On the Detection of Gene Network Interconnections using Directed Mutual Information

Abstract

In this paper, we suggest and validate a systematic method for inferring biological gene networks. So far, the identification of even a small portion of gene networks has been achieved by consensus over multiple cellular biology labs. A gene refers to the sequence of DNA that encodes a single protein. Proteins encoded by a gene can regulate other genes in the living cell, forming a complex network that determines cell growth, health, and disease. We view gene networks as dynamic systems, in discrete-time, formed by the interconnection among genes, which are abstracted as nodes whose state takes values in the range [-1, 1]. The state of each node is a function of the past values of the state of other nodes in the network. The edges of the gene network and their directions indicate functional dependence among the nodes state and their causality relationships, respectively. New engineering developments, such as quantum dot sensors, will allow measurement of gene dynamics inside living cells. From gene time-course data, we show how each edge in a gene network can be inferred using the concept of directed mutual information. We validated our method using small networks generated randomly, as well as for the known network for flagella biosynthesis in E.Coli, which we used to generate gene time-course data (with noise) in simulations. For acyclic graphs with 7 (or fewer) genes with summation operations only, we were able to infer all edges perfectly. We also present a heuristic method to deal with Boolean operations.