Inferring Boolean networks with perturbation from sparse gene expression data: a general model applied to the interferon regulatory network

Due to the large number of variables required and the limited number of independent experiments, the inference of genetic regulatory networks from gene expression data is a challenge of long standing within the microarray field. This report investigates the inference of Boolean networks with perturbation (BNp) from simulated data and observed microarray data. We interpret the discrete expression levels as attractor states of the underlying network and use the sequence of attractor states to determine the model. We consider the case where a complete sequence of attractors is known and the case where the known attractor states are arrived at by sampling from an underlying sequence of attractors. In the former case, a BNp can be inferred trivially, for an arbitrary number of genes and attractors. In the latter case, we use the constraints posed by the distribution of attractor states and the need to conserve probability to arrive at one of three possible solutions: an unique, exact network; several exact networks or a ‘most-likely’ network. In the case of several exact networks we use a robustness requirement to select a preferred network. In the case that an exact option is not found, we select the network that best fits the observed attractor distribution. We apply the resulting algorithm to the interferon regulatory network using expression data taken from murine bone-derived macrophage cells infected with cytomegalovirus.