Learning the shape of protein microenvironments with a holographic convolutional neural network.

Proteins play a central role in biology from immune recognition to brain activity. While major advances in machine learning have improved our ability to predict protein structure from sequence, determining protein function from its sequence or structure remains a major challenge. Here, we introduce holographic convolutional neural network (H-CNN) for proteins, which is a physically motivated machine learning approach to model amino acid preferences in protein structures. H-CNN reflects physical interactions in a protein structure and recapitulates the functional information stored in evolutionary data. H-CNN accurately predicts the impact of mutations on protein stability and binding of protein complexes. Our interpretable computational model for protein structure-function maps could guide design of novel proteins with desired function.

GAPS: a geometric attention-based network for peptide binding site identification by the transfer learning approach.

Protein-peptide interactions (PPepIs) are vital to understanding cellular functions, which can facilitate the design of novel drugs. As an essential component in forming a PPepI, protein-peptide binding sites are the basis for understanding the mechanisms involved in PPepIs. Therefore, accurately identifying protein-peptide binding sites becomes a critical task. The traditional experimental methods for researching these binding sites are labor-intensive and time-consuming, and some computational tools have been invented to supplement it. However, these computational tools have limitations in generality or accuracy due to the need for ligand information, complex feature construction, or their reliance on modeling based on amino acid residues. To deal with the drawbacks of these computational algorithms, we describe a geometric attention-based network for peptide binding site identification (GAPS) in this work. The proposed model utilizes geometric feature engineering to construct atom representations and incorporates multiple attention mechanisms to update relevant biological features. In addition, the transfer learning strategy is implemented for leveraging the protein-protein binding sites information to enhance the protein-peptide binding sites recognition capability, taking into account the common structure and biological bias between proteins and peptides. Consequently, GAPS demonstrates the state-of-the-art performance and excellent robustness in this task. Moreover, our model exhibits exceptional performance across several extended experiments including predicting the apo protein-peptide, protein-cyclic peptide and the AlphaFold-predicted protein-peptide binding sites. These results confirm that the GAPS model is a powerful, versatile, stable method suitable for diverse binding site predictions.

A geometric deep learning framework for drug repositioning over heterogeneous information networks.

Drug repositioning (DR) is a promising strategy to discover new indicators of approved drugs with artificial intelligence techniques, thus improving traditional drug discovery and development. However, most of DR computational methods fall short of taking into account the non-Euclidean nature of biomedical network data. To overcome this problem, a deep learning framework, namely DDAGDL, is proposed to predict drug-drug associations (DDAs) by using geometric deep learning (GDL) over heterogeneous information network (HIN). Incorporating complex biological information into the topological structure of HIN, DDAGDL effectively learns the smoothed representations of drugs and diseases with an attention mechanism. Experiment results demonstrate the superior performance of DDAGDL on three real-world datasets under 10-fold cross-validation when compared with state-of-the-art DR methods in terms of several evaluation metrics. Our case studies and molecular docking experiments indicate that DDAGDL is a promising DR tool that gains new insights into exploiting the geometric prior knowledge for improved efficacy.

Protein model quality assessment using rotation-equivariant transformations on point clouds.

Machine learning research concerning protein structure has seen a surge in popularity over the last years with promising advances for basic science and drug discovery. Working with macromolecular structure in a machine learning context requires an adequate numerical representation, and researchers have extensively studied representations such as graphs, discretized 3D grids, and distance maps. As part of CASP14, we explored a new and conceptually simple representation in a blind experiment: atoms as points in 3D, each with associated features. These features-initially just the basic element type of each atom-are updated through a series of neural network layers featuring rotation-equivariant convolutions. Starting from all atoms, we further aggregate information at the level of alpha carbons before making a prediction at the level of the entire protein structure. We find that this approach yields competitive results in protein model quality assessment despite its simplicity and despite the fact that it incorporates minimal prior information and is trained on relatively little data. Its performance and generality are particularly noteworthy in an era where highly complex, customized machine learning methods such as AlphaFold 2 have come to dominate protein structure prediction.

