Brain Dynamics:

Challenges of the Spike

If someone could poke special cells in your head called neurons they would most certainly see an action potential, or more commonly termed a spike. What's a spike? Like all cells, neurons have membranes that separate their insides from their outsides. Current can flow across the membrane creating the pattern of electrical activity shown here:

This shows neuron action potential - it goes rapidly up in voltage and then back down making a "spike" shape.

Figure from Hodgkin and Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, The Physiological Society, volume 117, 1952; Wiley-Blackwell Publishing.

What's the mathematical challenge in explaining spikes? There are three fundamental features of spikes that create the challenge. We'll explore them in turn, and then see how math meets them head-on.

Brain visualizations courtesy of Chris Johnson and Nathan Galli, Scientific Computing and Imaging Institute, University of Utah