I've spent so much time fiddling with the MatrixPlot settings to get the best visualization of the correlation analysis that Matrix Plot won't let me submit any more jobs. (Who knew the site had a limit of 50 jobs per 24 hr period?)
I've done the final analysis with a set of 3466 sequences, each 39bp) and each containing at least a rough match to the USS motif. These were obtained by motif searches told that 3000 sites were expect on each strand; 1650 and 1816 were found. 1454 of these contain perfect matches to the 9bp core consensus, 512 have one-off matches, 557 have two-off matches, and 943 have core sequences that match the consensus at no more than 6 places. I think having this many mismatched sequences gives the analysis the power to detect correlations even between the highly-conserved core positions.
First, look at the control figure to the left. This shows analysis of 3500 random sequences, each 39bp long, taken from random segments of both strands of the H. influenzae genome. The bar charts at the top and left can be ignored - they show the 'information' at each position, but the scale for these bars only goes from 0.0 to 0.00 (weird, I know. I guess '0.0' represents zero, and '0.00' represents less than 0.01),
It's a bit surprising (to me) that the few scores higher than 0.002 are mostly found between positions separated by 3 (positions 1 and 4, positions 3 and 6, positions 4 and 7, positions 9 and 12, etc.). I suspect this has something to do with the way coding for proteins constrains the genome, but it's not something I'm going to follow up.
Here's the 'experimental' image. It shows significant correlations only between close-neighbour positions, and only between neighbours within each of the two flanking conserved AT segments. I suspect that even these 'significant' correlations are quite weak (the highest correlation score is only 0.107), but I don't understand the analysis well enough to be sure. The documentation is very brief; I may need to send someone an email asking for clarification.
(Here's a logo as a reminder of the motif.)
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