A matrix perturbation method for computing the steady-state probability distributions of probabilistic Boolean networks with gene perturbations

Journal of Computational and Applied Mathematics

Volumn 235, Issue 8, 2011, Pages 2242-2251

  Xu, Wei Wei ^a   Ching, Wai Ki ^b   Zhang, Shu Qin ^c   Li, Wen ^d   Chen, Xiao Shan ^d  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

^c FUDAN UNIVERSITY   (China)

^d SOUTH CHINA NORMAL UNIVERSITY   (China)

Author keywords

Boolean networks; Gene perturbation; Perturbation matrix; Probabilistic Boolean networks; Steady state probability distribution

Indexed keywords

APPROXIMATION METHODS; BOOLEAN NETWORKS; GENETIC NETWORKS; MATRIX; MATRIX PERTURBATION; NUMERICAL EXPERIMENTS; PERTURBATION MATRIX; PROBABILISTIC BOOLEAN NETWORKS; REGULATORY INTERACTIONS; STEADY STATE PROBABILITIES; STORAGE REQUIREMENTS; SYSTEMS BIOLOGY; TRANSITION PROBABILITY MATRIX;

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; ELECTRIC POWER SYSTEM INTERCONNECTION; ERROR ANALYSIS; GENES; MATRIX ALGEBRA; NUMERICAL METHODS; PERTURBATION TECHNIQUES;

PROBABILITY DISTRIBUTIONS;

EID: 79251593423     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2010.10.021     Document Type: Article

References (18)

1. J.E. Celis Gene expression profiling: monitoring transcription and translation products using DNA microarrays and proteomics FEBS Lett. 480 2000 2 16
2. T.R. Hughes etc Expression profiling using microarrays fabricated by an ink-jet oligonucleotide synthesizer Nat. Biotechnol. 19 2001 342 347
3. K. Murphy, S. Mian, Modelling gene expression data using dynamic Bayesian networks, Technical Report, Berkeley, 1999.
4. T. Akutsu, S. Miyano, and S. Kuhara Identification of genetic networks from a small number of gene expression patterns under the Boolean network model Pac. Symp. Biocomput. 4 1999 17 28
5. T. Akutsu, M. Hayasida, W. Ching, and M. Ng Control of Boolean Networks: Hardness Results and Algorithms for Tree Structured Networks J. Theoret. Biol. 244 2007 670 679
6. I. Shmulevich, E.R. Dougherty, S. Kim, and W. Zhang Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks Bioinformatics 2 2002 261 274
7. I. Shmulevich, E.R. Dougherty, and W. Zhang Gene perturbation and intervention in probabilistic Boolean works Bioinformatics 18 2002 1319 1331
8. W. Ching, and M. Ng Markov Chains: Models, Algorithms and Applications, International Series on Operations Research and Management Science 2006 Springer New York
9. W. Ching, M. Ng, E. Fung, and T. Akutsu On construction of stochastic genetic networks based on gene expression sequences Int. J. Neural Syst. 15 2005 297 310
10. P. Smolen, D. Baxter, and J. Byrne Mathematical Modeling of Gene Network Neuron 26 2000 567 580
11. S.A. Kauffman Metabolic stability and epigenesis in randomly constructed genetic nets J. Theoret. Biol. 22 1969 437 467
12. S.A. Kauffman The Origins of Order: Self-Organization and Selection in Evolution 1993 Oxford University Press Oxford
13. S. Huang Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery J. Mol. Med. 77 1999 469 480
14. R. Pal, I. Ivanov, A. Datta, M.L. Bittner, and E.R. Dougherty Generating Boolean networks with a prescribed attractor structure Bioinformatics 21 2005 4021 4025
15. S. Zhang, W. Ching, M. Ng, and T. Akutsu Simulation study in probabilistic Boolean network models for genetic regulatory networks Int. J. Data Min. and Bioinform. 1 2007 217 240
16. W. Ching, S. Zhang, M. Ng, and T. Akutsu An approximation method for solving the steady-state probability distribution of probabilistic Boolean networks Bioinformatics 12 2007 1511 1518
17. G. Stewart, and J. Sun Matrix Perturbation Theory 1990 Academic Press San Diego
18. W. Xu, and W. Li New perturbation analysis for generalized saddle point systems CALCOLO 46 2009 25 36