Periodic Orbits and Equilibria in Glass Models for Gene Regulatory Networks

Autor: I. Zinovik, Yury Chebiryak, Daniel Kroening
Rok vydání: 2010
Předmět:
State transition diagram
Interaction graph
Computer science
Gene regulatory network
GENE REGULATION
REGULATION OF GENE-EXPRESSION (MOLECULAR BIOLOGY)
Library and Information Sciences
Data processing
computer science
Induced cycle
Gene interaction
Robustness (computer science)
Attractor
FOS: Mathematics
ddc:510
GRAPHENMODELLE (GRAPHENTHEORIE)
GRAPH MODELS (GRAPH THEORY)
MATHEMATICAL MODELING AND SIMULATION IN GENETICS
MODELLRECHNUNG UND SIMULATION IN DER GENETIK
Hypercube
Wiring diagram
Dominating codes
Pathway
LINEARE UND QUASILINEARE PARTIELLE DIFFERENTIALGLEICHUNGEN UND SYSTEME PARTIELLER DIFFERENTIALGLEICHUNGEN (ANALYSIS)
LINEAR AND QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS AND SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS (MATHEMATICAL ANALYSIS)
GENREGULATION
REGULATION DER GENEXPRESSION (MOLEKULARBIOLOGIE)
Numerical analysis
Graph
Computer Science Applications
ddc:004
Periodic graph (geometry)
Algorithm
Mathematics
Information Systems
Zdroj: IEEE Transactions on Information Theory. 56:805-820
ISSN: 1557-9654
0018-9448
DOI: 10.1109/tit.2009.2037078
Popis: Glass models are frequently used to model gene regulatory networks. A distinct feature of the Glass model is that its dynamics can be formalized as paths through multi-dimensional binary hypercubes. In this paper, we report a broad range of results about Glass models that have been obtained by computing the binary codes that correspond to the hypercube paths. Specifically, we propose algorithmic methods for the synthesis of specific Glass networks based on these codes. In contrast to existing work, bi-periodic networks and networks possessing both stable equilibria and periodic trajectories are considered. The robustness of the attractor is also addressed, which gives rise to hypercube paths with nondominated nodes and double coils. These paths correspond to novel combinatorial problems, for which initial experimental results are presented. Finally, a classification of Glass networks with respect to their corresponding gene interaction graphs for three genes is presented. © 2006 IEEE.
Databáze: OpenAIRE
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