Subsystems in the example Boolean network model. (A, B) Network and Boolean functions for a simple Boolean network model. If the logical condition in a Boolean function is satisfied (for node ni), then that node takes state 1 at the following time step (si(t + 1) = 1). Otherwise, if the logical condition fails, si(t + 1) = 0. Interactions in the model are summarised by the network edges in A (red arrow = activation, blue dot = inhibition). (C) A1, ..., A4 are the 4 possible attractors for the Boolean network model in A, B, which are consistent with both synchronous and asynchronous updating schemes. Each column corresponds to a node in the model, whilst each row corresponds to an attractor state. White/Black corresponds to the node having state 1/0 in the attractor state. Once the system enters an attractor it continually cycles through those attractor states (e.g. z0, z1, z2, z3, z0, z1, z2, z3, z0, z1 after the system enters A1). (D) 6 Subsystems identified for this model, corresponding to sub-dynamics that are conserved across/distinguish sets of attractors from C. These were identified by applying the new method from this paper to the 4 attractors A1, ..., A4. Each column corresponds to a node in the model, whilst each row corresponds to a partial state. White/Black corresponds to the node having state 1/0 in the partial state.
Irons and Monk BMC Bioinformatics 2007 8:413 doi:10.1186/1471-2105-8-413