Figure 1.
Attractors in Synchronous/Asynchronous Boolean Networks.
Figure 1. Diagrams of four types of attractors in Boolean networks. Attractors are outlined by slide boxes, and transient states by dashed boxes. (a) A self loop is a single state attractor. (b) A simple loop includes two or more states: each state is connected with only another state, and any two adjacent states differ from each other by only one bit. (c) A syn-complex loop is similar to simple loop, but any two adjacent states differ from each other by more than one bit. (d) A asyn-complex loop includes multiple interlinked states: each state is connected with more than one states, and there is only one bit difference between any two adjacent states. In Boolean networks, the self loop and simple loop can be identified in both synchronous Boolean networks and asynchronous Boolean networks. But the syn-complex loop only exists in the synchronous Boolean networks, and the asyn-complex loop only exists in asynchronous Boolean networks.
Figure 2.
An Asynchronous Attractor to Synchronous Attractor.
Figure 2. Diagrams of an attractor in asynchronous (a) and synchronous (b) Boolean networks. Each state is represented by a circle, and is designated as . The variable
represents that the
bit of the state
and
is different, which is also same as
and
. The numbers
indicate that state
and
differ by the
and
bits respectively. The
and
represents when state
and
differ at the
bit, state
and
will be different at the
bit, and vice versa. The difference between the two representations (i.e. synchronous versus asynchronous) of the attractor is that
and
differ in the
and
bits,
. That means we can use syn-complex loop to easily locate the states in asyn-complex_loop by asynchronous Boolean translation function
.
Table 1.
Characters of Five Different Biological Networks.
Table 2.
Performance Comparison between genYsis [10] and geneFAtt.