1. How do you modify the pairwise global alignment algorithm so that it outputs not only the optimal alignment but also the second best alignment? You do not need to give the modified algorithm. Instead, your answer should list the important changes that are necessary for you to achieve the new goal of finding and outputing the second best alignment.

2. The local pairwise alignment algorithm introduced in the class actually finds not only one but all conserved motifs that are above any given significance level. Please explain. Note that you do not need to modify the algorithm. Instead, your explanation should just be based on the given local pairwise alignment algorithm.

Team (one or two students) Project:

1. Construct a profile-HMM from a set of gene or motif sequences that are multiple-aligned. Based on the aligned data, discuss how the topology of the profile-HMM is determined and how the probablity parameters are computed.

2. Implement the standard Viterbi decoding algorithm for profile-HMMs so that it computes the optimal path for the constructed profile-HMM on any given sequence.

3. Apply the implemented Viterbi algorithm to search on genome sequences for additional candidates of the profile. Discuss how to ensure candidates identified are significant in their scores or probabilities.

4. Requirements:
   • You need to obtain your own multiple aligned data set for the profile-HMM construction. The data set needs to be sufficiently large (i.e., not just a few sequences);

   • Pseudocounts need to be considered for the data;

   • The implemented Viberti algorithm needs to be the standard version, not a verson specific to the profile you have constructed;

   • In addition to the Viberti algorithm, additional functions may be needed for accomplishing the genome search and candidate evaluation.

This homework is due on Friday March 4, 2016.