Modeling and Analysis of Gene Regulatory Networks - Modeling in Computational Biology and Biomedicine - page 47

Yet, the methods for design and analysis of GRN are still quite recent. The
Boolean and discrete approaches go back to works of Kauffmann (1969) and
Thomas (1973), the continuous differential approach was applied by Goodwin
(1963) to GRN, and the piecewise affine models were initiated by Glass and
Kauffman [ 22 ]; for references see the review by de Jong [ 16 ]. There are still many
open problems, mainly due to the large number of elements in a network. It is now
possible to describe the behavior of a network with dozens of genes, but what about
networks with several thousands of genes? These are still not attainable, even with
the power of present computers and algorithmic methods.
As we have seen, the choice of a modeling approach is dependent on the type and
amount of experimental data available, and on the nature of the biological questions
asked by the modeler. In this chapter, two fundamental strategies will be detailed:
continuous models and logical models. The first one gives quantitative predictions
but needs quantitative biological data in order to fit parameters. The second is mainly
based on a correct description of the logical links between biological entities (and
is for instance particularly adapted to DNA array data that describe if a given gene
is on/off). Nevertheless, both approaches can be used either to simulate biological
phenomena or to predict properties that are intrinsically linked to the structure of
the model, such as oscillatory or switch behaviors.

2.1.3 Chapter Overview

Public

This short introduction to GRN modeling is directed at Master level students whose
background is either in the biological or the mathematical sciences.

Outline

A short overview of the main mathematical tools and concepts is provided, both on
continuous (ordinary differential equations or hybrid systems) (see Sect. 2.2 )and
discrete (see Sect. 2.3 ) formalisms. For each type of formalism, simple examples
of how to model genetic networks are worked out in more detail. Some successful
applications of these methodologies to complex networks are also described.

2.2 Continuous and Hybrid Models of Genetic Regulatory

Networks

The concentrations of molecular species (such as proteins or messenger RNAs)
change in response to cellular signals. In this section, the concentrations are assumed
to vary in a continuous manner, and their dynamical behavior will be described
by systems of ordinary differential equations or the more abstract piecewise affine