A geometric deep learning model for display and prediction of potential drug-virus interactions against SARS-CoV-2.

Although the coronavirus epidemic spread rapidly with the Omicron variant, it lost its lethality rate with the effect of vaccine and immunity. The hospitalization and intense demand decreased. However, there is no definite information about when this disease will end or how dangerous the different variants could be. In addition, it is not possible to end the risk of variants that will continue to circulate among animals in nature. After this stage, drug-virus interactions should be examined in order to be able to prepare against possible new types of viruses and variants and to rapidly-produce drugs or vaccines against possible viruses. Despite experimental methods that are expensive, laborious, and time-consuming, geometric deep learning(GDL) is an alternative method that can be used to make this process faster and cheaper. In this study, we propose a new model based on geometric deep learning for the prediction of drug-virus interaction against COVID-19. First, we use the antiviral drug data in the SMILES molecular structure representation to generate too many features and better describe the structure of chemical species. Then the data is converted into a molecular representation and then into a graphical structure that the GDL model can understand. The node feature vectors are transferred to a different space with the Message Passing Neural Network (MPNN) for the training process to take place. We develop a geometric neural network architecture where the graph embedding values are passed through the fully connected layer and the prediction is actualized. The results indicate that the proposed method outperforms existing methods with 97% accuracy in predicting drug-virus interactions.

k-Space-based coil combination via geometric deep learning for reconstruction of non-Cartesian MRSI data.

PURPOSE: State-of-the-art whole-brain MRSI with spatial-spectral encoding and multichannel acquisition generates huge amounts of data, which must be efficiently processed to stay within reasonable reconstruction times. Although coil combination significantly reduces the amount of data, currently it is performed in image space at the end of the reconstruction. This prolongs reconstruction times and increases RAM requirements. We propose an alternative k-space-based coil combination that uses geometric deep learning to combine MRSI data already in native non-Cartesian k-space. METHODS: Twelve volunteers were scanned at a 3T MR scanner with a 20-channel head coil at 10 different positions with water-unsuppressed MRSI. At the eleventh position, water-suppressed MRSI data were acquired. Data of 7 volunteers were used to estimate sensitivity maps and form a base for simulating training data. A neural network was designed and trained to remove the effect of sensitivity profiles of the coil elements from the MRSI data. The water-suppressed MRSI data of the remaining volunteers were used to evaluate the performance of the new k-space-based coil combination relative to that of a conventional image-based alternative. RESULTS: For both approaches, the resulting metabolic ratio maps were similar. The SNR of the k-space-based approach was comparable to the conventional approach in low SNR regions, but underperformed for high SNR. The Cramér-Rao lower bounds show the same trend. The analysis of the FWHM showed no difference between the two methods. CONCLUSION: k-Space-based coil combination of MRSI data is feasible and reduces the amount of raw data immediately after their sampling.

Exploring palatal and dental shape variation with 3D shape analysis and geometric deep learning.

OBJECTIVES: Palatal shape contains a lot of information that is of clinical interest. Moreover, palatal shape analysis can be used to guide or evaluate orthodontic treatments. A statistical shape model (SSM) is a tool that, by means of dimensionality reduction, aims at compactly modeling the variance of complex shapes for efficient analysis. In this report, we evaluate several competing approaches to constructing SSMs for the human palate. SETTING AND SAMPLE POPULATION: This study used a sample comprising digitized 3D maxillary dental casts from 1,324 individuals. MATERIALS AND METHODS: Principal component analysis (PCA) and autoencoders (AE) are popular approaches to construct SSMs. PCA is a dimension reduction technique that provides a compact description of shapes by uncorrelated variables. AEs are situated in the field of deep learning and provide a non-linear framework for dimension reduction. This work introduces the singular autoencoder (SAE), a hybrid approach that combines the most important properties of PCA and AEs. We assess the performance of the SAE using standard evaluation tools for SSMs, including accuracy, generalization, and specificity. RESULTS: We found that the SAE obtains equivalent results to PCA and AEs for all evaluation metrics. SAE scores were found to be uncorrelated and provided an optimally compact representation of the shapes. CONCLUSION: We conclude that the SAE is a promising tool for 3D palatal shape analysis, which effectively combines the power of PCA with the flexibility of deep learning. This opens future AI driven applications of shape analysis in orthodontics and other related clinical disciplines.

