Math 485 -- Mathematical Modeling
Biophysical modeling
How cells move using Brownian ratchets
Small objects like pollen suspended in water will move in an irregular, random way due to constant bombardment by water molecules. This force, known as Brownian motion, can be an important source of energy for living organisms, for example some intracellular parasites.The first paper offers a short, historical overview of the topic. The second paper proposes a model for a specific mechanism called the Brownian ratchet.
- Brownian ratchets: Darwin's motors by G F Oster. Nature 417 (2002)
- Cellular motions and thermal fluctuations: the Brownian ratchet by C S Peskin, G M Odell, and G F Oster. Biophysical Journal 65 (1993) pp 316-324
Modeling nerve cells
Project proposed by Chris Bergevin.Nerve cells, or neurons, typically communicate information via propagation of electrical impulses. The propagation of these impulses involves some complex, yet approachable, nonlinear processes.
Note: This project is more open-ended. I suggest addressing a specific question of interest, for example: how does increasing the membrane capacitance affect the propagation speed of the electrical impulse? What is the effect of injecting an ever-increasing DC current into a cell?
- Wikipedia articles on the Hodgkin-Huxley neuron model and action potentials (these links are convenient starting points, but you will want to check all claims in published literature)
- Cellular Biophysics, Volume 2: Electrical Properties by T F Weiss, MIT Press 1997.