Systems Biology (Methods in Molecular Biology)

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.