Can Quantum Entanglement Between Ion Transition States Effect Action Potential Initiation?

Open Systems, Quantum Probability, and Logic for Quantum-like Modeling in Biology, Cognition, and Decision-Making

The aim of this review is to highlight the possibility of applying the mathematical formalism and methodology of quantum theory to model behavior of complex biosystems, from genomes and proteins to animals, humans, and ecological and social systems. Such models are known as quantum-like, and they should be distinguished from genuine quantum physical modeling of biological phenomena. One of the distinguishing features of quantum-like models is their applicability to macroscopic biosystems or, to be more precise, to information processing in them. Quantum-like modeling has its basis in quantum information theory, and it can be considered one of the fruits of the quantum information revolution. Since any isolated biosystem is dead, modeling of biological as well as mental processes should be based on the theory of open systems in its most general form-the theory of open quantum systems. In this review, we explain its applications to biology and cognition, especially theory of quantum instruments and the quantum master equation. We mention the possible interpretations of the basic entities of quantum-like models with special interest given to QBism, as it may be the most useful interpretation.

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 Optimized Conformation Dynamics of the KcsA Filter as a Probe for Lateral Membrane Effects: A First Principle Based Femto-Sec Resolution MD Study

We provide a high resolution, all-atom, femto-second molecular dynamics (MD) simulation of the passage of K⁺ ions and H₂O molecules through the selectivity filter of the KcsA potassium ion channel, based on first principle physical methods. Our results show that a change in the length of the selectivity filter of as little as 3%, regardless of whether the filter is made longer or shorter, will reduce the K⁺ ion current by around 50%. In addition, further squeezing or stretching by about 9% can effectively stop the current. Our results demonstrate optimized conformational dynamics that associate an increased mobility of parts in the filter linings with a standard configuration, leading to maximized conduction rates that are highly sensitive to geometrical distortions. We discuss this latter aspect in relation to lateral membrane effects on the filter region of ion channels and the 'force from lipids' hypothesis.

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.

Order-Stability in Complex Biological, Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.

Mathematical Modeling of Ion Quantum Tunneling Reveals Novel Properties of Voltage-Gated Channels and Quantum Aspects of Their Pathophysiology in Excitability-Related Disorders

Voltage-gated channels are crucial in action potential initiation and propagation and there are many diseases and disorders related to them. Additionally, the classical mechanics are the main mechanics used to describe the function of the voltage-gated channels and their related abnormalities. However, the quantum mechanics should be considered to unravel new aspects in the voltage-gated channels and resolve the problems and challenges that classical mechanics cannot solve. In the present study, the aim is to mathematically show that quantum mechanics can exhibit a powerful tendency to unveil novel electrical features in voltage-gated channels and be used as a promising tool to solve the problems and challenges in the pathophysiology of excitability-related diseases. The model of quantum tunneling of ions through the intracellular hydrophobic gate is used to evaluate the influence of membrane potential and gating free energy on the tunneling probability, single channel conductance, and quantum membrane conductance. This evaluation is mainly based on graphing the mathematical relationships between these variables. The obtained mathematical graphs showed that ions can achieve significant quantum membrane conductance, which can affect the resting membrane potential and the excitability of cells. In the present work, quantum mechanics reveals original electrical properties associated with voltage-gated channels and introduces new insights and implications into the pathophysiology of excitability- related disorders. In addition, the present work sets a mathematical and theoretical framework that can be utilized to conduct experimental studies in order to explore the quantum aspects of voltage-gated channels and the quantum bioelectrical property of biological membranes.

Quantum-like modeling in biology with open quantum systems and instruments

We present the novel approach to mathematical modeling of information processes in biosystems. It explores the mathematical formalism and methodology of quantum theory, especially quantum measurement theory. This approach is known as quantum-like and it should be distinguished from study of genuine quantum physical processes in biosystems (quantum biophysics, quantum cognition). It is based on quantum information representation of biosystem's state and modeling its dynamics in the framework of theory of open quantum systems. This paper starts with the non-physicist friendly presentation of quantum measurement theory, from the original von Neumann formulation to modern theory of quantum instruments. Then, latter is applied to model combinations of cognitive effects and gene regulation of glucose/lactose metabolism in Escherichia coli bacterium. The most general construction of quantum instruments is based on the scheme of indirect measurement, in that measurement apparatus plays the role of the environment for a biosystem. The biological essence of this scheme is illustrated by quantum formalization of Helmholtz sensation-perception theory. Then we move to open systems dynamics and consider quantum master equation, with concentrating on quantum Markov processes. In this framework, we model functioning of biological functions such as psychological functions and epigenetic mutation.

A Quantum-Like Model of Information Processing in the Brain

We present the quantum-like model of information processing by the brain’s neural networks. The model does not refer to genuine quantum processes in the brain. In this model, uncertainty generated by the action potential of a neuron is represented as quantum-like superposition of the basic mental states corresponding to a neural code. Neuron’s state space is described as complex Hilbert space (quantum information representation). The brain’s psychological functions perform self-measurements by extracting concrete answers to questions (solutions of problems) from quantum information states. This extraction is modeled in the framework of open quantum systems theory. In this way, it is possible to proceed without appealing to the state’s collapse. Dynamics of the state of psychological function F is described by the quantum master equation. Its stationary states represent classical statistical mixtures of possible outputs of F (decisions). This model can be used for justification of quantum-like modeling cognition and decision-making. The latter is supported by plenty of statistical data collected in cognitive psychology.

On Interpretational Questions for Quantum-Like Modeling of Social Lasing

The recent years were characterized by increasing interest to applications of the quantum formalism outside physics, e.g., in psychology, decision-making, socio-political studies. To distinguish such approach from quantum physics, it is called quantum-like. It is applied to modeling socio-political processes on the basis of the social laser model describing stimulated amplification of social actions. The main aim of this paper is establishing the socio-psychological interpretations of the quantum notions playing the basic role in lasing modeling. By using the Copenhagen interpretation and the operational approach to the quantum formalism, we analyze the notion of the social energy. Quantum formalizations of such notions as a social atom, s-atom, and an information field are presented. The operational approach based on the creation and annihilation operators is used. We also introduce the notion of the social color of information excitations representing characteristics linked to lasing coherence of the type of collimation. The Bose–Einstein statistics of excitations is coupled with the bandwagon effect, one of the basic effects of social psychology. By using the operational interpretation of the social energy, we present the thermodynamical derivation of this quantum statistics. The crucial role of information overload generated by the modern mass-media is emphasized. In physics laser’s resonator, the optical cavity, plays the crucial role in amplification. We model the functioning of social laser’s resonator by “distilling” the physical scheme from connection with optics. As the mathematical basis, we use the master equation for the density operator for the quantum information field.

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.

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.