Automated landmarking for palatal shape analysis using geometric deep learning.

OBJECTIVES: To develop and evaluate a geometric deep-learning network to automatically place seven palatal landmarks on digitized maxillary dental casts. SETTINGS AND SAMPLE POPULATION: The sample comprised individuals with permanent dentition of various ethnicities. The network was trained from manual landmark annotations on 732 dental casts and evaluated on 104 dental casts. MATERIALS AND METHODS: A geometric deep-learning network was developed to hierarchically learn features from point-clouds representing the 3D surface of each cast. These features predict the locations of seven palatal landmarks. RESULTS: Repeat-measurement reliability was <0.3 mm for all landmarks on all casts. Accuracy is promising. The proportion of test subjects with errors less than 2 mm was between 0.93 and 0.68, depending on the landmark. Unusually shaped and large palates generate the highest errors. There was no evidence for a difference in mean palatal shape estimated from manual compared to the automatic landmarking. The automatic landmarking reduces sample variation around the mean and reduces measurements of palatal size. CONCLUSIONS: The automatic landmarking method shows excellent repeatability and promising accuracy, which can streamline patient assessment and research studies. However, landmark indications should be subject to visual quality control.

[A Preliminary Study of Applying Geometric Deep Learning in Brain Morphometry for Diagnosis of Alzheimer's Disease].

OBJECTIVE: A predictive model of Alzheimer's disease (AD) was established based on brain surface meshes and geometric deep learning, and its performance was evaluated. METHODS: Seventy-six clinically diagnosed AD patients and 83 healthy older adults were enrolled and randomly assigned to the training set and the test set according to a 4-to-1 ratio. Brain surface mesh was constructed from 3-D T1-weighted high-resolution structural MR volumes of each participant. After applying a series of simplification to the surface meshes, the training set was fed into the geometric deep neural network for training. The performance of the prediction model was evaluated with the test set, and the evaluation metrics included accuracy, sensitivity and specificity. RESULTS: The prediction model trained on the right brain surface meshes with 6 000 faces achieved the best performance, with accuracy reaching 93.8%, sensitivity, 91.7%, and specificity, 94.1%. The evolution of the brain surface meshes during convolution and pooling revealed that AD patients had diffuse brain tissue loss compared with healthy older adults. CONCLUSION: Morphological brain analysis based on mesh data and geometric deep learning has great potential in the differential diagnosis of AD.

Geometric Deep Lean Learning: Deep Learning in Industry 4.0 Cyber-Physical Complex Networks.

In the near future, value streams associated with Industry 4.0 will be formed by interconnected cyber-physical elements forming complex networks that generate huge amounts of data in real time. The success or failure of industry leaders interested in the continuous improvement of lean management systems in this context is determined by their ability to recognize behavioral patterns in these big data structured within non-Euclidean domains, such as these dynamic sociotechnical complex networks. We assume that artificial intelligence in general and deep learning in particular may be able to help find useful patterns of behavior in 4.0 industrial environments in the lean management of cyber-physical systems. However, although these technologies have meant a paradigm shift in the resolution of complex problems in the past, the traditional methods of deep learning, focused on image or video analysis, both with regular structures, are not able to help in this specific field. This is why this work focuses on proposing geometric deep lean learning, a mathematical methodology that describes deep-lean-learning operations such as convolution and pooling on cyber-physical Industry 4.0 graphs. Geometric deep lean learning is expected to positively support sustainable organizational growth because customers and suppliers ought to be able to reach new levels of transparency and traceability on the quality and efficiency of processes that generate new business for both, hence generating new products, services, and cooperation opportunities in a cyber-physical environment.

Ear Detection Using Convolutional Neural Network on Graphs with Filter Rotation.

