Hidden Quantum Processes, Quantum Ion Channels, And 1/ F Θ-Type Noise

Abstract

In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from K+ and Na+ channel kinetics, in order to identify the source of 1/ f θ-type noise in neurological membranes.We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately 1/ f θ-type spectrum.We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activatedmeasurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hiddenMarkov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous 1/ f θ-type Lorentzian weights, in which the spectral exponent θ is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysicalmechanism by which channel and membrane kinetics can give rise to 1/ f θ-type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond 1/ f θ-type -noise, including applications to animal models and possible impact on quantum foundations.

Publication Date

7-1-2018

Publication Title

Neural Computation

Volume

30

Issue

7

Number of Pages

1830-1929

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1162/neco_a_01067

Socpus ID

85048936364 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85048936364

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