Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrative and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, large-scale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several points of view. We then introduce Boolean networks and discuss their relationships to nonlinear digital filters. The role of Boolean networks in understanding cell differentiation and cellular functional states is discussed. The inference of Boolean networks from real gene expression data is considered from the viewpoints of computational learning theory and nonlinear signal processing, touching on computational complexity of learning and robustness. Then, a discussion of the need to handle uncertainty in a probabilistic framework is presented, leading to an introduction of probabilistic Boolean networks and their relationships to Markov chains. Methods for quantifying the influence of genes on other genes are presented. The general question of the potential effect of individual genes on the global dynamical network behavior is considered using stochastic perturbation analysis. This discussion then leads into the problem of target identification for therapeutic intervention via the development of several computational tools based on first-passage times in Markov chains. Examples from biology are presented throughout the paper. 1
|
4828
|
Genetic Algorithms
– Goldberg
- 1989
|
|
4388
|
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
– Pearl
- 1988
|
|
1364
|
A theory of the learnable
– Valiant
- 1984
|
|
746
|
Image Analysis and Mathematical Morphology
– Serra
- 1992
|
|
742
|
System Identification: Theory for the User
– Ljung
- 1987
|
|
511
|
Molecular classification of cancer: class discovery and class prediction by gene expression monitoring
– Goloub, Slonim, et al.
- 1999
|
|
438
|
Origins of Order: Self-Organization and Selection in Evolution
– Kauffman
- 1993
|
|
336
|
Comprehensive identification of cell cycle-regulated genes of the yeast saccharomyces cerevisiae by microarray hybridization. Molecular Biology of the Cell
– SPELLMAN, SHERLOCK, et al.
- 1998
|
|
273
|
Quantitative monitoring of gene expression patterns with a complementary DNA microarray. Science 270:467–470
– Schena, Shalon, et al.
- 1995
|
|
178
|
Computational limitations on learning from examples
– Pitt, Valiant
- 1988
|
|
146
|
The Molecular Biology of the Cell
– Alberts, Bray, et al.
- 1989
|
|
136
|
Modeling and simulation of genetic regulatory systems: A literature review
– Jong
- 2000
|
|
119
|
Ratio-based decisions and the quantitative analysis of cDNA microarray images
– Chen, Dougherty, et al.
- 1997
|
|
118
|
Metabolic stability and epigenesis in randomly constructed genetic nets
– Kauffman
- 1969
|
|
113
|
Classification and diagnostic prediction of cancers using gene expression profiling and artificial neural networks
– Khan, Wei, et al.
- 2001
|
|
103
|
R: REVEAL, a general reverse engineering algorithm for inference of genetic network architectures. Pac Symp Biocomput
– Liang, Fuhrman, et al.
|
|
101
|
Computational Learning Theory
– Anthony, Biggs
- 1992
|
|
99
|
Yakhini Z: Tissue classification with gene expression profiles
– Ben-Dor, Bruhn, et al.
- 2000
|
|
99
|
Towards a General Theory of Adaptive Walks on Rugged Landscapes
– Kauffman, Levin
- 1987
|
|
86
|
Cellular Automata
– Codd
- 1968
|
|
83
|
Identification of genetic networks from a small number of gene expression patterns under the Boolean network model
– Akutsu, Miyano, et al.
- 1999
|
|
82
|
Probabilistic Boolean networks: A rule-based uncertainty model for gene regulatory networks
– Shmulevich, Dougherty, et al.
|
|
82
|
Evolving cellular automata to perform computations: Mechanisms and impediments
– Mitchell, Crutchfield, et al.
- 1994
|
|
78
|
High density synthetic oligonucleotide arrays
– Lipshutz, Fodor, et al.
- 1999
|
|
66
|
At Home in the Universe
– Kauffman
- 1995
|
|
66
|
Cause-effect relationships and partially defined boolean functions
– Crama, Hammer, et al.
- 1988
|
|
61
|
The logical analysis of continuous non-linear biochemical control networks
– Glass, Kauffman
- 1973
|
|
51
|
A methodology for solving Markov models of parallel systems
– Plateau, Fourneau
- 1991
|
|
50
|
Inferring qualitative relations in genetic networks and metabolic pathways
– Akutsu, Miyano, et al.
- 2000
|
|
45
|
EH: Genomic cis-regulatory logic: experimental and computational analysis of a sea urchin gene
– CH, Bolouri, et al.
- 1998
|
|
45
|
Dynamical behaviour of biological regulatory networks: I. Biological rool of feedback loops and practical use of the concept of the loop-characteristicstate
– Thomas, Thieffry, et al.
- 1995
|
|
45
|
2000. Discovery of regulatory interactions through perturbation: Inference and experimental design
– Ideker, Thorsson, et al.
|
|
40
|
Computational studies of gene regulatory networks: in numero molecular biology
– Hasty
|
|
40
|
Mathematical morphology in image processing
– Dougherty
- 1992
|
|
37
|
Stack filters
– Wendt, Coyle, et al.
- 1986
|
|
36
|
A theoretical analysis of the properties of median filters
– Gallagher, Wise
- 1981
|
|
35
|
Identification of gene regulatory networks by strategic gene disruptions and gene overexpressions
– Akutsu, Kuhara, et al.
- 1998
|
|
35
|
Error-free and best-fit extensions of partially defined Boolean functions
– Boros, Ibaraki, et al.
- 1998
|
|
33
|
The Nature of Statistical Learning Theory, second edition
– Vapnik
- 2000
|
|
32
|
The Nature of Statistical Learning Theory, 2nd ed
– Vapnik
- 2000
|
|
31
|
Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery
– Huang
- 1999
|
|
31
|
Genomic regulation modeled as a network with basins of attraction
– Wuensche
- 1998
|
|
31
|
Statistical Signal Processing
– Scharf
- 1991
|
|
29
|
Computational Modeling of Genetic and Biochemical Networks
– BOWER, H
|
|
29
|
Expression profiling using microarrays fabricated by an ink-jet oligonucleotide synthesizer
– TR, Mao, et al.
- 2001
|
|
28
|
Gene perturbation and intervention in probabilistic Boolean networks
– Shmulevich, Dougherty, et al.
- 2002
|
|
27
|
It’s a noisy business! Genetic regulation at the nanomolar scale
– McAdams, Arkin
- 1999
|
|
26
|
2001. Development of a system for the inference of large scale genetic networks
– Maki, Tominaga, et al.
|
|
26
|
Multivariate measurement of gene expression relationships
– Kim, Dougherty, et al.
- 2000
|
|
25
|
Hidden Order: How Adaptation Builds Complexity, Helix Books
– Holland
- 1995
|
