Functional data analysis of the dynamics of gene regulatory networks

A new method for constructing gene networks from microarray time-series gene expression data is proposed in the context of Bayesian network approach. An essential point of Bayesian network modeling is the construction of the conditional distribution of each random variable. When estimating the conditional distributions from gene expression data, a common problem is that gene expression data contain multiple missing values. Unfortunately, many methods for constructing conditional distributions require a complete gene expression value and may lose effectiveness even with a few missing value. Additionally, they treat microarray time-series gene expression data as static data, although time can be an important factor that affects the gene expression levels. We overcome these difficulties by using the method of functional data analysis. The proposed network construction method consists of two stages. Firstly, discrete microarray time-series gene expression values are expressed as a continuous curve of time. To account for the time dependency of gene expression measurements and the noisy nature of the microarray data, P-spline nonlinear regression models are utilized. After this preprocessing step, the conditional distribution of each random variable is constructed based on functional linear regression models. The effectiveness of the proposed method is investigated through Monte Carlo simulations and the analysis of Saccharomyces cerevisiae gene expression data.