Transcription factors are proteins that bind to motifs on the DNA and thus affect gene expression regulation. The qualitative description of the corresponding processes is therefore important for a better understanding of essential biological mechanisms. However, wet lab experiments targeted at the discovery of the regulatory interplay between transcription factors and binding sites are expensive. We propose a new, purely computational method for finding putative associations between transcription factors and motifs. This method is based on a linear model that combines sequence information with expression data. We present various methods for model parameter estimation and show, via experiments on simulated data, that these methods are reliable. Finally, we examine the performance of this model on biological data and conclude that it can indeed be used to discover meaningful associations. The developed software is available as a web tool and Scilab source code at http://biit.cs.ut.ee/gmat/.