Course Description
Broad introduction to mathematical modeling for molecular processes in living systems.
Athena Title
Systems Biology
Prerequisite
BINF(MIBO)(BCMB) 8211
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
The goal of the class is to make students competent to solve and identify practical problems in biology of the type dxi/dt=f(x1,x2,…,xi,…,xn) through the following student outcomes in which they are able to: 1. analyze the dynamics of a nonlinear dynamical system; 2. simulate complicated nonlinear dynamical systems; 3. identify complicated nonlinear dynamical systems; 4. design experiments to identify complicated nonlinear dynamical systems. In the first half of the course, students will be exposed to discrete and continuous models. There will be two unit exams and a final exam. Homework problems include analytical work and computational work. In the second half of the course, students will prepare weekly written reports and Powerpoint presentations on their work. Evaluation • Evaluation will be based on the ability to solve problems. • Evaluation will also be based on written reports submitted weekly in the second half of the course. The course will be writing intensive. • Evaluation will be by peers and instructor based on weekly oral reports in the second half of the course.
Topical Outline
1. Apply Buckingham's Pi theorem to produce a dynamical dimensionless system. 2. Determine fixed points of the dynamical system; that is, solve the system f(x) = 0. 3. Find the Jacobian matrix of f(x) and evaluate it at each one of the relevant fixed points. 4. Based upon eigenvalues, determine stability conditions, draw trajectories in the phase plane (if convenient), and, in general, describe the behavior of the dynamical system. 5. Determine and describe bifurcations in dynamical systems. The second half of the course will focus on tools that enable the modeling of synthetic and naturally occurring systems. The models will tend to be larger, and new approaches for identifying the models will be introduced so that students can become familiar with the data used to test systems biology models and its limitations. 6. Simulating a genetic network with application to the qa gene cluster of Neurospora crassa. 7. Building a genetic network using the toggle switch as an example. 8. Achieving stable oscillations with the repressilator. 9. Identifying genetic networks by ensemble methods using the repressilator as an example. 10. Microarray analysis using RNA profiling data on the biological clock in N. crassa. 11. Hypothesis testing in microarray analysis using ensemble methods on the qa gene cluster. 12. Model-guided discovery using the maximally informative next experiment (MINE).