In an animal cell, especially neuron and in particular its axon, while there is electrical resistance and capacitance mechanism in the cell, which play essential roles in the cable theory model of neuronal action potential transmission, is there a prominent self inductance mechanism in the sense of electromagnetism?
What one thinks, no matter how intuitive it may appear is not particularly relevant in science. The inductance associated with a neural axon has been well documented since Cole (1966). Its role in the propagation of neural signals is developed extensively in http://neuronresearch.net/hearing/pdf/7Projection.pdf#page=39 . The actual development begins earlier in Section 7.4 on page 322 of that document.
Failure to consider the inductance associated with any alternating electrical signal passed along a coaxial cable leads to disaster. The first undersea cable based on the ideas of William Thompson,Lord Kelvin, and described as an RC cable by Hermann (page 322 in the above document) was a technical and financial disaster. Two years later, a more sophisticated RLC cable based on Maxwell's Equations for a coaxial structure was laid with great success. No RC cable has ever been used in practice since that time. For unknown reasons, the biological community keeps trying to ignore the inductance of the coaxial myelinated axon (leading to ridiculous modeling data). This appears to be the result of introductory courses in electricity for non-engineers trying to avoid the necessary mathematics to understand electromagnetic signal propagation through space and along various types of cables and waveguides.
There surely is inductance in neurons. This inductance is introduced by two different mechanisms. 1. The coil structure of myelin sheaths can introduce a real electrical inductance. The solid evidence for this is the opposite spiraling directions between the adjacent myelin sheaths.
Here I quote the description on Wikipedia:At the junction of two Schwann cells along an axon, the directions of the lamellar overhang of the myelin endings are of opposite sense. You can also check the details in this paper: Uzmman B. G.; Nogueira-Graf G. (1957). "Electron microscope studies of the formation of nodes of Ranvier in mouse sciatic nerves". Journal of Biophysical and Biochemical Cytology. 3 (4): 589-597. doi:10.1083/jcb.3.4.589
The opposite spiraling directions can introduce a positive mutual inductance between adjacent myelin sheaths then further enhance the propagation speed of the neural signal. Meanwhile, it is easy to predict that the myelinated nerve can be stimulated by a magnetic field because of this coil inductor. Because of this opposite spiraling direction, the stimulation result is determined by the spatial gradient of the magnetic field. This phenomenon was validated by years and can be easily understood now.
- The piezoelectric effect of the plasma membrane. If you check the molecular structure of the lipid bilayer of the plasma membrane, you will find that it is naturally a piezoelectric layer. The definition of the piezoelectric layer is a layer consists of two crystal layer with opposite polarities, which is exactly the same as the lipid bilayer. The equivalent circuit of this piezoelectric layer will be a RLC circuit, which contains an equivalent inductor. Since the inductor is not a real one, the value is only used to match with the mechanical resonance frequency. When the mechanical resonance frequency is very low, which is the case for a soft and thin plasma membrane, this inductance will be huge. This is why in Cole's paper for measurement of the squid axon, this inductance is 0.2H. Then as a direct prediction, there should be a mechanical wave accompany with the electric signal of the action potential. This mechanical wave has been measured in this paper: Gonzalez-Perez, A., Mosgaard, L.D., Budvytyte, R., Villagran-Vargas, E., Jackson, A.D. and Heimburg, T., 2016. Solitary electromechanical pulses in lobster neurons. Biophysical chemistry, 216, pp.51-59.
I think here I already give a comprehensive answer to this question. You can check all the details in this paper on bioRix:https://www.biorxiv.org/content/early/2018/10/22/343905
Here I may talk something more, but these things will make most of the people in neuroscience unhappy. If this inductance introduced by the coil structure of myelin and the piezoelectric effect is true, then the whole neuroscience is wrong from the Day 1. The H-H model is built based on a RC circuit and so many people have developed their theories and models based on this H-H model. But ridiculously, everyone claims his model or theory is correct and can explain the data when tha basis is wrong. I have seen so many absurd explanations to bypass this inductance, such as the frequency-dependent capacitor, virtual cathode, negative resistor, and even negative capacitor. And indeed, more and more people begin to realize the so-called neuroscience is a complete failure. You can see in the homepage of Neuralink(https://neuralink.com/), they officially claim that they do not need any neuroscience experience, quote here:No neuroscience experience is required Also, there are many groups now only use deep learning or machine learning to study neurons.