Geometric deep learning (GDL) generalizes convolutional neural networks (CNNs) to non-Euclidean domains. In this work, a GDL technique, allowing the application of CNN on graphs, is examined. It defines convolutional filters with the use of the Gaussian mixture model (GMM). As those filters are defined in continuous space, they can be easily rotated without the need for some additional interpolation. This, in turn, allows constructing systems having rotation equivariance property. The characteristic of the proposed approach is illustrated with the problem of ear detection, which is of great importance in biometric systems enabling image based, discrete human identification. The analyzed graphs were constructed taking into account superpixels representing image content. This kind of representation has several advantages. On the one hand, it significantly reduces the amount of processed data, allowing building simpler and more effective models. On the other hand, it seems to be closer to the conscious process of human image understanding as it does not operate on millions of pixels. The contributions of the paper lie both in GDL application area extension (semantic segmentation of the images) and in the novel concept of trained filter transformations. We show that even significantly reduced information about image content and a relatively simple, in comparison with classic CNN, model (smaller number of parameters and significantly faster processing) allows obtaining detection results on the quality level similar to those reported in the literature on the UBEAR dataset. Moreover, we show experimentally that the proposed approach possesses in fact the rotation equivariance property allowing detecting rotated structures without the need for labor consuming training on all rotated and non-rotated images.

Geometric Deep Learning Autonomously Learns Chemical Features That Outperform Those Engineered by Domain Experts.

Artificial Intelligence has advanced at an unprecedented pace, backing recent breakthroughs in natural language processing, speech recognition, and computer vision: domains where the data is euclidean in nature. More recently, considerable progress has been made in engineering deep-learning architectures that can accept non-Euclidean data such as graphs and manifolds: geometric deep learning. This progress is of considerable interest to the drug discovery community, as molecules can naturally be represented as graphs, where atoms are nodes and bonds are edges. In this work, we explore the performance of geometric deep-learning methods in the context of drug discovery, comparing machine learned features against the domain expert engineered features that are mainstream in the pharmaceutical industry.

MuToN Quantifies Binding Affinity Changes upon Protein Mutations by Geometric Deep Learning.

Assessing changes in protein-protein binding affinity due to mutations helps understanding a wide range of crucial biological processes within cells. Despite significant efforts to create accurate computational models, predicting how mutations affect affinity remains challenging due to the complexity of the biological mechanisms involved. In the present work, a geometric deep learning framework called MuToN is introduced for quantifying protein binding affinity change upon residue mutations. The method, designed with geometric attention networks, is mechanism-aware. It captures changes in the protein binding interfaces of mutated complexes and assesses the allosteric effects of amino acids. Experimental results highlight MuToN's superiority compared to existing methods. Additionally, MuToN's flexibility and effectiveness are illustrated by its precise predictions of binding affinity changes between SARS-CoV-2 variants and the ACE2 complex.

Geometry-Complete Diffusion for 3D Molecule Generation and Optimization.

Motivation: Denoising diffusion probabilistic models (DDPMs) have recently taken the field of generative modeling by storm, pioneering new state-of-the-art results in disciplines such as computer vision and computational biology for diverse tasks ranging from text-guided image generation to structure-guided protein design. Along this latter line of research, methods have recently been proposed for generating 3D molecules using equivariant graph neural networks (GNNs) within a DDPM framework. However, such methods are unable to learn important geometric and physical properties of 3D molecules during molecular graph generation, as they adopt molecule-agnostic and non-geometric GNNs as their 3D graph denoising networks, which negatively impacts their ability to effectively scale to datasets of large 3D molecules. Results: In this work, we address these gaps by introducing the Geometry-Complete Diffusion Model (GCDM) for 3D molecule generation, which outperforms existing 3D molecular diffusion models by significant margins across conditional and unconditional settings for the QM9 dataset as well as for the larger GEOM-Drugs dataset. Importantly, we demonstrate that the geometry-complete denoising process GCDM learns for 3D molecule generation allows the model to generate realistic and stable large molecules at the scale of GEOM-Drugs, whereas previous methods fail to do so with the features they learn. Additionally, we show that extensions of GCDM can not only effectively design 3D molecules for specific protein pockets but also that GCDM's geometric features can effectively be repurposed to directly optimize the geometry and chemical composition of existing 3D molecules for specific molecular properties, demonstrating new, real-world versatility of molecular diffusion models. Availability: Our source code and data are freely available on GitHub.

