Classical Model
The first Boolean networks were proposed by Stuart A. Kauffman in 1969, as random models of genetic regulatory networks (Kauffman 1969, 1993).
Random Boolean networks (RBNs) are known as NK networks or Kauffman networks (Dubrova 2005). An RBN is a system of N binary-state nodes (representing genes) with K inputs to each node representing regulatory mechanisms. The two states (on/off) represent respectively, the status of a gene being active or inactive. The variable K is typically held constant, but it can also be varied across all genes, making it a set of integers instead of a single integer. In the simplest case each gene is assigned, at random, K regulatory inputs from among the N genes, and one of the possible Boolean functions of K inputs. This gives a random sample (of size one) of the ensemble of possible networks of size N and either connectivity =k or with connectivities with some deviation around k. The state of a network at any point in time is given by the current states of all N genes. Thus the size of the state space of any such network is 2N.
Simulation of RBNs is done in discrete time steps. The state of a node at time t+1 is computed by applying the boolean function associated with the node to the state of its input nodes at time t. The sequence of states of the whole network starting from some initial state is called the trajectory of that state.
The behavior of specific RBNs and generalized classes of them has been the subject of much of Kauffman's (and others) research.
Read more about this topic: Boolean Network
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