Systems Biology: Biomedical Modeling
3 credits

Course Director: Eric Sobie, IMI 12-70F, 8-1706, eric.sobie@mssm.edu
Instructors: Eric Sobie, Larry Sirovich, Avi Ma'ayan, Susana Neves, Kevin Costa, Fernand Hayot
Teaching Assistant: Kenneth Zhang
Special Guests: Steve Kleinstein(Yale), Uri Herschberg(Yale)

This course serves as Core III for the PSB curriculum, and runs from early April until the middle of June each year. Students in other MTAs are welcome to take this course as an elective.

We take a case-based approach to teach contemporary mathematical modeling techniques to graduate students. Lectures provide biological background and describe the development of both classical mathematical models and more recent representations of biological processes. Students are taught how to analyze the models and use computation to generate predictions that may be experimentally tested.

The course is useful for students who plan to use experimental techniques as their primary approach but who will employ computational modeling as a tool to obtain integrative understanding of complex systems. The course should also be valuable as an introductory overview for students planning to conduct their thesis research in computational modeling of biological systems.

The course has four sections to cover different modeling approaches that are currently being used in biomedical research. These approaches can be classified as: 1) graph theory and network analysis; 2) statistical models, including principal components and regression; 3) ordinary differential equation & partial differential equation-based models; and 4) stochastic models. Matlab will be the major modeling program used for the course, but other programs are used when they are more appropriate. For each section introductory lectures are followed by one or more cases that require the students to implement and analyze mathematical models. Considerable class time is therefore devoted to "hands on" problem solving sessions in which the students can get assistance from the instructors and teaching assistant.

Evaluation:

For each section, students are given an assignment, based on the material covered in class that generally involves: 1) implementing a mathematical model; 2) performing simulations and/or analysis of the model; and 3) interpreting the biological implications of the results. All assignments will be in take home format. Students can collaborate with peers regarding the details of model implementation but must provide their own answers to questions. The final grade will be the average of the grades on the individual homework assignments.

Outcome:
At the end of the course each student will be able to develop and compute simple models on their own, and to collaborate with experienced modelers for more complex problems. Students will also have an improved ability to design experiments that are useful for developing and constraining models.

Course Schedule 2010

Date	Topic	Reference	Instructor
4/6	Overview of course – Introduction to modeling		Sobie
4/8	Representation of biological systems as graphs		Ma'ayan
4/13	Making predictions using network analysis		Ma'ayan
4/15	Milestones in Network Analysis		Ma'ayan
4/20	Discussion/Problem Solving Session: Analysis of Network Models		Ma'ayan
4/22	Computing with Matlab		Sobie
4/27	Introduction to Dynamical Systems		Sobie
4/29	Statistical Modeling I		Sirovich
5/4	Promoter analysis and gene set enrichment	Subramanian, PNAS 2005	Kleinstein
5/6	Statistical Modeling II		Sirovich
5/11	Bistability in Biochemical Signaling I	Ferrell & Xiong, Chaos 2001	Sobie
5/13	Bistability in Biochemical Signaling II	Gardner, Cantor, & Collins, Nature 2000	Sobie
5/18	Development of Models I: Extracting constants from experimental literature, estimating errors	Bhalla & Iyengar, Science 1999	Neves
5/20	Development of Models II: Curve fitting and error estimation		Costas
5/25	ODE model of the cell cycle	Tyson, PNAS 1991	Sobie
5/27	ODE model of the action potential	Hodgkin & Huxley, J. Physiol. 1952	Sobie
6/1	PDE model of a propagating action potential	Quan & Rudy, Circ. Research, 1987	Sobie
6/3	Modeling in Virtual Cell: ODEs and PDEs		Neves
6/8	Stochastic models I		Hayot
6/10	Stochastic models II		Hayot
6/15	No class – Pharmacology and Systems Biology MTA retreat
6/17	Summary/Wrap Up		Sobie