Time lagged information theoretic approaches to the reverse engineering of gene regulatory networks

Background: A number of models and algorithms have been proposed in the past for gene regulatory network (GRN) inference; however, none of them address the effects of the size of time-series microarray expression data in terms of the number of time-points. In this paper, we study this problem by analyzing the behaviour of three algorithms based on information theory and dynamic Bayesian network (DBN) models. These algorithms were implemented on different sizes of data generated by synthetic networks. Experiments show that the inference accuracy of these algorithms reaches a saturation point after a specific data size brought about by a saturation in the pair-wise mutual information (MI) metric; hence there is a theoretical limit on the inference accuracy of information theory based schemes that depends on the number of time points of micro-array data used to infer GRNs. This illustrates the fact that MI might not be the best metric to use for GRN inference algorithms. To circumvent the limitations of the MI metric, we introduce a new method of computing time lags between any pair of genes and present the pair-wise time lagged Mutual Information (TLMI) and time lagged Conditional Mutual Information (TLCMI) metrics. Next we use these new metrics to propose novel GRN inference schemes which provides higher inference accuracy based on the precision and recall parameters. Results: It was observed that beyond a certain number of time-points (i.e., a specific size) of micro-array data, the performance of the algorithms measured in terms of the recall-to-precision ratio saturated due to the saturation in the calculated pair-wise MI metric with increasing data size. The proposed algorithms were compared to existing approaches on four different biological networks. The resulting networks were evaluated based on the benchmark precision and recall metrics and the results favour our approach. Conclusions: To alleviate the effects of data size on information theory based GRN inference algorithms, novel time lag based information theoretic approaches to infer gene regulatory networks have been proposed. The results show that the time lags of regulatory effects between any pair of genes play an important role in GRN inference schemes

Inference of gene regulatory networks from time series by Tsallis entropy

Background: The 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. Results: In 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. Conclusions: A 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/.Fundacao de Amparo e Amparo a Pesquisa do Estado de Sao Paulo (FAPESP)Coordenacao de Aperfeicofamento de Pessoal de Nivel Superior (CAPES)Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq