Response to Comment on "Pushing the frontiers of density functionals by solving the fractional electron problem".

Gerasimov et al. claim that the ability of DM21 to respect fractional charge (FC) and fractional spin (FS) conditions outside of the training set has not been demonstrated in our paper. This is based on (i) asserting that the training set has a ~50% overlap with our bond-breaking benchmark (BBB) and (ii) questioning the validity and accuracy of our other generalization examples. We disagree with their analysis and believe that the points raised are either incorrect or not relevant to the main conclusions of the paper and to the assessment of general quality of DM21.

Pushing the frontiers of density functionals by solving the fractional electron problem.

Density functional theory describes matter at the quantum level, but all popular approximations suffer from systematic errors that arise from the violation of mathematical properties of the exact functional. We overcame this fundamental limitation by training a neural network on molecular data and on fictitious systems with fractional charge and spin. The resulting functional, DM21 (DeepMind 21), correctly describes typical examples of artificial charge delocalization and strong correlation and performs better than traditional functionals on thorough benchmarks for main-group atoms and molecules. DM21 accurately models complex systems such as hydrogen chains, charged DNA base pairs, and diradical transition states. More crucially for the field, because our methodology relies on data and constraints, which are continually improving, it represents a viable pathway toward the exact universal functional.

Improved protein structure prediction using potentials from deep learning.

Protein structure prediction can be used to determine the three-dimensional shape of a protein from its amino acid sequence1. This problem is of fundamental importance as the structure of a protein largely determines its function2; however, protein structures can be difficult to determine experimentally. Considerable progress has recently been made by leveraging genetic information. It is possible to infer which amino acid residues are in contact by analysing covariation in homologous sequences, which aids in the prediction of protein structures3. Here we show that we can train a neural network to make accurate predictions of the distances between pairs of residues, which convey more information about the structure than contact predictions. Using this information, we construct a potential of mean force4 that can accurately describe the shape of a protein. We find that the resulting potential can be optimized by a simple gradient descent algorithm to generate structures without complex sampling procedures. The resulting system, named AlphaFold, achieves high accuracy, even for sequences with fewer homologous sequences. In the recent Critical Assessment of Protein Structure Prediction5 (CASP13)-a blind assessment of the state of the field-AlphaFold created high-accuracy structures (with template modelling (TM) scores6 of 0.7 or higher) for 24 out of 43 free modelling domains, whereas the next best method, which used sampling and contact information, achieved such accuracy for only 14 out of 43 domains. AlphaFold represents a considerable advance in protein-structure prediction. We expect this increased accuracy to enable insights into the function and malfunction of proteins, especially in cases for which no structures for homologous proteins have been experimentally determined7.

Protein structure prediction using multiple deep neural networks in the 13th Critical Assessment of Protein Structure Prediction (CASP13).

We describe AlphaFold, the protein structure prediction system that was entered by the group A7D in CASP13. Submissions were made by three free-modeling (FM) methods which combine the predictions of three neural networks. All three systems were guided by predictions of distances between pairs of residues produced by a neural network. Two systems assembled fragments produced by a generative neural network, one using scores from a network trained to regress GDT_TS. The third system shows that simple gradient descent on a properly constructed potential is able to perform on par with more expensive traditional search techniques and without requiring domain segmentation. In the CASP13 FM assessors' ranking by summed z-scores, this system scored highest with 68.3 vs 48.2 for the next closest group (an average GDT_TS of 61.4). The system produced high-accuracy structures (with GDT_TS scores of 70 or higher) for 11 out of 43 FM domains. Despite not explicitly using template information, the results in the template category were comparable to the best performing template-based methods.