HODGKIN AND HUXLEY’S WORK (5) revealing the origins of cellular excitability is one of the great triumphs of physiology. In an extraordinarily deft series of papers, they were able to measure the essential electrical characteristics of neurons and synthesize them into a quantitative model that accounts for the excitability of neurons and other cells. The Hodgkin-Huxley equations, a set of four differential equations, predict many of the electrical characteristics of neurons and muscle cells; however, these equations are somewhat beyond the ken of most undergraduate biology students. I will show that if one wants to truly understand the origins of excitability, one cannot avoid its mathematical underpinnings. In this article, I also will demonstrate how it is possible, resorting only to elementary mathematics, to show why the combination of certain ion channel makes cells excitable. What does it mean to understand a biological process? Is a description of what happens during some biological event enough? Some might claim that science simply describes how things happen, but this misses the essential power of science, which is to go beyond what has been observed into predicting what might happen, which can only be done through the agency of mathematics. To guide student’s understanding of the process in the classroom, we need to take them beyond rote recitation to a visceral understanding of the forces at play in the process. Most neuroscience textbook accounts of cellular excitability do not divulge the essence of what makes cells excitable because they seem reluctant to address the underlying mathematics and physics. This leads to students recounting what happens during an action potential but gives them little insight into the mechanism.
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