Model selection for factorial Gaussian graphical models with an application to dynamic regulatory networks

Data-driven dynamical modelling of a pathogen-infected plant gene regulatory network: A comparative analysis

Recent advances in synthetic biology have enabled the design of genetic feedback control circuits that could be implemented to build resilient plants against pathogen attacks. To facilitate the proper design of these genetic feedback control circuits, an accurate model that is able to capture the vital dynamical behaviour of the pathogen-infected plant is required. In this study, using a data-driven modelling approach, we develop and compare four dynamical models (i.e. linear, Michaelis-Menten with Hill coefficient (Hill Function), standard S-System and extended S-System) of a pathogen-infected plant gene regulatory network (GRN). These models are then assessed across several criteria, i.e. ease of identifying the type of gene regulation, the predictive capability, Akaike Information Criterion (AIC) and the robustness to parameter uncertainty to determine its viability of balancing between biological complexity and accuracy when modelling the pathogen-infected plant GRN. Using our defined ranking score, we obtain the following insights to the modelling of GRN. Our analyses show that despite commonly used and provide biological relevance, the Hill Function model ranks the lowest while the extended S-System model ranks highest in the overall comparison. Interestingly, the performance of the linear model is more consistent throughout the comparison, making it the preferred model for this pathogen-infected plant GRN when considering data-driven modelling approach.

ℓ 1-Penalized censored Gaussian graphical model

Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this estimator theoretically unfounded, even when the assumption of a multivariate Gaussian distribution is satisfied. Typical examples are data generated by polymerase chain reactions and flow cytometer. The combination of censoring and high-dimensionality make inference of the underlying genetic networks from these data very challenging. In this article, we propose an $\ell_1$-penalized Gaussian graphical model for censored data and derive two EM-like algorithms for inference. We evaluate the computational efficiency of the proposed algorithms by an extensive simulation study and show that, when censored data are available, our proposal is superior to existing competitors both in terms of network recovery and parameter estimation. We apply the proposed method to gene expression data generated by microfluidic Reverse Transcription quantitative Polymerase Chain Reaction technology in order to make inference on the regulatory mechanisms of blood development. A software implementation of our method is available on github (https://github.com/LuigiAugugliaro/cglasso).

Gene Regulatory Network Inference from Single-Cell Data Using Multivariate Information Measures

While single-cell gene expression experiments present new challenges for data processing, the cell-to-cell variability observed also reveals statistical relationships that can be used by information theory. Here, we use multivariate information theory to explore the statistical dependencies between triplets of genes in single-cell gene expression datasets. We develop PIDC, a fast, efficient algorithm that uses partial information decomposition (PID) to identify regulatory relationships between genes. We thoroughly evaluate the performance of our algorithm and demonstrate that the higher-order information captured by PIDC allows it to outperform pairwise mutual information-based algorithms when recovering true relationships present in simulated data. We also infer gene regulatory networks from three experimental single-cell datasets and illustrate how network context, choices made during analysis, and sources of variability affect network inference. PIDC tutorials and open-source software for estimating PID are available. PIDC should facilitate the identification of putative functional relationships and mechanistic hypotheses from single-cell transcriptomic data.

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PIDC infers gene regulatory networks from single-cell transcriptomic data

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Multivariate information measures and context in PIDC improve network inference

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Heterogeneity in single-cell data carries information about gene-gene interactions

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Fast, efficient, open-source software is made freely available

A Penalized Likelihood Framework for High-Dimensional Phylogenetic Comparative Methods and an Application to New-World Monkeys Brain Evolution

Working with high-dimensional phylogenetic comparative data sets is challenging because likelihood-based multivariate methods suffer from low statistical performances as the number of traits $p $ approaches the number of species $n $ and because some computational complications occur when $p $ exceeds $n$. Alternative phylogenetic comparative methods have recently been proposed to deal with the large $p $ small $n $ scenario but their use and performances are limited. Herein, we develop a penalized likelihood (PL) framework to deal with high-dimensional comparative data sets. We propose various penalizations and methods for selecting the intensity of the penalties. We apply this general framework to the estimation of parameters (the evolutionary trait covariance matrix and parameters of the evolutionary model) and model comparison for the high-dimensional multivariate Brownian motion (BM), Early-burst (EB), Ornstein-Uhlenbeck (OU), and Pagel's lambda models. We show using simulations that our PL approach dramatically improves the estimation of evolutionary trait covariance matrices and model parameters when $p$ approaches $n$, and allows for their accurate estimation when $p$ equals or exceeds $n$. In addition, we show that PL models can be efficiently compared using generalized information criterion (GIC). We implement these methods, as well as the related estimation of ancestral states and the computation of phylogenetic principal component analysis in the R package RPANDA and mvMORPH. Finally, we illustrate the utility of the new proposed framework by evaluating evolutionary models fit, analyzing integration patterns, and reconstructing evolutionary trajectories for a high-dimensional 3D data set of brain shape in the New World monkeys. We find a clear support for an EB model suggesting an early diversification of brain morphology during the ecological radiation of the clade. PL offers an efficient way to deal with high-dimensional multivariate comparative data.