Every second, a spike happens more than 100 billion times in your brain. Spikes are sudden electrical impulses, shot through one brain cell on its way to the next. Spikes are the currency of information in the brain and they drive everything we think and do. There are two basic questions that brain science must answer: how are spikes formed and what do they mean? Unraveling how neurons spike is a crown jewel of twentieth century neuroscience and mathematics was central to this resolution. Resolving the second question, that is, understanding the neural code, will be a central focus of twenty-first century neuroscience and mathematics will surely contribute to this resolution as well. A critical challenge that is not yet fully answered is to understand how spikes emerge from tiny neurons, hundreds per pinhead. How is it that spikes are produced by a huge variety of cells that look wildly different? How can different patterns of spikes be turned on and off in a single cell in normal operation or through medicines? And since vastly different inputs produce the same spike, just how does a neuron decide when to spike?
These questions have gripped the scientific community ever since spikes were first seen more than 100 years ago. Hodgkin and Huxley, two physiologists, showed how mathematics could solve all of them at once, laying the groundwork for their 1963 Nobel Prize and for modern neuroscience. Today, mathematicians are still building on Hodgkin and Huxley's theory of the spike to forge ahead in brain science.
Follow the links to the right to see how nonlinear mathematics provides the framework that unlocked the secret mechanics of the neuron. You’ll discover how this mathematical framework is a nexus for modern neuroscience, and meet Hodgkin and Huxley, the scientists who discovered it – and won a Nobel Prize.
This tutorial appears on Why Do Math.
|Author Institutional Affiliation
Brent Doiron and Eric Shea-Brown