An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series

Abstract Motivation Gene regulatory networks (GRNs) capture the regulatory interactions between genes, resulting from the fundamental biological process of transcription and translation. In some cases, the topology of GRNs is not known, and has to be inferred from gene expression data. Most of the existing GRNs reconstruction algorithms are either applied to time-series data or steady-state data. Although time-series data include more information about the system dynamics, steady-state data imply stability of the underlying regulatory networks. Results In this article, we propose a method for inferring GRNs from time-series and steady-state data jointly. We make use of a non-linear ordinary differential equations framework to model dynamic gene regulation and an importance measurement strategy to infer all putative regulatory links efficiently. The proposed method is evaluated extensively on the artificial DREAM4 dataset and two real gene expression datasets of yeast and Escherichia coli. Based on public benchmark datasets, the proposed method outperforms other popular inference algorithms in terms of overall score. By comparing the performance on the datasets with different scales, the results show that our method still keeps good robustness and accuracy at a low computational complexity. Availability and implementation The proposed method is written in the Python language, and is available at: https://github.com/lab319/GRNs_nonlinear_ODEs Supplementary information Supplementary data are available at Bioinformatics online.

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MODELING NONLINEAR GENE REGULATORY NETWORKS FROM TIME SERIES GENE EXPRESSION DATA

Journal of Bioinformatics and Computational Biology ◽

10.1142/s0219720008003746 ◽

2008 ◽

Vol 06 (05) ◽

pp. 961-979 ◽

Cited By ~ 15

Author(s):

ANDRÉ FUJITA ◽

JOÃO RICARDO SATO ◽

HUMBERTO MIGUEL GARAY-MALPARTIDA ◽

MARI CLEIDE SOGAYAR ◽

CARLOS EDUARDO FERREIRA ◽

...

Keyword(s):

Gene Expression ◽

Time Series ◽

Gene Regulatory Networks ◽

Regulatory Networks ◽

Expression Profiles ◽

A Priori ◽

Molecular Networks ◽

Biological Knowledge ◽

Vector Autoregressive ◽

Gene Regulatory

In cells, molecular networks such as gene regulatory networks are the basis of biological complexity. Therefore, gene regulatory networks have become the core of research in systems biology. Understanding the processes underlying the several extracellular regulators, signal transduction, protein–protein interactions, and differential gene expression processes requires detailed molecular description of the protein and gene networks involved. To understand better these complex molecular networks and to infer new regulatory associations, we propose a statistical method based on vector autoregressive models and Granger causality to estimate nonlinear gene regulatory networks from time series microarray data. Most of the models available in the literature assume linearity in the inference of gene connections; moreover, these models do not infer directionality in these connections. Thus, a priori biological knowledge is required. However, in pathological cases, no a priori biological information is available. To overcome these problems, we present the nonlinear vector autoregressive (NVAR) model. We have applied the NVAR model to estimate nonlinear gene regulatory networks based entirely on gene expression profiles obtained from DNA microarray experiments. We show the results obtained by NVAR through several simulations and by the construction of three actual gene regulatory networks (p53, NF-κB, and c-Myc) for HeLa cells.

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