Bioinformatics Homework: Sequence Alignment and Dynamic Programming, Assignments of Computer Science

Download Bioinformatics Homework: Sequence Alignment and Dynamic Programming and more Assignments Computer Science in PDF only on Docsity! Homework 1 Due: September 18, 8:30pm Problem 1 (5 points) • What is the complimentary sequence to the following string of nucleotides? Be sure to label the 5’ and 3’ ends. 5’- GCATATCGTAATGCCATA - 3’ • Show the mRNA transcript using the above sequence as a coding strand. • Show the final protein sequence. Problem 2 (15 points) In the lecture, I have mentioned that there are a few different ways of defining “distinct” alignments. Depending on the definition, the number of distinct alignments will be different. Consider for example the three alignments between abc and wxy: abc xyz , a-bc xy-z , and ab-c x-yz . They can be handled in two ways: (a) the three alignments are all different from each other; (b) the latter two are equivalent but distinct to the first one. The argument for (b) is that in the first alignment, a, b, c are aligned to x, y, and z respectively, while in the latter two cases, a is aligned to x, c is aligned to z, and b, y are aligned to gaps. Given two strings S, T of lengths m and n, let f(m,n) be the number of distinct alignments between them according to the second definition. In the lecture, we have discussed that f(m,n) can be obtained analytically using probability theory. The formula is f(m,n) = ( m + n n ) = (m+n)! m!n! . (Durbin book). In this assignment, you are asked to obtain the number of distinct align- ments, F(m, n), according to the first definition. There are two ways you can do it. The first is by using probability theory directly. The second is by using dynamic programming. You are free to choose either one, but the second is more related to the lectures. For this assignment, you don’t need to write a program. (1) Write down the recurrence or the formula. (2) Draw a table and fill in values from F(0, 0) to F(10, 10). (3) List all possible alignments between ab and xyz. See if the number agrees with the value F(2, 3) in your table. 1