Why is H. influenzae's CRP so feeble?

One discovery from the grad student's work on Sxy and CRP is that the H. influenzae CRP protein binds CRP sites much less strongly (with much lower affinity) than the E. coli CRP protein does. This is a bit surprising. The two proteins have quite similar sequences, and all the amino acid residues expected to directly contact the DNA are identical.

He's going to contact a lab that has done extensive structural analysis of E. coli CRP, to see how difficult it would be to see how well H. influenzae CRP will superimpose on the E. coli structure. One possibility he suggested is that the dimerization domain of H. influenzae CRP could be weak. This would cause the protein to spend less time assembled into the dimers that most readily bind DNA.

Until now we (at least I) had thought that the affinity of CRP for different genes was determined by how well the gene's CRP site matched the protein's requirements for binding. This would have been optimized for each gene by natural selection acting on mutations in its CRP site. But now I'm wondering whether natural selection has also acted differently on E. coli and H. influenzae CRP proteins to fine tune their affinity for all the sites in their respective genomes.

H. influenzae has only about 40% as many genes as E. coli, and about 40% as many CRP sites regulating them. But I can't think of any way that would favour a 100-fold difference in CRP affinity for the same CRP site, which is what the grad student has found.

The assays were done under exactly the same conditions, but this doesn't ensure that the proteins responded identically to these conditions. I wonder if the binding conditions used for these measurements (optimized for E. coli CRP) might be unsuitable for H. influenzae CRP.