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A neuron model with nonlinear membranes

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Abstract

One-layer membrane separates the gradient field in and out of the cell, while some two-layer membranes filled with excitable media/material are important to regulate the energy flow when ions are propagated and diffused. The intracellular and extracellular media can be effectively separated by the membrane. It is important to clarify and describe the biophysical function and then the capacitive property can be reproduced in equivalent neural circuit. Here, we suggest the cell membrane has certain thickness and becomes flexible under external stimuli, therefore, it is considered as a kind of nonlinear media. To mimic the physical property of the two-layer cell membrane, a nonlinear resistor is used to connect two linear circuits, which is used to describe the electrical characteristic of two sides of the cell membrane, respectively. The combination of two linear circuits via a nonlinear resistor can describe the energy characteristic and firing mode in the flexible membrane of biophysical neurons. Circuit equations are defined and converted into equivalent nonlinear oscillator like a neuron. The voltage difference for the two capacitors can be consistent with the membrane potential for the neuron. The Hamilton energy function for this neuron can be mapped from the field energy in the electronic components, and it is also derived by using Helmholtz’s theorem. The neuron can show similar spiking and bursting firing patterns, and uncertain diversity in membrane potentials is effective to support continuous firing patterns and mode transition under external stimulus. Furthermore, noisy disturbance is applied to induce coherence resonance. The results indicate that the lower coefficient variability and higher average energy level supports periodic firing in the neuron under coherence resonance. Therefore, this neuron model with nonlinear membranes (or two-layer form) is more suitable for identifying the biophysical property of biological neuron.

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The data are available from the corresponding author upon reasonable request.

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Acknowledgements

This project is supported by the National Natural Science Foundation of China under Grant No. 12072139.

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Authors and Affiliations

  1. College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

    Feifei Yang, Qun Guo & Jun Ma

  2. Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China

    Jun Ma

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  1. Feifei Yang
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  2. Qun Guo
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  3. Jun Ma
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Correspondence to Jun Ma.

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Yang, F., Guo, Q. & Ma, J. A neuron model with nonlinear membranes. Cogn Neurodyn 18, 673–684 (2024). https://doi.org/10.1007/s11571-023-10017-5

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