PKI: A bioinformatics method of quantifying the importance of nodes in gene regulatory network via a pseudo knockout index

Abstract

Background: Gene regulatory network (GRN) is a model that characterizes the complex relationships between genes and thereby provides an informatics environment to measure the importance of nodes. The evaluation of important nodes in a GRN can effectively refer to their functional implications severing as key players in particular biological processes, such as master regulator and driver gene. Currently, it is mainly based on network topological parameters and focuses only on evaluating a single node individually. However, genes and products play their functions by interacting with each other. It is worth noting that the effects of gene combinations in GRN are not simply additive. Key combinations discovery is of significance in revealing gene sets with important functions. Recently, with the development of single-cell RNA-sequencing (scRNA-seq) technology, we can quantify gene expression profiles of individual cells that provide the potential to identify crucial nodes in gene regulations regarding specific condition, e.g., stem cell differentiation.

Results: In this paper, we propose a bioinformatics method, called Pseudo Knockout Importance (PKI), to quantify the importance of node and node sets in a specific GRN structure using time-course scRNA-seq data. First, we construct ordinary differential equations to approach the gene regulations during cell differentiation. Then we design gene pseudo knockout experiments and define PKI score evaluation criteria based on the coefficient of determination. The importance of nodes can be described as the influence on the ODE system of removing variables. For key gene combinations, PKI is derived as a combinatorial optimization problem of quantifying the in silico gene knockout effects.

Conclusions: Here, we focus our analyses on the specific GRN of embryonic stem cells with time series gene expression profile. To verify the effectiveness and advantage of PKI method, we compare its node importance rankings with other twelve kinds of centrality-based methods, such as degree and Latora closeness. For key node combinations, we compare the results with the method based on minimum dominant set. Moreover, the famous combinations of transcription factors in induced pluripotent stem cell are also employed to verify the vital gene combinations identified by PKI. These results demonstrate the reliability and superiority of the proposed method.

Keywords: Embryonic stem cell; Gene importance evaluation; Gene regulatory network; Ordinary differential equation; Pseudo knockout index; Time series scRNA-seq data.