A quantum-mechanical description of ion motion within the confining potentials of voltage-gated ion channels

Mimicking classical noise in ion channels by quantum decoherence

The mechanism of selectivity in ion channels is still an open question in biology. Recent studies suggest that the selectivity filter may exhibit quantum coherence, which could help explain how ions are selected and conducted. However, environmental noise causes decoherence and loss of quantum effects. It is hoped that the effect of classical noise on ion channels can be modeled using the framework provided by quantum decoherence theory. In this paper, the behavior of the ion channel system was simulated using two models: the Spin-Boson model and the stochastic Hamiltonian model under classical noise. Additionally, using a different approach, the system's evolution was modeled as a two-level Spin-Boson model with tunneling, interacting with a bath of harmonic oscillators, based on decoherence theory. We investigated under what conditions the decoherence model approaches and deviates from the noise model. Specifically, we examined Gaussian noise and Ornstein-Uhlenbeck noise in our model. Gaussian noise shows a very good agreement with the decoherence model. By examining the results, it was found that the Spin-Boson model at a high hopping rate of potassium ions can simulate the behavior of the system in the classical noise approach for Gaussian noise.

Quantum Biology and the Potential Role of Entanglement and Tunneling in Non-Targeted Effects of Ionizing Radiation: A Review and Proposed Model

It is well established that cells, tissues, and organisms exposed to low doses of ionizing radiation can induce effects in non-irradiated neighbors (non-targeted effects or NTE), but the mechanisms remain unclear. This is especially true of the initial steps leading to the release of signaling molecules contained in exosomes. Voltage-gated ion channels, photon emissions, and calcium fluxes are all involved but the precise sequence of events is not yet known. We identified what may be a quantum entanglement type of effect and this prompted us to consider whether aspects of quantum biology such as tunneling and entanglement may underlie the initial events leading to NTE. We review the field where it may be relevant to ionizing radiation processes. These include NTE, low-dose hyper-radiosensitivity, hormesis, and the adaptive response. Finally, we present a possible quantum biological-based model for NTE.

A Quantum-Classical Model of Brain Dynamics

The study of the human psyche has elucidated a bipartite structure of logic reflecting the quantum-classical nature of the world. Accordingly, we posited an approach toward studying the brain by means of the quantum-classical dynamics of a mixed Weyl symbol. The mixed Weyl symbol can be used to describe brain processes at the microscopic level and, when averaged over an appropriate ensemble, can provide a link to the results of measurements made at the meso and macro scale. Within this approach, quantum variables (such as, for example, nuclear and electron spins, dipole momenta of particles or molecules, tunneling degrees of freedom, and so on) can be represented by spinors, whereas the electromagnetic fields and phonon modes can be treated either classically or semi-classically in phase space by also considering quantum zero-point fluctuations. Quantum zero-point effects can be incorporated into numerical simulations by controlling the temperature of each field mode via coupling to a dedicated Nosé-Hoover chain thermostat. The temperature of each thermostat was chosen in order to reproduce quantum statistics in the canonical ensemble. In this first paper, we introduce a general quantum-classical Hamiltonian model that can be tailored to study physical processes at the interface between the quantum and the classical world in the brain. While the approach is discussed in detail, numerical calculations are not reported in the present paper, but they are planned for future work. Our theory of brain dynamics subsumes some compatible aspects of three well-known quantum approaches to brain dynamics, namely the electromagnetic field theory approach, the orchestrated objective reduction theory, and the dissipative quantum model of the brain. All three models are reviewed.

The significance of bioelectricity on all levels of organization of an organism. Part 1: From the subcellular level to cells

Bioelectricity plays an essential role in the structural and functional organization of biological organisms. In this first article of our three-part series, we summarize the importance of bioelectricity for the basic structural level of biological organization, i.e. from the subcellular level (charges, ion channels, molecules and cell organelles) to cells.

