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.
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.
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.
The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described employing multiple connected electric circuits containing capacitors, voltage sources, and conductances. These conductances depend on previous depolarizing membrane voltages, which can be identified with a memory resistive element called memristor. Inspired by the recent quantization of the memristor, a simplified Hodgkin-Huxley model including a single ion channel has been studied in the quantum regime. Here, we study the quantization of the complete Hodgkin-Huxley model, accounting for all three ion channels, and introduce a quantum source, together with an output waveguide as the connection to a subsequent neuron. Our system consists of two memristors and one resistor, describing potassium, sodium, and chloride ion channel conductances, respectively, and a capacitor to account for the axon's membrane capacitance. We study the behavior of both ion channel conductivities and the circuit voltage, and we compare the results with those of the single channel, for a given quantum state of the source. It is remarkable that, in opposition to the single-channel model, we are able to reproduce the voltage spike in an adiabatic regime. Arguing that the circuit voltage is a quantum variable, we find a purely quantum-mechanical contribution in the system voltage's second moment. This work represents a complete study of the Hodgkin-Huxley model in the quantum regime, establishing a recipe for constructing quantum neuron networks with quantum state inputs. This paves the way for advances in hardware-based neuromorphic quantum computing, as well as quantum machine learning, which might be more efficient resource-wise.
The familiar Hodgkin-Huxley (HH) model describes transmission of a nerve impulse through an axon's membrane in terms of the dynamics of connected electrical circuits, featuring capacitors, voltage sources, and memristors. The recent quantization of the memristor's dynamics now allows study of a $q\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}m$ version of the HH circuit. The authors reproduce the behavior of the single-ion-channel HH circuit in the quantum regime, and exploring the possibility of this setup to be the building block for bioinspired quantum neural networks. Their results will impact the fields of superconducting devices, neuromorphic quantum computing, and hardware-based solutions for quantum machine learning.
With an increasing amount of experimental evidence pouring in from neurobiological investigations, it is quite appropriate to study viable reductionist models which may explain some of the features of brain activities. It is now quite well known that the Hodgkin-Huxley (HH) Model has been quite successful in explaining the neural phenomena. The idea of circuit equivalents and the membrane voltages corresponding to neurons have been remarkable which is essentially a classical result. In view of some recent results which show that quantum mechanics may be important at suitable length scales inside the brain, the question which becomes quite important is to find out a proper quantum analogue of the HH scheme which will reduce to the well known HH model in a suitable limit. From the ideas of neuro-manifold and the relevance of quantum mechanics at some length scales in the ion channels, we investigate this situation in this paper by taking into consideration the Schrödinger equation in an arbitrary manifold with a metric, which is in some sense a special case of the heat kernel equation. The next important approach we have taken in order to bring about it's relevance in brain studies and to make connection with HH models is to find out a plausible circuit equivalents of it. What we do realize is that for a proper quantum mechanical description and it's circuit implementation of the same we need to incorporate the non commutativity inside the circuit model. It has been realized here that the metric is a dynamical entity governing space time and for considering equivalent circuits it plays a very distinct role. We have used the methods of stochastic quantization and have constructed a specific case here and see that HH model inductances gets renormalized in the quantum limit.
Neuromuscular Junction (NMJ) is the place where the neuron meets with muscle fiber crating a synapse to propagate the electrochemical signals.The infolds of the endplate of muscle fiber play a vital role containing a huge number of sodium channels in contraction of NMJ transmission mechanism.We have studied here the entanglement of sodium channel activation particle ('m' particle).Through the simulation results we confirm that the entanglement of 'm' particle effects the initiation time, amplitude and the rate of change of membrane potential.
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').