Abstract
We introduce a novel algorithm for inference of causal gene interactions, termed CaSPIAN (Causal Subspace Pursuit for Inference and Analysis of Networks), which is based on coupling compressive sensing and Granger causality techniques. The core of the approach is to discover sparse linear dependencies between shifted time series of gene expressions using a sequential list-version of the subspace pursuit reconstruction algorithm and to estimate the direction of gene interactions via Granger-type elimination. The method is conceptually simple and computationally efficient, and it allows for dealing with noisy measurements. Its performance as a stand-alone platform without biological side-information was tested on simulated networks, on the synthetic IRMA network in Saccharomyces cerevisiae, and on data pertaining to the human HeLa cell network and the SOS network in E. coli. The results produced by CaSPIAN are compared to the results of several related algorithms, demonstrating significant improvements in inference accuracy of documented interactions. These findings highlight the importance of Granger causality techniques for reducing the number of false-positives, as well as the influence of noise and sampling period on the accuracy of the estimates. In addition, the performance of the method was tested in conjunction with biological side information of the form of sparse “scaffold networks”, to which new edges were added using available RNA-seq or microarray data. These biological priors aid in increasing the sensitivity and precision of the algorithm in the small sample regime.
Highlights
One of the unresolved open problems in systems biology is discovering causal relationships among different components of biological systems
We evaluated the performance of the proposed algorithms with respect to the choice of different parameters such as the sparsity level k, the significance value PF, the topology of network, the noise level, and the time-point sampling method
[42] and [43] employ the Compressive sensing (CS) framework to infer gene networks, there are crucial differences between CaSPIAN and the algorithms discussed in these papers
Summary
One of the unresolved open problems in systems biology is discovering causal relationships among different components of biological systems. Discovering causal relationships through experiments is a daunting task due to the technical precision and output volumes required from the experiments and due to the large number of interconnected and dynamically varying components of the system. It is of great importance to develop a precise analytical framework for quantifying causal connections between genes in order to elucidate the gene interactome based on limited and noisy experimental data. To date most reverse engineering algorithms have offered very few reliable outcomes for even moderately sized networks and were hardly ever experimentally tested – these and other shortcomings of existing inference techniques and models were described in detail in [3]. Algorithmic developments are focusing on small network components of prokaryotic or simple eukaryotic cell lines and on the more conservative – yet reliable – task of identifying a small number of highly accurate causal links
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