Genetic regulatory network model

Hartemink, A. J., D. K. Gifford, et al. (2002). "Combining location and expression data for principled discovery of genetic regulatory network models." Pac Symp Biocomput 437-449. 

Doyle and co-workers have used sensitivity and identifiability analyses in a complex genetic regulatory network to determine practically identifiable parameters (Zak et al., 2003), i.e., parameters that can be extracted from experiments with a certain confidence interval, e.g., 95%. The data used for analyses were based on simulation of their genetic network. Different perturbations (e.g., step, pulse) were exploited, and an identifiability analysis was performed. An important outcome of their analysis is that the best type of perturbations for maximizing the information content from hybrid multiscale simulations differs from that of the deterministic, continuum counterpart model. The implication of this interesting finding is that noise may play a role in systems-level tasks. 

R. Zhu, A.S. Ribeiro, D. Salahub, S.A. Kauffman, Studying genetic regulatory networks at the molecular level delayed reaction stochastic models. J. Theor. Biol. 246(4), 725-745 (2007)... 

Many more formulations exist and are in current use for modeling genetic regulatory networks. These are not discussed here for the sake of... 

Albert R. (2004). Boolean modeling of genetic regulatory networks. Nature. 650, pp 459 81. 

Using Graphical Models and Genomic Expression Data to Statistically Validate Models of Genetic Regulatory Networks. 

Serra, R., Villani, M., Graudenzi, A., Kauffman, S. Why a simple model of genetic regulatory networks describes the distribution of avalanches in gene expression data. J. Theor. Biol. 246(3), 449-460 (2007)... 

Abstract. In this paper we show that a well-known model of genetic regulatory networks, namely that of Random Boolean Networks (RBNs), allows one to study in depth the relationship between two important properties of complex systems, i.e. dynamical criticality and power-law distributions. The study is based upon an analysis of the response of a RBN to permanent perturbations, that may lead to avalanches of changes in activation levels, whose statistical properties are determined by the same parameter that characterizes the dynamical state of the network (ordered, critical or disordered). Under suitable approximations, in the case of large sparse random networks an analytical expression for the probability density of avalanches of different sizes is proposed, and it is shown that for not-too-smaU avalanches of critical systems it may be approximated by a power law. In the case of small networks the above-mentioned formula does not maintain its validity, because of the phenomenon of self-interference of avalanches, which is also explored by numerical simulations. 

It is also often assumed that the presence of power-law distributions is the hallmark of criticality. Indeed, slightly different (although overlapping) notions of criticality have been used [7]. In this paper we show that a well-known model of genetic regulatory networks, introduced hy one of us several years ago [8], i.e. that of Random Boolean Networks (RBNs), can he used to study the relationships between power-law distributions and criticality issues. 

In Section II, we demonstrate this approach with an equation that incorporates a nonlinear Hill function to model genetic control representing a mutually inhibitory network of two elements [26], and an inhibitory loop of three elements [27]. Although theoretical models of these types of networks have been known for at least 30 years [20, 32, 33], they took on new life in 2000 with the construction of genetic regulatory circuits in bacteria that were well described by the equations. 

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