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Stochastic
e.g. - Probabilistic
Boolean, Bayesian
models
e.g.- Reaction-Diffusion,
Fokker-Plank or Kolmororov
forward equation models
Discrete
Continuous
e.g.-Synchronous
Boolean, Fuzzy
logic models
e.g.- Mass-action
kinetics,
Enzyme kinetics
Deterministic
Fig. 4.1. Classification of mechanistic methods for modeling dynamics of biological systems. In
each quadrant we have given some of the common examples of modeling methods used in that
category. Most of the methods offer flexibility to incorporate resolution required for the specific
questions under examination.
that are maintained in a range of possible values. The kinetic details of molecular
and cellular interactions are rarely known. There is increasing evidence, however,
that the input-output curves of many regulatory relationships are strongly
sigmoidal and can be approximated by step functions (von Dassow
et al.
2000;
Bower 2001). Moreover, several models and experiments suggest that regulatory
networks maintain their function even when faced with fluctuations in
components and reaction rates (Alon, Surette
et al.
1999; von Dassow, Meir
et al.
2000; Eldar, Dorfman et al. 2002; Conant and Wagner 2004; Csete and Doyle
2004). These observations lend support to the applicability of Boolean and other
qualitative models .
Boolean modeling is a top-down approach that describes the regulation
between key players of the system and does not explicitly incorporate the
underlying biochemical details. Such a method is a powerful way to convert a
blackboard description of the biological system into a mathematical model.
Though it is simple in the manner it describes each component, the interplay
between the components of the system leads to rich emergent dynamic behaviors.
Boolean dynamic models have yielded significant insights into the behavior
of complex biological systems and into understanding the evolutionary principles
of biological networks. Most biological systems described by Boolean models
are gene regulatory networks but one of the advantages of such coarse-grained
method is that it can be easily extended to study systems at the physiological
level. The system under consideration is described by its components such as
