A

**gene regulatory network**(also called a

*GRN*or

*genetic regulatory network*) is a collection of DNA segments in a cell which interact with each other and with other substances in the cell, thereby governing the rates at which genes in the network are transcribed into mRNA.

Mathematical models of GRNs have been developed to allow predictions of the models to be tested. Various modeling techniques have been used, including boolean networks, Petri nets, Bayesian networks, and sets of differential equations. Conversely, techniques have been proposed for generating models of GRNs that best explain a set of time series observations.

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## Example: Boolean network

The following example illustrates how a Boolean network can model a GRN together with its gene products (the outputs) and the substances from the environment that affect it (the inputs). Stuart Kauffman was amongst the first biologists to use the metaphor of Boolean networks to model genetic regulatory networks.

- Each gene, each input, and each output is represented by a node in a directed graph in which there is an arrow from one node to another if and only if there is a causal link between the two nodes.
- Each node in the graph can be in one of two states: on or off.
- For a gene, "on" corresponds to the gene being expressed; for inputs and outputs, "on" corresponds to the substance being present.
- Time is viewed as proceeding in discrete steps. At each step, the new state of a node is a boolean function of the prior states of the nodes with arrows pointing towards it.