Curvature-enhanced graph convolutional network for biomolecular interaction prediction

Geometric deep learning has demonstrated a great potential in non-Euclidean data analysis. The incorporation of geometric insights into learning architecture is vital to its success. Here we propose a curvature-enhanced graph convolutional network (CGCN) for biomolecular interaction prediction. Our CGCN employs Ollivier-Ricci curvature (ORC) to characterize network local geometric properties and enhance the learning capability of GCNs. More specifically, ORCs are evaluated based on the local topology from node neighborhoods, and further incorporated into the weight function for the feature aggregation in message-passing procedure. Our CGCN model is extensively validated on fourteen real-world bimolecular interaction networks and analyzed in details using a series of well-designed simulated data. It has been found that our CGCN can achieve the state-of-the-art results. It outperforms all existing models, as far as we know, in thirteen out of the fourteen real-world datasets and ranks as the second in the rest one. The results from the simulated data show that our CGCN model is superior to the traditional GCN models regardless of the positive-to-negative-curvature ratios, network densities, and network sizes (when larger than 500).

Geometric graph neural networks on multi-omics data to predict cancer survival outcomes

The advance of sequencing technologies has enabled a thorough molecular characterization of the genome in human cancers. To improve patient prognosis predictions and subsequent treatment strategies, it is imperative to develop advanced computational methods to analyze large-scale, high-dimensional genomic data. However, traditional machine learning methods face a challenge in handling the high-dimensional, low-sample size problem that is shown in most genomic data sets. To address this, our group has developed geometric network analysis techniques on multi-omics data in connection with prior biological knowledge derived from protein-protein interactions (PPIs) or pathways. Geometric features obtained from the genomic network, such as Ollivier-Ricci curvature and the invariant measure of the associated Markov chain, have been shown to be predictive of survival outcomes in various cancers. In this study, we propose a novel supervised deep learning method called geometric graph neural network (GGNN) that incorporates such geometric features into deep learning for enhanced predictive power and interpretability. More specifically, we utilize a state-of-the-art graph neural network with sparse connections between the hidden layers based on known biology of the PPI network and pathway information. Geometric features along with multi-omics data are then incorporated into the corresponding layers. The proposed approach utilizes a local-global principle in such a manner that highly predictive features are selected at the front layers and fed directly to the last layer for multivariable Cox proportional-hazards regression modeling. The method was applied to multi-omics data from the CoMMpass study of multiple myeloma and ten major cancers in The Cancer Genome Atlas (TCGA). In most experiments, our method showed superior predictive performance compared to other alternative methods.

Discrete Ricci curvatures capture age-related changes in human brain functional connectivity networks

Introduction

Geometry-inspired notions of discrete Ricci curvature have been successfully used as markers of disrupted brain connectivity in neuropsychiatric disorders, but their ability to characterize age-related changes in functional connectivity is unexplored.

Methods

We apply Forman-Ricci curvature and Ollivier-Ricci curvature to compare functional connectivity networks of healthy young and older subjects from the Max Planck Institute Leipzig Study for Mind-Body-Emotion Interactions (MPI-LEMON) dataset (N = 225).

Results

We found that both Forman-Ricci curvature and Ollivier-Ricci curvature can capture whole-brain and region-level age-related differences in functional connectivity. Meta-analysis decoding demonstrated that those brain regions with age-related curvature differences were associated with cognitive domains known to manifest age-related changes-movement, affective processing, and somatosensory processing. Moreover, the curvature values of some brain regions showing age-related differences exhibited correlations with behavioral scores of affective processing. Finally, we found an overlap between brain regions showing age-related curvature differences and those brain regions whose non-invasive stimulation resulted in improved movement performance in older adults.

Discussion

Our results suggest that both Forman-Ricci curvature and Ollivier-Ricci curvature correctly identify brain regions that are known to be functionally or clinically relevant. Our results add to a growing body of evidence demonstrating the sensitivity of discrete Ricci curvature measures to changes in the organization of functional connectivity networks, both in health and disease.

Robustness of Brain Structural Networks Is Affected in Cognitively Impaired MS Patients

The robustness of brain structural networks, estimated from diffusion MRI data, may be relevant to cognition. We investigate whether measures of network robustness, such as Ollivier-Ricci curvature, can explain cognitive impairment in multiple sclerosis (MS). We assessed whether local (i.e., cortical area) and/or global (i.e., whole brain) robustness, differs between cognitively impaired (MSCI) and non-impaired (MSNI) MS patients. Fifty patients, with Expanded Disability Status Scale mean (m): 3.2, disease duration m: 12 years, and age m: 40 years, were enrolled. Cognitive impairment scores were estimated from the Minimal Assessment of Cognitive Function in Multiple Sclerosis. Images were obtained in a 3T MRI using a diffusion protocol with a 2 min acquisition time. Brain structural networks were created using 333 cortical areas. Local and global robustness was estimated for each individual, and comparisons were performed between MSCI and MSNI patients. 31 MSCI and 10 MSNI patients were included in the analyses. Brain structural network robustness and centrality showed significant correlations with cognitive impairment. Measures of network robustness and centrality identified specific cortical areas relevant to MS-related cognitive impairment. These measures can be obtained on clinical scanners and are succinct yet accurate potential biomarkers of cognitive impairment.