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

Sapna Kumari, Wenping Deng, Chathura Gunasekara, Vincent Chiang, Huann-sheng Chen, Hao Ma, Xin Davis, Hairong Wei

Multilayered 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. A 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. We 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.