??? Math 319: Applied Probability and Stochastic Processes for Biology


Applied Probability and Stochastic Processes for Biology

MATH 319 / BIOL 319-419 / PHOL 419 / EBME 419 / EECS 319

Catalog Description

Applications of probability and stochastic processes to biological systems. Mathematical topics will include: introduction to discrete and continuous probability spaces (including numerical generation of pseudo random samples from specified probability distributions), Markov processes in discrete and continuous time with discrete and continuous sample spaces, point processes including homogeneous and inhomogeneous Poisson processes and Markov chains on graphs, and diffusion processes including Brownian motion and the Ornstein-Uhlenbeck process. Biological topics will be determined by the interests of the students and the instructor. Likely topics include: stochastic ion channels, molecular motors and stochastic ratchets, actin and tubulin polymerization, random walk models for neural spike trains, bacterial chemotaxis, signaling and genetic regulatory networks, and stochastic predator-prey dynamics. The emphasis will be on practical simulation and analysis of stochastic phenomena in biological systems. Numerical methods will be developed using both MATLAB and the R statistical package. Student projects will comprise a major part of the course. Offered as BIOL 319/419, MATH 319, EECS 319, EBME 419, PHOL 419. Students enrolled for graduate credit will have additional expectations related to the course projects.

New for Spring 2011

Thanks to a generous award from UCITE's Glennan Fellows Program, the course will be significantly revised to emphasize the use of MCell. MCell is a specialized numerical platform designed for state of the art Monte Carlo simulations of Cellular microphysiology, developed jointly by the Pittsburgh Supercomputer Center (http://www.mcell.psc.edu/) and the Computational Neurobiology Laboratory at the Salk Institute for Biological Studies (http://www.mcell.cnl.salk.edu/). The course syllabus has been totally redesigned so that students will learn the practical details of simulating and visualizing stochastic microscale biological systems at the same time as they learn the mathematical framework for stochastic modeling. MCell will play a major role in the course along with some use of Matlab or similar platforms for data visualization and analysis. Class will meet two days a week in a lecture hall and one day a week in the Department of Mathematics' computer laboratory. Students will be expected to complete a course project using MCell, and will have access to the CWRU High Performance Computing Cluster as part of the course. Also, there is a class trip to visit the MCell developers at the Pittsburgh Supercomputer Center in the works.

Syllabus

Course description, how the course is being updated, rules and regulations etc.

Course Flyer

An attractive flyer.

Course Schedule on Google Calendar

Under construction. Check back here for reading assignments etc.

Google Docs Page

Check back to the Google Docs page for classwork assignments and other course information.

MCell Tutorial Pages

These tutorials were adapted for the CWRU course from materials provided by the developers of MCell. For the tutorials provided by the developers click here.

Background & Topics

Mathematical models of biological systems frequently involve systems of ordinary or partial differential equations. While these deterministic models can give important insights into biological behavior, they fail to include the effects of chance fluctuations on biological dynamics. This course will explore applications of probability theory and stochastic processes in biological systems. It is a natural extension of the biological dynamics courses (BIOL 300 or BIOL 306) or a first course in differential equations (MATH 224 or 228) and any of these can serve as a prerequisite. Students should be comfortable with multivariable calculus (MATH 223 or 227) and linear algebra (MATH 201 or MATH 307). While the mathematical content will be appropriate for a 300 level undergraduate course, the emphasis will be on applications and practical matters such as numerically simulating biological stochastic phenomena using numerical platforms such as the R statistical package, MATLAB, scientific/numerical python, and MCell. Mathematical topics to be covered include applications of: Biological applications will be determined by the mutual interests of the students and the instructor. Suggestions are welcomed. A list of tentative topics includes:

Matlab References


For more information, please contact Dr. Thomas.

Updated: February 6, 2011