Prior to including explicit solvent, we first consider a model trained on DNA only data (Table 1) to assess the strategy of fragmenting the DNA base-pair step. We compare density prediction errors ∊ r ML and ∊ r true (see Computational Methods for definitions of these errors) from the current fragment-trained model and the previous model trained on the entire DNA base-pair step [21,30]. Note that the accuracy of the previous model has been improved from what was reported [21] by normalizing the coefficients to electron populations (see S1 Appendix).…”

Accurate Hellmann-Feynman forces with optimized atom-centered Gaussian basis sets

“…DNA fragment geometries were obtained from MD simulations performed in a previous study [39] using the Amber 20 package [40] and the BSC1 force field [41]. DNA was modeled as 12 base pair strands ("12-mers") in the canonical B [42] form, the most common structural form of DNA.…”