# Math 127 Homepage, Fall 2008.

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

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 TACGA**G**TACGA,ACTGAC**G**ACTGAC 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