Abstract
This book deals with algorithms for inferring and analyzing Gene Regulatory Networks using mainly gene expression data. What precisely are the Gene Regulatory Networks that are inferred by such algorithms from this type of data? There is still much confusion in the current literature and it is important to start a book about computational methods for Gene Regulatory Networks with a definition that is as unambiguous as possible. In this chapter, I provide a definition and try to clearly explain what Gene Regulatory Networks are in terms of the underlying biochemical processes. To do the latter in a formal way, I will use a linear approximation to the in general non-linear kinetics underlying interactions in biochemical systems and show how a biochemical system can be ‘condensed’ into the more compact description of Gene Regulatory Networks. Important differences between the defined Gene Regulatory Networks and other network models for gene regulation, such as Transcriptional Regulatory Networks and Co-Expression Networks, will be highlighted.
TopGene Regulatory Networks
I start out by giving a possible formal definition for Gene Regulatory Networks. The remainder of the chapter is entirely dedicated to provide a detailed explanation of this definition.
Definition – Gene Regulatory Network (GRN): a Gene Regulatory Network is a mixed graph G:= (V, U, D) over a set V of nodes, corresponding to gene-activities, with unordered pairs U, the undirected edges, and ordered pairs D, the directed edges. A directed edge dij from vi to vj is present iff a causal effect runs from node vi to vj and there exist no nodes or subsets of nodes in V that are intermediating the causal influence (it may be mediated by hidden variables, i.e. variables not in V). An undirected edge uij between nodes vi and vj is present iff gene-activities vi and vj are associated by other means than a direct causal influence, and there exist no nodes or subsets of nodes in V that explain that association (it is caused by a variable hidden to V).
What do the nodes in GRNs precisely represent? The nodes in GRNs are often said to correspond to ‘genes’. More precisely, they rather correspond to ‘gene-activities’ (‘gene expression levels’ or ‘RNA concentrations’) as these are the dynamical and quantitative variables that are related by the algorithms discussed in this book. Of course ‘gene-activity’ could be included in the definition of ‘gene’. Therefore, there will be no need to adapt the name ‘Gene-activity Regulatory Networks’.
Key Terms in this Chapter
Cyclic network: A network with at least one directed path that starts and ends in the same node.
Transcriptional Regulatory Network: A network model of transcription factor-target relationships. Directed edges run from transcription factor nodes to target nodes.
Undirected graph: A network with only undirected edges between the nodes.
Co-Expression Network: A network model in which nodes represent gene-activities and the undirected edges represent significant associations.
Hidden variables: Variables that are not explicietely represented in the network model, often because these have not been experimentally observed.
Gene Regulatory Network: A network model in which nodes represent gene-activities and the directed edges represent direct causal influences and undirected edges represent associations due to confounding.
Directed graph: A network with only directed edges between the nodes.
Mixed graph: A network with undirected as well as directed edges between the nodes.