Abstract: Transcription factor proteins control the temporal and spatial expression of genes by binding specific regulatory elements, or motifs, in DNA. Mapping a transcription factor to its motif is an important step towards defining the structure of transcriptional regulatory networks and understanding their dynamics. The information to map a transcription factor to its DNA binding specificity is in principle contained in the protein sequence. Nevertheless, methods that map directly from protein sequence to target DNA sequence have been lacking, and generation of regulatory maps has required experimental data. Here we describe a purely computational method for predicting transcription factor binding. The method calculates the free energy of binding between a transcription factor and possible target DNA sequences using thermodynamic integration. Approximations of additivity (each DNA basepair contributes independently to the binding energy) and linear response (the DNA-protein and DNA-solvent couplings are linear in an effective reaction coordinate representing the basepair character at a specific position) make the computations feasible and can be verified by more detailed simulations. Results obtained for MAT-alpha2, a yeast homeodomain transcription factor, are in good agreement with known results. This method promises to provide a general, computationally feasible route from a genome sequence to a gene regulatory network.