Quantum coherence on selectivity and transport of ion channels

Recently, it has been suggested that ion channel selectivity filter may exhibit quantum coherence, which may be appropriate to explain ion selection and conduction processes. Potassium channels play a vital role in many physiological processes. One of their main physiological functions is the efficient and highly selective transfer of K⁺ ions through the membranes into the cells. To do this, ion channels must be highly selective, allowing only certain ions to pass through the membrane, while preventing the others. The present research is an attempt to investigate the relationship between hopping rate and maintaining coherence in ion channels. Using the Lindblad equation to describe a three-level system, the results in different quantum regimes are examined. We studied the distillable coherence and the second order coherence function of the system. The oscillation of distillable coherence from zero, after the decoherence time, and also the behavior of the coherence function clearly show the point that the system is coherent in ion channels with high throughput rates.

Transport threshold in a quantum model for the KscA ion channel

The mechanism behind the high throughput rate in K⁺channels is still an open problem. However, recent simulations have shown that the passage of potassium through the K⁺channel core, the so-called selectivity filter (SF), is water-free against models where the strength of Coulomb repulsion freezes ions conduction. Thus, it has been suggested that coherent quantum hopping might be relevant in mediating ion conduction. Within the quantum approach and the hypothesis of desolvated ions along the pathway, we start with several particles in a source to see how they go across a SF, modeled by a linear chain of sites, to be collected in a drain. We show that the average SF occupancy is three ions, and the ion transfer rate is ∼10⁸ions s^-1, results which agree with the recent findings in the literature.

A primary model of THz and far-infrared signal generation and conduction in neuron systems based on the hypothesis of the ordered phase of water molecules on the neuron surface I: signal characteristics

In this paper, we use the theory of quantum optics and electrodynamics to study the electromagnetic field problem in the nervous system based on the assumption of an ordered arrangement of water molecules on the neuronal surface. Using the Lagrangian of the water molecule-field ion, the dynamic equations for neural signal generation and transmission are derived. Perturbation theory and the numerical method are used to solve the dynamic equations, and the characteristics of high-frequency signals (the dispersion relation, the time domain of the field, the frequency domain waveform, etc.) are discussed. This model predicts some intrinsic vibration modes of electromagnetic radiation on the neuronal surface. The frequency range of these vibration modes is in the THz and far-infrared ranges.

Excitation energy transport with noise and disorder in a model of the selectivity filter of an ion channel

A selectivity filter is a gate in ion channels that is responsible for the selection and fast conduction of particular ions across the membrane (with high throughput rates of 10⁸ ions s^-1 and a high 1:10⁴ discrimination rate between ions). It is made of four strands as the backbone, and each strand is composed of sequences of five amino acids connected by peptide units H-N-C=O in which the main molecules in the backbone that interact with ions in the filter are carbonyl (C=O) groups that mimic the transient interactions of ion with binding sites during ion conduction. It has been suggested that quantum coherence and possible emergence of resonances in the backbone carbonyl groups may play a role in mediating ion conduction and selectivity in the filter. Here, we investigate the influence of noise and disorder on the efficiency of excitation energy transfer (EET) in a linear harmonic chain of N  =  5 sites with dipole-dipole couplings as a simple model for one P-loop strand of the selectivity filter backbone in biological ion channels. We include noise and disorder inherent in real biological systems by including spatial disorder in the chain, and random noise within a weak coupling quantum master equation approach. Our results show that disorder in the backbone considerably reduces EET, but the addition of noise helps to recover high EET for a wide range of system parameters. Our analysis may help for better understanding of the coordination of ions in the filter as well as the fast and efficient functioning of the selectivity filters in ion channels.

Quantum Dynamics and Non-Local Effects Behind Ion Transition States during Permeation in Membrane Channel Proteins

We present a comparison of a classical and a quantum mechanical calculation of the motion of K⁺ 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.

