AMATH 410:

Introduction to Computational Biology and Chemistry


SLN 19428, MTWF 8:30-9:20

LOCATION: MWF, GUG 416. ***Tues, Room B022 of ICL lab ** .


Instructor:

Professor Eric Shea-Brown
Guggenheim 414F
etsb@amath.washington.edu
office hours: M 1:15-2:45, Guggenheim 415F; T 9:20-9:50, Room B022 of ICL lab


Description and Objectives Textbook and Notes Syllabus Schedule and Homework

Description and Objectives

In AMATH 410, you will learn about models that arise in biology in chemistry and how they're analyzed using modern mathematical and computational techniques. We will cover statistical models, discrete- and continuous- time dynamical models, and stochastic models. Applications will sample a wide range of scales, from biomolecules to population dynamics, with an emphasis on common mathematical concepts and computational techniques. Throughout, our themes will include interpretation of existing data and predictions for new experiments.

MATLAB will be used for numerical computation, visualization, and data analysis -- and mathematical tools taught in parallel with their computational implementation.

This course is designed for students in a wide variety of departments and with backgrounds across the sciences. A working knowledge of calculus is assumed, together with a desire to learn more about the underlying science, mathematics, or both.

Textbooks, Notes, and Course Resources

The required text for this course is "Dynamic Models in Biology," by Stephen Ellner and John Guckenhiemer (called EG below). A few chapters (including CHAPTER 1) are available free online, here. The text should be in the bookstore, is available on Amazon, and is on reserve in the library.

The "Lab Manual" for this course is also required reading. Freely available from the webpage here, this manual introduces MATLAB and computational methods -- and how to use them to solve and analyze the models and problems in the main text.

OTHER COURSE RESOURCES -- Mathematical models and analysis

These useful texts are also on course reserve in the library:

A course in Mathematical Biology, by de Vries, Hillen, Lewis, Muller, Schonfisch

Mathematical Models in Biology, by Leah Edelstein-Keshet

OTHER COURSE RESOURCES -- Computational methods and MATLAB

The notes of Prof. Nathan Kutz for AMATH 301 are a valuable course reference. Prof. Kutz has provided them online here: (.pdf)

There are a variety of MATLAB resource books available at the library. An excellent one is "Matlab Guide," by Desmond and Nicholas Higham. It is currently on "Math Reserve" in the library ( QA297 .H5217 2005).

For other MATLAB resources, including online tutorials, see below.

 

Syllabus

(1) Course overview and introduction to mathematical models in the life sciences (1 week).
Reading: EG Chapter 1, EG lab manual sections 1-6.

Partial lecture notes, codes, and sampling of papers referred to in class:

(2) Matrix models -- discrete time, linear maps (2 weeks)
Reading: EG Chapter 2.

(3) Stochastic models (2.5 weeks)
Reading: EG Chapter 3.1-3.3, EG Lab manual (section 11). Also: Anderson and Stevens (1973), below. Additional resources on stochastic ion channels: (1) Foundations of Cellular Neurophysiology, by Johnston and Wu, (2) Introduction to Theoretical Neurobiology, Volume 2, by H. Tuckwell.

(4) Continuous time models (3.5 weeks)
Reading: EG Chapter 4, 5.1-5.4, 5.7, 6.1-6.3. Also: section 5 of Amath301 notes by N. Kutz (see link above).
(5) More on fitting and testing models (1 weeks)
Reading: EG Chapter 9

Schedule and Homework

Follow links in the table below to obtain a copy of the homework in Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems. For additional information regarding viewing and printing the homework and solution sets, click here.

Homework, Exams, and Events Date Problem sets, etc.
First day of class Monday, Jan. 7
Homework#1 Due Wed. Jan 16, 8:30 AM Homework #1 (.pdf) Homework #1 solutions (.pdf)
M.L. King Day Monday, January 21 no classes
Homework#2 Due Wed. Jan 30, 8:30 AM
Homework#3 (note due date) Due Fri. Feb 8, 8:30 AM
Midterm Review Mon. Feb 11
Midterm Wed. Feb 13, in class Midterm
No class Fri. Feb 15 Start preparing case studies
President's Day Monday, February 18 no classes
Case study presentations IN CLASS Mon. Feb 25 and Weds. Feb 27 8:30 AM
Homework#4 Due Wed. March 5, 8:30 AM Homework#5 Due Fri. March 14, 8:30 AM
Last day of classes Friday, March 14
Final Presentations Tuesday, March 18, 9:00-10:20am

Final Presentations

Location: GUG 416

Homework submission and course policies

Homework is due at the beginning of class on the days above. Please take careful note of these dates, as they are somewhat irregularly spaced. Please also note that these dates might change somewhat as the course progresses -- webpage and email updates will be provided.

No late homework will be accepted. However, for all students, I will drop the lowest ONE homework grade (i.e., one out of the five) when calculating the homework average.

 

Grading

Your course grade will be calculated via the following weights:

Homework 40%

Midterm 20%

Case study presentation 5%

Course project 35%

The test schedule is in the table above.

Case study and final project presentation -- follow link to more details.

Each student will give a brief in-class presentation of a paper that applies the modeling and computational techniques we have learned in the course (case study). These studies will be developed into course projects. FOLLOW THIS LINK TO PROJECT AND CASE STUDY DETAILS.

Matlab Resources

In this course, we will make extensive use of Matlab, a technical computing environment for numerical computation and visualization produced by The MathWorks, Inc. Computers running with MATLAB, as well as the accompanying documentation, are available in the ICL Lab. If you are working in the Windows environment, be sure to check out the Matlab notebook feature that integrates Matlab with Microsoft Word.

There are many additional Matlab resources available on the net, such as the below and many tutorials.