  Much of the complexity observed in gene regulation originates from
cooperative protein-DNA binding. While studies of the target search of proteins
for their specific binding sites on the DNA have revealed design principles for
the quantitative characteristics of protein-DNA interactions, no such
principles are known for the cooperative interactions between DNA-binding
proteins. We consider a simple theoretical model for two interacting
transcription factor (TF) species, searching for and binding to two adjacent
target sites hidden in the genomic background. We study the kinetic competition
of a dimer search pathway and a monomer search pathway, as well as the
steady-state regulation function mediated by the two TFs over a broad range of
TF-TF interaction strengths. Using a transcriptional AND-logic as exemplary
functional context, we identify the functionally desirable regime for the
interaction. We find that both weak and very strong TF-TF interactions are
favorable, albeit with different characteristics. However, there is also an
unfavorable regime of intermediate interactions where the genetic response is
prohibitively slow.
