Information Technology Reference
In-Depth Information
Chapter 5
Complexity of Boolean Dynamics in Simple Models of Signaling
Networks and in Real Genetic Networks
Albert D az-Guilera
1;2
and Elena R. Alvarez-Buylla
3
1
Departament de Fsica Fonamental, Universitat de Barcelona,
Barcelona, 08028, Spain
2
Department of Chemical and Biological Engineering, Northwestern University
Evanston, IL 60202, USA
3
Instituto de Ecologa, Departamento de Ecologa Funcional,
Universidad Nacional Autonoma de Mexico, Mexico, D.F. 04510, Mexico
5.1. Introduction
Complex systems are composed of interacting units that communicate among them-
selves and process external environmental stimuli [Buchman (2002)]. Generally, the
dynamical properties of such systems are analyzed in terms of the time series of
some relevant property of the system. In this sense, the complexity of the dynamics
is understood as the existence of non-trivial correlations of the uctuations. The
Fourier transform of the correlation function of the uctuations (the spectrum)
measures the degree of complexity of the system. When correlations span across
multiple time scales the spectrum has a power-law behavior and it is the expo-
nent of the power-law that quanties the complexity of the generated dynamics
[Bassingthwaighte et al. (1994); Malik and Camm (1995); Goldberger et al. (2002)].
One of the crucial ndings in the last decade concerning the structure of many
complex systems is the fact that the topology of the interactions between single units
plays a crucial role. Real topologies are far from being regular or completely ran-
dom and the topological correlations add new ingredients to the dynamical models
considered so far [Watts and Strogatz (1998); Albert and Barabasi (2002)].
Thus, trying to understand how complex systems dynamically evolve and process
information has stimulated the development of network theory [Boccaletti et al.
(2006)]. In Biology, the concerted action of multiple interconnected genes and
proteins underlie developmental processes and phenotypical traits. Several years
ago, Kauman (1969) proposed that cellular states or types corresponded to steady
states or attractors of such dynamic complex networks and recent experimental
evidence supports this hypothesis [Huang et al. (2005)].
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