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Fig. 4.4. Classification of random Boolean networks according to their updating scheme. DDNs -
Discrete Dynamic Networks, MxRBNs - Mixed context RBNs, GARBNs - Generalized
Asynchrnous RBNs, ARBNs - Asynchronous RBNs, DGARBN - Deterministic Generalized
Asynchronous RBNs, CRBN - classical RBNs, CA - Cellular Automata, DARBNs - Deterministic
Asynchronous RBNs. Figure adapted from (Gershenson 2004)
The variations to describe the activity includes using more than two states,
incorporating weights to define the strengths of the input interactions and
implementing independent thresholds for each components. The hybrid Boolean
approach, also known as piece-wise linear formalism (Glass
et al.
1973),
combines Boolean synthesis with continuous decay. Each node is characterized
by two variables, a continuous variable akin to a concentration and a discrete
variable akin to an activity. The rate of change of the continuous variable
is
= −
, and the Boolean variable
X
i
switches states when
the continuous variable
x
i
passes a threshold θ. The limiting values 0 and 1 of the
continuous variable represent, respectively, the absence of species
i
and maximal
concentration of species
i
. With all this said it's important to note that all the
above variations maintain the fixed points (steady states) of the traditional
Boolean models.
Qualitative models such as Boolean network models have the common
feature of most closely reflecting the topology of the regulatory network based on
experimental data and of describing the signal processing through the network.
During the network assembly perturbations can be performed to verify the
network topology by comparing the outcome of the perturbed network to the
experimental observations. Perturbations often include permanent silencing or
activation of the nodes of the network which can be directly compared to knock-
out or over-expression experiments respectively. Thus in this chapter first we will
t
t
t
dx
dt
B
(
X
,
X
..
X
)
x
i
i
i
2
k
i
