Formalized Quantum Stochastic Processes and Hidden Quantum Models with Applications to Neuron Ion Channel Kinetics

TL;DR

This paper introduces hidden quantum models based on quantum stochastic processes to analyze ion channel kinetics, linking energy theories with phenomenological models and explaining 1/f noise in neural signals.

Contribution

It formalizes hidden quantum models for ion channel analysis, integrating energy-based quantum channels with classical Markov schemes and deriving spectral properties of neural signals.

Findings

Calculated activation energies for Hodgkin-Huxley ion channels.

Derived noise spectral densities approximating 1/f^α.

Linked quantum models with biophysical explanations of neural noise.

Abstract

A new class of formal latent-variable stochastic processes called hidden quantum models (HQM's) is defined in order to clarify the theoretical foundations of ion channel signal processing. HQM's are based on quantum stochastic processes which formalize time-dependent observation. They allow the calculation of autocovariance functions which are essential for frequency-domain signal processing. HQM's based on a particular type of observation protocol called independent activated measurements are shown to to be distributionally equivalent to hidden Markov models yet without an underlying physical Markov process. Since the formal Markov processes are non-physical, the theory of activated measurement allows merging energy-based Eyring rate theories of ion channel behavior with the more common phenomenological Markov kinetic schemes to form energy-modulated quantum channels. Using the simplest quantum channel model consistent with neuronal membrane voltage-clamp experiments, activation eigenenergies are calculated for the Hodgkin-Huxley K+ and Na+ ion channels. It is also shown that maximizing entropy under constrained activation energy yields noise spectral densities approximating $S(f) \sim 1/f^\alpha$, thus offering a biophysical explanation for the ubiquitous $1/f$-type in neurological signals.