Cellular Biophysics and Modeling is a required mathematical course in William & Mary‘s Neuroscience program. The course curriculum was initially developed as part of an NSF CAREER grant to this blog’s author, Greg Conradi Smith. For more than a decade, Cellular Biophysics and Modeling has been taught once per academic year to 50-100 undergraduate students.
Cellular Biophysics and Modeling is an integrated exposition of electrophysiology of excitable cells and introductory nonlinear dynamics. The course includes challenging readings from the primary literature and weekly homework assignments. The prerequisites are calculus and a 200-level introduction to cell and molecular biology.
Topics include: the biophysics of excitable membranes, the gating of voltage- and ligand-gated ion channels, neuronal calcium signaling, Hodgkin-Huxley-style mathematical modeling of the neuronal action potential, the geometry of electrical bursting, central pattern generation, and the role of inhibition, network connectivity, synaptic dynamics, and synchronization in brain function.
The course notes – units 1 & 2 (of 3) – have recently been developed into a 400-page textbook: Cellular Biophysics and Modeling: A Primer on the Computational Biology of Excitable Cells, Cambridge University Press, 2019. [CUP] [Amazon] [AppleBooks]
An electronic version of this required text is freely available to W&M students via SWEM library.
How should you prepare for Cellular Biophysics and Modeling?
Short answer: review core math skills and read the Preface and Chapter 1 of the textbook (see above).
Make sure you can:
- graph polynomial functions
- take derivatives of polynomial functions
- multiply small matrices and vectors
These show up all the time, so if those feel shaky, it’s worth reviewing before the course starts.
If you want some quick refreshers:
- Khan Academy (great for brushing up on calculus and algebra): https://www.khanacademy.org/math
- Paul’s Online Math Notes (clear, no-nonsense explanations): https://tutorial.math.lamar.edu/
- 3Blue1Brown (excellent intuition for calculus and linear algebra): https://www.youtube.com/c/3blue1brown
Beyond mechanics, it really helps to understand what derivatives mean—rates of change, how things evolve over time, etc. A lot of what we do is take biological systems (especially cells and neurons) and describe how they change using math.
On the biology side, you don’t need anything too advanced, but being familiar with basic cell biology is helpful—things like membranes, ion channels, and signaling.
See you soon!