title: Estimating time-varying directed gene regulation networks.
abstract: The problem of modeling the dynamical regulation process within a gene network has been of great interest for a long time. We propose to model this dynamical system with a large number of nonlinear ordinary differential equations (ODEs), in which the regulation function is estimated directly from data without any parametric assumption. Most current research assumes the gene regulation network is static, but in reality, the connection and regulation function of the network may change with time or environment. This change is reflected in our dynamical model by allowing the regulation function varying with the gene expression and forcing this regulation function to be zero if no regulation happens. We introduce a statistical method called functional SCAD to estimate a time-varying sparse and directed gene regulation network, and simultaneously, to provide a smooth estimation of the regulation function and identify the interval in which no regulation effect exists. The finite sample performance of the proposed method is investigated in a Monte Carlo simulation study. Our method is demonstrated by estimating a time-varying directed gene regulation network of 20 genes involved in muscle development during the embryonic stage of Drosophila melanogaster.
authors.affiliation: Department of Statistics and Actuarial Science, Simon Fraser University, British Columbia, Canada.
authors.forename: Yunlong
authors.initials: Y
authors.lastname: Nie
authors.affiliation: Department of Statistics and Actuarial Science, Simon Fraser University, British Columbia, Canada.
authors.forename: LiangLiang
authors.initials: L
authors.lastname: Wang
authors.affiliation: Department of Statistics and Actuarial Science, Simon Fraser University, British Columbia, Canada.
authors.forename: Jiguo
authors.identifier: 0000-0001-7417-6330
authors.initials: J
authors.lastname: Cao
mesh_terms: D000818:Animals; D004331:Drosophila melanogaster / Q000196:embryology; D053263:Gene Regulatory Networks; D009010:Monte Carlo Method; D024510:Muscle Development; D017711:Nonlinear Dynamics; D013997:Time Factors
keywords: Ordinary differential equation; Smoothing spline; Sparse estimation; System identification