Transcriptional regulatory network models can be reconstructed ab initio from DNA sequence data by locating the binding sites, defined by position specific score matrices, and identifying transcription factors by homology with known ones in other organisms. In general the resulting network contains spurious elements, because the pattern matching methods for binding site location have low specificity, while homology to known transcription factors does not always identify correctly new ones. In the case of A. ferrooxidans, one of the bacterias involved in industrial bioleaching processes, the sequence based network reconstruction results in 66 transcription factors and 182 binding site motifs represented in 27 435 sites. In this work we use differential expression experimental data, in the form of Mutual Information, as logical constraints to be satisfied by any valid regulatory network subgraph. These rules are expressed as an Answer Set Program, a logical programming paradigm, and used to determine the minimal sets of motif and transcription factors which constitute a genetic regulatory network compatible with the experimental evidence. The resulting network comprises 27 transcription factors and 14 motifs in 2428 instances, satisfying all constraints.