1. Given two indices i and j, mutual information measures the amount of information that I (or the
probability distribution of which nucleotides can appear in column i) conveys about the
probability distribution of nucleotides in position j. If the mutual information between these two
distributions is high, this implies that a lot of information about the probability distribution of
column j can be gained by studying the probability of distribution of nucleotides of column i (or
vice versa). This would imply that the distributions are not independent, and that the data from
those two columns can likely be compressed.
2. Given tRNA’s folded structure, we would expect that there would be some high values of mutual
information among certain columns. The columns that have a high mutual information content
are those that are more likely to be bonded to one another in the tRNA molecule. So it is likely
that the nucleotides in the top 20 columns are bonded. For the nucleotides in the top 50
columns, the probability that they are bonded is somewhat less high, perhaps indicating the
presence of an evolutionary change or other type of mutation. As you can see in the attached
graphs, when plotting I vs. J, with the size of the plot marks proportional to their information
content, the result looks similar to that produced by the probability plots that we used in
homework 4. It stands to reason that similar conclusions can be drawn from the plot of mutual
information.