Boolean Network - Updating Schemes

Updating Schemes

Classical RBNs (CRBNs) use a synchronous updating scheme and a criticism of CRBNs as models of genetic regulatory networks is that genes do not change their states all at the same moment. Harvey and Bossomaier introduced this criticism and defined asynchronous RBNs (ARBNs) where a random node is selected at each time step and updated (Harvey and Bossomaier, 1997). Since a random node is updated ARBNs are non-deterministic and do not have the cycle attractors found in CRBNs (Gershenson, 2004).

Deterministic asynchronous RBNs (DARBNs) were introduced by Gershenson as a way to have RBNs that do not have asynchronous updating but still are deterministic. In DARBNs each node has two randomly generated parameters P_i and Q_i (P_i, Q_i ∈ ℕ, P_i > Q_i). These parameters remain fixed. A node i will be updated when t ≡ Q_i (mod P_i) where t is the time step. If more than one node is to be updated at a time step the nodes are updated in a pre-defined order, e.g. from lowest to highest i. Another way to do this is to synchronously update all nodes that fulfill the updating condition. The latter scheme is called deterministic semi-synchronous or deterministic generalized asynchronous RBNs (DGARBNs) (Gershenson, 2004).

RBNs where one or more nodes are selected for updating at each time step and the selected nodes are then synchronously updated are called generalized asynchronous RBNs (GARBNs). GARBNs are semi-synchronous, but non-deterministic (Gershenson, 2002).