Computer simulations and experimental studies of gel mobility patterns for weak and strong non-cooperative protein binding to two targets on the same DNA: application to binding of tet repressor variants to multiple and single tet operator sites.

A series of computer simulations of gel patterns assuming non-cooperative binding of a protein to two targets on the same DNA fragment was performed and applied to interprete gel mobility shift experiments of Tet repressor-tet operator binding. While a high binding affinity leads to the expected distribution of free DNA, DNA bound by one repressor dimer and DNA bound by two repressor dimers, a lower affinity or an increased electrophoresis time results in the loss of the band corresponding to the singly occupied complex. The doubly occupied complex remains stable under these conditions. This phenomenon is typical for protein binding to DNA fragments with two identical sites. It results from statistical disproportionation of the singly occupied complex in the gel. The lack of the singly occupied complex is commonly taken to indicate cooperative binding, however, our analysis shows clearly, that cooperativity is not needed to interprete these results. Tet repressor proteins and small DNA fragments with two tet operator sites have been prepared from four classes of tetracycline resistance determinants. The results of gel mobility shift analyses of various complexes of these compounds confirm the predictions. Furthermore, calculated gel patterns assuming different gel mobilities of the two singly occupied complexes show discrete bands only if the electrophoresis time is shorter than the inverse of the microscopic dissociation rate constant. Simulations assuming increasing dissociation rates predict that the two bands first merge into one, which then disappears. This behavior was verified by gel mobility analyses of Tet repressor-tet operator titrations at increased salt concentrations as well as by direct footprinting of the complexes in the gel. It is concluded that comparison of the intensities of the single and the double occupation bands allow a rough estimation of the dissociation rate constant. On this basis the sixteen possible Tet repressor-tet operator combinations can be ordered with decreasing binding affinities by a simple gel shift experiment. The implications of these results for gel mobility analyses of other protein-DNA complexes are discussed.