And is it also correct when there are multiple independent copies on a single DNA molecule. Also, how binding kinetics differs between a titration based experiment and in vivo when there is a single copy of chromosome per cell.
The Hill slope for a monovalent ligand binding to a monovalent receptor should be 1, indicating no cooperativity, since there can be no cooperativity between ligand binding sites if there is only one site.
This reasoning also applies to multiple copies of the binding site on the same DNA molecule, as long as the receptor (repressor) is monomeric. The only change in the analysis is that the concentration of ligand (binding sites) is higher than the concentration of DNA molecules, so the former concentration should be used.
If the repressor is multimeric, there is the possibility of cooperativity, and a non-unity Hill slope.
It seems likely that the kinetics of binding, as well as the thermodynamics, will differ between in vitro and in vivo experiments because of differences in the conditions, including ionic strength, composition of the medium, viscosity of the medium, and accessibility of the binding site.
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