Statistical field theory of the transmission of nerve impulses

Gianluigi Zangari Del Balzo

doi:10.1186/s12976-020-00132-9

Gianluigi Zangari Del Balzo

Open Access

https://doi.org/10.1186/s12976-020-00132-9

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Abstract

BackgroundStochastic processes leading voltage-gated ion channel dynamics on the nerve cell membrane are a sufficient condition to describe membrane conductance through statistical mechanics of disordered and complex systems.ResultsVoltage-gated ion channels in the nerve cell membrane are described by the Ising model. Stochastic circuit elements called “Ising Neural Machines” are introduced. Action potentials are described as quasi-particles of a statistical field theory for the Ising system.ConclusionsThe particle description of action potentials is a new point of view and a powerful tool to describe the generation and propagation of nerve impulses, especially when classical electrophysiological models break down.The particle description of action potentials allows us to develop a new generation of devices to study neurodegenerative and demyelinating diseases as Multiple Sclerosis and Alzheimer’s disease, even integrated by connectomes. It is also suitable for the study of complex networks, quantum computing, artificial intelligence, machine and deep learning, cryptography, ultra-fast lines for entanglement experiments and many other applications of medical, physical and engineering interest.

Highlights

Stochastic processes leading voltage-gated ion channel dynamics on the nerve cell membrane are a sufficient condition to describe membrane conductance through statistical mechanics of disordered and complex systems
From our model we define a stochastic circuit element which we call for convenience of reading “Ising Neural Machine” (INM), briefly “Ising Machine” and we indicate it with a rhomboid frame icon
We place the INMs in the equivalent circuit with single compartment of Fig. 7 defined for two superfamilies of ion channels (Na+ and K+)

Summary

Introduction

Stochastic processes leading voltage-gated ion channel dynamics on the nerve cell membrane are a sufficient condition to describe membrane conductance through statistical mechanics of disordered and complex systems. In 1952 British physiologists Sir Alan Lloyd Hodgkin (1914–1998) and Sir Andrew Fielding Huxley (1917– 2012) at the University of Cambridge demonstrated the existence of selective and voltage-dependent ion channels in the nerve cell membrane with five famous pioneers works published in the Journal of Physiology. They received the Nobel Prize for Medicine in 1963 together with the Australian physiologist Sir John Carew Eccles (1903–1997) [1,2,3,4,5]. The stochastic dynamics of opening/closing (“gating”) of each ion channel

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