Methods of robustness analysis for Boolean models of gene control networks

As a discrete approach to genetic regulatory networks, Boolean models provide an essential qualitative description of the structure of interactions among genes and proteins. Boolean models generally assume only two possible states (expressed or not expressed) for each gene or protein in the network, as well as a high level of synchronisation among the various regulatory processes. Two possible methods of adapting qualitative models to incorporate the continuous-time character of regulatory networks, are discussed and compared. The first method consists of introducing asynchronous updates in the Boolean model. In the second method, the approach introduced by Glass is adopted to obtain a set of piecewise linear differential equations that continuously describe the states of each gene or protein in the network. Both methods are applied to a Boolean model of the segment polarity gene network of Drosophila melanogaster. The dynamics of the model is analysed, and a theoretical characterisation of the model's gene pattern prediction is provided as a function of the timescales of the various processes.