Recording and modeling of pinched hysteresis loops, the fingerprint of a memristor, in neurons

A variant of the Hodgkin-Huxley model has been proposed in which time-varying Na⁺ and K⁺ ion conductances are replaced by memristors, based on the proposal that ion channels are memristors. This hypothesis predicts that current-voltage plots of neurons subjected to sinusoidal stimulation should exhibit a pinched hysteresis loop, the fingerprint of a memristor. We tested this using whole-cell patch clamp recordings from human neurons derived from neural progenitor cells and observed pinched hysteresis loops in 16% of all recorded neurons. Recordings with current clamp and voltage clamp with a holding potential of 0 mV yielded a higher success rate than voltage clamp recordings with a holding potential of around - 60 mV. In addition, more neurons exhibited pinched hysteresis loops when the applied voltage or current amplitude was high, and the frequency was low. The recording of pinched hysteresis loops in neurons gives evidence that these contain memristors and this is the first time to be shown experimentally. This is not just an indication that the memristor-based Hodgkin-Huxley model is valid; it also demonstrates that models of neurons based on memristors actually resemble nature. We then subjected simulated neurons expressing Hodgkin-Huxley voltage-gated Na⁺ and K⁺ channels to sinusoidal membrane potential oscillations and found that the presence of pinched hysteresis loops depended strongly on the density of voltage-gated K⁺ channels and on the membrane capacitance but not on the presence of voltage-gated Na⁺ channels. Because Na⁺ channels are expected to be largely inactivated in neurons at a holding potential of 0 mV, these findings together suggest that it is the presence of voltage-gated K⁺ channels that is critical for the observed memristive behavior.