Corrections and Addenda

1. Important clarification: The svd() function returns the square roots of the eigenvalues of RR^T and R^TR, rather than the eigenvalues themselves. See the "Comparing Protein Structures" section of the updated project description for more details.
2. The pickCA() function will not retrieve the CA coordinates correctly for several assigned proteins. Instead, download pickAtom.m. It works just like pickCA(), but is more general in that it can retrieve the coordinates of any specified backbone atom. Type help pickAtom for more information.
3. If you downloaded the file alignments.txt before Wednesday, October 10, please re-download it here. The new version fixes a problem with the sequence of the protein 1DO1.
4. If you downloaded drawCluster.m before Friday, October 12, you can re-download it here. This is not necessary, though: all it will do is draw a nicer graphical representation of your clustering output than the previous version.

General Information

• The projects are individual. You should not be working with partners.
• For information on how to hand in the project, see the deliverables section at the bottom of the page.

Part 1: Determining Distances Between Protein Structures

1. Read the project description.
2. Download the following sequences from the protein databank:

      1) 1MBC         5) 1BZ6         9) 1YOI
      2) 1DO1         6) 1MBO        10) 4MBN
      3) 1A6G         7) 1BZR        11) 1LH1
      4) 1VXH         8) 1YMB
   

   Throughout the assignment, these proteins will be numbered as above. When you refer to protein #1, for example, it will be clear you are referring to 1MBC. If you plan to change this convention, please make it clear in your code.
   
   
3. Download the following three files into your project directory:

   alignments.txt

   File of all pairwise sequence alignments

   loadAlignments.m

   Matlab function to parse the alignments.txt file and extract and store all pairswise sequence alingments.

   getAlignment.m

   Matlab function to retrieve a specific pairwise alignment from the structure returned by loadAlignments().

   
   You are encouraged to use the provided Matlab functions, although you are free to write your own Matlab code or modify the provided code in order to retrieve the alignments. Once you've downloaded the functions, you can use the help command in order to find out how to use them.
   
   
4. Use the pickAtom() function to extract the CA coordinates for each protein structure.
   
   The following three steps can be intergrated together, though it is better style to write separate functions for each:
5. Write the code to extract the relevant CA coordinate vectors to be compared, based on the sequence alignment.
6. Write the code to compute the distance between a pair coordinate matrices.
7. Using the code from (5) and (6) above, generate an 11x11 matrix of distances between each possible pair of structures. Print out this matrix to complete this part of the assignment.

Part 2: Building Similarity Clusters

1. Read the project description.
2. Download the cluster library below. The cluster library has been provided in order to make it easy to manage clusters. It consists of the following files:

   makeCluster.m

   Create a leaf cluster containing a specified value. Can be used to associate a leaf cluster with a protein.

   combineClusters.m

   Create a compound cluster containing two specified clusters

   isLeafCluster.m

   Return true if a cluster is a leaf cluster, false if it is a compound.

   getClusterValue.m

   Return a value stored in a leaf cluster. Could be used to retrieve an associated protein from a leaf cluster.

   getSubClusters.m

   Get the sub-clusters of a compound cluster.

   drawCluster.m

   Draws a nice graphical representation of a cluster and all its nested subclusters. Useful to display the entire cluster structure once the clustering has been completed.

   
   You are encouraged to use the provided Matlab functions, although you are free to write your own Matlab code or modify the provided code in order to handle clusters. Once you've downloaded the functions, you can use the help command in order to find out how to use them.
   
   
3. Implement the clustering algorithm.
   
   
4. Using your clustering algorithm and the distance matrix generated in the last step of Part 1, perform clustering on the proteins. Output the resulting nested cluster structure. You can either use the drawCluster() function of the cluster library, write your own code for outputting the clusters, or draw the clusters by hand.
   
   
5. What conclusions can you draw about the evolutionary relationship of the proteins based on your clustering output?

Bonus: Explaining the Clustering Output

• All the code that you wrote. That is, all the code for computing the distances, clustering, all matlab commands you've used, and any supporting functions that you wrote. In addition, if you modified any of the provided code, you must submit the modified versions: however, if you used the provided code "as is" you do not need to submit it. Basically, you should submit everything that the TA would need to successfully run your program.

  All code must be submitted both electronically and on paper. The electronic version will be tested, so if there are any special execution instructions, please include them with your code. Needless to say, the electronic and paper versions of your code should be identical.

• The matrix of pairwise distances between structures. This should be submitted on paper only.

• The outcome of your clustering algorithm, along with a paragraph interpreting these results. Should be submitted on paper only.

• If you choose to do the bonus part of the project, submit a short report relating biological information about each protein to the results of your clustering algorithm. This submission is also paper-only.