Systems Biology (Methods in Molecular Biology)

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few time points) and uncertain (lake of replicates and precision)
[49]. Logic-based models are qualitative and do not require detail
quantitative parameters which make it suitable for large-scale bio-
chemical networks [50–52]. In such a modeling formalism, a net-
work is represented as a graph with nodes and edges, where a node
represents any molecular specie and edges depict the type of effect
that one specie exerts on the state of other in terms of activation
and inactivation (Fig.7). The state of each species is determined by
a logic-based function that links the incoming effect to a state.
Logic-based models can provide predictive testable hypotheses,
which are especially valuable in poorly understood large-scale sys-
tems [53, 54].
The basic/simplest logic-based model is the Boolean model
popularized by Kauffmann [55] where the components of a net-
work can be in one of two states: (1) “on” state (also denoted by
1 or “true” state) which represents the “active” or “expressed” state
of the component; (2) “off” state (also denoted by 0 state or “false”
state) which represents the “inactive” or “not expressed” state of
the component. In the Boolean models, nodes (X1,...,n) of a net-
work correspond to the Boolean variables that can have values
either 1 or 0, and edges define the type of interactions (e.g.,
activation or inhibition). The future stateX(tþ1) of a node is a
Boolean function (BF) of the current stateX(t) of the nodes
regulating it, i.e.,Xi(t+1)¼BF(X 1 (t),X 2 (t),...,Xn(t)) (Fig.8).
Boolean functions determine the states of the node using Boolean
gates (NOT, ACTIVE, OR, and AND), where the NOT gate is

Small number of
interacting components

Interaction maps

Large number of
interacting components

t

ODE-based modeling

(^0) t
1
Logic-based modeling
Modeling formalisms Pros and cons



  • Widely use to study non-linear
    dynamics.

  • Produce high quality predictions
    of the system ́s dynamics.

  • Require accurate kinetic
    parameters.

  • Not suitable for large systems.

  • Provide predictive hypotheses
    for poorly understood
    large-scale systems.

  • Inappropriate for networks
    enriched with feedback/-
    feedforward loops.


Hybrid modeling
Core regulatory
module

Target genes

Interface

Phenotypical
output

ODE

model

Logic-

based model

ODE or Logic-based model

Interface

Transactivation/de-
activation

Feedback/forward
loops

Phenotypical
analysis

= , ; 0 =

In Out

Fig. 7Selection of appropriate mathematical modeling formalism: The choice of suitable modeling formalism
is based on available information of a system, the structure and the size of a network. ODE-based models are
widely used for small non-linear system with detailed information available. For a large network size and little
available knowledge, logic-based models are preferably used for their dynamics understanding. Hybrid
modeling is a strategy to model large-scale non-linear systems by combing ODEs and logic-based models


258 Faiz M. Khan et al.

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