Modeling Genome-Wide Dynamic Regulatory Network in Mouse Lungs with Influenza Infection Using High- Dimensional Ordinary Differential Equations Shuang Wu . , Zhi-Ping Liu . , Xing Qiu, Hulin Wu* Department of Biostatistics and Computational Biology, University of Rochester, Rochester, New York, United States of America Abstract The immune response to viral infection is regulated by an intricate network of many genes and their products. The reverse engineering of gene regulatory networks (GRNs) using mathematical models from time course gene expression data collected after influenza infection is key to our understanding of the mechanisms involved in controlling influenza infection within a host. A five-step pipeline: detection of temporally differentially expressed genes, clustering genes into co-expressed modules, identification of network structure, parameter estimate refinement, and functional enrichment analysis, is developed for reconstructing high-dimensional dynamic GRNs from genome-wide time course gene expression data. Applying the pipeline to the time course gene expression data from influenza-infected mouse lungs, we have identified 20 distinct temporal expression patterns in the differentially expressed genes and constructed a module-based dynamic network using a linear ODE model. Both intra-module and inter-module annotations and regulatory relationships of our inferred network show some interesting findings and are highly consistent with existing knowledge about the immune response in mice after influenza infection. The proposed method is a computationally efficient, data-driven pipeline bridging experimental data, mathematical modeling, and statistical analysis. The application to the influenza infection data elucidates the potentials of our pipeline in providing valuable insights into systematic modeling of complicated biological processes. Citation: Wu S, Liu Z-P, Qiu X, Wu H (2014) Modeling Genome-Wide Dynamic Regulatory Network in Mouse Lungs with Influenza Infection Using High- Dimensional Ordinary Differential Equations. PLoS ONE 9(5): e95276. doi:10.1371/journal.pone.0095276 Editor: Alberto de la Fuente, Leibniz-Institute for Farm Animal Biology (FBN), Germany Received September 29, 2013; Accepted March 26, 2014; Published May 6, 2014 Copyright: ß 2014 Wu et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This research was partially supported by the NIH grants HHSN272201000055C, AI087135; the University of Rochester CTSI pilot award (UL1RR024160) from the National Center For Research Resources; and Award Number UL1TR000042 from the National Center for Advancing Translational Sciences of the National Institutes of Health. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: Hulin_Wu@urmc.rochester.edu . These authors contributed equally to this work. Introduction Influenza A virus is an important respiratory pathogen that poses a considerable threat to public health each year during seasonal epidemics and even more so when a pandemic strain emerges. The immune response to viral infection is a dynamic process and is regulated by an intricate network of many genes and their products. Understanding the dynamics of this network will shed light on the mechanisms involved in controlling influenza infection within a host and is also important for developing new and effective treatment strategies. Recently, several studies have been performed to monitor the within host genome-wide expression patterns of immune responses over time to influenza infection [1,2]. Analyzing such time course gene expression data requires the use of advanced statistical and computational approaches developed specifically for time series data instead of the standard methods for the traditional snap-shot or vector expression data. In particular, reverse engineering the gene regulatory networks (GRNs) from the time course expression data using mathematical models, especially dynamic network models, is of increasing research interest. In this paper, we will use a high- dimensional ordinary differential equation (ODE) model to construct the genome-wide dynamic GRN of influenza infected mouse lungs. This model will provide quantitative measures of the global response of the immune system to influenza infection in vivo and also help us better understand the virus-mediated immuno- pathology in a systematic way. Previously developed computational approaches for inferring GRNs from gene expression data are either not efficient in describing dynamic regulations between genes or restricted to small-scale networks. For example, information theory models [3– 5] are basically correlation networks. They are simple and easy to compute, but they are static models and do not take into account that multiple genes could co-regulate a target gene. Boolean networks [6–9] are discrete dynamic networks in which the state of a gene is represented by a binary variable that is either on or off. Such models are limited because the continuous nature of gene expressions cannot be described adequately by only two states. Bayesian networks (BNs) [10–16] make use of the Bayesian rule and provide a flexible framework for combining different types of data and prior knowledge. Time course data can be used to reconstruct dynamic BNs [13,15], but the optimization of the network usually requires very high computational cost, so the applications are mostly limited to small systems. The vector autoregressive (VAR) and state space models (SSM) models are PLOS ONE | www.plosone.org 1 May 2014 | Volume 9 | Issue 5 | e95276