Model-Checking Signal Transduction Networks through Decreasing Reachability Sets

Our goal is to construct a model for genetic regulatory networks such that the model class: (i) incorporates rule-based dependencies between genes; (ii) allows the systematic study of global network dynamics; (iii) is able to cope with uncertainty, both in the data and the model selection; and (iv) permits the quantification of the relative influence and sensitivity of genes in their interactions with other genes. We introduce Probabilistic Boolean Networks (PBN) that share the appealing rule-based properties of Boolean networks, but are robust in the face of uncertainty. We show how the dynamics of these networks can be studied in the probabilistic context of Markov chains, with standard Boolean networks being special cases. Then, we discuss the relationship between PBNs and Bayesian networks--a family of graphical models that explicitly represent probabilistic relationships between variables. We show how probabilistic dependencies between a gene and its parent genes, constituting the basic building blocks of Bayesian networks, can be obtained from PBNs. Finally, we present methods for quantifying the influence of genes on other genes, within the context of PBNs. Examples illustrating the above concepts are presented throughout the paper.

Computational modeling of biological systems is becoming increasingly important in efforts to better understand complex biological behaviors. In this review, we distinguish between two types of biological models--mathematical and computational--which differ in their representations of biological phenomena. We call the approach of constructing computational models of biological systems 'executable biology', as it focuses on the design of executable computer algorithms that mimic biological phenomena. We survey the main modeling efforts in this direction, emphasize the applicability and benefits of executable models in biological research and highlight some of the challenges that executable biology poses for biology and computer science. We claim that for executable biology to reach its full potential as a mainstream biological technique, formal and algorithmic approaches must be integrated into biological research. This will drive biology toward a more precise engineering discipline.

Flowers are icons in developmental studies of complex structures. The vast majority of 250,000 angiosperm plant species have flowers with a conserved organ plan bearing sepals, petals, stamens, and carpels in the center. The combinatorial model for the activity of the so-called ABC homeotic floral genes has guided extensive experimental studies in Arabidopsis thaliana and many other plant species. However, a mechanistic and dynamical explanation for the ABC model and prevalence among flowering plants is lacking. Here, we put forward a simple discrete model that postulates logical rules that formally summarize published ABC and non-ABC gene interaction data for Arabidopsis floral organ cell fate determination and integrates this data into a dynamic network model. This model shows that all possible initial conditions converge to few steady gene activity states that match gene expression profiles observed experimentally in primordial floral organ cells of wild-type and mutant plants. Therefore, the network proposed here provides a dynamical explanation for the ABC model and shows that precise signaling pathways are not required to restrain cell types to those found in Arabidopsis, but these are rather determined by the overall gene network dynamics. Furthermore, we performed robustness analyses that clearly show that the cell types recovered depend on the network architecture rather than on specific values of the model's gene interaction parameters. These results support the hypothesis that such a network constitutes a developmental module, and hence provide a possible explanation for the overall conservation of the ABC model and overall floral plan among angiosperms. In addition, we have been able to predict the effects of differences in network architecture between Arabidopsis and Petunia hybrida.