Journal
IEEE CIRCUITS AND SYSTEMS MAGAZINE
Volume 14, Issue 1, Pages 12-36Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/MCAS.2013.2296414
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Funding
- US Air Force Grant [FA9550-13-1-0136]
- National Research Foundation of Korea (NRF)
- Korea government [2013R1A1A2062282, 2013R1A2A2A01068683]
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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.
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