Math 260-022: Modeling in Biology and Physics

UC Riverside, Fall 2020

Lecture: MW 12:30pm – 1:50pm. Lectures will be launched online through Zoom and will be recorded.

Instructor: Qixuan Wang

Email: qixuanw@ucr.edu

Office: MRB 3120

Office hours and location: By appointment

Website: https://sites.google.com/ucr.edu/qixuanwang/

Course Description: In this course, we will 1) talk about several modeling topics in biology and physics, with a focus on cell and developmental biology, and 2) using these model systems, we will introduce both analytical and computational methods that are commonly used in mathematical biology and biophysics study. The goal of this course is to help students that are interested in applied math and interdisciplinary research to get prepared with basic modeling and computational skills before they join a research lab.

Prerequisites for Graduate Students: None.

Prerequisites for Undergraduate Students: Math 146AB, Math 135AB. *Please consult with your undergraduate advisors before registering this course.

Course Topics: Tentative course topics include:

· Reaction Kinetics: Reaction rate equations, Law of mass action, Enzyme kinetics, Michaelis and Menten model.

· Differential Equation Models: ODE models, Linear stability analysis, Stochastic differential equation models, Numerical methods of differential equation models.

· Scales in Nature: Non-dimensionalization, Microswimming, Singular perturbation theory.

· Gene Regulation and Cell Signaling: Gene regulatory network, Applications of Bifurcation Theory, Boolean network, Chemical master equation and stochastic simulation

· Growth and Remodeling: Theories, Discrete computational Models, Continuum mechanics introduction, Morphoelasticity Theory.

· Pattern formation: Turing mechanism, Traveling waves, Excitability.

(Students are encouraged to suggest any topic they are interested in.)

Grading: Course grades are determined by the combined total of the bi-weekly homework (60%), final presentation (40%), listed as follows.

Bi-weekly homework (60%): Homework will be assigned every 2 weeks. The homework problems will be related to course materials, and include both written and coding problems. We highly recommend Matlab, Python or C++ for coding problems, but if you prefer other languages (R, Java, etc.), it is also fine.

Presentation (40%): At the end of the quarter, each student will give a 20-30 minutes presentation. If you are doing modeling related research, you are encouraged to present your own research. Otherwise you can present a paper suggested by the lecturer, or any paper you are interested as long as it is related to the course topics.