**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). |