ABSTRACT
As molecular data accumulates, the use of mathematical and computational tools for understanding how the concerted actions of genes underlie developmental processes and phenotypical traits is becoming both necessary and possible. This has stimulated network theory, as a tool for understanding complex systems comprised of many connected elements with correlated behaviours and non-linear interactions. In this chapter we first present the concept of basic dynamic gene regulatory network (GRN) models and discuss which mathematical tools can be used to integrate data from complex biological processes at different space-time scales. We then explain key concepts of dynamic systems as exemplified by the Boolean case. In the following section we discuss two concepts basic to understanding GRNs of developmental processes: epistasis and robustness. After that we review work on two main approaches to studying GRN in animal and plant development. The first approach focuses on modules or subnetworks, in which behaviour is relatively autonomous and for which dynamical analyses with direct functional and/or structural interpretations are possible. By reviewing a repertoire of such small networks, we point to some generalities that are starting to emerge concerning their robust dynamic behaviour in the face of environmental and genetic perturbations. Detailed dynamical studies of specific modules enable detection of holes in experimental data and lead to novel predictions that may be tested experimentally and then fed back to refine the models. Furthermore, the application of the modular approach to understanding the genetic basis of body plan evolution in plants and animals has allowed us to hypothesize that a number of regulatory processes underlying developmental problems have evolutionarily conserved solutions. The second approach aims at recovering the complete GRN for an organism. Such studies rely on different inference methods to reverse engineer the GRN structure from genomic-wide expression arrays from different genetic backgrounds and under different environmental conditions. Dynamic analyses of genome-level GRN are still a challenge that lies ahead in both the experimental and theoretical-computational research fronts.
