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Chapter 4
Boolean Networks in Inference and Dynamic Modeling of Biological
Systems at the Molecular and Physiological Level
Juilee Thakar and RĂ©ka Albert
Department of Physics, 104 Davey Laboratory, Pennsylvania State University,
University Park, PA 16802, USA
4.1. Introduction
Mathematical modeling is a valuable tool for understanding biological systems,
especially since vast amounts of data are getting produced with increasing
technical efficiency. Modeling frameworks range from empirical methods driven
by the analysis of the available data to mechanistic models encapsulating prior
knowledge. The latter models are usually classified along two axes: from discrete
to continuous based on the resolution of the variables, and from deterministic to
stochastic based on the incorporation of fluctuations and noise (Fig. 4.1). We will
focus in this chapter on discrete and continuous-discrete hybrid models, with
particular focus on the Boolean formalism that assumes only two levels for each
variable. Boolean modeling methods are used both to infer causal relationships
from expression data and to analyze the dynamic behavior of systems whose
network of interactions is known.
Theoretical and computational analysis of biochemical networks has a long
history (Heinrich et al. 1996; Voit 2000; Bower 2001; Fall 2002). Most
theoretical models focus on experimentally well-studied cellular pathways that
have relatively few components, and they use differential equations based on
mass-action (or more general) kinetics for the production and decay of
components (Tyson, Novak et al. 1996; Barkai and Leibler 1997; Spiro,
Parkinson et al . 1997; Ciliberto and Tyson 2000; Tyson, Chen et al. 2001;
Hoffmann, Levchenko et al . 2002; Dillon, Gadgil et al. 2003; Lee, Salic et al.
2003). The drawback of the differential equation-based method is the necessity to
know the kinetic parameters of the underlying reactions. Parameter estimation or
systematic search in parameter space is usually employed to find general features
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