# Superconducting Bio-Inspired Au-Nanowire-Based Neurons

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## Abstract

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## 1. Introduction

## 2. Results and Discussion

#### 2.1. Preparation of Samples and Experimental Results

#### 2.2. Bio-Inspired Neuron

**Regular mode**shows the typical response of a neuron to external stimulation. A short input current pulse of a sufficient amplitude causes single spike, whereafter the system returns to a stable state, see Figure 4a. A long pulse leads to repeated overcoming of the firing threshold. Thus, a series of spikes is observed, Figure 4b. The interspike interval is determined by a neuron refractory period, which, in consequence, is related to the recovery of $N{a}^{+}$ channels.**Steady state mode**(Figure 4c) is characterized by the weak damped output pulses. This is analog of the maintenance of constant internal concentrations of ions in the cell in response to an under threshold stimulation.**Injury mode**(Figure 4d) is characterized by the losses of spikes, or vice versa, the generation of “extra” spikes. This mimics the biophysical abnormality caused by different nervous diseases and neuron injuries.**Bursting mode**(Figure 4e) demonstrates the generation of a series of spikes in response to singe stimulating current pulse. Such behavior may be the result of the complex neuron interaction in the network. However, this can also be a consequence of internal processes in a neuron. In the last case, the reason is the after-depolarization (ADP), a membrane depolarisation at the last stages of repolarisation (circled “4” on the spike shown in Figure 4a) [59,60]. A slow sodium current appears at membrane voltage ∼−50…−70 mV and overcomes outward ${K}^{+}$ current, causing a membrane voltage to rise again. Such current is resistant to inactivation and may last for long times. The bursting pattern parameters—the spike sequence frequency and its length—are determined by the concentration of ion channels of different kinds, properties of these channels, and ionic concentrations in extracellular space. Though only relatively small cohort of neurons in vivo exhibits a bursting behavior [61,62,63], it plays an important role in synaptic plasticity [64,65], synchronization of big neuron groups [66], detection of frequency features of input stimuli [67], information encoding [68,69], and reliability of synaptic transmission [64,70], which may be crucial for processing of important stimuli [71].- Figure 4f illustrates the bursting dynamics of biological neuron simulated in the frame of the fractional-order Izhikevich model [72,73] for comparison, see also Supplementary Materials.

## 3. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Sketch of a biological neuron and its artificial counterpart made of a superconducting material with a normal metal nanowire.

**Figure 2.**Scanning electron microscope images of (

**a**) sample A (insert—Zoom of the Josephson junction), (

**b**) sample B, and (

**c**) sample C with zoom of the central part of the sample C. The scale bar is 1 $\mathsf{\mu}$m. The corresponding sets of current-voltage characteristics in various magnetic fields for these samples are shown in panels (

**d**–

**f**); voltage scale is in $\mathsf{\mu}$V (displayed in color).

**Figure 3.**(

**a**) Sketch of the proposed superconducting bio-inspired neuron with nanowire-based Josephson junctions. (

**b**) Schematic of the proposed bio-inspired neuron.

**Figure 4.**Simulations of the superconducting bio-inspired neuron dynamics in the various operation modes: (

**a**,

**b**) regular mode ($\beta =0.5$, $\eta =0.2$), (

**c**) steady state mode ($\beta =0.5$, $\eta =0.7$), (

**d**) injury mode ($\beta =0.4$, $\eta =0.9$), and (

**e**) bursting mode ($\beta =1.5$, $\eta =0.14$). The figures show the output voltage across the second Josephson junction of the cell stimulated by the input current pulse. The circuit parameters are ${i}_{b}=1.9$, $l=5$, ${l}_{S}=3.85$. (

**f**) Bursting dynamics obtained in the framework of the Izhikevich model, see Figure S3d of Supplementary Materials and its description therein.

**Figure 5.**Map of the proposed bio-inspired neuron operating modes on the plane of parameters ($\beta $, $\eta $). White boundaries represent the areas where transient processes complicating identification of a particular mode take place. Stars mark parameters taken for simulations presented in Figure 4. The regular, steady state, and injury modes can be obtained in the overdamped circuits ($\beta \u27f60$) such as the studied experimental samples. Implementation of the bursting mode requires underdamped system.

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**MDPI and ACS Style**

Skryabina, O.V.; Schegolev, A.E.; Klenov, N.V.; Bakurskiy, S.V.; Shishkin, A.G.; Sotnichuk, S.V.; Napolskii, K.S.; Nazhestkin, I.A.; Soloviev, I.I.; Kupriyanov, M.Y.;
et al. Superconducting Bio-Inspired Au-Nanowire-Based Neurons. *Nanomaterials* **2022**, *12*, 1671.
https://doi.org/10.3390/nano12101671

**AMA Style**

Skryabina OV, Schegolev AE, Klenov NV, Bakurskiy SV, Shishkin AG, Sotnichuk SV, Napolskii KS, Nazhestkin IA, Soloviev II, Kupriyanov MY,
et al. Superconducting Bio-Inspired Au-Nanowire-Based Neurons. *Nanomaterials*. 2022; 12(10):1671.
https://doi.org/10.3390/nano12101671

**Chicago/Turabian Style**

Skryabina, Olga V., Andrey E. Schegolev, Nikolay V. Klenov, Sergey V. Bakurskiy, Andrey G. Shishkin, Stepan V. Sotnichuk, Kirill S. Napolskii, Ivan A. Nazhestkin, Igor I. Soloviev, Mikhail Yu. Kupriyanov,
and et al. 2022. "Superconducting Bio-Inspired Au-Nanowire-Based Neurons" *Nanomaterials* 12, no. 10: 1671.
https://doi.org/10.3390/nano12101671