Reconstruction of gene regulatory networks for Caenorhabditis elegans using tree-shaped gene expression data

Abstract

Constructing gene regulatory networks is a widely adopted approach for investigating gene regulation, offering diverse applications in biology and medicine. A great deal of research focuses on using time series data or single-cell RNA-sequencing data to infer gene regulatory networks. However, such gene expression data lack either cellular or temporal information. Fortunately, the advent of time-lapse confocal laser microscopy enables biologists to obtain tree-shaped gene expression data of Caenorhabditis elegans, achieving both cellular and temporal resolution. Although such tree-shaped data provide abundant knowledge, they pose challenges like non-pairwise time series, laying the inaccuracy of downstream analysis. To address this issue, a comprehensive framework for data integration and a novel Bayesian approach based on Boolean network with time delay are proposed. The pre-screening process and Markov Chain Monte Carlo algorithm are applied to obtain the parameter estimates. Simulation studies show that our method outperforms existing Boolean network inference algorithms. Leveraging the proposed approach, gene regulatory networks for five subtrees are reconstructed based on the real tree-shaped datatsets of Caenorhabditis elegans, where some gene regulatory relationships confirmed in previous genetic studies are recovered. Also, heterogeneity of regulatory relationships in different cell lineage subtrees is detected. Furthermore, the exploration of potential gene regulatory relationships that bear importance in human diseases is undertaken. All source code is available at the GitHub repository https://github.com/edawu11/BBTD.git.

Keywords: Bayesian statistics; Boolean network; data integration; gene regulatory network; tree-shaped gene expression data.

Figure 1

Comparison of two cell lineage subtrees; the figure shows a part of two cell lineage subtrees, which are, respectively, derived from two real data files: CD20060629_pha4_b2.csv and CD20081014_ref-1_2_L1.csv; both subtrees start from ‘Ea’ cell at time zero; the length of each vertical line corresponds to the lifetime of a single cell; each horizontal line represents an event of cell division; the color of lines corresponds to the fluorescent intensity of two labeled gene: pha-4 and ref-1; the cell names are from [9], which are signed on the right side of each vertical line.

Figure 2

A four-step process of data integration for each cell lineage subtree; Step 1: normalize the lifetime of each cell to a standardized unit; Step 2: compute the first-order difference of the raw data and interpolate them for each cell to the same number; Step 3: discretize the expression rates into binary values; Step 4: merge the multiple copies of the same gene.

Figure 3

An example of the probabilistic Boolean network model with time delay; (a) depicts a 5-gene GRN; each node corresponds to a gene, and the regulatory relationships are illustrated by solid deep green arrows (indicating positive regulations) and dashed orange arrows (indicating negative regulations); (b) presents the matrix corresponding to the GRN representation in (a); a deep green grid signifies , an orange grid represents , and a white grid represents ; (c) demonstrates the state transition process of the 5-gene GRN; the gray circle represents an active state of the gene, while the white circle represents an inactive state; specifically, (c) illustrates the regulatory mechanism governing the gene states at time with different time delay as an example.

Figure 4

Performance of synthesized data with difference methods: BBTD, BB, BFE, and ATEN; the figure shows the comparisons of average TPR and average PPR for five synthesized subtrees.

Figure 5

The inferred GRNs of the five cell lineage subtrees: ‘AB’, ‘C’, ‘D’, ‘E’, and ‘MS’; sub-figures (a) to (e) illustrate the GRNs of these subtrees in sequential order; each solid circle in the inferred GRN represents a gene; the presence of a solid (dashed) arrow indicates a positive (negative) regulatory relationship extending from regulator genes to regulated ones; the color of the arrow corresponds to the respective time delay associated with the regulatory relationship.