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     A genetic regulatory network is a collection of genes that regulate each other's expression. The nodes in this network are the genes themselves and the links between them represent the regulatory interactions. So, two genes are connected if one regulates the expression of the other. 
 
In 1961  Francois Jacob and Jacques Monod introduced the first model of a genetic network, which was a set of differential equations for the activation-deactivation of the set of genes controlling the transport and metabolisim of lactose in  E. coli. This little genetic circuit, known as the lac operon,  has since been a prototype for the modeling of genetic networks. In fact, some biologists think that the only valid approach for the modeling of genetic networks is through differential equations, i.e. la Jacob and Monod.     
 
However, in 1969 Stuart A. Kauffman proposed a different model of a genetic network. In this model one is interested in the state of expression of the genes ("on" or "off") rather than in the concentration of their products. The genome is then represented as a collection of Boolean variables that interact between them via some logical rules. For many years the Kauffman model was consider as an over simplification of a genetic network and nobody (except, perhaps, Kauffman himself ) expected this model to yield accurate descriptions of real biological systems.  Nonetheless.... 
 
To everyone's surprise, the Kauffman model was much more powerful than it was originally thought. Elena Alvarez, Sui Huang, and Reka Albert, among others, have given experimental and numerical evidence that gene expression profiles of real organisms can be recovered by using the Kauffman approach. Additionally, Sui Huang and Donald Ingber have investigated and confirmed experimentally the hypothesys, formulated by Kauffman, stating that the dynamical attractors of the genetic network correspond to cell fates or cell types.
 
So, it seems that the Kauffman model, far from being an "over simplification" of real genetic networks, actually captures the essential aspects of the interactions between the genes and gives results that have  held out the confrontation with experiment.     
 
Although the model has been around for over 30 years, there is still a lot to be done. One of my main lines of research is the study of the dynamical stability and robustness  of the Kauffman model under perturbations and mutations. In a recent work (here) we discuss how robusness and evolvability can be put together within the same framework and give a mechanism for the emergence of new phenotypes.   
Structure of the state space of the Kauffman model. The tiangle at the center is the dynamical attractor, which corresponds to a cell type or cell fate. The basin of attraction represents all the possible differentiation pathways that eventually produce this cell type.