Modeling a gene's expression from its intergenic locus and trans-regulatory context is a fundamental goal in computational biology. Owing to the distributed nature of cis-regulatory information and the poorly understood mechanisms that integrate such information, gene locus modeling is a more challenging task than modeling individual enhancers. Here we report the first quantitative model of a gene's expression pattern as a function of its locus. We model the expression readout of a locus in two tiers: 1) combinatorial regulation by transcription factors bound to each enhancer is predicted by a thermodynamics-based model and 2) independent contributions from multiple enhancers are linearly combined to fit the gene expression pattern. The model does not require any prior knowledge about enhancers contributing toward a gene's expression. We demonstrate that the model captures the complex multi-domain expression patterns of anterior-posterior patterning genes in the early Drosophila embryo. Altogether, we model the expression patterns of 27 genes; these include several gap genes, pair-rule genes, and anterior, posterior, trunk, and terminal genes. We find that the model-selected enhancers for each gene overlap strongly with its experimentally characterized enhancers. Our findings also suggest the presence of sequence-segments in the locus that would contribute ectopic expression patterns and hence were "shut down" by the model. We applied our model to identify the transcription factors responsible for forming the stripe boundaries of the studied genes. The resulting network of regulatory interactions exhibits a high level of agreement with known regulatory influences on the target genes. Finally, we analyzed whether and why our assumption of enhancer independence was necessary for the genes we studied. We found a deterioration of expression when binding sites in one enhancer were allowed to influence the readout of another enhancer. Thus, interference between enhancer activities was a possible factor necessitating enhancer independence in our model.