VN-EGNN: E(3)-Equivariant Graph Neural Networks with Virtual Nodes Enhance Protein Binding Site Identification

Being able to identify regions within or around proteins, to which ligands can potentially bind, is an essential step to develop new drugs. Binding site identification methods can now profit from the availability of large amounts of 3D structures in protein structure databases or from AlphaFold predictions. Current binding site identification methods heavily rely on graph neural networks (GNNs), usually designed to output E(3)-equivariant predictions. Such methods turned out to be very beneficial for physics-related tasks like binding energy or motion trajectory prediction. However, the performance of GNNs at binding site identification is still limited potentially due to the lack of dedicated nodes that model hidden geometric entities, such as binding pockets. In this work, we extend E(n)-Equivariant Graph Neural Networks (EGNNs) by adding virtual nodes and applying an extended message passing scheme. The virtual nodes in these graphs are dedicated quantities to learn representations of binding sites, which leads to improved predictive performance. In our experiments, we show that our proposed method VN-EGNN sets a new state-of-the-art at locating binding site centers on COACH420, HOLO4K and PDBbind2020.

GNN-VPA: A Variance-Preserving Aggregation Strategy for Graph Neural Networks

Graph neural networks (GNNs), and especially message-passing neural networks, excel in various domains such as physics, drug discovery, and molecular modeling. The expressivity of GNNs with respect to their ability to discriminate non-isomorphic graphs critically depends on the functions employed for message aggregation and graph-level readout. By applying signal propagation theory, we propose a variance-preserving aggregation function (VPA) that maintains expressivity, but yields improved forward and backward dynamics. Experiments demonstrate that VPA leads to increased predictive performance for popular GNN architectures as well as improved learning dynamics. Our results could pave the way towards normalizer-free or self-normalizing GNNs.

Redundancy-aware unsupervised rankings for collections of gene sets

The biological roles of gene sets are used to group them into collections. These collections are often characterized by being high-dimensional, overlapping, and redundant families of sets, thus precluding a straightforward interpretation and study of their content. Bioinformatics looked for solutions to reduce their dimension or increase their intepretability. One possibility lies in aggregating overlapping gene sets to create larger pathways, but the modified biological pathways are hardly biologically justifiable. We propose to use importance scores to rank the pathways in the collections studying the context from a set covering perspective. The proposed Shapley values-based scores consider the distribution of the singletons and the size of the sets in the families; Furthermore, a trick allows us to circumvent the usual exponential complexity of Shapley values' computation. Finally, we address the challenge of including a redundancy awareness in the obtained rankings where, in our case, sets are redundant if they show prominent intersections. The rankings can be used to reduce the dimension of collections of gene sets, such that they show lower redundancy and still a high coverage of the genes. We further investigate the impact of our selection on Gene Sets Enrichment Analysis. The proposed method shows a practical utility in bioinformatics to increase the interpretability of the collections of gene sets and a step forward to include redundancy into Shapley values computations.

Redundancy-aware unsupervised ranking based on game theory -- application to gene enrichment analysis

Gene set collections are a common ground to study the enrichment of genes for specific phenotypic traits. Gene set enrichment analysis aims to identify genes that are over-represented in gene sets collections and might be associated with a specific phenotypic trait. However, as this involves a massive number of hypothesis testing, it is often questionable whether a pre-processing step to reduce gene sets collections' sizes is helpful. Moreover, the often highly overlapping gene sets and the consequent low interpretability of gene sets' collections demand for a reduction of the included gene sets. Inspired by this bioinformatics context, we propose a method to rank sets within a family of sets based on the distribution of the singletons and their size. We obtain sets' importance scores by computing Shapley values without incurring into the usual exponential number of evaluations of the value function. Moreover, we address the challenge of including a redundancy awareness in the rankings obtained where, in our case, sets are redundant if they show prominent intersections. We finally evaluate our approach for gene sets collections; the rankings obtained show low redundancy and high coverage of the genes. The unsupervised nature of the proposed ranking does not allow for an evident increase in the number of significant gene sets for specific phenotypic traits when reducing the size of the collections. However, we believe that the rankings proposed are of use in bioinformatics to increase interpretability of the gene sets collections and a step forward to include redundancy into Shapley values computations.

