## From Boolean to Probabilistic Boolean Networks as Models of Genetic Regulatory Networks (2002)

Venue: | Proc. IEEE |

Citations: | 90 - 16 self |

### BibTeX

@INPROCEEDINGS{Shmulevich02fromboolean,

author = {Ilya Shmulevich and Edward R. Dougherty and Wei Zhang},

title = {From Boolean to Probabilistic Boolean Networks as Models of Genetic Regulatory Networks},

booktitle = {Proc. IEEE},

year = {2002},

pages = {1778--1792}

}

### Years of Citing Articles

### OpenURL

### Abstract

Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrarive 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

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Citation Context ... is given by with probability with probability where is component-wise addition modulo 2 and , is the transition function representing a possible realization of the entire PBN, as discussed above. In =-=[96]-=-, an explicit formulation of the state-transition probabilities in terms of the Boolean functions and the probability of perturbation , was derived. It is fairly easy to show [96] that, for , the Mark... |

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Citation Context ...tion and Cellular Functional States Boolean networks qualitatively reflect the nature of complex adaptive systems in that they are “systems composed of interacting agents described in terms of rules=-=” [51]-=-. A central concept in dynamical systems is that of structural stability, which is the persistent behavior of a system under perturbation. Structural stability formally captures the idea of behavior t... |