Innovations in Biological Network Modeling: Unraveling Omics Data Analysis

Modern RNA sequencing technologies provide gene expression measurements from single cells that promise refined insights on regulatory relationships among genes. Directed graphical models are well-suited to explore such (cause-effect) relationships. However, statistical analyses of single cell data are complicated by the fact that the data often show zero-inflated expression patterns. To address this challenge, we propose directed graphical models that are based on Hurdle conditional distributions parametrized in terms of polynomials in parent variables and their 0/1 indicators of being zero or nonzero. While directed graphs for Gaussian models are only identifiable up to an equivalence class in general, we show that, under a natural and weak assumption, the exact directed acyclic graph of our zero-inflated models can be identified. We propose methods for graph recovery, apply our model to real single-cell RNA-seq data on T helper cells, and show simulated experiments that validate the identifiability and graph estimation methods in practice. 

Single-cell RNA sequencing (scRNA-seq) experiments have become instrumental in developmental and differentiation studies, enabling the profiling of cells at a single or multiple time-points to uncover subtle variations in expression profiles reflecting underlying biological processes. However, researchers encounter routine challenges in their analysis due to uncertainty with respect to selecting the most appropriate methods and parameters. Additionally, trajectory methods' performances are highly dataset-specific. We developed Escort, a novel framework for evaluating a dataset's suitability for trajectory inference and quantifying trajectory-specific properties influenced by analysis decisions. We demonstrate Escort's ability to both alleviate the decision burden inherent to trajectory inference analysis and in obtaining more accurate trajectories based on data-driven evaluations. Escort is implemented in an accessible R package and R/Shiny application, providing researchers with the necessary tools to make informed decisions during trajectory analysis and enabling new insights into dynamic biological processes at single-cell resolution. 

Modern spatial transcriptomic profiling techniques facilitate spatially resolved, high-dimensional assessment of cellular gene transcription across the tumor domain. The characterization of spatially varying gene networks enables the discovery of heterogeneous regulatory patterns and biological mechanisms underlying cancer etiology. We propose a spatial Graphical Regression (sGR) model to infer spatially varying graphs for high-resolution multivariate spatial data. Unlike existing graphical models, sGR explicitly incorporates spatial information to infer non-linear conditional dependencies through Gaussian processes. It conducts sparse estimation and selection of spatially varying edges, at both spatial and sub-spatial levels. Extensive simulation studies illustrate the profitability of sGR for spatial graph structural recovery and estimation accuracy. Our methods are motivated by and applied to two spatial transcriptomics data sets in breast and prostate cancer, to investigate spatially varying gene connectivity patterns across the tumor microenvironment. 

Network theory has proven invaluable in unraveling complex protein interactions. Previous studies have employed statistical methods rooted in network theory, including the Gaussian graphical model, to infer networks among proteins, identifying hub proteins based on key structural properties of networks such as degree centrality. However, there has been limited research examining a prognostic role of hub proteins on outcomes, while adjusting for clinical covariates in the context of high-dimensional data. To address this gap, we propose a network-guided penalized regression method. First, we construct a network using the Gaussian graphical model to identify hub proteins. Next, we preserve these identified hub proteins along with clinically relevant factors, while applying penalization non-hub proteins for variable selection. Our network-guided estimators are shown to have variable selection consistency and asymptotic normality. Simulation results suggest that our method produces better results compared to existing methods and demonstrates promise for advancing biomarker identification in proteomics research. Lastly, we apply our method to the real proteomics data and identified hub proteins that may serve as prognostic biomarkers for various diseases, including rare genetic disorders and immune checkpoint for cancer immunotherapy.