Brains Are Made of Memristors

This exposition shows that the potassium ion-channels and the sodium ion-channels that are distributed over the entire length of the axons of our neurons are in fact locally-active memristors. In particular, they exhibit all of the fingerprints of memristors, including the characteristic pinched hysteresis Lissajous figures in the voltage-current plane, whose loop areas shrink as the frequency of the periodic excitation signal increases. Moreover, the pinched hysteresis loops for the potassium ion-channel memristor, and the sodium ion-channel memristor, from the Hodgkin-Huxley axon circuit model are unique for each periodic excitation signal. An in-depth circuit-theoretic analysis and characterizations of these two classic biological memristors are presented via their small-signal memristive equivalent circuits, their frequency response, and their Nyquist plots. Just as the Hodgkin-Huxley circuit model has stood the test of time, its constituent potassium ion-channel and sodium ion-channel memristors are destined to be classic examples of locally-active memristors in future textbooks on circuit theory and bio-physics.