From the analysis of BC3NET for the gene expression data set from S. cerevisiae
, we find in addition to a significant enrichment of over
GO-terms in the category Biological Process, the significance of
GO-terms in Cellular Component for protein complexes. The largest complexes we identified are the ribosome (
) and proteasome protein complex (
). There are two main reasons why edges of these protein complexes are highly abundant in the yeast BC3NET network. First, the ribosome and proteasome protein complexes are well annotated because they have been extensively studied in yeast 
. Second, the ribosome and proteasome protein complex are mainly regulated on the gene expression level and, where observed, having highly dependent gene expression patterns 
. Therefore, it is plausible that GRN inference methods can also pick-up signals from physical interactions between protein subunits of protein complexes.
We want to note that we are not the first to recognize that gene expression data contain information about protein-protein interactions. For example, 
provide evidence that proteins from the same complex show a significant coexpression of their corresponding genes. Also in 
it is mentioned that inferred interactions from gene expression data ‘may represent an expanded class of interactions’ 
. However, when it comes to the experimental assessment of the inferred networks, usually, only interactions related to the transcriptional regulation are studied, e.g., with ChIP-chip experiments 
. To our knowledge we are the first to provide a large-scale analysis of an inferred GRN from gene expression data with respect to the presence of protein-protein interactions.
BC3NET is an ensemble method that uses as base network inference algorithm C3NET 
. As for other ensemble methods based on bagging, e.g., random forests, the interpretability and characteristics of the base method does usually not translate to the resulting ensemble method 
. In our case this means that the inferred network can actually have more than
edges, despite the fact that networks inferred by C3NET can not. However, in our case this is a desirable property because it improves BC3NET leading ultimately to a richer connectivity structure of the inferred network. Specifically, our numerical results demonstrate that BC3NET gains in average more than
true positive edges compared to C3NET (see ). Another more general advantage of an ensemble approach is that it is straight forward to use on a computer cluster because a parallelization is naturally given by the base inference methods. Given the increasing availability of computer clusters this appears to be a conceptual advantage over none ensemble methods, likely to gain even more importance in the future. In this paper we pursued a conservative approach by using a Bonferroni procedure for MTC to demonstrate that even in this setting our method is capable of inferring many significant interactions that can be confirmed biologically. However, there is certainly potential to use more adopted MTC procedures that are less conservative. For example, procedures controlling the false discovery rate
(FDR) could be investigated 
Further, we want to note that despite the fact that the network inference method C3NET is no Bayesian method 
, BC3NET is. The reason for this is that it is known for the bootstrap distribution of a parameter to correspond approximately to the Bayesian posterior distribution for a noninformative prior, and the bagged estimate thereof is the approximate mean of the Bayesian posterior 
. Hence, BC3NET can be considered as a Bayesian method with noninformative priors for the connectivity structure among the genes. Given the problem to define informative priors for a Bayesian approach in a genomics context, either because not enough reliable information about a specific organism is available or because it is difficult to select this information in an uncontroversial manner, a noninformative prior is in the current state of genomics research still a prevalent choice. From a theoretical point of view, a bootstrap implementation is easier to accomplish than the corresponding (full) Bayesian method. Hence, our approach is more elementary 
. Employing a similar argument as above, one can also see that BC3NET performs a model averaging of the individual networks inferred by C3NET.
From a conceptual point of view, one may wonder if an inferred GRN using BC3NET corresponds to a causal or an association network 
. Here, by causal
we denote an edge that corresponds to a direct
interaction between gene products, e.g., the binding of a transcription factor to the promoter region on the DNA for regulating the expression of this genes. The quantitative evaluation of our simulated data, provide actually a quantification of the causal content
of the inferred networks in the form of F-scores. It is clear that due to the statistical nature of the data, any inference is accompanied by a certain amount of uncertainty leading to an inferred GRN that contains false positive as well as false negative edges. However, as demonstrated by our numerical analysis, BC3NET is an important improvement toward the inference of causal gene regulatory networks.
Despite the fact that the presented inference method BC3NET was introduced by using gene expression data from DNA microarray experiments, it can also be used in connection with data from RNA-seq experiments. Given the rapidly increasing importance of this new technology we expect that within the next few years datasets with sufficient large sample size are available to infer GRN.