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- Title
A Scale-Free Structure Prior for Graphical Models with Applications in Functional Genomics.
- Authors
Sheridan, Paul; Kamimura, Takeshi; Shimodaira, Hidetoshi
- 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, P(k) of nodes in a network with degree k is roughly described by a power-law P(k)∝k-γ with exponent γ between 2 and 3. 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.
- Subjects
GRAPHICAL modeling (Statistics); FUNCTIONAL genomics; GENETIC regulation; BAYESIAN analysis; GENE expression; DISTRIBUTION (Probability theory); BREAST cancer; GRAPHIC methods for multivariate analysis; MATHEMATICAL models
- Publication
PLoS ONE, 2010, Vol 5, Issue 11, p1
- ISSN
1932-6203
- Publication type
Article
- DOI
10.1371/journal.pone.0013580