Math 127 Homepage, Fall 2008.

Mathematical and Computational Methods in Molecular Biology (CCN: 54852)

Instructor: Lior Pachter.


Phone: (510) 642-2028.
Office hours: Tuesdays and Thursdays 11am-12:30pm in 1081 Evans.
Lectures: Tuesdays and Thursdays, 9:30am-11:00am, 75 Evans.
Course Control Number: 54772


Syllabus

The course provides an introduction to the mathematical aspects of computational genomics with an emphasis on evolutionary biology. This year we will focus on sequence alignment- the problem of distinguishing homology from matching among related biological sequences. Students in the course will have the opportunity to experiment with (and contribute ideas to) a novel approach to sequence alignment. The resulting projects (see grading policy below) are expected to lead to a published research paper coauthored by class participants.

Textbook: Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids

Grading policy: The grade will be based on the homework (50%), a midterm (20%), and a final presentation/project (30%).

Introduction (pdf of slides) and homework 1 (due September 4th)
Homework 2 (due September 11th): 2.8,2.9 in the textbook. Draw the rooted X-forest for all the hierarchies on the set X={1,2}. How many hierarchies are there on the set X={1,2,3}?
Homework 3 (due September 18th): 2.1,2.2,2.3,2.4 in the textbook. Find the optimal alignment(s) for the pair of sequences TACGAGTACGA,ACTGACGACTGAC where the boldface characters are required to be aligned. How many distinct summaries (M,X,S) can there be for the two sequences GAGG,GAT?
Homework 4 (due September 25th): Show that the distance function introduced in class is a metric.
Homework 5 (due October 2): 3.1,3.2,3.3,3.5.
Homework 6 (due October 16): Show that for the Jukes-Cantor model the probability that a pair of characters are equal + probabilitiy that they are not equal = 1. 8.1, 8.3.

Midterm: Thursday October 16th.
Homework 7 (due October 30): Show that Z=-L-Q (where Z,L,Q are as defined in class).


Related courses and seminars of interest:

Mathematical and computational biology seminar
Statistics and genomics seminar
Seminars in statistical phylogenetics
Introduction to computational biology