Abstract
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.
Scientific Reports, 2025: https://doi.org/10.1038/s41598-025-21035-0
Several measurements in current clamp or voltage clamp mode showed a pinched hysteresis loop, the fingerprint of a memristor. A simplified equivalent electrical circuit of a neuron during the recording (adapted (two noise sources added) from4, which itself is an adapted version of the Hodgkin-Huxley model6). Note that not all kinds of ion channels potentially expressed in the recorded neurons are shown. In the original Hodgkin-Huxley model, the potassium ion channel conductance GK(n) depends on the dimensionless potassium gate-activation variable n, and the sodium ion channel conductance GNa(m, h) depends on both the dimensionless sodium gate-activation variable m and the dimensionless sodium gate-inactivation variable h4.
The n, m and h variables represent probabilities that channels are open and arise from the original mathematical modeling conducted by Hodgkin and Huxley in which differential equations were derived that fit experimentally observed conductance changes6. In the memristor-based Hodgkin-Huxley model4, the time-varying potassium resistor and sodium resistor6 are replaced by the (first order) potassium ion channel memristor expressed by the memductance GK(n) and the (second order) sodium ion channel memristor expressed by the memductance GNa(m, h), respectively4. GL represents the conductance of the leakage ion channels. ENa and EK are the voltages created by the ion gradients (between intracellular and extracellular space) of sodium and potassium, respectively. EL denotes the voltage created by the gradient of ions to which the membrane leak channels are permeant. The capacitive properties of the membrane are represented by CM.
Stochastic opening and closing of ion channels leads to random inward or outward currents, also called intrinsic noise16, which is represented by Nintrinsic, The component Nextern represents all noise voltages caused by the measurement setup and the environment (including 50 Hz noise from the electrical mains).