Hodgkin-Huxley Circuit Research Articles

Are There an Infinite Number of Passive Circuit Elements in the World?

We found that a second-order ideal memristor [whose state is the charge, i.e., in ] degenerates into a negative nonlinear resistor with an internal power source. After extending analytically and geographically the above local activity (experimentally verified by the two active higher-integral-order memristors extracted from the famous Hodgkin–Huxley circuit) to other higher-order circuit elements, we concluded that all higher-order passive memory circuit elements do not exist in nature and that the periodic table of the two-terminal passive ideal circuit elements can be dramatically reduced to a reduced table comprising only six passive elements: a resistor, inductor, capacitor, memristor, mem-inductor, and mem-capacitor. Such a bounded table answered an open question asked by Chua 40 years ago: Are there an infinite number of passive circuit elements in the world?

Firing activity in an N-type locally active memristor-based Hodgkin–Huxley circuit

Firing activity in an N-type locally active memristor-based Hodgkin–Huxley circuit

Modeling the effect of magnetoelectric nanoparticles on neuronal electrical activity: An analog circuit approach.

This paper introduces a physical neuron model that incorporates magnetoelectric nanoparticles (MENPs) as an essential electrical circuit component to wirelessly control local neural activity. Availability of such a model is important as MENPs, due to their magnetoelectric effect, can wirelessly and noninvasively modulate neural activity, which, in turn, has implications for both finding cures for neurological diseases and creating a wireless noninvasive high-resolution brain-machine interface. When placed on a neuronal membrane, MENPs act as magnetic-field-controlled finite-size electric dipoles that generate local electric fields across the membrane in response to magnetic fields, thus allowing to controllably activate local ion channels and locally initiate an action potential. Herein, the neuronal electrical characteristic description is based on ion channel activation and inhibition mechanisms. A MENP-based memristive Hodgkin-Huxley circuit model is extracted by combining the Hodgkin-Huxley model and an equivalent circuit model for a single MENP. In this model, each MENP becomes an integral part of the neuron, thus enabling wireless local control of the neuron's electric circuit itself. Furthermore, the model is expanded to include multiple MENPs to describe collective effects in neural systems.

Fractional order memcapacitive neuromorphic elements reproduce and predict neuronal function

There is an increasing need to implement neuromorphic systems that are both energetically and computationally efficient. There is also great interest in using electric elements with memory, memelements, that can implement complex neuronal functions intrinsically. A feature not widely incorporated in neuromorphic systems is history-dependent action potential time adaptation which is widely seen in real cells. Previous theoretical work shows that power-law history dependent spike time adaptation, seen in several brain areas and species, can be modeled with fractional order differential equations. Here, we show that fractional order spiking neurons can be implemented using super-capacitors. The super-capacitors have fractional order derivative and memcapacitive properties. We implemented two circuits, a leaky integrate and fire and a Hodgkin–Huxley. Both circuits show power-law spiking time adaptation and optimal coding properties. The spiking dynamics reproduced previously published computer simulations. However, the fractional order Hodgkin–Huxley circuit showed novel dynamics consistent with criticality. We compared the responses of this circuit to recordings from neurons in the weakly-electric fish that have previously been shown to perform fractional order differentiation of their sensory input. The criticality seen in the circuit was confirmed in spontaneous recordings in the live fish. Furthermore, the circuit also predicted long-lasting stimulation that was also corroborated experimentally. Our work shows that fractional order memcapacitors provide intrinsic memory dependence that could allow implementation of computationally efficient neuromorphic devices. Memcapacitors are static elements that consume less energy than the most widely studied memristors, thus allowing the realization of energetically efficient neuromorphic devices.

Periodic and chaotic spiking behaviors in a simplified memristive Hodgkin-Huxley circuit

The famous Hodgkin-Huxley circuit contains two time-varying resistors to describe the electrophysiological characteristics of sodium and potassium ion channels. But the time-varying resistors are expressed by mixed exponential equations, which are unavailable to directly implement in analog circuit and hinders hardware application of the Hodgkin-Huxley circuit. To hit this issue, a simplified memristive Hodgkin-Huxley (m-HH) circuit is proposed, which only involves two locally active memristors (LAMs) to depict the sodium and potassium ion channels, a capacitor to describe the neuron membrane, a DC current to represent external stimulus, and two DC voltages to express the reversal potentials. MATLAB-based numerical simulations and analog circuit-based hardware measurements display that the simplified m-HH circuit can generate memristor parameter- and DC current-related periodic spiking behaviors with different periodicities and chaotic spiking behavior. This delights that electrophysiological characteristics of ion channels and external stimulus can be employed for regulating these periodic and chaotic spiking behaviors. It is interesting that the simplified m-HH circuit can generate frequency self-adaptation and coexisting firing patterns. The inter-spike interval bifurcation diagram shows that the frequency of the periodic spiking behavior increases with the increase of externally applied DC current. Besides, the hybrid parameter bifurcation diagram displays that the simplified m-HH circuit can generate memristor initial state-related coexisting firing patterns of period-6 with chaos, period-3 with chaos, and period-3 with period-8. These offer us the unique insight into explaining some biological firing patterns. The most significance is that the analog hardware circuit is feasible in reproducing these periodic and chaotic spiking behaviors and benefits for developing spiking-based neuromorphic hardware.

