Hands-on activity: Di-nucleotide frequency differences in organisms#
Objective#
The objective of this assignment is to compare the nucleotide and di-nucleotide frequencies in the human and fruit fly genomes, and to discuss possible biological justifications for the observations. You will be replicating parts of the results in [Burge et al., 1992, Gentles and Karlin, 2001].
Your genome sequence can be represented by a string over the alphabet {a,c,g,t}. Are the frequencies of a,c,g,t uniform? How about di-nucleotides, are their frequencies uniform?
Method#
Perform the following for human and fruit-fly genome.
Step 1: Let \(S\) be a DNA string of length 50 kilo-bases, taken from a random position in the genome.
Step 2: Observe the frequencies of all possible dinucleotides (see notes below on how to deal with double-strandedness of DNA).
Step 3: Compute the over-representation or under-representation of the dinucleotides by computing the odds ratio of observed and expected frequencies.
Step 4: Repeat 100 times.
Step 5: Visualize and discuss your results.
A note on computing (di)nucleotide frequencies#
If we were to treat \(S\) as a single string (i.e. ignore the double-stranded-ness of RNA), for a dinucleotide \(xy\) , its odds ratio (i.e. ratio of observed frequency and expected frequency) would be \( R_{xy} = f_{xy}/f_xf_y\), where \(f_{xy}\) is the observed frequency of \(xy\) in \(S\) and \(f_x\) is the frequency of nucleotide \(x\) in \(S\).
However, since \(S\) is double stranded, we need to consider its reverse complementary sequence \(S_{RC}\). Let \(S'\) be the sequence obtained by concatenating \(S\) and \(S_{RC}\). The presence of say a \(\tt{ cc}\) in \(S\) means there is a \(\tt{ gg}\) in \(S_{RC}\), and the frequency of \(\tt{ cc}\) and \(\tt{ gg}\) in \(S'\) would be the same. So we could club together \(\tt{ cc}\) and \(\tt{ cc}\) into one group. Overall there will be ten groups from the 16 possible dinulceotides.
For a nucleotide \(x\), its frequency \(f'_{x}\) in \(S'\) is:
\(f'_{x} = (1/2) \times (f_{x} + f_{\bar{x}})\),
where \(f_x\) and \(f_{\bar{x}}\) are the frequencies \(x\) and its reverse complement nucleotide \(\bar{x}\) in \(S\).
Similarly, the frequency of a di-nucleotide \(xy\) in \(S'\) is:
\(f'_{xy} =(1/2) \times (f_{xy} + f_{\bar{y}\bar{x}})\),
where \(f_{xy}\) and \(f_{\bar{y}\bar{x}}\) are the frequencies of \(xy\) and its reverse complement dinucleotide \(\bar{y}\bar{x}\) in \(S\).
Therefore the odds ratio that considers both strands is:
\(R'_{xy} = \frac{f'_{xy}}{f'_{x}f'_{y}}.\)
References#
C Burge, A M Campbell, and S Karlin. Over- and under-representation of short oligonucleotides in DNA sequences. Proc. Natl. Acad. Sci. U. S. A., 89(4):1358–1362, February 1992.
A J Gentles and S Karlin. Genome-scale compositional comparisons in eukaryotes. Genome Res., 11(4):540–546, April 2001.