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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum entanglement of K+ions, multiple channel states, and the role of noise in the brain

Gustav Bernroider, Sisir Roy

Published May 23, 2005• 37 citations
Publisher

Abstract

We propose a quantum information scheme that builds on the interference properties of entangled ion states that are transiently confined by local potentials within the permeation path of voltage-gated, ion-conducting membrane proteins. We show, that the sub-molecular organization of parts of the protein, as revealed by the recent progress in high-resolution atomic-level spectroscopy and accompaning molecular dynamics simulations, carries a logical coding potency that goes beyond the pure catalytic function of the channel, subserving the transmembrane crossing of an electrodiffusive barrier. As we argue that 'within channel states' can become super-correlated with the environment , this also sheds new light on the role of noise in controlling the access of ions to voltage-gated ion channels ('channel noise').

DOI
10.1117/12.609227

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We propose a quantum information scheme that builds on the interference properties of entangled ion states that are transiently confined by local potentials within the permeation path of voltage-gated, ion-conducting membrane proteins. We show, that the sub-molecular organization of parts of the protein, as revealed by the recent progress in high-resolution atomic-level spectroscopy and accompaning molecular dynamics simulations, carries a logical coding potency that goes beyond the pure catalytic function of the channel, subserving the transmembrane crossing of an electrodiffusive barrier. As we argue that 'within channel states' can become super-correlated with the environment , this also sheds new light on the role of noise in controlling the access of ions to voltage-gated ion channels ('channel noise').
We investigate the effects of a quantum entanglement regime within an ion conducting molecule (ion channel) of the neuronal plasma membrane on the onset dynamics of propagating nerve pulses (action potentials). In particular, we model the onset parameters of the sodium current in the Hodgkin Huxley equation as three similar but independent probabilistic mechanisms which become quantum entangled. The underlying physics is general and can involve entanglement between various degrees of freedom underlaying ion transition states or 'gating states' during conduction, e.g. Na+^++ ions in different channel locations, or different 'affinity' states of ions with atoms lining the sub-regions of the channel protein ('filter-states'). We find that the 'quantum corrected' Hodgkin Huxley equation incorporating entangled systems states can reproduce action potential pulses with the critical onset dynamics observed recently in neocortical neurons in vivo by Naundorf et al. [Nature {\bf 440}, 1060 (20 April 2006)]. Interestingly, the suggested entanglement term can also slow down action potential initiation.
ions in the highly conserved KcsA selectivity filter motive of voltage gated ion channels. We first show that the de Broglie wavelength of thermal ions is not much smaller than the periodic structure of Coulomb potentials in the nano-pore model of the selectivity filter. This implies that an ion may no longer be viewed to be at one exact position at a given time but can better be described by a quantum mechanical wave function. Based on first principle methods, we demonstrate solutions of a non-linear Schrödinger model that provide insight into the role of short-lived (~1 ps) coherent ion transition states and attribute an important role to subsequent decoherence and the associated quantum to classical transition for permeating ions. It is found that short coherences are not just beneficial but also necessary to explain the fast-directed permeation of ions through the potential barriers of the filter. Certain aspects of quantum dynamics and non-local effects appear to be indispensable to resolve the discrepancy between potential barrier height, as reported from classical thermodynamics, and experimentally observed transition rates of ions through channel proteins.
We showed that quantum mechanical superposition can sustain in the process of ion transfer in protein membrane for a substantial period, in spite of the presence of the interactions with environmental modes of molecular vibration. The spectral temperature, as defined in quantum thermodynamical framework plays a significant role in maintaining the coherence. The ratio of decoherence time and dwell time has been calculated, which can be directly related to the degree of coherence. The results shead new light to build quantum information system of entangled ionic states in the voltage gated biological channels.
This chapter discusses several previously published results on possible applications of quantum information theory to neuroscience and will present a number of open questions that deserve further study. Applying the quantum information theory of consciousness to modeling the electric processes that occur in neuronal networks in the brain is an open scientific problem that deserves further study. The quantum behavior of individual ion channels is clearly manifested in the discrete changes observed in their channel conductance. Neurons communicate with each other at synaptic contacts that permit the transmission of electric or chemical signals from one neuron to another. Electrical synapses provide a direct electrical coupling between the two neurons through gap junctions that are nanopores constructed from connexin proteins. Multiple protein subunits, each possessing its own geometric shape, may further bind into protein complexes with a quaternary structure. Voltage-gated ion channels provide a typical example of protein complexes that are composed of multiple protein subunits.
Understanding neural excitability and action potential generation is a cornerstone of neuroscience, relying on the complex interplay of biophysical mechanisms governed by ion channels in neuronal membranes. Traditional approaches, such as the Hodgkin-Huxley model, have provided a robust framework for simulating these processes using classical computational techniques. However, the advent of quantum computing opens new avenues for exploring neuronal dynamics, particularly due to ion movement's inherently quantum mechanical properties at atomic scales. In this study, I investigated the intersection of quantum computing and membrane biophysics, evaluating how quantum algorithms could revolutionize simulations of ion channel behavior and neuronal signaling. I began by analyzing the limitations of classical methods in handling high-dimensional, nonlinear systems. Next, I introduced key quantum computing principles, including qubits, superposition, and entanglement, and their potential applications in solving molecular dynamics and differential equations relevant to neuronal activity. Despite promising theoretical advantages, practical challenges such as qubit coherence, error rates, and hardware scalability must be addressed before quantum models can outperform classical simulations. I also discussed hybrid classical-quantum approaches as a transitional strategy, leveraging the strengths of both paradigms. By bridging neuroscience, biophysics, and quantum information science, I aimed to stimulate interdisciplinary research toward more efficient and accurate models of neural excitability.
Neural Coding Abstract. Quantum models of higher level brain functions such as conscious experience, suggest that the neural correlate of mentation requires dynamical properties instantiated at the Planck-scale. Several candidate quantum processes have been suggested, but it remains to be seen how these quantum properties can relate to the established classical signals in the brain involving physical action twenty magnitudes above the quantum domain. In this paper we show the results of a systematic analysis of Lagrangian action order to brain processes at different scales of resolution. The results encompass processes at the macroscopic single cell level to processes at the sub-molecular and concerted molecular population level. It is shown that the state of ions in the permeation filter of channel proteins, as for example indicated by the MacKinnon KcsA K+ channel model, is a quantum phenomenon involving a Lagrangian in the order of 10–34 Js. Further, we show that the brain spans at least 20 orders of magnitudes of physical action with physiologically significant signal properties. We suggest that the quantum-classical correspondence in the brain is resolved by the spread of quantum-witness states that correlate with the gating states of voltage sensitive ion channels. 1.