Assignment 3 Phylogenetic Tree Reconstruction and Motif Finding

Transcription

1 ssignment Phylogenetic ree Reconstruction and Motif Finding Lecturer: Michal Ziv-Ukelson ssignment hecker: Dina Svetlitsky You may submit the assignment in pairs. Explain your answers as clearly as possible and include as many details as possible. he assignment must be typed and submitted in PDF format to the submission system. Behatzlaha!

2 Question Small Parsimony (25 points):. ( pts) Run Fitch s algorithm on the following phylogenetic tree. Draw the tree computed after each of the algorithm s phases (bottom up & top down). 2. ( pts) Using the substitution matrix below, run Sankoff s algorithm on the tree from.. Draw the tree computed (including any values computed per each node) after each of the algorithm s phases, and write the final tree s score. From(row): o(column:) (5 pts) ompare the algorithms you used in. and.2. Which one is more general? How so?

3 Question 2 Maximum likelihood (5 points):. ( pts) iven the substitution probability table below, compute the likelihood of the following tree topology. Show your computation. V V 2 V V iven that the sum likelihood of all assignments of v, v2, v, v 4 is.2, except for v, v, v, v,,, (which means you have to compute it). he base frequencies are (f, f, f, f ) = (.,.2,.5,.2). short reminder: topology s likelihood is a sum of all possible inner nodes assignments likelihoods. In this question, all but one assignment have already been computed and summed ( pts) Describe the process of computing the maximum likelihood of m sequences of length. What output is expected from this process?. (5 pts) In order to compute the maximum likelihood of m sequences of length n>, what needs to be assumed? Describe how the process works.

4 Question UPM & trees (5 points):. Is the distance matrix given below dditive? Explain (5 pts) ow Pig Horse Mouse Dog at ow Pig Horse Mouse 99 Dog 88 at 2. Run UPM to compute a phylogenetic tree from the distance matrix above. Write down in detail each and every step in your computation. ( pts). In this question, a distance matrix is a matrix in which the cell i, j contains the hamming distance between sequence i and sequence j. Write the distance matrix resulting from the following sequences (5 pts): S = S2 = S = S4 = 4. Run UPM on the distance matrix from.2 and explain whether the resulting tree preserves the original distances. (5 pts) 5. How many rooted phylogenetic trees can be drawn for m sequences? Explain. (5 pts) 6. How many unrooted phylogenetic trees can be drawn for m sequences? Explain. (5 pts)

5 Question 4 Motif Discovery (25 points): he following algorithm is a cousin of one of the two motif finding algorithms we have considered in class. he parameters are named similarly to the notation used in the class slides. ssume that DN is globally available to any procedure run by the algorithm and thus does not need to be passed in the parameter list of the procedure call. ssume that s[y] denotes index y in vector s. NOHER_MOIF_SERH(DN, t, n, l) s [,,..., ] 2 bestmotif FINDINSEQ(s,, t, n, l) return bestmotif FINDINSEQ(s, currentseq, t, n, l) bestscore 2 for j to n l + s[currentseq] j 4 if currentseq t 5 s FINDINSEQ(s, currentseq +, t, n, l) 6 if Score(s) > bestscore 7 bestscore Score(s) 8 bestmotif s 9 return bestmotif. Identify which algorithm is a cousin of NOHERMOIFSERH and find the similarities and differences between these two algorithms. (7 pts) 2. What does Procedure FindInSeq compute? (6 pts). What is the time complexity of this algorithm? (6 pts) 4. How does the time complexity of the above algorithm compare to the time complexity of the other two motif-finding algorithms learned in class? (6 pts)