title: A scale-free structure prior for graphical models with applications in functional genomics.
abstract: The problem of reconstructing large-scale, gene regulatory networks from gene expression data has garnered considerable attention in bioinformatics over the past decade with the graphical modeling paradigm having emerged as a popular framework for inference. Analysis in a full Bayesian setting is contingent upon the assignment of a so-called structure prior-a probability distribution on networks, encoding a priori biological knowledge either in the form of supplemental data or high-level topological features. A key topological consideration is that a wide range of cellular networks are approximately scale-free, meaning that the fraction, , of nodes in a network with degree is roughly described by a power-law with exponent between and . The standard practice, however, is to utilize a random structure prior, which favors networks with binomially distributed degree distributions. In this paper, we introduce a scale-free structure prior for graphical models based on the formula for the probability of a network under a simple scale-free network model. Unlike the random structure prior, its scale-free counterpart requires a node labeling as a parameter. In order to use this prior for large-scale network inference, we design a novel Metropolis-Hastings sampler for graphical models that includes a node labeling as a state space variable. In a simulation study, we demonstrate that the scale-free structure prior outperforms the random structure prior at recovering scale-free networks while at the same time retains the ability to recover random networks. We then estimate a gene association network from gene expression data taken from a breast cancer tumor study, showing that scale-free structure prior recovers hubs, including the previously unknown hub SLC39A6, which is a zinc transporter that has been implicated with the spread of breast cancer to the lymph nodes. Our analysis of the breast cancer expression data underscores the value of the scale-free structure prior as an instrument to aid in the identification of candidate hub genes with the potential to direct the hypotheses of molecular biologists, and thus drive future experiments.
authors.affiliation: Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan. sherida6@is.titech.ac.jp
authors.forename: Paul
authors.initials: P
authors.lastname: Sheridan
authors.forename: Takeshi
authors.initials: T
authors.lastname: Kamimura
authors.forename: Hidetoshi
authors.initials: H
authors.lastname: Shimodaira
mesh_terms: D000465:Algorithms; D001943:Breast Neoplasms / Q000235:genetics / Q000473:pathology; D027682:Cation Transport Proteins / Q000235:genetics; D003198:Computer Simulation; D005260:Female; D020869:Gene Expression Profiling; D053263:Gene Regulatory Networks; D023281:Genomics / Q000379:methods*; D006801:Humans; D008207:Lymphatic Metastasis; D008957:Models, Genetic; D009363:Neoplasm Proteins / Q000235:genetics
chemical_list: D027682:Cation Transport Proteins; D009363:Neoplasm Proteins; C418627:SLC39A6 protein, human