Boolean Models of Cellular Signaling Networks - Systems Biology Concepts and Insights - page 191

FIGURE 10.4 A four-node signal transduction network in which A is activated by Input, and its activation also requires the absence of B.
(A) Network representation; (B) the list of Boolean rules.

Finally, consider yet another example ( Figure 10.8 ). The
characteristic feature of this network is two paths that both
connect the Input and the Output, but functionally contradict
each other. Given the AND rule for theOutput, the steady state
of Output is OFF, and more importantly, this outcome is
independent of the state of the Input: the Output is decoupled
from the Input in this case. If OR is used in the transfer
function of the Output, its statewill be at constant ON instead,
but it will still be independent from the Input state.
Now let's apply the dynamic analysis to the network in
Figure 10.2 and see whether a steady state of the Output is

possible. Given that the Input node is ON, the negative
feedback on node Awill generate an oscillation of states for
node A as well as node B. However, since the Boolean rule
for node C is C*

(NOT A) OR Input, the oscillation
coming from branch Awill be combined by an OR rule with
the ON state of the Input. The Output node will henceforth
reach an ON steady state. The attractor for the state vector
of the system, on the other hand, will be a limit cycle, since
a subset of the nodes is oscillating.
In general, multiple network motifs can be present in
the graph representation of a system under study, and each

¼

FIGURE 10.5 The state transition graph of the system described in Figure 10.4. The 3-digit vectors inside the circles represent the state of node A,
B, and Output from left to right. The state of the Input is fixed at 1, indicating a constant ON signal to the system (not shown in the graph). A self-loop on
a certain state indicates that if one of the nodes is updated, the system state remains the same. For 3 nodes, a total of 8 states exist. (A) Synchronous update.
All 8 states are located in the same basin of attraction, of which 4 form the attractor. (B) General asynchronous update. The attractor is formed by all 8
states. These figures were generated by BooleanNet.