Computational Biology

EE550

Computational Biology

Homework 1 – due 17.03.2020 Instructions: Please return your homework by e-mail as a single PDF document by the due date with “EE550” in the subject line. Sharing of ideas and discussions is encouraged, but sharing of results and/or text is not. Show the details of your work including the intermediary results if applicable. Question (100 points) For this question, generate a random transition rate matrix 𝑄 to model the rates of nucleic acid substitutions in such a way that the off-diagonal entries vary between 0 and 1 and the diagonal entries are set so that each row sums to 0. a) (50 points) Calculate the transition probability matrix 𝑃(𝑡) corresponding to the transition rate matrix 𝑄 above and plot the corresponding transition probabilities between each nucleotide pair in a 4 × 4 table for 𝑡 ∈ [0,5]. (Hint: You need to figure out how to calculate matrix exponentials.) b) (50 points) Given the transition probability matrix 𝑃(𝑡) above, calculate the functional relationship between the sequence distance 𝐷 and the evolutionary distance 𝑑 between two nucleotide sequences. Show the calculated relationship as a graph of 𝑑 versus 𝐷.