Graduate School of Biological Sciences

This course will be offered as a Core III for the PSB curriculum. The course will run from early April till the end of June and will be offered each year.

Days & Time: M-F
Lectures: 1-2 pm
Computer Lab 2-5 pm Room: IMI 12-34 and 12-52
Start Date: 04/07/09
Ends Date: 06/23/09

This course will take a case-based approach to teach current mathematical modeling techniques to graduate students. The approach will be to use numerical computations to develop models that can be used to analyze and predict behaviors that may be experimentally tested. The course should be useful for students planning to use experimental techniques as their primary approach and use computational modeling as a tool to enhance the experimental approaches. The course should also be valuable as an introductory overview for students planning to conduct their thesis research in modeling biomedical systems. The course will have four sections to cover different modeling approaches that are currently being used in biomedical research. These approaches include graph theory and network analysis, statistical models and principal component analysis, ordinary differential equation & partial differential equation-based models and stochastic & hybrid models.

MatLab will be the major modeling program used for the course. Other programs may be used as needed. For each section there will be introductory lectures followed by one or more cases that the students will model and analyze. The majority of class time will be spent in the computer laboratory with the students developing and analyzing models. There will be one teaching assistant per 3 students who will be available to help the students during the computer lab. Class size will be limited to 6 students.

At the end of each section, the student will be given a model to compute and analyze as an exam. These exams will be in the take home format. Students will be expected to compute the model individually without consulting other students. Final grade will be the average of the four exams. At the end of the course each student should be able to develop and compute simple models on their own and collaborate with experienced modelers to compute more complex models. Students should also be able to gather experimental data in a manner that will be useful in developing and constraining models.

Date	Topic	Format	Reference	Instructor
4/7/2009	Representation of biological systems as graphs	Lecture/Lab		Ma'ayan
4/9/2009	Signaling and metabolic networks	Lecture/Lab		Ma'ayan
4/14/2009	Identifying motifs and inferring regulation from motifs	Lecture/Lab		Ma'ayan
4/16/2009	Discussion/problem solving session:  analysis of network models	Lecture		Ma'ayan
4/21/2009	Computing with matlab I	Lecture		Sobie
4/23/2009	Computing with matlab II	Lecture		Sobie
4/28/2009	Analysis of genomic data: Part I	Lecture/Lab	tba	Sirovich
4/30/2009	Analysis of genomic data: Part II	Lecture/Lab	tba	Sirovich
5/5/2009	Introduction to dynamical systems: Part I	Lecture		Sirovich
5/7/2009	Introduction to dynamical systems: Part II	Lecture		Sirovich
5/12/2009	ODE model of the Cell Cycle	Lecture/Lab	Tyson, PNAS 1991	Sobie
5/14/2009	Development of Models:  Extracting constants from experimental literature, estimating errors	Lecture		Neves
5/19/2009	ODE model of MAP-kinase bistable switch	Lecture/Lab	Bhalla, Ram, Iyengar, Science 2002	Sobie
5/21/2009	ODE model of action potential	Lecture/Lab	Hodgkin & Huxley, J. Physiol. 1952	Sobie
5/26/2009	PDE model of calcium spark	Lecture/Lab	Smith et al., Biophysical Journal, 1998	Sobie
5/28/2009	Modeling in Virtual Cell	Lecture/Lab		Neves
6/2/2009	PDE models of cAMP microdomains	Lab	Neves et al Cell 2008	Neves
6/4/2009	Discussion/problem solving session:  Analysis of ODE and PDE models			Sobie
6/9/2009	Stochastic phenomena in biology	Lecture		Sirovich
6/11/2009	Neurotransmitter release, retinal photon arrivals	Lecture/Lab	Hecht, Shlaer, Pirenne, JGP 1942; delCastillo & Katz, J. Physiol. 1954	Sirovich
6/16/2009	Gene expression I	Lecture/Lab		Hayot
6/18/2009	Gene expression II:  hybrid models	Lecture/Lab		Hayot
6/23/2009	Discussion/problem solving session:  Analysis of stochastic models	Lecture		Sirovich/Hayot