Firing activity in a simplified Hodgkin–Huxley circuit with memristive sodium and potassium ion channels

Firing activity in a simplified Hodgkin–Huxley circuit with memristive sodium and potassium ion channels

Firing pattern in a memristive Hodgkin–Huxley circuit: Numerical simulation and analog circuit validation

Spiking firing patterns and their hardware implementation can assist us in exploring spike-based applications. The classical Hodgkin–Huxley circuit can generate spiking firing patterns, but it is hard to implement on analog platform because of the involvement of complex exponential nonlinearities for characterizing the sodium and potassium ion channels. To solve this issue, this paper proposes a second-order local active memristor (LAM) and a first-order LAM to respectively characterize the sodium and potassium ion channels in the Hodgkin–Huxley circuit, thereby obtains a memristive Hodgkin–Huxley circuit. Numerical simulations demonstrate that the memristive Hodgkin–Huxley circuit can generate abundant spiking firing patterns, i.e. periodic and chaotic spiking firing patterns. These abundant firing patterns can be effectively regulated by memristor- and stimulus-related parameters. Moreover, a PCB-based analog circuit employing off-the-shelf discrete circuit components is manually constructed and hardware experiments are executed. Experimental results captured from hardware measurements satisfactorily verify the numerically simulated spiking firing patterns and effectively exhibit the availability of the memristive Hodgkin–Huxley circuit in generating spiking firing patterns.

Topological electronics: from infinity to six

Topology captures the essence of what remains unchanged under a transformation. This study was motivated by a newly found topological invariant called super conformality that leads to local activity of a higher-integral-order electric element. As a result, the traditional periodic table of the electric elements can be dramatically reduced to have only six passive ones (resistor, inductor, capacitor, memristor, meminductor, and memcapacitor), in contrast to the unbounded table predicted 40 years ago. Our claim was experimentally verified by the fact that the two higher-integral-order memristors in the famous Hodgkin–Huxley circuit are locally active with an internal battery.

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.

Anti-electromagnetic interference analysis of equivalent circuit of ion channel based on the Hodgkin-Huxley model

With the continuous improvement of circuit integration and working clock frequency in the electronic system, it is increasingly easy for the system to be affected by electromagnetic waves, and electromagnetic susceptibility and vulnerability become more severe. However, living beings in nature have shown extraordinary compatibility, immunity and adaptability to the electromagnetism at the same time. In addition, the ion channel on the neuron cytomembrane is a typical representation of "bioelectrical immunity". So the Hodgkin-Huxley circuit model with one capacitor in parallel with some power supplies and resistors was adopted to simulate the ion channel on the neuron cytomembrane. Through analysis, the circuit model can be used to simulate some electrical characteristics of biological neuron cells, and then acquire a certain level of anti-electromagnetic interference ability. This method will be useful for improving the reliability, compatibility and anti-interference capability of the electronic system in the complicated electromagnetic environment.

Energy and information in Hodgkin-Huxley neurons

The generation of spikes by neurons is energetically a costly process and the evaluation of the metabolic energy required to maintain the signaling activity of neurons a challenge of practical interest. Neuron models are frequently used to represent the dynamics of real neurons but hardly ever to evaluate the electrochemical energy required to maintain that dynamics. This paper discusses the interpretation of a Hodgkin-Huxley circuit as an energy model for real biological neurons and uses it to evaluate the consumption of metabolic energy in the transmission of information between neurons coupled by electrical synapses, i.e., gap junctions. We show that for a single postsynaptic neuron maximum energy efficiency, measured in bits of mutual information per molecule of adenosine triphosphate (ATP) consumed, requires maximum energy consumption. For groups of parallel postsynaptic neurons we determine values of the synaptic conductance at which the energy efficiency of the transmission presents clear maxima at relatively very low values of metabolic energy consumption. Contrary to what could be expected, the best performance occurs at a low energy cost.

The modelling of a burst-generating neuron with a field-effect transistor analog

An electronic analog that models the burst generating neuronR 15 of theAplysia abdominal ganglion is described. The analog is based on the four branch Hodgkin-Huxley equivalent circuit for a patch of squid axon membrane, with a choice of parameter values appropriate to theAplysia cell membrane. To realize the slow subthreshold oscillations seen in cellR 15 upon exposure to the drug tetrodotoxin (TTX), it was necessary to include two additional conductance branches,g? Na andg? K, to the basic Hodgkin-Huxley circuit. Without these, the analog was capable of generating only action potentials and hence termed the "suprathreshold" analog. With all six branches operative, bursts very similar to those seen inR 15 were realized, and subsequent inhibition of the Hodgkin-Huxley sodium conductanceg Na resulted in the desired subthreshold oscillations. The electronic circuitry and the performance of the "suprathreshold" and complete analog are described. An explanation is offered for the progressive widening of the action potentials within a burst seen inR 15. The analog also simulates the phenomenon of potassium ion accumulation outside the cell membrane during a burst, using a local feedback loop to reduce the potassium equilibrium potential in a manner roughly proportional to the logarithm of the time integral of the outward potassium current. Some consequences of this effect are also discussed.