Dinucleotide frequencies

On p. 48-50 Deonier outline an analysis of dinucleotide frequencies. They use (what I think is) a modification of the Chi-square statistic, where the standard square of (O - E) divided by E is also divided by a normalizing constant they call c. This is some kind of correction for the fact that nucleotide frequencies aren't equal. I'm not going to post my code here, but I'll put a copy of the file up on the .mac server and it'll last as long as I renew my subscription. I really wish there was a way to post text files to Blogger. The first 1000 bp of genomic sequence for E. coli and M. genitalium were obtained from Genbank (NC_000913 and L43967). What took me more time than anything was to re-discover that string's count method is not suitable for this sort of thing. That's because of this behavior:

>>> s = 'GAAATTC' >>> s.count('AA') 1 >>> s = 'GAAAAAAAAAAAAAAAAAAAAAATTC' >>> s.count('AA') 11

This is what I get using the nucleotide frequencies assumed by Deonier. The first block is for E. coli. The second is for M. genitalium.

The columns are: dinucleotide, observed count, expected count, Chi-square, c, Chi-square/c. Note that my values are close but not quite the same as in the book. Also there is (not shown) quite a bit of difference when the true nucleotide frequencies are used, even though they aren't very different than those assumed for this analysis. The values in the last column > 1 indicate a discrepancy between the value expected based on single nucleotide frequency and that observed in the sequence.

AA 86 62.5000 8.8360 1.3125 6.7322 AC 64 62.5000 0.0360 0.8125 0.0443 AG 45 62.5000 4.9000 0.8125 6.0308 AT 63 62.5000 0.0040 0.8125 0.0049 CA 74 62.5000 2.1160 0.8125 2.6043 CC 64 62.5000 0.0360 1.3125 0.0274 CG 69 62.5000 0.6760 0.8125 0.8320 CT 47 62.5000 3.8440 0.8125 4.7311 GA 52 62.5000 1.7640 0.8125 2.1711 GC 85 62.5000 8.1000 0.8125 9.9692 GG 63 62.5000 0.0040 1.3125 0.0030 GT 53 62.5000 1.4440 0.8125 1.7772 TA 45 62.5000 4.9000 0.8125 6.0308 TC 41 62.5000 7.3960 0.8125 9.1028 TG 76 62.5000 2.9160 0.8125 3.5889 TT 72 62.5000 1.4440 1.3125 1.1002 AA 197 202.5000 0.1494 1.2925 0.1156 AC 47 40.5000 1.0432 0.8785 1.1875 AG 43 40.5000 0.1543 0.8785 0.1757 AT 167 166.5000 0.0015 0.5005 0.0030 CA 42 40.5000 0.0556 0.8785 0.0632 CC 10 8.1000 0.4457 1.1557 0.3856 CG 2 8.1000 4.5938 0.9757 4.7082 CT 39 33.3000 0.9757 0.9001 1.0840 GA 37 40.5000 0.3025 0.8785 0.3443 GC 11 8.1000 1.0383 0.9757 1.0641 GG 7 8.1000 0.1494 1.1557 0.1293 GT 29 33.3000 0.5553 0.9001 0.6169 TA 179 166.5000 0.9384 0.5005 1.8750 TC 25 33.3000 2.0688 0.9001 2.2984 TG 32 33.3000 0.0508 0.9001 0.0564 TT 132 136.9000 0.1754 1.3293 0.1319