Controllability of Boolean control networks via the Perron–Frobenius theory

Boolean control networks (BCNs) are recently attracting considerable interest as computational models for genetic and cellular networks. Addressing control-theoretic problems in BCNs may lead to a better understanding of the intrinsic control in biological systems, as well as to developing suitable...

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Published inAutomatica (Oxford) Vol. 48; no. 6; pp. 1218 - 1223
Main Authors Laschov, Dmitriy, Margaliot, Michael
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 01.06.2012
Elsevier
Subjects
Algebra
Applied sciences
Biological
Biological and medical sciences
Boolean algebra
Cellular communication
Computer science; control theory; systems
Control system analysis
Control systems
Control theory. Systems
Controllability
Exact sciences and technology
Fundamental and applied biological sciences. Psychology
Gene regulating networks
General aspects
Genetics
Logical systems
Mathematical models
Modelling and identification
Molecular and cellular biology
Nonnegative matrices
Reachability
Systems biology
Logical systems
Controllability
Systems biology
Nonnegative matrices
Reachability
Gene regulating networks
Necessary and sufficient condition
Boolean Network
Modular system
Perron value
Cell network
Forbidden state
Modeling
Biological system
Non negative matrix
Genetic algorithm
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Summary:Boolean control networks (BCNs) are recently attracting considerable interest as computational models for genetic and cellular networks. Addressing control-theoretic problems in BCNs may lead to a better understanding of the intrinsic control in biological systems, as well as to developing suitable protocols for manipulating biological systems using exogenous inputs. We introduce two definitions for controllability of a BCN, and show that a necessary and sufficient condition for each form of controllability is that a certain nonnegative matrix is irreducible or primitive, respectively. Our analysis is based on a result that may be of independent interest, namely, a simple algebraic formula for the number of different control sequences that steer a BCN between given initial and final states in a given number of time steps, while avoiding a set of forbidden states.
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ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2012.03.022