Network inference of pal-1 lineage-specific regulation in the C. elegans embryo by structural equation modeling

Abstract

The elucidation of spatial and temporal control during developmental stages is one of the central tasks for systems biology, and a variety of intracellular factors are known as regulators for specific gene expression. The activity information of those various factors is not directly reflected in their gene expression profiles. Hence, a method based on Structural Equation Modeling (SEM) is described. SEM can include the latent variables within the constructed model and infer the relationships among latent and observed variables, as a network model. An improved SEM approach for the construction of an optimal model is applied to infer the regulatory network for the determination of C lineage fate in C. elegans development. The inferred network model shows that the 13 analysed transcription factor genes were regulated by several other factors in addition to pal-1 expression. The other regulatory factors are those involved in protein accumulation and localization as important regulatory factors for normal development. Those regulatory factors were regulated sequentially in the network model. The regulation of the known pal-1 regulated genes was dependent on this sequential control of the regulatory factors. The interpretation of the network model shows insights to the complex regulation occurring during the C lineage determination by pal-1.

Keywords: Developmental Control; Embryo; Gene Network; Structural Equation Modeling.

Figure 1

Inferred network model of pal-1 regulation. The estimated network structure of the pal-1 regulatory system shows for lineage-specific differentiation. Genes, which are observed variables, are displayed as rectangles, and estimated regulatory factors, which are latent variables, are displayed as circles. Arrows show the causal relationships among the variables in the model. Error terms are omitted in this figure, but all error terms were calculated by SEM. The relationships between the errors are considered to represent other regulatory systems in the cell. For simplicity, these relationships are not shown. (a) Network model between genes and regulatory factors; (b) Relationships between pal-1-dependent genes. Each gene is classified by its regulatory factor, shown on the left side; (c) Goodness-of-fit scores. The calculations for these scores included the relationships between errors. Four criteria were mainly used: GFI>0.90, AGFI>0.90, CFI >0.90 and RMSEA<0.05. All four scores indicated that the model fit the measured data well.

Figure 2

Biological interpretation of the inferred model. Biological interpretations of regulatory factors are expressed within the network. All genes are displayed as rectangles, and the color of the gene name indicates the detected cell type or developmental phase in embryogenesis: Green: Early embryo, Red: Muscle cell, Blue: Epidermal cell and Black: Both muscle and epidermal cells. The pal-1 rectangle indicates the quantity of pal-1 mRNA, and thus the first regulatory factor is considered to be the pal-1 protein. From the sequential regulation of the regulatory factors, all factors and relationships were interpreted.