Biology Reference
In-Depth Information
analysis about the interweaving of system components and
the cascade of information flow, and enable in silico node
knockout experiments that produce informative predictions
about the system. Discrete dynamic models have been
successfully implemented in numerous biological systems,
facilitating the study and greater understanding of biolog-
ical processes such as flower development
[17,18]
, the
yeast cell cycle
[8,9,19]
, Drosophila embryonic develop-
ment
[20
e
24]
, hormone signaling in plants
[10,25]
, the
immune response
[11]
, and T-cell signaling and differen-
tiation
[12,13, 26
e
28]
.
Boolean network modeling of biological systems is the
simplest of the discrete dynamic models. Each node can
have one of two discrete states, namely 0 and 1, instead of
a continuously varying concentration. 0 or OFF means that
the element represented by the node is inactive (e.g., an
enzyme or transcription factor), or has a below-threshold
concentration (e.g., a small molecule). 1 or ON represents
the opposite, which is active or an above-threshold
concentration
[6,7]
. The state of a system that has N nodes
is therefore represented by an N-dimensional vector with
each value being 0 or 1. The state space of such system
contains a total of 2
N
states. In order to carry out dynamic
simulations, time is usually discretized into time steps. As
time evolves, starting from one initial state vector, either
predetermined or randomly generated, the system state
vector can traverse the state space, reaching different parts
of the space. It is not necessary that a dynamic trajectory
traverse all 2
N
states in the space; indeed, the observed
trajectories converge into a stationary state or set of states
after a much smaller number of state transitions.
In this chapter, we first explain the correspondence
between Boolean networks and biological systems, then
introduce the basic concepts of Boolean network modeling
and elaborate in a step-by-step fashion the modeling
procedure, starting from network reconstruction based on
biological information compilation to model validation. We
will present two successful applications of this method-
ology in cellular biology
[11,12]
.
BOOLEAN NETWORKS AND BIOLOGICAL
SYSTEMS
Here we introduce the basics of Boolean algebra and its
connection with biological systems. In order to summarize
all available information and graphically represent the
system we are studying, the elements of the system, such as
genes or proteins, become the nodes of the network. Nodes
that represent a phenomenon or a certain biological result
can also be included, for instance Stomatal Closure, or
Apoptosis.
Edges are drawn between biologically or chemically
related nodes to represent the relationship between them.
Since the flow of signals and reaction fluxes is directional,
the edges in the network will each have a direction that is
consistent with biology; edges may also be characterized
by a sign (
) that denotes the property of that edge:
positive for activation and negative for inhibition. For
example, a common representation of the synthesis reac-
tion C
þ
/
E connects the two reactants with the product
of the reaction, as in
Figure 10.1
(A).
This representation does not, however, directly reflect
the fact that C and D are both required for the reaction to
take place. Thus the network must be complemented with
rules that specify the ways in which all upstream compo-
nents are combined. A natural and economical method is to
use the Boolean operators AND, OR, NOT. A combination
of these operators can describe most possible relationships
or reactions between substances and components in a bio-
logical system. The logic dependence underlying
a synthesis reaction can be described by the Boolean
operator AND, so the reaction C
þ
D
/
þ
D
E becomes C AND
/
D
E* in Boolean language, where for simplicity the node
names stand for the state of the node. Similarly, if a certain
¼
FIGURE 10.1
Three different ways to represent the same synthesis reaction relationship between 3 nodes. (A) Two separate edges directed from the
reactants to the product. (B) Two edges from the reactants first merged together and then directed at the product. (C) An intermediate node (green circle)
denoting the synergy between the two reactants is added. The reactants are connected to this intermediary node, which is in turn connected to the product.