The Soul, as an Uninhibited Mental Activity, is Reduced into Consciousness by Rules of Quantum Physics

This paper is an effort to describe, in neuroscientific terms, one of the most ambiguous concepts of the universe-the soul. Previous efforts to understand what the soul is and where it may exist have accepted the soul as a subjective and individual entity. We will make two additions to this view: (1) The soul is a result of uninhibited mental activity and lacks spatial and temporal information; (2) The soul is an undivided whole and, to become divided, the soul has to be reduced into unconscious and conscious mental events. This reduction process parallels the maturation of the frontal cortex and GABA becoming the main inhibitory neurotransmitter. As examples of uninhibited mental activity, we will discuss the perceptual differences of a newborn, individuals undergoing dissociation, and individuals induced by psychedelic drugs. Then, we will explain the similarities between the structure of the universe and the structure of the brain, and we propose that consideration of the rules of quantum physics is necessary to understand how the soul is reduced into consciousness.

Linoleic acid: Is this the key that unlocks the quantum brain? Insights linking broken symmetries in molecular biology, mood disorders and personalistic emergentism

In this paper we present a mechanistic model that integrates subneuronal structures, namely ion channels, membrane fatty acids, lipid rafts, G proteins and the cytoskeleton in a dynamic system that is finely tuned in a healthy brain. We also argue that subtle changes in the composition of the membrane's fatty acids may lead to down-stream effects causing dysregulation of the membrane, cytoskeleton and their interface. Such exquisite sensitivity to minor changes is known to occur in physical systems undergoing phase transitions, the simplest and most studied of them is the so-called Ising model, which exhibits a phase transition at a finite temperature between an ordered and disordered state in 2- or 3-dimensional space. We propose this model in the context of neuronal dynamics and further hypothesize that it may involve quantum degrees of freedom dependent upon variation in membrane domains associated with ion channels or microtubules. Finally, we provide a link between these physical characteristics of the dynamical mechanism to psychiatric disorders such as major depression and antidepressant action.

Quantum Interference and Selectivity through Biological Ion Channels

The mechanism of selectivity in ion channels is still an open question in biology for more than half a century. Here, we suggest that quantum interference can be a solution to explain the selectivity mechanism in ion channels since interference happens between similar ions through the same size of ion channels. In this paper, we simulate two neighboring ion channels on a cell membrane with the famous double-slit experiment in physics to investigate whether there is any possibility of matter-wave interference of ions via movement through ion channels. Our obtained decoherence timescales indicate that the quantum states of ions can only survive for short times, i.e. ≈100 picoseconds in each channel and ≈17-53 picoseconds outside the channels, giving the result that the quantum interference of ions seems unlikely due to environmental decoherence. However, we discuss our results and raise few points, which increase the possibility of interference.

The quantum mitochondrion and optimal health

A sufficiently complex set of molecules, if subject to perturbation, will self-organize and show emergent behaviour. If such a system can take on information it will become subject to natural selection. This could explain how self-replicating molecules evolved into life and how intelligence arose. A pivotal step in this evolutionary process was of course the emergence of the eukaryote and the advent of the mitochondrion, which both enhanced energy production per cell and increased the ability to process, store and utilize information. Recent research suggest that from its inception life embraced quantum effects such as 'tunnelling' and 'coherence' while competition and stressful conditions provided a constant driver for natural selection. We believe that the biphasic adaptive response to stress described by hormesis-a process that captures information to enable adaptability, is central to this whole process. Critically, hormesis could improve mitochondrial quantum efficiency, improving the ATP/ROS ratio, whereas inflammation, which is tightly associated with the aging process, might do the opposite. This all suggests that to achieve optimal health and healthy aging, one has to sufficiently stress the system to ensure peak mitochondrial function, which itself could reflect selection of optimum efficiency at the quantum level.

