The axes of biology: a novel axes-based network embedding paradigm to decipher the functional mechanisms of the cell.

Summary: Common approaches for deciphering biological networks involve network embedding algorithms. These approaches strictly focus on clustering the genes' embedding vectors and interpreting such clusters to reveal the hidden information of the networks. However, the difficulty in interpreting the genes' clusters and the limitations of the functional annotations' resources hinder the identification of the currently unknown cell's functioning mechanisms. We propose a new approach that shifts this functional exploration from the embedding vectors of genes in space to the axes of the space itself. Our methodology better disentangles biological information from the embedding space than the classic gene-centric approach. Moreover, it uncovers new data-driven functional interactions that are unregistered in the functional ontologies, but biologically coherent. Furthermore, we exploit these interactions to define new higher-level annotations that we term Axes-Specific Functional Annotations and validate them through literature curation. Finally, we leverage our methodology to discover evolutionary connections between cellular functions and the evolution of species. Availability and implementation: Data and source code can be accessed at https://gitlab.bsc.es/sdoria/axes-of-biology.git.

A functional analysis of omic network embedding spaces reveals key altered functions in cancer.

MOTIVATION: Advances in omics technologies have revolutionized cancer research by producing massive datasets. Common approaches to deciphering these complex data are by embedding algorithms of molecular interaction networks. These algorithms find a low-dimensional space in which similarities between the network nodes are best preserved. Currently available embedding approaches mine the gene embeddings directly to uncover new cancer-related knowledge. However, these gene-centric approaches produce incomplete knowledge, since they do not account for the functional implications of genomic alterations. We propose a new, function-centric perspective and approach, to complement the knowledge obtained from omic data. RESULTS: We introduce our Functional Mapping Matrix (FMM) to explore the functional organization of different tissue-specific and species-specific embedding spaces generated by a Non-negative Matrix Tri-Factorization algorithm. Also, we use our FMM to define the optimal dimensionality of these molecular interaction network embedding spaces. For this optimal dimensionality, we compare the FMMs of the most prevalent cancers in human to FMMs of their corresponding control tissues. We find that cancer alters the positions in the embedding space of cancer-related functions, while it keeps the positions of the noncancer-related ones. We exploit this spacial 'movement' to predict novel cancer-related functions. Finally, we predict novel cancer-related genes that the currently available methods for gene-centric analyses cannot identify; we validate these predictions by literature curation and retrospective analyses of patient survival data. AVAILABILITY AND IMPLEMENTATION: Data and source code can be accessed at https://github.com/gaiac/FMM.

Probabilistic graphlets capture biological function in probabilistic molecular networks.

MOTIVATION: Molecular interactions have been successfully modeled and analyzed as networks, where nodes represent molecules and edges represent the interactions between them. These networks revealed that molecules with similar local network structure also have similar biological functions. The most sensitive measures of network structure are based on graphlets. However, graphlet-based methods thus far are only applicable to unweighted networks, whereas real-world molecular networks may have weighted edges that can represent the probability of an interaction occurring in the cell. This information is commonly discarded when applying thresholds to generate unweighted networks, which may lead to information loss. RESULTS: We introduce probabilistic graphlets as a tool for analyzing the local wiring patterns of probabilistic networks. To assess their performance compared to unweighted graphlets, we generate synthetic networks based on different well-known random network models and edge probability distributions and demonstrate that probabilistic graphlets outperform their unweighted counterparts in distinguishing network structures. Then we model different real-world molecular interaction networks as weighted graphs with probabilities as weights on edges and we analyze them with our new weighted graphlets-based methods. We show that due to their probabilistic nature, probabilistic graphlet-based methods more robustly capture biological information in these data, while simultaneously showing a higher sensitivity to identify condition-specific functions compared to their unweighted graphlet-based method counterparts. AVAILABILITYAND IMPLEMENTATION: Our implementation of probabilistic graphlets is available at https://github.com/Serdobe/Probabilistic_Graphlets. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.