Latent disentanglement in mesh variational autoencoders improves the diagnosis of craniofacial syndromes and aids surgical planning.

BACKGROUND AND OBJECTIVE: The use of deep learning to undertake shape analysis of the complexities of the human head holds great promise. However, there have traditionally been a number of barriers to accurate modelling, especially when operating on both a global and local level. METHODS: In this work, we will discuss the application of the Swap Disentangled Variational Autoencoder (SD-VAE) with relevance to Crouzon, Apert and Muenke syndromes. The model is trained on a dataset of 3D meshes of healthy and syndromic patients which was increased in size with a novel data augmentation technique based on spectral interpolation. Thanks to its semantically meaningful and disentangled latent representation, SD-VAE is used to analyse and generate head shapes while considering the influence of different anatomical sub-units. RESULTS: Although syndrome classification is performed on the entire mesh, it is also possible, for the first time, to analyse the influence of each region of the head on the syndromic phenotype. By manipulating specific parameters of the generative model, and producing procedure-specific new shapes, it is also possible to approximate the outcome of a range of craniofacial surgical procedures. CONCLUSION: This work opens new avenues to advance diagnosis, aids surgical planning and allows for the objective evaluation of surgical outcomes. Our code is available at github.com/simofoti/CraniofacialSD-VAE.

Geometric deep learning for the prediction of magnesium-binding sites in RNA structures.

Magnesium ions (Mg2+) are essential for the folding, functional expression, and structural stability of RNA molecules. However, predicting Mg2+-binding sites in RNA molecules based solely on RNA structures is still challenging. The molecular surface, characterized by a continuous shape with geometric and chemical properties, is important for RNA modelling and carries essential information for understanding the interactions between RNAs and Mg2+ ions. Here, we propose an approach named RNA-magnesium ion surface interaction fingerprinting (RMSIF), a geometric deep learning-based conceptual framework to predict magnesium ion binding sites in RNA structures. To evaluate the performance of RMSIF, we systematically enumerated decoy Mg2+ ions across a full-space grid within the range of 2 to 10 Å from the RNA molecule and made predictions accordingly. Visualization techniques were used to validate the prediction results and calculate success rates. Comparative assessments against state-of-the-art methods like MetalionRNA, MgNet, and Metal3DRNA revealed that RMSIF achieved superior success rates and accuracy in predicting Mg2+-binding sites. Additionally, in terms of the spatial distribution of Mg2+ ions within the RNA structures, a majority were situated in the deep grooves, while a minority occupied the shallow grooves. Collectively, the conceptual framework developed in this study holds promise for advancing insights into drug design, RNA co-transcriptional folding, and structure prediction.

A novel interactive deep cascade spectral graph convolutional network with multi-relational graphs for disease prediction.

Graph neural networks (GNNs) have recently grown in popularity for disease prediction. Existing GNN-based methods primarily build the graph topological structure around a single modality and combine it with other modalities to acquire feature representations of acquisitions. The complicated relationship in each modality, however, may not be well highlighted due to its specificity. Further, relatively shallow networks restrict adequate extraction of high-level features, affecting disease prediction performance. Accordingly, this paper develops a new interactive deep cascade spectral graph convolutional network with multi-relational graphs (IDCGN) for disease prediction tasks. Its crucial points lie in constructing multiple relational graphs and dual cascade spectral graph convolution branches with interaction (DCSGBI). Specifically, the former designs a pairwise imaging-based edge generator and a pairwise non-imaging-based edge generator from different modalities by devising two learnable networks, which adaptively capture graph structures and provide various views of the same acquisition to aid in disease diagnosis. Again, DCSGBI is established to enrich high-level semantic information and low-level details of disease data. It devises a cascade spectral graph convolution operator for each branch and incorporates the interaction strategy between different branches into the network, successfully forming a deep model and capturing complementary information from diverse branches. In this manner, more favorable and sufficient features are learned for a reliable diagnosis. Experiments on several disease datasets reveal that IDCGN exceeds state-of-the-art models and achieves promising results.

