Bottom-up GGM algorithm for constructing multilayered hierarchical gene regulatory networks that govern biological pathways or processes

Abstract

BackgroundMultilayered hierarchical gene regulatory networks (ML-hGRNs) are very important for understanding genetics regulation of biological pathways. However, there are currently no computational algorithms available for directly building ML-hGRNs that regulate biological pathways.ResultsA bottom-up graphic Gaussian model (GGM) algorithm was developed for constructing ML-hGRN operating above a biological pathway using small- to medium-sized microarray or RNA-seq data sets. The algorithm first placed genes of a pathway at the bottom layer and began to construct a ML-hGRN by evaluating all combined triple genes: two pathway genes and one regulatory gene. The algorithm retained all triple genes where a regulatory gene significantly interfered two paired pathway genes. The regulatory genes with highest interference frequency were kept as the second layer and the number kept is based on an optimization function. Thereafter, the algorithm was used recursively to build a ML-hGRN in layer-by-layer fashion until the defined number of layers was obtained or terminated automatically.ConclusionsWe validated the algorithm and demonstrated its high efficiency in constructing ML-hGRNs governing biological pathways. The algorithm is instrumental for biologists to learn the hierarchical regulators associated with a given biological pathway from even small-sized microarray or RNA-seq data sets.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-0981-1) contains supplementary material, which is available to authorized users.

Recursive random forest algorithm for constructing multilayered hierarchical gene regulatory networks that govern biological pathways

“…A total of 14 positive TFs including MYB43, MYB46, MYB52, MYB58, MYB63 MYB83, MYB85, MYB103, SND1, 2, 3 and NST1, 2 and KNAT7 [ 22 , 23 ] were identified as known positive regulators of lignocellulosic biosynthesis. In a previous work, 20 positive known TFs were identified by bottom-up GGM algorithm when 25 pathway genes and 1622 TFs were used [ 7 ]. However, these 20 positive TFs were identify by bottom-up GGM in a total of 1507 edges while the BWERF identified the 14 positive TFs in a total of 90 edges.…”

“…The bottom-up GGM algorithm evaluates the triple genes by comparing the difference between the correlation coefficient of the two bottom-layered genes and the partial correlation coefficient of the two bottom-layered genes given a TF at the immediately upper layer. When the difference is statistically significant, the TF was defined to be the regulator of the two bottom-layered genes [ 7 ]. This is because the correlation coefficient of the two bottom-layered genes represents their coordination in the presence of the TF, whereas the partial correlation coefficient reflects their coordination after the effect of the TF on both bottom-layered genes is removed.…”

“…Although ML-hGRNs are important, there is a lack of statistical or computational methods for directly constructing ML-hGRNs from high-throughput gene expression data [ 7 ]. Currently there are many methods that are available for constructing GRNs [ 15 – 20 ], but these methods are not specifically tailored for constructing ML-hGRNs that mimic the hierarchical regulation [ 7 ].…”

“…Although ML-hGRNs are important, there is a lack of statistical or computational methods for directly constructing ML-hGRNs from high-throughput gene expression data [ 7 ]. Currently there are many methods that are available for constructing GRNs [ 15 – 20 ], but these methods are not specifically tailored for constructing ML-hGRNs that mimic the hierarchical regulation [ 7 ]. We have recently developed an algorithm called Bottom-up Gaussian graphical model (GGM) algorithm [ 5 , 7 ] for directly constructing ML-hGRNs from high-throughput gene expression data.…”

“…Currently there are many methods that are available for constructing GRNs [ 15 – 20 ], but these methods are not specifically tailored for constructing ML-hGRNs that mimic the hierarchical regulation [ 7 ]. We have recently developed an algorithm called Bottom-up Gaussian graphical model (GGM) algorithm [ 5 , 7 ] for directly constructing ML-hGRNs from high-throughput gene expression data. Although it can recognize the known positive regulators with high efficiency, it usually builds a large number of regulatory relationships (edges) into ML-hGRNs, resulting in possible false positive relationships (edges) and making it hard to identify implicit “top-down chains-of-commands” for experimental validation.…”