Inference of gene regulatory networks from time series by Tsallis entropy

Fabrício Martins Lopes,Evaldo A De Oliveira,Roberto M Cesar

doi:10.1186/1752-0509-5-61

Fabrício Martins Lopes, Evaldo A De Oliveira + Show 1 more

Open Access

https://doi.org/10.1186/1752-0509-5-61

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Journal: BMC systems biology	Publication Date: May 5, 2011
Citations: 91	License type: CC BY 2.0

Abstract

BackgroundThe inference of gene regulatory networks (GRNs) from large-scale expression profiles is one of the most challenging problems of Systems Biology nowadays. Many techniques and models have been proposed for this task. However, it is not generally possible to recover the original topology with great accuracy, mainly due to the short time series data in face of the high complexity of the networks and the intrinsic noise of the expression measurements. In order to improve the accuracy of GRNs inference methods based on entropy (mutual information), a new criterion function is here proposed.ResultsIn this paper we introduce the use of generalized entropy proposed by Tsallis, for the inference of GRNs from time series expression profiles. The inference process is based on a feature selection approach and the conditional entropy is applied as criterion function. In order to assess the proposed methodology, the algorithm is applied to recover the network topology from temporal expressions generated by an artificial gene network (AGN) model as well as from the DREAM challenge. The adopted AGN is based on theoretical models of complex networks and its gene transference function is obtained from random drawing on the set of possible Boolean functions, thus creating its dynamics. On the other hand, DREAM time series data presents variation of network size and its topologies are based on real networks. The dynamics are generated by continuous differential equations with noise and perturbation. By adopting both data sources, it is possible to estimate the average quality of the inference with respect to different network topologies, transfer functions and network sizes.ConclusionsA remarkable improvement of accuracy was observed in the experimental results by reducing the number of false connections in the inferred topology by the non-Shannon entropy. The obtained best free parameter of the Tsallis entropy was on average in the range 2.5 ≤ q ≤ 3.5 (hence, subextensive entropy), which opens new perspectives for GRNs inference methods based on information theory and for investigation of the nonextensivity of such networks. The inference algorithm and criterion function proposed here were implemented and included in the DimReduction software, which is freely available at http://sourceforge.net/projects/dimreduction and http://code.google.com/p/dimreduction/.

Highlights

The inference of gene regulatory networks (GRNs) from large-scale expression profiles is one of the most challenging problems of Systems Biology nowadays
2.1 Experiments In order to verify the effect of the entropic parameter q, we carried out inference experiments considering two types of network topologies: the uniformly-random Erdös-Rényi (ER) and the scale-free Barabási-Albert (BA) models [23,24,25]
The present work opens new perspectives for methods based on information theory, in face of all results discussed which show a relevant improvement on the inference accuracy by adopting nonextensive entropies proposed by Tsallis

Summary

Introduction

The inference of gene regulatory networks (GRNs) from large-scale expression profiles is one of the most challenging problems of Systems Biology nowadays. Gene regulatory networks (GRNs) are used to indicate the interrelation among genes in the genomic level [2] Such information is very important for disease treatment design, drugs creation purposes and to understand the activity of living organisms in the molecular level. The development of techniques for sampling expression levels of genes along time has increased the possibility of important advances in the understanding of regulatory mechanisms of gene transcription and protein synthesis. In this context, an important task is the study and identification of high-level properties of gene networks and their interactions, without the necessity of low-level biochemical descriptions. The objective is to recover the gene connections in a global and simple way, by identifying the most significant connections (relationships)

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