  Gene regulation is one of the most important fundamental biological processes
in living cells. It involves multiple protein molecules that locate specific
sites on DNA and assemble gene initiation or gene repression multi-molecular
complexes. While the protein search dynamics for DNA targets has been
intensively investigated, the role of inter-molecular interactions during the
genetic activation or repression remains not well quantified. Here we present a
simple one-dimensional model of target search for two interacting molecules
that can reversibly form a dimer molecular complex, which also participates in
the search process. In addition, the proteins have finite residence times on
specific target sites, and the gene is activated or repressed when both
proteins are simultaneously present at the target. The model is analyzed using
first-passage analytical calculations and Monte Carlo computer simulations. It
is shown that the search dynamics exhibits a complex behavior depending on the
strength of inter-molecular interactions and on the target residence times. We
also found that the search time shows a non-monotonic behavior as a function of
the dissociation rate for the molecular complex. Physical-chemical arguments to
explain these observations are presented. Our theoretical approach highlights
the importance of molecular interactions in the complex process of gene
activation/repression by multiple transcription factor proteins.
