Introduction | | | Supplementary Data
version 1.0 (4/26/2010)
with sample data (172k)
Introduction   Top

A gene regulatory relation often changes over time rather than being constant. But many gene regulatory networks available in databases or literatures are static in the sense that they are either snapshots of gene regulatory relations at a time point or union of successive gene regulations over time. Such static networks cannot represent temporal aspects of gene regulatory interactions such as the order of gene regulations or the pace of gene regulations.

We have developed GeneNetFinder to qualitatively infer dynamic gene regulatory interactions from gene expression data. From the time-series data of gene expression, GeneNetFinder identifies not only gene regulatory interactions but also the temporal aspects of the regulatory interactions using two types of scores, R1 and R2. As for the temporal aspect of gene regulatory relations, it identifies the order of the gene regulatory relations and the pace of the relations. The identified gene regulatory interactions and their temporal aspects are stored in the regulation list and visualized as a gene regulatory network. In the network visualized, gene regulations and their temporal aspects are represented by edge types and edge labels.

Identification of gene regulations   Top

The regulatory interactions between genes are identified using two scores: R1 and R2. The regulatory relation between two genes is first evaluated using R1(X; Y; i; p) in Equation 1. R1 represents the correlation between gene X at time point i and gene Y at time point i + p. p is the time span of the gene regulation.

[Equation (1) for the R1 score]

In Equation 1, N is the total number of time points contained in the time span, Xk and Yk are the expression levels of genes X and Y at time k, and X and Y are the average gene expression levels at all time points of the time span. Among the total i X p candidate regulations, the regulation with the maximum absolute value of R1(X; Y; i; p) is selected as the regulatory relation between genes X and Y .

The R1 score of each gene regulation is iteratively calculated using Algorithm 1. For genes A and B, the regulation with the largest absolute R1 score is chosen for the regulation between the genes and represented as R1(A; B; t1; p) with t2 = t1 + p.

After we construct a regulation list, we compute the R2 score for the gene pairs in the regulation list to distinguish the gene regulatory relations with the same correlation but different gene expression levels. R2 is basically the Euclidean distance of the expression levels of the two genes.

where, [Equation (2) for the R2 score]

In Equation 2, X and Y are the average gene expression levels at all time points in the time span. Xmax is the maximum gene expression value of gene X. Ymax and Ymin are the maximum and minimum gene expression value of gene Y , respectively.

When computing the R2 score in a time span, the time span is divided into smaller sub-timespans as follows. The R2 score is not computed for sub-timespans with less than 6 time points.

1. A time point with the minimum expression level of the regulator gene becomes a splitting point of the time span.

2. Each sub-timespan starts with at least 3 consecutive time points that have a positive slope of a curve representing gene expression levels, and ends with at least 3 consecutive time points with a negative slope.

3. Each sub-timespan encompasses at least 6 time points, including the start and ending time points.

Visualization of gene regulatory networks   Top

All gene regulations identified are visualized as a 2-dimensional gene regulatory network, in which a node represents a gene. Edge types and edge labels of the network represent gene regulatory relations. Arrows represent inductive interactions (relations +A(t1) -> +B(t2) and -A(t1) -> +B(t2)) and blocked arrows represent inhibitory interactions (relations +A(t1) -> -B(t2) and -A(t1) -> -B(t2)). The regulator gene, type of regulation (+ for induction and - for inhibition), and time delay of the regulation are annotated as edge labels. Each edge is labeled with R/s/T to indicate a regulator gene R, sign s of the log-ratio of the expression level of R, and the time delay T of the regulation. For visualization of gene regulatory networks, two layout algorithms have been developed: grid layout and layered layout.

Figure 1: Example of grid layout. (A) Node S with the highest degree is place in the center grid, and the nodes connected to S are placed in the adjacent grids in the specified order. (B) Grid drawing by GeneNetFinder.
(A) (B) (C) (D)
Figure 2: Visualization of layered layout in the GeneNetFinder. (A) Put the node with the maximum degree at layer 1. If there is a tie, select a node with a higher out-degree. Assign the nodes connected the nodes at layer i to layer i+1.(B) 3. Repeat steps 1 and 2 for the remaining nodes. (C) If two nodes at the same layer are connected to each other, make a new layer between the layer and the upper layer and move the node with a smaller degree to the new layer (node 4 in C). Nodes with 0 out-degrees (node 1 in C) are also moved to the new layer. (D) Order the nodes in each layer by the Barycenter method to reduce the number of edge crossings

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