BIOPHYS 433 001 WN 2025

BIOCOMPLEXITY

BIOPHYSICS433 / PHYSICS433

Instructor  Magdalena Ivanova, PhD  Email: mivanova@umich.edu

Class Schedule   11:30am - 1:00pm/TuTh    Rm: 3401MH   

Office hours  11AM-12PM Wed via Zoom https://zoom.us/my/amyloid PW 430440 

Class Calendar Refer to for information on class topics, guest lectures, homework, and assignment due dates.

Maizey An AI tutor trained specifically on the class materials.

Course description

Biophysics 433 focuses on understanding how complex behaviors and patterns emerge in biological systems, such as how cancer cell groups behave or embryos develop. The course introduces students to mathematical tools used to describe these systems. For instance, students will learn about bifurcations, which occur when a small change in conditions causes a system to switch from one behavior to another, like how a heart might go from regular to irregular beating. The course will also cover dynamical systems, both linear (predictable) and nonlinear (where small changes can have significant, unpredictable effects). The network theory for studying interconnected elements, such as brain neurons or ecosystem species, is also discussed. The class also covers the basics of chaos theory, which helps explain why some systems, like the weather or population growth, can be unpredictable even though they follow specific rules. Finally, the course will introduce spatiotemporal dynamics and pattern formation to examine how cells in developing organisms create complex, organized structures, like the stripes on a zebra or the branching of blood vessels. These models are essential for explaining how complex biological systems behave and predicting their behavior. By applying these frameworks, students will learn how to describe and analyze biological complexity, from the dynamics of cell populations to the emergent properties of entire ecosystems.

Assignments in the course will be designed to help students apply their knowledge to practical problems. You will gain hands-on experience using R-Studio, a powerful platform for data analysis and model application.

Reading and Materials

The course is based on many sources, including research papers, textbooks, and online articles. The primary resources are listed below:

• Newman (Networks): Networks: An Introduction
• Edelstein-Keshet (MMB). Mathematical Models in Biology. Classics in Applied Mathematics Series 46, SIAM
• Strogatz (NDC).  Nonlinear Dynamics and Chaos:  With Applications to Physics, Biology, Chemistry, and Engineering. 
• Nelson.  Physical Models of Living Systems – e-version from google
• Hobbie & Roth (IPMB): Intermediate Physics for Medicine and Biology
• Ivanova & Dinov (BPAD): Biomedical Physics with Applications to Disease
• Dinov: R and Rmarkdown orientation
• Dinov: Data Science and Predictive Analytics

Lecture availability    Lectures will be recorded via Zoom and posted on Canvas under Pages. You can also download the lectures in PDF format from Canvas under Files > Lectures.

Accommodations for Students with Disabilities

If you need accommodation for a disability, please let me know at your earliest convenience. Your information is private and confidential and will be treated as such.

Religious holidays and other time conflicts

Please let me know during the first two weeks of the semester if you have conflicts with the listed examination dates.

Grading

Grades will be based on four homework (40%), one in-class paper discussions (30%),  and a final exam 30%.

20% will be deducted for each late submission.

Homework

Homework assignments will be distributed every 1-2 weeks and may include computational tasks. These tasks can be completed using R-Studio, MATLAB, Mathematica, Python, or any other numerical computing platform of your choice.

Exams

The exams will be based on material covered in lectures, homework, and handouts.

Final grades will be calculated using a standard scale