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Antigen specific immune responses are regulated by the T helper cell types,
thus the differentiation of T cells has been the focus of many studies. Mendoza
and Xenarios (Mendoza
et al.
2006) developed a generalized formulation to
describe any static network using discrete and hybrid dynamic models. The
hybrid formalism is similar to the piecewise linear formalism described in the
previous section except the activation term is a sigmoidal function of activating
and inhibiting interactions. This method has been applied to the cytokine
interaction network implicated in T cell differentiation. The authors have studied
the steady states leading to the activation of IL12 or IL4 leading to the
differentiation of naïve T helper cells into their subtypes, T helper 1 and T helper
2 respectively. Smaller systems have also been successful in integrating known
information into Boolean models to formulate a constructive hypothesis. A five
component model for T cell receptor mediated signaling was studied to reveal the
mechanisms by which the receptor can induce alternative cellular responses
(Kaufman
et al.
1999). The authors show that different signaling conditions can
occur for a single ligand-binding event per receptor in time-dependent manner so
that the relative time of binding of the ligand and the tyrosine kinase activity
decides the outcome. The model predicts two different stable states can be
reached after ligand dissociation, one corresponding to immunocompetence and
another to unresponsiveness (anergy). Another interesting example is a multi-
scale model of the genetic and molecular features of the evolution of colorectal
cancer (Ribba
et al.
2006). A Boolean model of genes involved in cell
proliferation and death pathways that are frequently mutated in colorectal cancer
patients is integrated with a discrete model of the cell cycle and a fluid dynamics
tissue model. Such multi-scale model can incorporate regulating factors such as
hypoxia, tumor geometry and tissue dynamics in predicting and improving radio-
therapeutic efficacy.
4.7. Conclusions
Theoretical models developed in close collaborations with experimentalists are
required to analyze the implications of a set of observations and also to design
novel explanatory hypotheses. We reviewed here applications of the Boolean
approach in inferring the network of interactions from expression data and in
modeling the dynamics of a network of interactions. The Boolean approach is a
coarse grained method which is usually used to analyze systems with limited
time course and kinetic information. Boolean networks thus show a way to start
modeling dynamics of molecular networks at an earlier stage than we are used to
today. The success of these models in describing specific systems and processes
