SigFlux: a novel network feature to evaluate the importance of proteins in signal transduction networks

Abstract

Background: Measuring each protein's importance in signaling networks helps to identify the crucial proteins in a cellular process, find the fragile portion of the biology system and further assist for disease therapy. However, there are relatively few methods to evaluate the importance of proteins in signaling networks.

Results: We developed a novel network feature to evaluate the importance of proteins in signal transduction networks, that we call SigFlux, based on the concept of minimal path sets (MPSs). An MPS is a minimal set of nodes that can perform the signal propagation from ligands to target genes or feedback loops. We define SigFlux as the number of MPSs in which each protein is involved. We applied this network feature to the large signal transduction network in the hippocampal CA1 neuron of mice. Significant correlations were simultaneously observed between SigFlux and both the essentiality and evolutionary rate of genes. Compared with another commonly used network feature, connectivity, SigFlux has similar or better ability as connectivity to reflect a protein's essentiality. Further classification according to protein function demonstrates that high SigFlux, low connectivity proteins are abundant in receptors and transcriptional factors, indicating that SigFlux candescribe the importance of proteins within the context of the entire network.

Conclusion: SigFlux is a useful network feature in signal transduction networks that allows the prediction of the essentiality and conservation of proteins. With this novel network feature, proteins that participate in more pathways or feedback loops within a signaling network are proved far more likely to be essential and conserved during evolution than their counterparts.

Figure 1

SigFlux, connectivity and the clustering coefficient of mouse proteins in different phenotype groups. Mutant phenotypes of genes in mouse are grouped into the following 3 categories: group 1 corresponds to no obvious phenotype, group 2 is a viable phenotype, and group 3 is a lethal phenotype, as shown on the x-axis. The median and standard deviation of SigFlux, connectivity and the clustering coefficient in different groups are shown on the y-axis, respectively. (a) A positive correlation exists between SigFlux and essentiality. (b) A positive correlation exists between connectivity and essentiality. (c) No obvious correlation exists between the clustering coefficient and essentiality.

Figure 2

SigFlux is plotted as a function of connectivity. High-SigFlux is assigned to proteins with above average SigFlux value, otherwise low-SigFlux. High-connectivity and low-connectivity proteins are defined in the same way. Region A includes all high-SigFlux, low-connectivity proteins, Region B high-SigFlux, high-connectivity proteins, Region C low-SigFlux, low-connectivity proteins, and Region D low-SigFlux, high-connectivity proteins.

Figure 3

The distribution of SigFlux follows a power law. The value of SigFlux is divided into ten equal sections, and the number of proteins whose SigFlux locate in each section is counted. The distribution of SigFlux follows a power law, with P(SigFlux) ~ SigFlux^-γ, γ = 2.72 ± 0.16 (p = 1.34 × 10^-7).

Figure 4

Proteins are classified according to their function in the signaling network. All proteins are classified according to their function in the signaling network as shown in (a), and HSLC proteins as shown in (b). Corresponding hypergeometric p-values of receptors and transcriptional factors are 4.486 × 10^-5 and 5.317 × 10^-6, respectively. The result shows that HSLC proteins are abundant in receptors and transcriptional factors.

Figure 5

A simple example is shown to illustrate how breadth-first search method works. Given a network G, first label all the nodes of G and get its parent index. Then generate paths starting from a root node. The nodes with shorter distance to the root node are explored preferentially. Paths starting from root to target are returned when all the nodes are visited. In the network below, take A as the root node and E, F as target nodes. The resulting path sets are {A,B,E}, {A,C,E}, {A,B,C,E}, {A,C,F}, {A,D,F}, {A,C,D,F}, {A,B,C,F} and {A, B,C,D,F}.