How to correlate the pattern by which CAP activator from E.coli binds to DNA and its mechanism of action?
I found a great article that might help. To summarize the contents of the article, there are two classes of CAP dependent promoters/genes, and the distance of the CAP bindings site in these classes are different. Also the actions in which CAP is involved are different in the two classes of promoters. In the first class it does not overlap with the promoter region and is only involved in RNAP recruitment. In the second class it overlaps with -35 element of the core promoter and is involved in multiple interactions. 
So the binding distance of the CAP is determines what interactions is it involved. 

You can see the difference between the two classes on the picture below (taken from the article i linked). And I think this answers your question on why the patterns are multiples of ten - because this is the space needed for alpha-CTD to make a bridge between the protein complexes, or the CAP to interact with the RANP complex.



I only took a glance at the paper I linked and quickly extracted the info, but I hope it still helps