Unsupervised Features Ranking via Coalitional Game Theory for Categorical Data

Not all real-world data are labeled, and when labels are not available, it is often costly to obtain them. Moreover, as many algorithms suffer from the curse of dimensionality, reducing the features in the data to a smaller set is often of great utility. Unsupervised feature selection aims to reduce the number of features, often using feature importance scores to quantify the relevancy of single features to the task at hand. These scores can be based only on the distribution of variables and the quantification of their interactions. The previous literature, mainly investigating anomaly detection and clusters, fails to address the redundancy-elimination issue. We propose an evaluation of correlations among features to compute feature importance scores representing the contribution of single features in explaining the dataset's structure. Based on Coalitional Game Theory, our feature importance scores include a notion of redundancy awareness making them a tool to achieve redundancy-free feature selection. We show that the deriving features' selection outperforms competing methods in lowering the redundancy rate while maximizing the information contained in the data. We also introduce an approximated version of the algorithm to reduce the complexity of Shapley values' computations.

Boundary Graph Neural Networks for 3D Simulations

The abundance of data has given machine learning huge momentum in natural sciences and engineering. However, the modeling of simulated physical processes remains difficult. A key problem in doing so is the correct handling of geometric boundaries. While triangularized geometric boundaries are very common in engineering applications, they are notoriously difficult to model by machine learning approaches due to their heterogeneity with respect to size and orientation. In this work, we introduce Boundary Graph Neural Networks (BGNNs), which dynamically modify graph structures to address boundary conditions. Boundary graph structures are constructed via modifying edges, augmenting node features, and dynamically inserting virtual nodes. The new BGNNs are tested on complex 3D granular flow processes of hoppers and rotating drums which are standard parts of industrial machinery. Using precise simulations that are obtained by an expensive and complex discrete element method, BGNNs are evaluated in terms of computational efficiency as well as prediction accuracy of particle flows and mixing entropies. Even if complex boundaries are present, BGNNs are able to accurately reproduce 3D granular flows within simulation uncertainties over hundreds of thousands of simulation timesteps, and most notably particles completely stay within the geometric objects without using handcrafted conditions or restrictions.

Learning 3D Granular Flow Simulations

Recently, the application of machine learning models has gained momentum in natural sciences and engineering, which is a natural fit due to the abundance of data in these fields. However, the modeling of physical processes from simulation data without first principle solutions remains difficult. Here, we present a Graph Neural Networks approach towards accurate modeling of complex 3D granular flow simulation processes created by the discrete element method LIGGGHTS and concentrate on simulations of physical systems found in real world applications like rotating drums and hoppers. We discuss how to implement Graph Neural Networks that deal with 3D objects, boundary conditions, particle - particle, and particle - boundary interactions such that an accurate modeling of relevant physical quantities is made possible. Finally, we compare the machine learning based trajectories to LIGGGHTS trajectories in terms of particle flows and mixing entropies.

Cross-Domain Few-Shot Learning by Representation Fusion

In order to quickly adapt to new data, few-shot learning aims at learning from few examples, often by using already acquired knowledge. The new data often differs from the previously seen data due to a domain shift, that is, a change of the input-target distribution. While several methods perform well on small domain shifts like new target classes with similar inputs, larger domain shifts are still challenging. Large domain shifts may result in high-level concepts that are not shared between the original and the new domain. However, low-level concepts like edges in images might still be shared and useful. For cross-domain few-shot learning, we suggest representation fusion to unify different abstraction levels of a deep neural network into one representation. We propose Cross-domain Hebbian Ensemble Few-shot learning (CHEF), which achieves representation fusion by an ensemble of Hebbian learners acting on different layers of a deep neural network that was trained on the original domain. On the few-shot datasets miniImagenet and tieredImagenet, where the domain shift is small, CHEF is competitive with state-of-the-art methods. On cross-domain few-shot benchmark challenges with larger domain shifts, CHEF establishes novel state-of-the-art results in all categories. We further apply CHEF on a real-world cross-domain application in drug discovery. We consider a domain shift from bioactive molecules to environmental chemicals and drugs with twelve associated toxicity prediction tasks. On these tasks, that are highly relevant for computational drug discovery, CHEF significantly outperforms all its competitors. Github: https://github.com/ml-jku/chef

Large-scale ligand-based virtual screening for SARS-CoV-2 inhibitors using deep neural networks

Due to the current severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic, there is an urgent need for novel therapies and drugs. We conducted a large-scale virtual screening for small molecules that are potential CoV-2 inhibitors. To this end, we utilized "ChemAI", a deep neural network trained on more than 220M data points across 3.6M molecules from three public drug-discovery databases. With ChemAI, we screened and ranked one billion molecules from the ZINC database for favourable effects against CoV-2. We then reduced the result to the 30,000 top-ranked compounds, which are readily accessible and purchasable via the ZINC database. Additionally, we screened the DrugBank using ChemAI to allow for drug repurposing, which would be a fast way towards a therapy. We provide these top-ranked compounds of ZINC and DrugBank as a library for further screening with bioassays at https://github.com/ml-jku/sars-cov-inhibitors-chemai.