Many eukaryotic transcription factors function after forming oligomers. The choice of protein partners is a nonrandom event that has distinct functional consequences for gene regulation. In the present work we examine three dimers of transcription factors in the NF kappa B family: p50p50, p50p65, and p65p65. The NF kappa B dimers bind to a myriad of genomic sites and switch the targeted genes on or off with precision. The p65p50 heterodimer of NF kappa B is the strongest DNA binder, and its unbinding is controlled kinetically by molecular stripping from the DNA induced by I kappa B. In contrast, the homodimeric forms of NF kappa B, p50p50 and p65p65, bind DNA with significantly less affinity, which places the DNA residence of the homodimers under thermodynamic rather than kinetic control. It seems paradoxical that the heterodimer should bind more strongly than either of the symmetric homodimers since DNA is a nearly symmetric target. Using a variety of energy landscape analysis tools, here we uncover the features in the molecular architecture of NF kappa B dimers that are responsible for these drastically different binding free energies. We show that frustration in the heterodimer interface gives the heterodimer greater conformational plasticity, allowing the heterodimer to better accommodate the DNA. We also show how the elastic energy and mechanical strain in NF kappa B dimers can be found by extracting the principal components of the fluctuations in Cartesian coordinates as well as fluctuations in the space of physical contacts, which are sampled via simulations with a predictive energy landscape Hamiltonian. These energetic contributions determine the specific detailed mechanisms of binding and stripping for both homo- and heterodimers.