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Ivan V. Ivanov (Texas A&M University, USA)

Copyright: © 2010
|Pages: 18

DOI: 10.4018/978-1-60566-685-3.ch014

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TopOne can think of a *Gene Regulatory Network (GRN)* as a network of relations among strands of DNA (genes) and the regulatory activities associated with those genes (Dougherty and Braga-Neto, 2006). This general definition allows for many mathematical (usually dynamical) systems to be called GRNs. The goodness of each such model is evaluated using several important criteria: the level of description of the biochemical reactions involved, complexity of the model, model parameter estimation, and the predictive power of the model. There have been many attempts to model the structure and dynamical behavior of GRNs, ranging from deterministic with discrete time space to fully stochastic with continuous time space. One can find a good review of such attempts in (de Jong, 2002). The so called central ‘dogma’ of molecular biology (Crick, 1970) implies that genes communicate via the proteins they encode. Both stages of protein production, transcription and translation, are controlled by a multitude of biochemical reactions, and are influenced by both internal and external to the cell factors. This perspective suggests that the expression of a given gene *i*, i.e. the quantity of either protein or messenger RNA, should be considered as a random function *X _{i}*(

Reduction Mapping: A mapping that solves the reduction problem for the PBN model of genomic regulation without increasing the number of the constituent BNs.

DIRE Algorithm: An algorithm that construct a mapping that solves the reduction problem using the state transition diagram of a given PBN as a constraint.

Probabilistic Boolean network (PBN): A mathematical model that describes genomic regulation as a stochastic discrete dynamical system.

Projection Mapping: A mapping that solves the reduction problem for the PBN model of genomic regulation under a specific set of constraints.

Reduction Problem: The ill-posed inverse problem for reducing the size and the complexity of a given computational model of genomic regulation under a given set of constraints.

Boolean Network (BN): A mathematical model that describes genomic regulation as a deterministic discrete dynamical system.

Gene Regulatory Network: A network of relations among strands of DNA (genes) and the regulatory activities associated with those genes.

Complexity: Understood in the context of either complex system or algorithmic information theory.

Cost of Reduction: A measure for evaluating the complexity of a given reduction mapping.

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