The tetracycline operon is an important gene network component, commonly used in synthetic biology applications because of its switch-like character. At the heart of this system is the highly specific interaction of the tet repressor protein (TetR) with its cognate DNA sequence (tetO). TetR binding on tetO practically stops expression of genes downstream of tetO by excluding RNA polymerase from binding the promoter and initiating transcription. Mutating the tetO sequence alters the strength of TetR-tetO binding and thus provides a tool to synthetic biologists to manipulate gene expression levels. We employ molecular dynamics (MD) simulations coupled with the free energy perturbation method to investigate the binding affinity of TetR to different tetO mutants. We also carry out in vivo tests in Escherichia coli for a series of promoters based on these mutants. We obtain reasonable agreement between experimental green fluorescent protein (GFP) repression levels and binding free energy differences computed from molecular simulations. In all cases, the wild-type tetO sequence yields the strongest TetR binding, which is observed both experimentally, in terms of GFP levels, and in simulation, in terms of free energy changes. Two of the four tetO mutants we tested yield relatively strong binding, whereas the other two mutants tend to be significantly weaker. The clustering and relative ranking of this subset of tetO mutants is generally consistent between our own experimental data, previous experiments with different systems and the free energy changes computed from our simulations. Overall, this work offers insights into an important synthetic biological system and demonstrates the potential, as well as limitations of molecular simulations to quantitatively explain biologically relevant behavior.