Membrane Capacitive Memory Alters Spiking in Neurons Described by the Fractional-Order Hodgkin-Huxley Model

Abstract

Excitable cells and cell membranes are often modeled by the simple yet elegant parallel resistor-capacitor circuit. However, studies have shown that the passive properties of membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduce capacitive memory effects, i.e., dynamics are influenced by a weighted sum of the membrane potential prior history. However, it is not clear to what extent fractional-order dynamics may alter the properties of active excitable cells. In this study, we investigate the spiking properties of the neuronal membrane patch, nerve axon, and neural networks described by the fractional-order Hodgkin-Huxley neuron model. We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced. In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order. Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity.

Ferroelectric Fractional‐Order Capacitors

“…[1][2][3] The concept of a fractional-order element provides an additional degree of freedom in modeling, characterizing, and implementing novel circuit components in a wide spectrum of disciplines: viz. energy-storage and generation device modeling, [4][5] supercapacitor modeling, [6][7] sensor design, [8][9] corrosion modeling and characterization, [10][11] neural-system modeling, [12][13][14] bio-impedance characterization, [15][16] control-system design, [17][18] heat diffusion control, [19][20] electromagnetic system design [21][22] and electronic circuit design. [23][24][25][26][27][28] In particular, a fractional-order element with 0 < a < 1 (i. e. À908 > f> 08) is called a fractional-order capacitor (FOC).…”

An ultra-broadband single-component fractional-order capacitor using MoS2-ferroelectric polymer composite

“…[1][2][3][4][5][6][7][8][9][10][11] Thanks to the additional parameter, namely, the fractional order (see supplementary material Sec. S1 and Fig.…”

“…S1), FOCs offer increased flexibility in modeling and designing various electrical devices and systems, such as filters, 12,13 oscillators, 14,15 neural circuits, 2 transmission lines, 16 supercapacitors and batteries, [17][18][19][20][21] impedance matching networks, 22 phase-locked loops, 23 and proportional-integral-derivative controllers, 24 and open the door to several unconventional properties that cannot be obtained using traditional circuit elements. For example, unlike a conventional capacitor, an FOC supports a capacitive memory, which enables temporal history of signals to be "stored" by electrical circuits, and therefore, it can be used to more accurately mimic/model electrical pulses communicated by neurons 2 and memory regeneration phenomena observed in dielectrics. 25,26 Another example is the use of an FOC in a temperature controller instead of a conventional controller: The FOC reduces drastically both the overshoot amplitude and the time required to stabilize the temperature.…”

“…It is clear that these FOCs are not suitable for many electronic systems, which work at low frequencies, such as fractional controllers 7 and neural networks. 2,31,32 To alleviate this problem, in this work, an FOC is fabricated using PDVF polymer composites embedding molybdenum disulfide (MoS 2 ) nanosheets [see Fig. 1(a)].…”

“…The MoS 2 nanosheets, which are used as fillers in polymers, are exfoliated from a bulk MoS 2 nanosheets are distributed uniformly inside the polymer without any aggregation. Furthermore, the structural composition of the composite is investigated using XRD, which confirms that no additional complex molecular structures are generated.…”