Noise assisted excitation energy transfer in a linear model of a selectivity filter backbone strand

In this paper, we investigate the effect of noise and disorder on the efficiency of excitation energy transfer (EET) in a N = 5 sites linear chain with 'static' dipole-dipole couplings. In fact, here, the disordered chain is a toy model for one strand of the selectivity filter backbone in ion channels. It has recently been discussed that the presence of quantum coherence in the selectivity filter is possible and can play a role in mediating ion-conduction and ion-selectivity in the selectivity filter. The question is 'how a quantum coherence can be effective in such structures while the environment of the channel is dephasing (i.e. noisy)?' Basically, we expect that the presence of the noise should have a destructive effect in the quantum transport. In fact, we show that such expectation is valid for ordered chains. However, our results indicate that introducing the dephasing in the disordered chains leads to the weakening of the localization effects, arising from the multiple back-scatterings due to the randomness, and then increases the efficiency of quantum energy transfer. Thus, the presence of noise is crucial for the enhancement of EET efficiency in disordered chains. We also show that the contribution of both classical and quantum mechanical effects are required to improve the speed of energy transfer along the chain. Our analysis may help for better understanding of fast and efficient functioning of the selectivity filters in ion channels.

On the classical vibrational coherence of carbonyl groups in the selectivity filter backbone of the KcsA ion channel

It has been suggested that quantum coherence in the selectivity filter of ion channel may play a key role in fast conduction and selectivity of ions. However, it has not been clearly elucidated yet why classical coherence is not sufficient for this purpose. In this paper, we investigate the classical vibrational coherence between carbonyl groups oscillations in the selectivity filter of KcsA ion channels based on the data obtained from molecular dynamics simulations. Our results show that classical coherence plays no effective role in fast ionic conduction.

Quantum decoherence time scales for ionic superposition states in ion channels

There are many controversial and challenging discussions about quantum effects in microscopic structures in neurons of the brain and their role in cognitive processing. In this paper, we focus on a small, nanoscale part of ion channels which is called the "selectivity filter" and plays a key role in the operation of an ion channel. Our results for superposition states of potassium ions indicate that decoherence times are of the order of picoseconds. This decoherence time is not long enough for cognitive processing in the brain, however, it may be adequate for quantum superposition states of ions in the filter to leave their quantum traces on the selectivity filter and action potentials.

Quantum effects in the understanding of consciousness

This paper presents a historical perspective on the development and application of quantum physics methodology beyond physics, especially in biology and in the area of consciousness studies. Quantum physics provides a conceptual framework for the structural aspects of biological systems and processes via quantum chemistry. In recent years individual biological phenomena such as photosynthesis and bird navigation have been experimentally and theoretically analyzed using quantum methods building conceptual foundations for quantum biology. Since consciousness is attributed to human (and possibly animal) mind, quantum underpinnings of cognitive processes are a logical extension. Several proposals, especially the Orch OR hypothesis, have been put forth in an effort to introduce a scientific basis to the theory of consciousness. At the center of these approaches are microtubules as the substrate on which conscious processes in terms of quantum coherence and entanglement can be built. Additionally, Quantum Metabolism, quantum processes in ion channels and quantum effects in sensory stimulation are discussed in this connection. We discuss the challenges and merits related to quantum consciousness approaches as well as their potential extensions.

A study of quantum mechanical probabilities in the classical Hodgkin-Huxley model

The Hodgkin-Huxley (HH) model is a powerful model to explain different aspects of spike generation in excitable cells. However, the HH model was proposed in 1952 when the real structure of the ion channel was unknown. It is now common knowledge that in many ion-channel proteins the flow of ions through the pore is governed by a gate, comprising a so-called "selectivity filter" inside the ion channel, which can be controlled by electrical interactions. The selectivity filter (SF) is believed to be responsible for the selection and fast conduction of particular ions across the membrane of an excitable cell. Other (generally larger) parts of the molecule such as the pore-domain gate control the access of ions to the channel protein. In fact, two types of gates are considered here for ion channels: the "external gate", which is the voltage sensitive gate, and the "internal gate" which is the selectivity filter gate (SFG). Some quantum effects are expected in the SFG due to its small dimensions, which may play an important role in the operation of an ion channel. Here, we examine parameters in a generalized model of HH to see whether any parameter affects the spike generation. Our results indicate that the previously suggested semi-quantum-classical equation proposed by Bernroider and Summhammer (BS) agrees strongly with the HH equation under different conditions and may even provide a better explanation in some cases. We conclude that the BS model can refine the classical HH model substantially.