We discuss a method for analysing the number of GFP-LacI fusion transcription factors bound to a construct of 256 contiguous LacI binding sites using photon bleaching statics. We show by using a combination of imaging of the construct in nanochannels, photon statistics and addition of IGFP that the binding coefficient of the LacI decreases with increasing occupation of the construct, with a binding coefficient of 10(-6) M when only 15 of the 256 possible sites are occupied. We model this effect by assuming that the GFP-LacI dimer introduces elastic strain into the helix by generalized deformations, and that this strain propagates over distances at least as large as the persistence length.