Modeling And Estimation Of Dynamic Gene Regulatory Network Based On Functional Convolution Model

The research on gene regulatory network is of great significance to reveal the life activities and the evolution of diseases,and it is one of the hottest research topics in the field of bioinformatics.At present,many studies have focused on the static gene network assuming that the regulation is constant and does not change with time.However,in practice,gene regulation often changes with time or environment,and there is a time lag effect in gene regulation,that is,the expression level of one gene is affected by the historical expression level of other genes.In addition,the highdimensional characteristics of gene data make gene network modeling very challenging.In this paper,we try to model and estimate the dynamic gene regulation network based on functional data and consider time lag effect at the same time.Firstly,a series of functional convolution models with time delay term are used to model the dynamic process of regulation,and the nonparametric method is used to estimate coefficient functions.The functional convolution model not only allows coefficient functions to change with time(if the regulation does not exist,the coefficient function will be compressed to 0),but also can flexibly consider the time lag effect of the regulation.The functional SCAD method is introduced to estimate the directed dynamic regulation network with dual sparsity of both time and variables.By penalizing coefficient function on the subdivisions of the support set,we can not only obtain the smooth estimation of coefficient functions using functional SCAD,but also identify the time intervals in which the regulation does exist,as well as realizing variable selection.Through a large number of simulations,this paper verifies that the functional convolution model combined with functional SCAD method can pick out the real regulatory variables and estimate coefficient functions accurately.The more observation points of a single gene curve,the more accurate the model estimation results and the narrower the confidence band,which also shows that the estimators are consistent.In the real data analysis,we first uses the clustering method based on functional principal component to cluster Drosophila gene data into 23 clusters.The expression levels of genes in the same cluster,which is called coexpressive gene,are similar and the cluster composed of coexpressive genes is called functional module.Finally,the functional convolution model is used to model the dynamic regulation process between different functional gene modules and the mutual regulation relationship between different functional gene modules is found.