3D physiologically-informed deep learning for drug discovery of a novel vascular endothelial growth factor receptor-2 (VEGFR2).

Angiogenesis is an essential process in tumorigenesis, tumor invasion, and metastasis, and is an intriguing pathway for drug discovery. Targeting vascular endothelial growth factor receptor 2 (VEGFR2) to inhibit tumor angiogenic pathways has been widely explored and adopted in clinical practice. However, most drugs, such as the Food and Drug Administration -approved drug axitinib (ATC code: L01EK01), have considerable side effects and limited tolerability. Therefore, there is an urgent need for the development of novel VEGFR2 inhibitors. In this study, we propose a novel strategy to design potential candidates targeting VEGFR2 using three-dimensional (3D) deep learning and structural modeling methods. A geometric-enhanced molecular representation learning method (GEM) model employing a graph neural network (GNN) as its underlying predictive algorithm was used to predict the activity of the candidates. In the structural modeling method, flexible docking was performed to screen data with high affinity and explore the mechanism of the inhibitors. Small -molecule compounds with consistently improved properties were identified based on the intersection of the scores obtained from both methods. Candidates identified using the GEM-GNN model were selected for in silico modeling using molecular dynamics simulations to further validate their efficacy. The GEM-GNN model enabled the identification of candidate compounds with potentially more favorable properties than the existing drug, axitinib, while achieving higher efficacy.

Neural deformation fields for template-based reconstruction of cortical surfaces from MRI.

The reconstruction of cortical surfaces is a prerequisite for quantitative analyses of the cerebral cortex in magnetic resonance imaging (MRI). Existing segmentation-based methods separate the surface registration from the surface extraction, which is computationally inefficient and prone to distortions. We introduce Vox2Cortex-Flow (V2C-Flow), a deep mesh-deformation technique that learns a deformation field from a brain template to the cortical surfaces of an MRI scan. To this end, we present a geometric neural network that models the deformation-describing ordinary differential equation in a continuous manner. The network architecture comprises convolutional and graph-convolutional layers, which allows it to work with images and meshes at the same time. V2C-Flow is not only very fast, requiring less than two seconds to infer all four cortical surfaces, but also establishes vertex-wise correspondences to the template during reconstruction. In addition, V2C-Flow is the first approach for cortex reconstruction that models white matter and pial surfaces jointly, therefore avoiding intersections between them. Our comprehensive experiments on internal and external test data demonstrate that V2C-Flow results in cortical surfaces that are state-of-the-art in terms of accuracy. Moreover, we show that the established correspondences are more consistent than in FreeSurfer and that they can directly be utilized for cortex parcellation and group analyses of cortical thickness.

DilatedToothSegNet: Tooth Segmentation Network on 3D Dental Meshes Through Increasing Receptive Vision.

The utilization of advanced intraoral scanners to acquire 3D dental models has gained significant popularity in the fields of dentistry and orthodontics. Accurate segmentation and labeling of teeth on digitized 3D dental surface models are crucial for computer-aided treatment planning. At the same time, manual labeling of these models is a time-consuming task. Recent advances in geometric deep learning have demonstrated remarkable efficiency in surface segmentation when applied to raw 3D models. However, segmentation of the dental surface remains challenging due to the atypical and diverse appearance of the patients' teeth. Numerous deep learning methods have been proposed to automate dental surface segmentation. Nevertheless, they still show limitations, particularly in cases where teeth are missing or severely misaligned. To overcome these challenges, we introduce a network operator called dilated edge convolution, which enhances the network's ability to learn additional, more distant features by expanding its receptive field. This leads to improved segmentation results, particularly in complex and challenging cases. To validate the effectiveness of our proposed method, we performed extensive evaluations on the recently published benchmark data set for dental model segmentation Teeth3DS. We compared our approach with several other state-of-the-art methods using a quantitative and qualitative analysis. Through these evaluations, we demonstrate the superiority of our proposed method, showcasing its ability to outperform existing approaches in dental surface segmentation.